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*                                       *
*  h   h  ooo  w     w ttttttt ooo      *
*  h   h o   o w     w 	  t   o   o     *
*  hhhhh o   o w  w  w    t   o   o     *
*  h   h o   o w  w  w    t   o   o     *
*  h   h  ooo   ww ww     t    ooo      *
*                                       *
*                                       *
*      use wprime_1.0.1_v4/ model       *
*             Version 1.0.1             *
*  Based on MadGraph/MadEvent V4.4.33   *
*  (Modified for use w/ MadEvent 5+)    *
*                                       *
* Zack Sullivan<[email protected]>  *
*            and Yaofu Zhou             *
*          Physics Department           *
*    Illinois Institute of Technology   *
*                                       *
*            Jan. 19, 2011              *
*                                       *
*****************************************

Note: wprime_1.0.1_v4/ is the current directory, but is referred to as
wprime/ below.

The wprime/ model is an extension of the Standard Model (i.e. smckm/) that
contains a W-prime boson with arbitrary vector and axial-vector couplings
to Standard Model fermions (with no right-handed neutrinos).

The most general Lorentz invariant Lagrangian describing the coupling of a
W-prime to fermions can be written as

\mathcal{L}=

\frac{g}{\sqrt{2}}\bar{f_{i}}\gamma_{\mu}
(C_{f_{i}f_{j}}^{R}P_{R}+C_{f_{i}f_{j}}^{L}P_{L})W'f_{j}+
\mathrm{H.c.}=                                                       (1)

\frac{1}{\sqrt{2}}\bar{f_{i}}\gamma_{\mu}
(g_{R}e^{i\omega}\cos\zeta V_{f_{i}f_{j}}^{R}P_{R}+
 g_{L}\sin\zeta V_{f_{i}f_{j}}^{L}P_{L})W'f_{j}+
\mathrm{H.c.}=                                                       (2)

\frac{g}{\sqrt{2}}\bar{f_{i}}\gamma_{\mu}
(S_{R}e^{i\omega}V_{f_{i}f_{j}}^{R}P_{R}+
 S_{L}V_{f_{i}f_{j}}^{L}P_{L})W'f_{j}+
\mathrm{H.c.},                                                       (3)

Form (3) is used in wprime/ model, where the left-right mixing factors
\cos\zeta and \sin\zeta in form (2) are absorbed into S_{R} and S_{L},
respectively.

To configure an arbitrary model with a given W-prime boson,
SMLeftRight.wpmod can be modified to include any possible couplings to
fermions. If only left- or right-handed W-prime bosons are needed, only
param_card.dat needs to be modified for the mass and handedness.

1. param_card.dat

1.1. The mass of the W-prime boson is set by "WPMASS".

1.2. There is no need to set the "WPWIDTH", as it will be reevaluated
according to the W-prime mass and couplings. (Note the LO mass used is
written out in MadEvent 4, but MadEvent 5 suppresses output.)

1.3.1. If the W-prime boson in the model couples to the fermions like
the Standard Model left-handed W boson does (same CKM matrix), up to a
scaling factor for the left- and right-handed couplings, "model" can
be set to either 0 or 1. If "model" is set to 1, go to Step 1.3.2; if
"model" set to 0,

1.3.1.1. "glscale" and "grscale" are used to set the scaling factors
for the left- and right-handed couplings, respectively.

1.3.1.2. There is no need to touch SMLeftRight.wpmod.

1.3.1.3. Run

$ make checkmodel
$ ./checkmodel

to check whether good values are assigned to good variables.

1.3.2. If "model" is set to 1, wpmodelfile is read in to set the base
couplings. "glscale" and "grscale" are ALWAYS used to quickly rescale
left- and right-handed couplings. For example, use them to switch
on/off left- or right-handed couplings by setting them to either 1e0
or 0e0. Additional multipliers are available in the .wpmod model file
(base file is SMLeftRight.wpmod).

2. SMLeftRight.wpmod

2.1. Follow the instructions in SMLeftRight.wpmod if you wish to
modify it.

2.2. Enable logging in SMLeftRight.wpmod and Run

$ make checkmodel
$ ./checkmodel

to check if the parameters are set correctly. W-prime couplings,
generalized CKM matrices, W-prime mass, W-prime width, branching
ratios of W-prime decay, and R_{t}'s and R_{u}'s for the s-channel
cross sections are printed to the terminal, which can be redirected to
files. For complete definitions of R_{t} and R_{u}, see Z. Sullivan,
Phys. Rev. D 66, 075011 (2002) [hep-ph/0207290].

Note that this log is only printed by running the ./checkmodel
command, and is not printed while running MadGraph/MadEvent.

2.3. Note that if all R_{u}'s are 0, the model is purely right- or
left-handed, it scales like the Standard Model, and the ratio between
the effective coupling constant and the Standard Model coupling
constant for each s-channel diagram can be extracted. See the
footnote for info on R_{u} and R_{t}.

3. Generating events with MadGraph/MadEvent 4

3.1. In [run directory]/Cards/proc_card.dat, enter "wprime_1.0.1_v4"
in Model information.

3.2. Edit the processes as desired. The symbol of W-prime boson is wp-
for the particle and wp+ for the antiparticle. The W-prime boson in
wprime/ model directory couples only to the Standard Model fermions.
You may refer to wprime/particles.dat or wprime/internations.dat for
more details. Example processes involving W-prime boson are

p p > wp+ > t b~
p p > wp- > e- ev~

Interference can occur between a left-handed W-prime boson and the
Standard Model W boson in

p p > t b~

as the intermediate boson is not specified.

3.3. In [run directory]/ Run

$ ./bin/newprocess

This replace the default model of [run directory]/ with the wprime/
model. Further changes to param_card.dat and SMLeftRight.wpmod can be
made in [run directory]/Cards/param_card.dat, and
[run directory]/Source/MODEL/SMLeftRight.wpmod

3.4. Configure [run directory]/Cards/run_card.dat, go to [run directory]/
and run

$ ./bin/generate_events

to generate events.

3.5. The default compiler in the makefile in wprime/ is f77 as in other
codes in MadGraph/MadEvent V4.4.33. f77 can be changed to gfortran
when wprime/ is running independently, minor effects may occur in the
log.

4. Generating events with MadEvent 5 (or mg5_aMC)

4.1. MadEvent 5 (and the newer mg5_aMC) have adopted a python-based
approach to reading files. The only change required to run in
MadEvent 5 is to change the compiler in the makefile from f77 to
gfortran.

4.2. To load the model into ME5 use:
import model_v4 wprime_1.0.1_v4

4.3. Remember to change the mass in param_card.dat to the mass you
desire, and set glscale or grscale. Otherwise, all other features are
the same between MadEvent 4 and 5.

==================================================================
Footnote

R_{t}=
(|V_{i}|^{2}+|A_{i}|^{2})(|V_{f}|^{2}+|A_{f}|^{2})+
4\mathrm{Re}(V_{i}A_{i}^{*})\mathrm{Re}(V_{f}A_{f}^{*})

R_{u}=
(|V_{i}|^{2}+|A_{i}|^{2})(|V_{f}|^{2}+|A_{f}|^{2})-
4\mathrm{Re}(V_{i}A_{i}^{*})\mathrm{Re}(V_{f}A_{f}^{*})

where

|V|^{2}+|A|^{2}=
(|S_{R}V_{f_{i}f_{j}}^{R}|^{2}+|S_{L}V_{f_{i}f_{j}}^{L}|^{2})/4

2\mathrm{Re}(VA^{*})=
(|S_{R}V_{f_{i}f_{j}}^{R}|^{2}-|S_{L}V_{f_{i}f_{j}}^{L}|^{2})/4

If All R_{u}'s are 0, the model is purely right- or left-handed, and
scales like the Standard Model, otherwise there are
non-Standard-Model-like kinematics. This is correctly accounted for
by MadEvent, but might require modifying SMLeftRight.wpmod if the
couplings are not simple scalings of the Standard Model-like ones.