Hi Vladyslav,
When I tried to do TID to a rank-2 3-point loop tensor, TID with UsePaVeBasis set to be true or false give me different results (tid2-tid1 doesn't vanish). Do you know why this happens.
In[24]:=
ClearScalarProducts;
SPD[p1, p1] = 0;
SPD[p2, p2] = 0;
SPD[p1, p2] = s/2;
tid1 = (ToPaVe[
TID[FV[q, mu] FV[q, nu] FAD[{q, m}, {q + p1, m}, {q + p2, m}],
q, UsePaVeBasis -> False], q] /. D -> 4);
tid2 = (ToPaVe[
TID[FV[q, mu] FV[q, nu] FAD[{q, m}, {q + p1, m}, {q + p2, m}],
q, UsePaVeBasis -> True], q] /. D -> 4 // PaVeReduce);
FullSimplify[tid1 - tid2]
Out[30]= -((I \[Pi]^2 (s Overscript[g, _]^(munu)-2 (Overscript[p2, _]^mu Overscript[p1, _]^nu+Overscript[p1, _]^mu Overscript[p2, _]^nu)))/(4 s))
Cheers,
Xing
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