Name: Vladyslav Shtabovenko (email_not_shown)
Date: 11/03/14-11:58:59 PM Z

Hi,

I'm terribly sorry for the very late reply, I must have overlooked your
e-mail.

OneLoop is generally designed to do the D->4 limit at the end of the
computation, so that it is not really the purpose of this function to
leave everything in D-dimensions.

However, there are other functions that can do similar things. For the
tensor integral decomposition you can use TID. If you also want the loop
integrals to be identified, use ToTFI. This will give you the integrals
in Tarcer's notation (see arXiv:hep-ph/9801383) , but they are trivially
related to the PaVe integrals via a prefactor.

So, for your example you can do

\$LoadPhi = False;
\$LoadTARCER = True;
\$LoadFeynArts = False;
<< HighEnergyPhysics`FeynCalc`;

-(-I/Pi^2) FVD[p, mu] FAD[{p - q, I M}] // TID[#, q] & //
ToTFI[#, q, p] & //FCI

This gives you

(I*Pair[LorentzIndex[mu, D], Momentum[p, D]]*TAI[D, 0, {{1, I*M}}])/Pi^21

To convert between TAI and A0 use:

TAI[D, 0, {{1, M}}] = (I*(Pi)^(2-D/2) (2Pi)^(D-4)) A0[M^2]

For examples of doing these kind of things, you can look at the files
in:

https://github.com/FeynCalc/feyncalc/tree/master/FeynCalc/fcexamples/QCD

And by the way, a D-dimensional vector should really be

Pair[LorentzIndex[\[Eta], D], Momentum[p, D]] and not just

Pair[LorentzIndex[\[Eta]], Momentum[p, D]] as in your original code.

This is because

Pair[LorentzIndex[\[Eta]], Momentum[p, D]]

evaluates to

Pair[LorentzIndex[\[Eta]], Momentum[p]]

which is a four dimensional vector.

Cheers,
Vladyslav

Am 13.08.2014 um 19:24 schrieb Marcela:
> Hi,
> when I use OneLoop in D dimension I lose the Dimension D at the end, for example:
> a = OneLoop[
> q, -(-I/Pi^2) Pair[LorentzIndex[\[Eta]],
> Momentum[p, D]] FAD[{p - q, I M}], Dimension -> D]
> a[[3]] // StandardForm
>
> Gives Pair[LorentzIndex[\[Eta]], Momentum[p]] instead of Pair[LorentzIndex[\[Eta]], Momentum[p,D]]
>
> How can I do to obtain Pair[LorentzIndex[\[Eta]], Momentum[p,D]]? I want to be sure tha all the expressions I have are in dimension D.
>
> Thank you!
>

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