**Next message:**Steffen Schwertfeger: "Error in PaVeReduce?"**Previous message:**Vladyslav Shtabovenko: "Re: $LimitTo4 and PaVeReduce"**Maybe in reply to:**Nefedov Maxim: "Fwd: Box-diagrams, rational parts and OneLoop"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Hi Maxim,

let me contribute to the resolution of the discrepancy.

The point is that at the end of the computation OneLoop converts

all the D-dimensional 4-vectors and metric tensors to 4-dimensions.

This is also what one normally does when doing computation by hand,

so there is no issue here. However, if the output of OneLoop is not the

full expression that you want to evaluate but just a part of it, one has to

be careful.

In particular, if the output of OneLoop contains metric tensors and you

want to contract it with D-dimensional metric tensors, then you have to

convert your expression back to D-dimensions first. Otherwise, from

contracting g^{mu nu} g_{mu nu} you obtain 4 instead of D, which gives

the rise to the discrepancy that you have been observing.

The correct way of writing the code is

ScalarProduct[q1, q1] = 0;

ScalarProduct[q2, q2] = 0;

ScalarProduct[q3, q3] = 0;

den = FAD[{q, 0}, {q - q1, 0}, {q - q1 - q2, 0}, {q - q1 - q2 - q3,

0}];

ex1 = Contract[(OneLoop[q, den*SP[q, q]*FV[q, mu]*FV[q, nu]] //

ChangeDimension[#, D] &)*MTD[mu, nu]] // PaVeReduce

ex2 = OneLoop[q, den*SP[q, q]^2] // PaVeReduce //

ChangeDimension[#, D] &

and the difference is zero, as it should be.

Cheers,

Vladyslav

*> -----
*

----- ðÅÒÅÎÁÐÒÁ×ÌÅÎÎÏÅ ÓÏÏÂÝÅÎÉÅ ----------

*> ïÔ: *Nefedov Maxim*
*

*> äÁÔÁ: ÓÕÂÂÏÔÁ, 11 ÍÁÑ 2013 Ç.
*

*> ôÅÍÁ: Box-diagrams, rational parts and OneLoop
*

*> ëÏÍÕ: feyncalc@feyncalc.org
*

*>
*

*> Hi!
*

*> Trying to calculate box diagrams with OneLoop (Mathematica 7 + FC 8.2.0)
*

*> I obtained the different results in the seemingly equivalent calculations:
*

*> ------------------------------------------------------------------
*

*> ScalarProduct[q1, q1] = 0;
*

*> ScalarProduct[q2, q2] = 0;
*

*> ScalarProduct[q3, q3] = 0;
*

*> den = FAD[{q, 0}, {q - q1, 0}, {q - q1 - q2, 0}, {q - q1 - q2 - q3,
*

*> 0}];
*

*>
*

*> (*Doing OneLoop with q^2*q^mu*q^nu in numerator and then contracting with
*

*> g_munu*)
*

*> ex1 = PaVeReduce[
*

*> Contract[OneLoop[q, den*SP[q, q]*FV[q,mu]*FV[q, nu]]*
*

*> MT[mu, nu]]]
*

*>
*

*> (*Doing OneLoop with q^4 in numerator*)
*

*> ex2 = PaVeReduce[OneLoop[q, den*SP[q, q]^2]]
*

*> ------------------------------------------------------------------
*

*> The results are different:
*

*>
*

*> ex1-ex2=I*Pi^2/2
*

*>
*

*> It looks like that in this two cases, the rational part of the answer (the
*

*> part which is finite in the limit D->4, but not proportional to the basis
*

*> scalar integrals) is treated in a different way, and I can not guess how to
*

*> use OneLoop to obtain always the correct answers.
*

*> Thanks in advance for any help.
*

*> Maxim Nefedov
*

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