Name: Vladyslav Shtabovenko Date: 05/07/15-12:34:46 PM Z

Dear Manuel,

in the meantime you can try to use the improved TID function (that does
tensor integral decompositions at 1-loop), that I’ve just commited to
the repository. It still misses some convenience features but is
hopefully quite stable.

Please find the notebook with your integral attached.

Since your integral has a vanishing Gram determinant, it is a bit tricky
to reduce, so that I included two ways of doing this.

In the first case TID will first cancel scalar products of z in the
numerator before doing the reduction. This greatly reduces the amount of
work needed to reduce the integral. The result that you get is actually
zero, since you have a difference of two B0 functions with the same
arguments, as (-p1+p2)^2 = (-p1+p2-k)^2

In the second case, cancelling of scalar products is turned off, so that
TID will have to reduce the full 4-point function of rank 4. This takes
some time and the result has to be given in terms of Dxxxx coefficient
functions because of the vanishing Gram determinants. However, in this
case it is easier to see that the integral actually vanishes because of
the kinematics of the external momenta. To make this more clear, we can
disable the expansion of scalar products in the final result (third
command). Then you see all the Dxxxx functions multiplied by scalar
products of the external momenta that vanish
upon expansion.

P.S. TID is also invoked by OneLoopSimplify, so you can that one as
well, e.g. OneLoopSimplify[amp,z]

Hope that helps.

Cheers,
Vladyslav

Am 07.05.2015 um 01:59 schrieb Vladyslav Shtabovenko:
> Dear Manuel,
>
> thanks for you patience. I’m investigating the issue.
>
> 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
>>
>