Name: Nikita Belyaev Date: 07/25/15-06:39:48 PM Z
Hello, Vladyslav
We’ve faced with a problem that we couldn’t solve. It is related to
imaginary parts of the traces. We have some of them to calculate and a
lot of them were already calculated correctly but for one specific term
we cannot get the result without imaginary part.
We’ve spent a lot of time using a FeynCalcFormLink procedure and also
trying to apply the Scouten identity as you told us some time ago but we
did not succeed because as I understand there is no common algorithm to
check such kind of equivalence in the general case.
Could you probably help us to check that the trace included contains no imaginary part?
Here is the code of our calculation:
Clear[“Global`*”];
<<HighEnergyPhysics`FeynCalc`
Needs[“FeynCalcFormLink`”]
$LeviCivitaSign = -1;
ScalarProduct[p,p]=m^2;
ScalarProduct[p1,p1]=m^2;
ScalarProduct[p2,p2]=m^2;
ScalarProduct[k1,k1]=0;
ScalarProduct[k2,k2]=0;
ScalarProduct[q,q] = u^2;
ScalarProduct[q,s] =0;
Line13:=
(GS[p2]-m).GA[\[Beta]1].(GS[p1]+m).GA[\[Beta]].(GS[p]-m).GA[\[Alpha]1].GS[k2].GA[\[Alpha]].(1-GA[5]);
Line14:=
GS[k1].GA[\[Alpha]1].(GS[q]-GS[p1]-GS[p2]-u).GA[\[Beta]1].(GS[q]-u).(1+GA[5].GS[s]).GA[\[Beta]].(GS[q]-GS[p1]-GS[p]-u).GA[\[Alpha]].(1-GA[5]);
Line15:=
(GS[p]-m).GA[\[Beta]1].(GS[p1]+m).GA[\[Beta]].(GS[p2]-m).GA[\[Alpha]1].GS[k2].GA[\[Alpha]].(1-GA[5]);
Line16:=
GS[k1].GA[\[Alpha]1].(GS[q]-GS[p1]-GS[p]-u).GA[\[Beta]1].(GS[q]-u).(1+GA[5].GS[s]).GA[\[Beta]].(GS[q]-GS[p1]-GS[p2]-u).GA[\[Alpha]].(1-GA[5]);
Tr13= DiracTrace[Line13];
Tr14= DiracTrace[Line14];
Tr15= DiracTrace[Line15];
Tr16= DiracTrace[Line16];
TrA2B2=FeynCalcFormLink[Tr13.Tr14+Tr15.Tr16];
ComplexExpand[FullSimplify[TrA2B2/1024]] //Schouten
Thanks for your help!
With the Best Regards,
Nikita Belyaev