**Next message:**Vladyslav Shtabovenko: "Re: Oneloop Bug? OneLoop on a combination of loop and non-loop terms"**Previous message:**Vladyslav Shtabovenko: "Re: OneLoop gets different results with/without OneLoopSimplify"**In reply to:**Vladyslav Shtabovenko: "Re: OneLoop Dimension D"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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!
*

*>>
*

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