Name: Marco V (email_not_shown)
Date: 04/19/18-12:54:01 AM Z


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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