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
>
>FYI: Tensor integrals of rank higher than 3 encountered; Please use the
> option CancelQP -> True or OneLoopSimplify->True or use another program.
>
>However, it appears that CancelQP->True is the default, and OneLoopSimplify
>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
>
>(k.p1)^3 / [k^2-lam^2][(k-q)^2-lam^2][(k-p1)^2-m^2][(k+p2)^2-M^2]
>
>where p1^2=m^2 and p2^2=M^2. This term looks innocent enough, and in fact
>looks to me like it IS of rank 3. By a lot of fudging and manipulating I
>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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