Name: Vladyslav Shtabovenko (email_not_shown)
Date: 05/11/16-10:37:54 AM Z


Hi James,

tools that do IBP reduction usually deal only with scalar integrals. So
you need to do tensor reduction first.

num = C GA[mu].(GS[k] - M).GA[mu].(GS[k] - GS[q] - M).GA[
    nu].(GS[q] - M).GA[nu]
amp = FAD[{k - p, M}, {k, mw}, {k - q, M}, {q, M}, {-p + q, mw}]
fullamp = (num amp) // DiracSimplify // FCMultiLoopTID[#, {k, q}] & //
    DiracSimplify;

tfiamp = fullamp // ToTFI[#, k, q, p] & // ChangeDimension[#, 4] &;
tfiamp2 = TarcerRecurse[tfiamp]

Since you want to use 4-dim Dirac algebra I must warn you that this is
where one has to be very careful. Tensor reduction needs to work with
D-dim integrals, so things like

g^mu l_mu (...),

where g is 4dim and l is a loop momentum get uncontracted and l is
"upgraded" to D-dimensions. After the reduction the tensor integral

l_mu (...) is purely D-dimensional and it is the task of the user to
convert the appearing external momenta back to 4-dimensions.

Furthermore, for 4-dim+D-dim algebra only t'Hooft Veltman scheme is
supported. Dimensional reduction is NOT supported.

Cheers,
Vladyslav

Am 11.05.2016 um 01:50 schrieb James:
> Hello,
>
> I am trying to use FeynArts -> FeynCalc -> Tarcer to compute some 2-loop self
> energy integrals. However, I find that the ToTFI function won't deal with terms in
> the numerator which contain an internal loop momentum. I see this when trying to
> convert complicated FeynArts output, and I can reproduce the problem with a
> simple example, which I copy below.
>
>
> -------------------
>
> dm[mu_] := DiracMatrix[mu, Dimension -> 4]
> dm[5] := DiracMatrix[5]
> ds[p_] := DiracSlash[p]
> SetOptions[DiracSlash, Dimension -> 4, FeynCalcInternal -> True];
>
> num := C dm[mu].(ds[k] - M).dm[mu].(ds[k] - ds[q] - M).
> dm[nu].(ds[q] - M).dm[nu]
> amp := FeynAmpDenominator[PropagatorDenominator[k - p, M],
> PropagatorDenominator[k, mw], PropagatorDenominator[k - q, M],
> PropagatorDenominator[q, M], PropagatorDenominator[q - p, mw]] //
> Contract // FCI
>
>
> tfiamp := ToTFI[DiracSimplify[num SPC[amp, k, q]], k, q, p]
> tfiamp
>
> -----------------------
>
>
> The output I get is half made up of nice integrals terms like F and V and so on, but
> the rest is basically just the original input, for all the terms which contain an internal
> momentum (slashed) in the numerator. Is there something I am fundamentally
> doing wrong with the input? I am unsure because the ToTFI instructions don't have
> an example where there is a dot product of internal momentum and a gamma matrix
> like this in the numerator. If I can find the problem in this example then it should
> help with also converting the FeynArts output.
>
>
> Thanks,
> James
>



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