Name: Vladyslav Shtabovenko 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!
>