Name: Vladyslav Shtabovenko Date: 05/19/15-12:20:59 PM Z

> 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)

OK, with the new ToPaVe function

<https://github.com/FeynCalc/feyncalc/commit/b451fac89e4aa990d6dff248e13a3890dd832f76>

we can finally convert scalar integrals written as FAD[…] to PaVe
functions without using OneLoop:

ToPaVe[FAD[{q, m}, {q + p, m2}], q]

-> I*Pi^2*B0[Pair[Momentum[p, D], Momentum[p, D]], m^2, m2^2]

This way we can obtain an output purely in terms of PaVe functions
without OneLoop.

Thanks again to Manuel for his mail. In this case ToPaVe turns out to be
quite useful:

«FeynCalc`

ClearScalarProducts;
bb = xx;
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}];

int = TID[amp, z]

int
% // ExpandScalarProduct // Simplify
% // ToPaVe[#, z] &

As of now you have to invoke ToPaVe by hand, but I’m planning to
integrate it into TID in a clever way, in particular to detect integrals
that look different but actually evaluate to same value as in the above
example.

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
>>