Name: Vladyslav Shtabovenko (email_not_shown)
Date: 01/18/17-07:03:35 PM Z


Dear Pilar,

many thanks for your question. I realized that there was a bug in TID
related to the loop integrals with uncontracted loop momenta in 4 and
D-4 dimensions that should be now fixed, so if you reinstall FeynCalc via

Import["https://raw.githubusercontent.com/FeynCalc/feyncalc/master/install.m"]
InstallFeynCalc[]

and then evaluate

$BreitMaison = True;
trs = DiracTrace[GAD[a].GAD[mu].GA[6].GAD[b].GAD[nu].GA[6]] /.
   DiracTrace -> Tr
amp = Contract[trs FVD[l, a] FVD[k + l, b] FAD[{l, 0}, {k + l, 0}]]
TID[amp, l, ToPaVe -> True] // Simplify

then the result should be correct. You can also use

TID[amp, l, ToPaVe -> True, FCVerbose->3]

to show different steps of the tensor decomposition.

As for the result of OneLoop, you are putting the finger on the
sore spot. The issue is that OneLoop (carelessly) converts the input
expression to D dimensions and puts the dimension of momenta and metric
tensors to 4 at the very end. This is "ok" for NDR, but messes things up
in BMHV for obvious reasons. It is difficult to tell how and why it came
to that situation, at least it was already like that when I joined the
project.

For now I blocked OneLoop for calculations in the BMHV scheme. For the
next stable release of FeynCalc it should be fixed, which would involve
some serious changes in the behavior of OneLoop.

Sorry for the trouble.

Cheers,
Vladyslav

Am 18.01.2017 um 08:31 schrieb Pilar Hernandez:
> Hello, I am confused about the differences in the output of OneLoop and TID & ToPaVe
> in an amplitude where I use the BMHV prescription for gamma5.
>
> trs =DiracTrace[
> GAD[a] . GAD[mu] . DiracMatrix[6] . GAD[b] . GAD[nu] .
> DiracMatrix[6]]\ \ /. \ DiracTrace -> Tr
> amp = Contract[trs FVD[l, a] FVD[k + l, b] FAD[{l, 0}, {k + l, 0}] ]
>
> I don't get the same result if I integrate with OneLoop[l, amp] or if I use TID[amp,l] and ToPaVe...
>
> What is the proper way to treat this amplitude ?
> Thanks, Pilar
>



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