**Next message:**V. Shtabovenko: "Re: a problem about \gamma^0 matrix"**Previous message:**V. Shtabovenko: "Re: Feyncalc refuses to expand LC"**Next in thread:**Frederik Orellana: "Re: Problem using OneLoop"**Maybe reply:**Frederik Orellana: "Re: Problem using OneLoop"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

In general, the best strategy for such complicated integrals is to first

rewrite them in terms of the coefficient functions

amp = Pair[Momentum[k], Momentum[p1]]^3 FAD[{k, lam}, {(k - q),

lam}, {(k - p1), m}, {(k + p2), M}];

res = TID[amp, k, UsePaVeBasis -> True, ToPaVe -> True]

which quickly returns a rather compact result

-3 I \[Pi]^2 PaVe[0, 0,

1, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2],

SPD[p2, p2] + 2 SPD[p2, q] + SPD[q, q], SPD[q, q], SPD[p2, p2],

SPD[p1, p1] - 2 SPD[p1, q] + SPD[q, q]}, {lam^2, m^2, M^2, lam^2},

PaVeAutoOrder -> True, PaVeAutoReduce -> True] SP[p1, p1]^2 -

...

Then, depending on what one wants to do, one can

1) Evaluate the coefficient functions numerically using LoopTools,

Collier or whatever other package

2) Evaluate the coefficient functions analytically via Package-X by

using PaXEvaluate from the FeynHelpers extension

3) Reduce the coefficient functions to scalar integral, which would of

course generate a huge amount of terms, e.g.

res[[1]] // PaVeReduce

Cheers,

Vladyslav

*> I'm trying to do an integral that FeynCalc chokes on. The message returned
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*> is the usual
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*>
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*> FYI: Tensor integrals of rank higher than 3 encountered; Please use the
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*> option CancelQP -> True or OneLoopSimplify->True or use another program.
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*>
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*> However, it appears that CancelQP->True is the default, and OneLoopSimplify
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*> expresses the results in terms of Contract3, which doesn't seem to exist.
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*>
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*> The integrals are box diagrams, and a typical term would look something like
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*>
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*> (k.p1)^3 / [k^2-lam^2][(k-q)^2-lam^2][(k-p1)^2-m^2][(k+p2)^2-M^2]
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*>
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*> where p1^2=m^2 and p2^2=M^2. This term looks innocent enough, and in fact
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*> looks to me like it IS of rank 3. By a lot of fudging and manipulating I
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*> managed to get a result using ScalarProductCancel, but it is hit and miss
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*> for various terms in the amplitude.
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*>
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*> Is there a fix in FeynCalc, or do I have to use another program (and if so,
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*> which one)?
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**Next message:**V. Shtabovenko: "Re: a problem about \gamma^0 matrix"**Previous message:**V. Shtabovenko: "Re: Feyncalc refuses to expand LC"**Next in thread:**Frederik Orellana: "Re: Problem using OneLoop"**Maybe reply:**Frederik Orellana: "Re: Problem using OneLoop"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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