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The decomposition of four-point functions rapidly gets very large with the

tensor rank (in the integration momentum). Does anyone have any experience

with doing this kind of integrals with straight-forward Feynman parameter

integration?

FeynCalc provides the function TID for doing tensorial decomposition. This

function is used internally be OneLoopSimplify. So, setting the

OneLoopSimplify -> True when using OneLoop, should allow the calculation of

the integral you mention. This presumably also requires a good deal of

patience.

I have done the integral using something like the sequence of commands

given below. The result was, as expected, a monstruously large polynomial

in the masses and external momenta with scalar functions B_0, C_0, D_0 as

coefficients.

The WriteString commands are just there to be able to follow the progress.

You may also want to set $VeryVerbose to 1 or 2.

If you have suggestions on how to optimize things (FeynCalc code or

calculational procedure), please let me know.

Frederik

amp=Pair[Momentum[k],Momentum[p1]]^3 FeynAmpDenominator[

PropagatorDenominator[k,lam], PropagatorDenominator[(k-q),lam],

PropagatorDenominator[(k-p1),m], PropagatorDenominator[(k+p2), M]]

res=TID[amp, k, ScalarProductCancel -> False];

res // Length;

res1=(WriteString["stdout","."]; OneLoop[k,#])& /@ res;

res1 // Length;

(WriteString["stdout","."]; PaVeReduce[#])& /@ Expand[res1];

At 18:59 17-03-2003 -0500, you wrote:

*>I'm trying to do an integral that FeynCalc chokes on. The message returned
*

*>is the usual
*

*>
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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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*>
*

*>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.
*

*>
*

*>The integrals are box diagrams, and a typical term would look something like
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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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*>
*

*>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
*

*>for various terms in the amplitude.
*

*>
*

*>Is there a fix in FeynCalc, or do I have to use another program (and if so,
*

*>which one)?
*

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