Name: Nikita Belyaev (email_not_shown)
Date: 07/28/15-03:49:57 PM Z


Hi Vladyslav ,

>actually I have some doubts that your expression should have no
>imaginary part. At least, if I look at the pieces of the imaginary >part
>that are proportional to u^3:
>
>SelectNotFree[FCE[TrA2B2], Complex];
>u3Piece = SelectNotFree[%, u^3] // EpsEvaluate
>
>-512 I u^3 SP[p1, p2] LC[][k1, k2, p, s] +
> 512 I u^3 SP[p, p2] LC[][k1, k2, p1, s] -
> 512 I u^3 SP[p, p1] LC[][k1, k2, p2, s] +
> 512 I u^3 SP[k1, p2] LC[][k2, p, p1, s] -
> 512 I u^3 SP[k1, p] LC[][k2, p1, p2, s]
>
>Schouten[%]
>
>then it is clear that they do not vanish by the Schouten identity.

And this is exactly the thing we are worrying about. We've checked by hand that expressions with u^3 are cancelled out and there is totally no imaginary part (you also can check it by hand if you want, it isn't long calculation).
 
Moreover we can provide you additional example:

Line29:= (GS[p]-m).GA[\[Beta]1].(GS[p]+GS[p1]+GS[p2]-m).GA[\[Alpha]1].GS[k2].GA[\[Alpha]].(1-GA[5]);
Line30:= GA[\[Beta]].(GS[p2]-m).GA[\[Beta]1].(GS[p1]+m);
Line31:= GS[k1].GA[\[Alpha]1].(GS[q]-u).(1+GA[5].GS[s]).GA[\[Beta]].(GS[q]-GS[p1]-GS[p2]-u).GA[\[Alpha]].(1-GA[5]);
Line32:= (GS[p]+GS[p1]+GS[p2]-m).GA[\[Beta]].(GS[p]-m).GA[\[Alpha]1].GS[k2].GA[\[Alpha]].(1-GA[5]);
Line33:= GA[\[Beta]].(GS[p2]-m).GA[\[Beta]1].(GS[p1]+m);
Line34:= GS[k1].GA[\[Alpha]1].(GS[q]-GS[p1]-GS[p2]-u).GA[\[Beta]1].(GS[q]-u).(1+GA[5].GS[s]).GA[\[Alpha]].(1-GA[5]);

We've calculated this term by hand and it also contains no imaginary part while FeynCalc give us the same set of it in the output as in the previous case.

Best Regards,
Nikita Belyaev



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