**Next message:**Yan: "Re: Tacer in FeynCalc mathematica 10.4 mac os"**Previous message:**Vladyslav Shtabovenko: "Re: Tacer in FeynCalc mathematica 10.4 mac os"**In reply to:**James: "ToTFI with momentum in numertor"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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
*

*>
*

**Next message:**Yan: "Re: Tacer in FeynCalc mathematica 10.4 mac os"**Previous message:**Vladyslav Shtabovenko: "Re: Tacer in FeynCalc mathematica 10.4 mac os"**In reply to:**James: "ToTFI with momentum in numertor"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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