Name: Vladyslav Shtabovenko Date: 05/17/15-02:03:31 AM Z

Dear Manuel,

I found the reason for the problem. Effectively, it was because
ScalarProductCancel was not cancelling a z^2 in the denominator
which allowed it to slip into the tensor decomposition routine,
where it lead to an additional factor of four in one of the terms.

I improved SPC when working with sums of different integrals and added
a cross-check in OneLoop to ensure that this would not happen again.

<https://github.com/FeynCalc/feyncalc/commit/4f1d8fd12f2ebe57215b39a69be38994b0f8a71d>

<https://github.com/FeynCalc/feyncalc/commit/a96bb2028faf8841ddda9f1d6246f9a27d0814ee>

Now the result is zero in both cases you mentioned (see attachment).

The changes are already in the nightly version.

If you are curious, you can also see the explicit cancellation using
the new option “UsePaVeBasis” in TID, which makes TID return output in
terms of PaVe coefficient functions (well, some pieces are still FAD’s,
but I’ll improve on that soon)

Those PaVe functions can then e.g. evaluated using H. Patel’s PackageX.
Again, the integral gives 0.

P.S. Note that PaVe functions of FeynCalc and Package X are actually
differently normalized, but in this case it is just an overall prefactor
that I ignored.

Cheers,
Vladyslav

Am 06.05.2015 um 14:38 schrieb manuel J.Vicente:
> Dear Vladyslav,
> thanks for your prompt answer. I’ve also found another problem with OneLoop. It fails in the 8.2.0 and in today’s nightly version. Results from default options and OneLoopSimplify->True differ.
>
> Notice the first line: bb=k. It corresponds to an external momentum. Changing its name to anything alphabetically after p (e.g. bb=x) seems to solve the problem??
>
> ===================================================================
> «FeynCalc`
> bb = k;
> ScalarProduct[bb, p1] = 0; ScalarProduct[bb, bb] = 0;
> ScalarProduct[p1, p1] = m^2; ScalarProduct[p2, p2] = m^2;
> ScalarProduct[p1, r] = 0; ScalarProduct[bb, r] = 0;
> ScalarProduct[bb, p2] = 0; ScalarProduct[r, p2] = 1;
> ScalarProduct[p1, p2] = 0;
>
> amp = SPD[r, z] SPD[bb, z] SPD[p2, z] SPD[p1,
> z] FAD[{z, 0}, {p1 + bb - z, m}, {p2 - z, m}, {p1 - z, m}];
>
> FI; OneLoop[z, amp] // PaVeReduce
>
> (-I/24)*m^2*Pi^2
>
> OneLoop[z, amp, OneLoopSimplify -> True]
>
> 0
> ======================================
>
> best regards and thanks again!
>
> M.J. Vicente
>