Name: Vladyslav Shtabovenko Date: 05/07/15-03:54:14 PM Z

Another late follow-up. With OneLoopSimplify and the refactored TID
you will get general D-dimensional results without D->4 being taken
anywhere:

a = OneLoopSimplify[-(-I/Pi^2) Pair[LorentzIndex[\[Eta],D],
    Momentum[p, D]] FAD[{p - q, I M}], q]

Cheers,
Vladyslav

Am 03.11.2014 um 23:58 schrieb Vladyslav Shtabovenko:
> 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!
>>