· FeynCalc

Name: Lingxiao Xu Date: 11/03/14-05:40:00 AM Z

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Maybe reply: Lingxiao Xu: “Re: Problems of two QCD processes calculating by FeynCalc and bugs of Contract?”
Maybe reply: Lingxiao Xu: “Re: Problems of two QCD processes calculating by FeynCalc and bugs of Contract?”

hi，recently I’ve calculated some QCD processes using FeynCalc.Here comes my questions: firstly, the result of the process “quark,quarkbar to quark,quarkbar” obtained by FeynCalc is wrong.Secondly,when calculating the process of quark gluon scattering, the commmand “Contract” seems not working right. There is still Lorentz indexes after using it.
Here are my Codes for two processes:

Q,Qbar to Q,Qbar:
Quit;

«HighEnergyPhysics`FeynCalc`

ClearScalarProducts;
{ScalarProduct[p1, p1] =
   ScalarProduct[p2, p2] =
    ScalarProduct[p3, p3] = ScalarProduct[p4, p4] = 0,
  ScalarProduct[p1, p2] = ScalarProduct[p3, p4] = s/2,
  ScalarProduct[p1, p3] = ScalarProduct[p2, p4] = -t/2,
  ScalarProduct[p1, p4] = ScalarProduct[p2, p3] = -u/2
  };
ScPr[p_, m_] := -I/(ScalarProduct[p] - m^2) // ExpandScalarProduct;
ftrace = {DiracTrace -> Tr2, D -> 4};
SUNN = 3;
SetOptions[SUNSimplify, SUNNToCACF -> False];
qav = 6;

f1 = SpinorVBar[p2, 0].QGV[\[Alpha], k].SpinorU[p1, 0] ScPr[p1 + p2,
     0] SpinorUBar[p3, 0].QGV[\[Alpha], k].SpinorV[p4, 0] // Explicit;
f2 = SpinorUBar[p3, 0].QGV[\[Alpha], k].SpinorU[p1, 0] ScPr[p1 - p3,
     0] SpinorVBar[p2, 0].QGV[\[Alpha], k].SpinorV[p4, 0] // Explicit;
f = f1 + f2
f1s = SpinorUBar[p1, 0].QGV[\[Beta], l].SpinorV[p2,
      0] (-ScPr[p1 + p2, 0]) SpinorVBar[p4, 0].QGV[\[Beta],
      l].SpinorU[p3, 0] // Explicit;
f2s = SpinorUBar[p1, 0].QGV[\[Beta], l].SpinorU[p3,
      0] (-ScPr[p1 - p3, 0]) SpinorVBar[p4, 0].QGV[\[Beta],
      l].SpinorV[p2, 0] // Explicit;
fstar = f1s + f2s

Msq = FermionSpinSum[
f fstar // Explicit // Expand]/(qav^2 Gstrong^4) /. ftrace //
Contract // Simplify // SUNSimplify // Expand

standard = 4/9 ((s^2 + u^2)/t^2 + (u^2 + t^2)/s^2 - 2/3 u^2/(s t))
TrickMandelstam[Msq - standard, {s, t, u, 0}]

Quark Gluon Scattering:

Quit[];

«HighEnergyPhysics`FeynCalc`
ClearScalarProducts;
{
  ScalarProduct[p1, p1] =
   ScalarProduct[p2, p2] =
    ScalarProduct[p3, p3] = ScalarProduct[p4, p4] = 0,
  ScalarProduct[p1, p2] = ScalarProduct[p3, p4] = s/2,
  ScalarProduct[p1, p3] = ScalarProduct[p2, p4] = -t/2,
  ScalarProduct[p1, p4] = ScalarProduct[p2, p3] = -u/2
  };
QPr[p_, m_] :=
  I (DiracSlash[p] + m)/(ScalarProduct[p] - m^2) //
   ExpandScalarProduct;
SUNN = 3;
SetOptions[SUNSimplify, SUNNToCACF -> False];
{qav = 6, gav = 16, eav = 2};
ftrace := {DiracTrace -> Tr2, D -> 4};

f1munu = SpinorUBar[p3, 0].QGV[\[Nu], j].QPr[p1 + p2, 0].QGV[\[Mu],
    i].SpinorU[p1, 0] // Explicit
f2munu = SpinorUBar[p3, 0].QGV[\[Mu], i].QPr[p1 - p4, 0].QGV[v,
    j].SpinorU[p1, 0] // Explicit
fmunu = f1munu + f2munu;
f1s = -SpinorUBar[p1, 0].QGV[\[Rho], i].QPr[p1 + p2, 0].QGV[\[Sigma],
     j].SpinorU[p3, 0] // Explicit
f2s = -SpinorUBar[p1, 0].QGV[\[Sigma], j].QPr[p1 - p4, 0].QGV[\[Rho],
     i].SpinorU[p3, 0] // Explicit
fmunus = f1s + f2s;

Pols = PolarizationSum[\[Mu], \[Rho], p2,
p1] PolarizationSum[\[Nu], \[Sigma], p4, p3]

Msqmunu = FermionSpinSum[fmunu fmunus /(gav qav) // Expand]

SUNSimplify[SUNTrace[%], Explicit -> True]
% /. DiracTrace -> TR;

Msq = Pols % // Contract // Simplify

I’m appreciate for the help,cheers!