Name: Vladyslav Shtabovenko Date: 11/03/14-11:27:29 PM Z

Hi,

for the q qbar -> q qbar see my next e-mail.

As far as the q g -> q g process is concerned, you have two syntax
errors in your code:

1)

f2munu = SpinorUBar[p3, 0].QGV[\[Mu], i].QPr[p1 - p4, 0].QGV[v,
j].SpinorU[p1, 0] // Explicit

should be

f2munu = SpinorUBar[p3, 0].QGV[\[Mu], i].QPr[p1 - p4, 0].QGV[\Nu,
j].SpinorU[p1, 0] // Explicit

2) You forgot to multiply Msqmunu by the polarization sum:

Msqmunu =
 FermionSpinSum[fmunu fmunus/(gav qav ) // Expand] Pols // Contract //
     SUNSimplify //
   ReplaceAll[#,
     DiracTrace[x_] :> DiracTrace[x, DiracTraceEvaluate -> True]] & //
   Simplify

Apart from that, the computation still will not give you the correct
result, since you are missing a diagram with the three gluon vertex.

Cheers,
Vladyslav

Am 03.11.2014 um 05:40 schrieb Lingxiao Xu:
> 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!
>