From 21add0c01b5942bb959ca9f31feb83be6af8f538 Mon Sep 17 00:00:00 2001 From: Vladyslav Shtabovenko Date: Sun, 7 Jun 2020 12:59:51 +0200 Subject: [PATCH] Fixed a bug in ToSFAD for massive propagators. --- FeynCalc/LoopIntegrals/FCLoopBasis.m | 3 +- FeynCalc/LoopIntegrals/ToSFAD.m | 2 +- Tests/LoopIntegrals/FCLoopBasis.test | 15 +- .../FCLoopMixedToCartesianAndTemporal.test | 4 +- Tests/LoopIntegrals/TID.test | 207 ++++++------------ Tests/LoopIntegrals/ToSFAD.test | 30 +-- 6 files changed, 94 insertions(+), 167 deletions(-) diff --git a/FeynCalc/LoopIntegrals/FCLoopBasis.m b/FeynCalc/LoopIntegrals/FCLoopBasis.m index 210dcda90..8dcf19ecc 100755 --- a/FeynCalc/LoopIntegrals/FCLoopBasis.m +++ b/FeynCalc/LoopIntegrals/FCLoopBasis.m @@ -297,7 +297,8 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), ]; If[ OptionValue[ToSFAD] && !FreeQ[expAsList,PropagatorDenominator], - expAsList = ToSFAD[expAsList] + expAsList = ToSFAD[expAsList]; + FCPrint[3,"FCLoopBasisIntegralToPropagators: After ToSFAD: ", expAsList, FCDoControl->itpVerbose]; ]; diff --git a/FeynCalc/LoopIntegrals/ToSFAD.m b/FeynCalc/LoopIntegrals/ToSFAD.m index e589e862e..e8a613efe 100755 --- a/FeynCalc/LoopIntegrals/ToSFAD.m +++ b/FeynCalc/LoopIntegrals/ToSFAD.m @@ -65,7 +65,7 @@ }; pdsConverted = pds /. { - PropagatorDenominator[a_,b_] :> StandardPropagatorDenominator[a,0,b^2,{1, optEtaSign}] + PropagatorDenominator[a_,b_] :> StandardPropagatorDenominator[a,0,-b^2,{1, optEtaSign}] }; ruleFads = Thread[Rule[fads,fadsConverted]]; diff --git a/Tests/LoopIntegrals/FCLoopBasis.test b/Tests/LoopIntegrals/FCLoopBasis.test index bc60447fb..763394af8 100644 --- a/Tests/LoopIntegrals/FCLoopBasis.test +++ b/Tests/LoopIntegrals/FCLoopBasis.test @@ -836,9 +836,18 @@ Tally -> True, FCE -> True]", Pair[Momentum[-k2/2, D], Momentum[l, D]]) FAD[{l, 0, 2}, {-k1/2 - k2/2 + l, m}, {k1/2 - k2/2 + l, m}], {l}, MomentumCombine -> True, Tally -> False]", -"{FeynAmpDenominator[StandardPropagatorDenominator[0, -Pair[Momentum[k1 + k2, D], Momentum[l, D]]/2, 0, {-1, 1}]], -FeynAmpDenominator[StandardPropagatorDenominator[Momentum[l, D], 0, 0, {1, 1}]], FeynAmpDenominator[StandardPropagatorDenominator[-Momentum[k1, D]/2 - Momentum[k2, D]/2 + Momentum[l, D], -0, m^2, {1, 1}]], FeynAmpDenominator[StandardPropagatorDenominator[Momentum[k1, D]/2 - Momentum[k2, D]/2 + Momentum[l, D], 0, m^2, {1, 1}]]}"}, +"{FeynAmpDenominator[ +StandardPropagatorDenominator[ +0, -Pair[Momentum[k1 + k2, D], Momentum[l, D]]/2, 0, {-1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[l, D], 0, 0, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[k1, D]/2 - + Momentum[k2, D]/2 + Momentum[l, D], 0, -m^2, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[ +Momentum[k1, D]/2 - Momentum[k2, D]/2 + Momentum[l, D], +0, -m^2, {1, 1}]]}"}, {"fcstFCLoopBasisIntegralToPropagators-ID32", "FCLoopBasisIntegralToPropagators[GFAD[{p1.q p2.q + x}] SFAD[p1], {p1, p2}, FCE -> True]", "{GFAD[{{x + p1.q p2.q, 1}, 1}], SFAD[{{p1, 0}, {0, 1}, 1}]}"}, diff --git a/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test b/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test index f3ac49a23..211a82e6c 100644 --- a/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test +++ b/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test @@ -78,8 +78,8 @@ FCE->True]", "-CFAD[{{0, p . q}, {-(TC[p]*TC[q]), -1}, 3}]"}, {"fcstFCLoopMixedToCartesianAndTemporal-ID19", "FCLoopMixedToCartesianAndTemporal[ \ FCI[TC[k]FAD[{k,m3},{k-pH,m2},{k-pE1,pPH}]],{k},FCE\[Rule]True]", -"-(CFAD[{{k, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - \ -TC[k - pH]^2, -1}, 1}, {{k - pE1, 0}, {-pPH^2 - TC[k - pE1]^2, -1}, \ +"-(CFAD[{{k, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - \ +TC[k - pH]^2, -1}, 1}, {{k - pE1, 0}, {pPH^2 - TC[k - pE1]^2, -1}, \ 1}]*TC[k])"}, {"fcstFCLoopMixedToCartesianAndTemporal-ID20", "FCLoopMixedToCartesianAndTemporal[FCI[TC[k] FVD[k,mu] \ diff --git a/Tests/LoopIntegrals/TID.test b/Tests/LoopIntegrals/TID.test index a7159cc0e..7a36eebf5 100644 --- a/Tests/LoopIntegrals/TID.test +++ b/Tests/LoopIntegrals/TID.test @@ -949,151 +949,68 @@ Pair[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D]]*TC[k]^3)/ {"fcstTID-ID50", "TID[GSD[k] FAD[-pE1-pPh] \ FAD[{k,m2},k+pE1-pH+pPh,{k-pH,m2},{k-pH,m3}] TC[k],k,FCE\[Rule]True]", - "(CFAD[{{k, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}, {{k + pE1 - pH + \ -pPh, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}]*(CGSD[pH] - CGSD[-pE1 - pPh] \ -- CGSD[pE1 + pH + pPh])*(CSPD[pE1, pH] + CSPD[pH, pPh])*FAD[pE1 + \ -pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ -(CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ -- pH]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, \ -pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ -m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ -pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-m3^2 - \ -TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ -1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ -CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ -m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ -pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-TC[k - \ -pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {-m2^2 - TC[k]^2, -1}, \ -1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ -2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ -CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ -m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ -pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-TC[k - \ -pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {-m3^2 - TC[k]^2, -1}, \ -1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ -2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ -CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ -m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ -pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-m2^2 - \ -TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - \ -pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ -1}]*(CGSD[pH]*CSPD[pE1, pE1]*CSPD[pH, pH] + CGSD[-pE1 - \ -pPh]*CSPD[pE1, pH]*CSPD[pH, pH] + 2*CGSD[pH]*CSPD[pE1, pPh]*CSPD[pH, \ -pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pH, \ -pH]*CSPD[pPh, pPh] - CGSD[pH]*CSPD[pE1, pH]*(m2^2 + CSPD[pE1, pE1] + \ -2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) - CGSD[-pE1 - pPh]*CSPD[pH, \ -pH]*(m2^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) - \ -CGSD[pH]*CSPD[pH, pPh]*(m2^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ -CSPD[pPh, pPh]))*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, \ -pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, \ -pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ -1}, {{k + pH, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, \ -0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1]*(m2^2 - \ -m3^2 - CSPD[pH, pH]) + CGSD[-pE1 - pPh]*CSPD[pE1, pH]*(m2^2 - m3^2 - \ -CSPD[pH, pH]) + 2*CGSD[pH]*CSPD[pE1, pPh]*(m2^2 - m3^2 - CSPD[pH, \ -pH]) + CGSD[-pE1 - pPh]*(m2^2 - m3^2 - CSPD[pH, pH])*CSPD[pH, pPh] + \ -CGSD[pH]*(m2^2 - m3^2 - CSPD[pH, pH])*CSPD[pPh, pPh] + \ -CGSD[pH]*CSPD[pE1, pH]*(m3^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ -CSPD[pPh, pPh]) + CGSD[-pE1 - pPh]*CSPD[pH, pH]*(m3^2 + CSPD[pE1, \ -pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) + CGSD[pH]*CSPD[pH, \ -pPh]*(m3^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, \ -pPh]))*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - \ -CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ -CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - \ -pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - \ -pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - \ -(CFAD[{{k, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ -- pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ -1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - (CFAD[{{k, 0}, \ -{-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - TC[k]^2, -1}, \ -1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ -1}]*(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - \ -pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - \ -pPh]*CSPD[pH, pH] - CGSD[pH]*CSPD[pH, pPh] + CGSD[-pE1 - \ -pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + \ -pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ -(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ -TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ --1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pE1 + pH + pPh]*CSPD[pE1, \ -pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - pPh]*CSPD[pH, pH] - \ -CGSD[pE1 + pH + pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 \ -+ pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 \ -- CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) \ -+ (CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 \ -- TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ --1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ -2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ -CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - \ -TC[pH])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ -(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ -TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ --1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ -2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ -CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - \ -TC[pH])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ -(FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}]*(GSD[pH]*SPD[pE1, pH] + \ -GSD[-pE1 - pPh]*SPD[pH, pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/(2*(m2^2 \ -- m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, \ -pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, \ -m2}, {k - pH, m3}]*(GSD[pH]*SPD[pE1, pH] + GSD[-pE1 - pPh]*SPD[pH, \ -pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] \ -- SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ -SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, m2}, k - pE1 - \ -pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + \ -2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + \ -GSD[pH]*SPD[pPh, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - \ -SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ -SPD[pPh, pPh]))) + (FAD[pE1 + pPh]*FAD[{k, m3}, k - pE1 - \ -pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + \ -2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + \ -GSD[pH]*SPD[pPh, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - \ -SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ -SPD[pPh, pPh]))) + (FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}, k - pE1 \ -- pPh]*(GSD[pH]*SPD[pE1, pE1]*SPD[pH, pH] + GSD[-pE1 - pPh]*SPD[pE1, \ -pH]*SPD[pH, pH] + 2*GSD[pH]*SPD[pE1, pPh]*SPD[pH, pH] + GSD[-pE1 - \ -pPh]*SPD[pH, pH]*SPD[pH, pPh] + GSD[pH]*SPD[pH, pH]*SPD[pPh, pPh] - \ -GSD[pH]*SPD[pE1, pH]*(m2^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ -SPD[pPh, pPh]) - GSD[-pE1 - pPh]*SPD[pH, pH]*(m2^2 + SPD[pE1, pE1] + \ -2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[pH]*SPD[pH, pPh]*(m2^2 + \ -SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) + \ -2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, \ -pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh])))*TC[pH])/(2*(m2^2 - \ -m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] \ -+ 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, m3}, \ -{k - pH, m2}, k - pE1 - pPh]*(-(GSD[pH]*SPD[pE1, pE1]*(m2^2 - m3^2 - \ -SPD[pH, pH])) - GSD[-pE1 - pPh]*SPD[pE1, pH]*(m2^2 - m3^2 - SPD[pH, \ -pH]) - 2*GSD[pH]*SPD[pE1, pPh]*(m2^2 - m3^2 - SPD[pH, pH]) - GSD[-pE1 \ -- pPh]*(m2^2 - m3^2 - SPD[pH, pH])*SPD[pH, pPh] - GSD[pH]*(m2^2 - \ -m3^2 - SPD[pH, pH])*SPD[pPh, pPh] - GSD[pH]*SPD[pE1, pH]*(m3^2 + \ -SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[-pE1 - \ -pPh]*SPD[pH, pH]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, \ -pPh]) - GSD[pH]*SPD[pH, pPh]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] \ -+ SPD[pPh, pPh]) + 2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - \ -SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, \ -pPh])))*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - \ -SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - \ -(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - \ -TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ --1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ -CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - \ -TC[pPh])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ -(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ -TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ --1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ -CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - \ -TC[pPh])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ -CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ -(CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ -- pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ -1}]*FAD[pE1 + pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2) + (CFAD[{{k, 0}, \ -{-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ -1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + \ -pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2)"}, + "-(CFAD[{{k, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {m2^2 - TC[k]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] + + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - +(CFAD[{{k, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {m3^2 - TC[k]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] + + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1]*CSPD[pH, pH] + CGSD[-pE1 - pPh]*CSPD[pE1, pH]*CSPD[pH, pH] + 2*CGSD[pH]*CSPD[pE1, pPh]*CSPD[pH, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH]*CSPD[pH, pPh] + + CGSD[pH]*CSPD[pE1, pH]*(m2^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + CGSD[-pE1 - pPh]*CSPD[pH, pH]*(m2^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + + CGSD[pH]*CSPD[pH, pPh]*(m2^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + CGSD[pH]*CSPD[pH, pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1]*(m2^2 - m3^2 + CSPD[pH, pH]) + CGSD[-pE1 - pPh]*CSPD[pE1, pH]*(m2^2 - m3^2 + CSPD[pH, pH]) + 2*CGSD[pH]*CSPD[pE1, pPh]*(m2^2 - m3^2 + CSPD[pH, pH]) + + CGSD[-pE1 - pPh]*(m2^2 - m3^2 + CSPD[pH, pH])*CSPD[pH, pPh] + CGSD[pH]*CSPD[pE1, pH]*(m3^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + + CGSD[-pE1 - pPh]*CSPD[pH, pH]*(m3^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + CGSD[pH]*CSPD[pH, pPh]*(m3^2 - CSPD[pE1, pE1] - 2*CSPD[pE1, pPh] - CSPD[pPh, pPh]) + + CGSD[pH]*(m2^2 - m3^2 + CSPD[pH, pH])*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - +(CFAD[{{k, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pE1 + pH + pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - pPh]*CSPD[pH, pH] - CGSD[pE1 + pH + pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])* +FAD[pE1 + pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pE1 + pH + pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - pPh]*CSPD[pH, pH] - CGSD[pE1 + pH + pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])* +FAD[pE1 + pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pH])^2)/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pH])^2)/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}]*(GSD[pH]*SPD[pE1, pH] + GSD[-pE1 - pPh]*SPD[pH, pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - +(FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m3}]*(GSD[pH]*SPD[pE1, pH] + GSD[-pE1 - pPh]*SPD[pH, pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - +(FAD[pE1 + pPh]*FAD[{k, m2}, k - pE1 - pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + 2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + GSD[pH]*SPD[pPh, pPh])*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) + +(FAD[pE1 + pPh]*FAD[{k, m3}, k - pE1 - pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + 2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + GSD[pH]*SPD[pPh, pPh])*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) + +(FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}, k - pE1 - pPh]*(GSD[pH]*SPD[pE1, pE1]*SPD[pH, pH] + GSD[-pE1 - pPh]*SPD[pE1, pH]*SPD[pH, pH] + 2*GSD[pH]*SPD[pE1, pPh]*SPD[pH, pH] + + GSD[-pE1 - pPh]*SPD[pH, pH]*SPD[pH, pPh] + GSD[pH]*SPD[pH, pH]*SPD[pPh, pPh] - GSD[pH]*SPD[pE1, pH]*(m2^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - + GSD[-pE1 - pPh]*SPD[pH, pH]*(m2^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[pH]*SPD[pH, pPh]*(m2^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) + + 2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh])))*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - +(FAD[pE1 + pPh]*FAD[{k, m3}, {k - pH, m2}, k - pE1 - pPh]*(-(GSD[pH]*SPD[pE1, pE1]*(m2^2 - m3^2 - SPD[pH, pH])) - GSD[-pE1 - pPh]*SPD[pE1, pH]*(m2^2 - m3^2 - SPD[pH, pH]) - + 2*GSD[pH]*SPD[pE1, pPh]*(m2^2 - m3^2 - SPD[pH, pH]) - GSD[-pE1 - pPh]*(m2^2 - m3^2 - SPD[pH, pH])*SPD[pH, pPh] - GSD[pH]*(m2^2 - m3^2 - SPD[pH, pH])*SPD[pPh, pPh] - + GSD[pH]*SPD[pE1, pH]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[-pE1 - pPh]*SPD[pH, pH]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - + GSD[pH]*SPD[pH, pPh]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) + + 2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh])))*TC[pH])/ +(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - TC[pPh])^2)/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + +(CFAD[{{k, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]* +(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - TC[pPh])^2)/ +(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - +(CFAD[{{k, 0}, {m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2) + +(CFAD[{{k, 0}, {m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2)"}, {"fcstTID-ID51","TID[DCHN[-GSD[k] + me, Dir3, Dir4] FAD[{k, me}, k - q], k, FCE -> True]","(DCHN[GSD[q], Dir3, Dir4] FAD[{k, me}])/(2 SPD[q, q]) - (1/( 2 SPD[q, q]))*FAD[k, {k - q, me}] (DCHN[GSD[q], Dir3, Dir4] (me^2 - SPD[q, q]) - diff --git a/Tests/LoopIntegrals/ToSFAD.test b/Tests/LoopIntegrals/ToSFAD.test index 8c8414cfc..cbae57f1e 100644 --- a/Tests/LoopIntegrals/ToSFAD.test +++ b/Tests/LoopIntegrals/ToSFAD.test @@ -40,41 +40,41 @@ Tests`LoopIntegrals`ToSFAD = 0, 0, {1, 1}]]"}, {"fcstToSFAD-ID11", "ToSFAD[FCI[FAD[{p,m}]]]", "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ -0, m^2, {1, 1}]]"}, +0, -m^2, {1, 1}]]"}, {"fcstToSFAD-ID12", "ToSFAD[FCI[FAD[{p,m,2}]]]", "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ -0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[p, D], 0, \ -m^2, {1, 1}]]"}, +0, -m^2, {1, 1}], StandardPropagatorDenominator[Momentum[p, D], 0, \ +-m^2, {1, 1}]]"}, {"fcstToSFAD-ID13", "ToSFAD[FCI[FAD[{p,m},q]]]", "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ -0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +0, -m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ {1, 1}]]"}, {"fcstToSFAD-ID14", "ToSFAD[FCI[FAD[{p,m1},q,{r-q,m2,2}]]]", "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ -0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +0, -m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, \ -D], 0, m2^2, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ -Momentum[r, D], 0, m2^2, {1, 1}]]"}, +D], 0, -m2^2, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ +Momentum[r, D], 0, -m2^2, {1, 1}]]"}, {"fcstToSFAD-ID15", "ToSFAD[FCI[FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]]", "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ -0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +0, -m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ {1, 1}]]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, \ -D], 0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], \ +D], 0, -m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], \ 0, 0, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ -Momentum[r, D], 0, m2^2, {1, 1}], \ +Momentum[r, D], 0, -m2^2, {1, 1}], \ StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, D], 0, \ -m2^2, {1, 1}]]"}, +-m2^2, {1, 1}]]"}, {"fcstToSFAD-ID16", "ToSFAD[FCI[x+FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]]", "x + FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, \ -D], 0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, \ +D], 0, -m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, \ 0, {1, 1}]]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[\ -p, D], 0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, \ +p, D], 0, -m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, \ D], 0, 0, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ -Momentum[r, D], 0, m2^2, {1, 1}], \ +Momentum[r, D], 0, -m2^2, {1, 1}], \ StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, D], 0, \ -m2^2, {1, 1}]]"}, +-m2^2, {1, 1}]]"}, {"fcstToSFAD-ID17", "ToSFAD[FAD[p, Dimension -> X]]", "SFAD[{{p, 0}, {0, 1}, 1}, Dimension -> X]"}