**Next message:**Vladyslav Shtabovenko: "Re: How to deal with the Gamma5 in DiracTrace"**Previous message:**Xing: "Re: OneLoop without CancelQP"**In reply to:**Xing: "Re: OneLoop without CancelQP"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Am 04.11.2015 um 18:45 schrieb Xing:

*> Hi Vladyslav,
*

*> Thank you very much.
*

*> But TID reduces everything into scalar integrals, which could be sort of lengthy. I wonder if there is a function other than the "legacy" OneLoop that can give tensor coefficients instead of scalar integrals.
*

Of course. This is what the option UsePaVeBasis and the function ToPaVe

are for.

In your example there is nothing to reduce, since the q1^2 term in the

nominator can be knocked off by trivial partial fractioning. Hence,

your result consists of only Passarino-Veltman *scalar* functions (e.g.

A0,B0,C0,D0) .

If you want, you can convert the resulting scalar integrals to this form

explicitly:

TID[SP[q1, q1] FAD[{q1, m1}, {q1 + kk1, m2}, {q1 + kk2, m3}], q1] //

ToPaVe[#, q1] &

Now suppose that you would have a q1.q1^3 there. Then you need a proper

reduction. As you wrote, the reduction into scalar integrals is quite

lengthy. With

TID[SP[q1, q1]^3 FAD[{q1, m1}, {q1 + kk1, m2}, {q1 + kk2, m3}], q1,

UsePaVeBasis -> True] // ToPaVe[#, q1] &

you get the quick result entirely in terms of the PaVe coefficient

functions.

Notice that the result also contains some non-loop terms, because

FeynCalc knows some relations between different PaVe functions (there

are plenty of those described in papers by Denner and Dittmaier, see

https://github.com/FeynCalc/feyncalc/wiki/Literature). You can "disable"

this "knowledge" by setting $LimitTo4 = False:

$LimitTo4 = False

TID[SP[q1, q1]^3 FAD[{q1, m1}, {q1 + kk1, m2}, {q1 + kk2, m3}], q1,

UsePaVeBasis -> True] // ToPaVe[#, q1] &

gives a very compact result.

Cheers,

Vladyslav

*>
*

*> Cheers,
*

*> Xing
*

*>
*

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