Name: V. Shtabovenko (email_not_shown)
Date: 01/18/18-03:38:01 PM Z

Am 18.01.2018 um 22:17 schrieb Duarte:
> Oh, sorry!, right. Thank you very much.
> So the two problems are solved: I can compute both ampW1 and the
> loop of ampF1.
> But with all these changes, I now face 2 new problems! The first
> of them shows up when I compute ampW1. Here, I get some objects
> (at least metric tensors and 4-momenta) both with and without
> hat. What do they mean? How I am supposed to deal with them?

This is the standard notation of the BMHV scheme, the objects with hats
live in D-4 dimensions, without hats in D dimensions and those with bars
in 4 dimensions.

The BMHV scheme is not a magical think to solve your problems with
gamma^5. It also has its drawbacks, such as the breakage of axial Ward
identities, which requires an additional counter-term. In general, I can
tell you that gamma^5 in D-dimensions is always "a mess", so you should
make sure that you understand the scheme (there are many of them!) that
you are using and its implications. FeynCalc just follows the known
prescription to compute traces in this scheme, but it does not solve the
physical problems for you.

> The second problem has to do with the following. As I am working in
> dimensional regularization, I will have to make D -> 4 - epsilon,
> (and I will want to obtain, on the one hand, the non-divergent term
> coming from the product between epsilon and the PaVe functions, and to
> make, on the other hand, epsilon -> 0 in the end; by the way, I do
> all of this manually, but maybe there is some automatic function to
> help me with these steps). But as I make D -> 4 - epsilon, some funny
> objects show up: basically, gamma matrices and 4-momenta with
> subscript "4-epsilon" (or just "epsilon"). I have the same questions:
> what do they mean? How I am supposed to deal with them?

When you substitute the results for the PaVe functions, you should
use FCReplaceD[exp,D->4-Epsilon]. This will keep the dimensions of the
Dirac matrices and 4-vectors unchanged. Only after the expansion around
eps=0 you can finally do D->4 to get the 4D result.

As for automatizing the evaluation:


$LoadAddOns = {"FeynHelpers"};
<< FeynCalc`


res = TID[ampF1, k, UsePaVeBasis -> True, ToPaVe -> True]
res2 = PaXEvaluate[res, PaXImplicitPrefactor -> 1/(2 Pi)^D]

DotSimplify[res2 /. D -> 4]

This is the raw (unrenormalized) result (Package-X uses D=4-2Epsilon,
keep that in mind!).
As I wrote before, gamma^5 in the BMHV scheme normally requires a
special counter term that you should work out separately.


> Thanks again,
> Duarte

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