Name: V. Shtabovenko (email_not_shown)
Date: 04/19/18-06:02:27 AM Z


Hi,

just add the option ToPaVe->True to TID.

MBOX = ChangeDimension[(1/(16 Pi^4)) TID[integrandBOX, k,
      UsePaVeBasis -> True, ToPaVe -> True], 4] // Simplify

that's all. ToPaVe is also a separate function

?ToPaVe

ToPaVe[expr,q] converts all the scalar 1-loop integrals that depend on
the momentum q to scalar Passarino Veltman functions A0, B0, C0, D0 etc.

Cheers,
Vladyslav

Am 19.04.2018 um 06:54 schrieb Marco V:
> Hello,
>
> I am using FeynCalc 9.2.0 and I am trying to compute the amplitude for a box diagram in QED, but when I use TID to decompose the loop integral, it seems that FC does not convert a denominator into a PaVe scalar function.
>
> Setting the integrand
>
> numBOX = e^4 (SpinorUBarD[q1,
> m\[Mu]].GAD[\[Alpha]].(GSD[p1 - k] +
> m\[Mu]).GAD[\[Beta]].SpinorUD[p1, m\[Mu]] SpinorUBarD[q2,
> me].GAD[\[Alpha]].(GSD[k + p2] + me).GAD[\[Beta]].SpinorUD[p2,
> me]);
>
> integrandBOX =
> numBOX*FAD[{p1 - k, m\[Mu]}, {k + p2, me}, {k + p2 - q2,
> SmallVariable[\[Lambda]]}, {k, SmallVariable[\[Lambda]]}];
>
>
> and putting it in TID
>
> MBOX = ChangeDimension[(1/(16 Pi^4)) TID[integrandBOX, k,
> UsePaVeBasis -> True], 4] // Simplify
>
>
> the result I obtain is mostly in terms of D coefficient functions and independent from the loop momentum k (as I expect), but there is also a term
>
> -2 (me^2 + m\[Mu]^2 - s) Spinor[Momentum[q1], m\[Mu],
> 1].GA[\[Alpha]].Spinor[Momentum[p1], m\[Mu], 1] Spinor[
> Momentum[q2], me, 1].GA[\[Alpha]].Spinor[Momentum[p2], me,
> 1] FAD[{k, SmallVariable[\[Lambda]]}, {k + p1, m\[Mu]}, {k - p2,
> me}, {k - p2 + q2, SmallVariable[\[Lambda]]}, Dimension -> 4]
>
> which I understand should correspond to a D0 but it is not transformed in it.
>
> If I try to use TID on the last expression, it remains unchanged.
> If instead I use OneLoop it gives me exactly the D0 which I was looking for.
>
> I suppose the problem is related to the choice of dimension, but I don't understand why the rest of the result is correctly in terms of PaVes. Can you explain what I am doing wrong?
>
> Many Thanks
>



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