TID for contributions to the flow of the Graviton 4-point function

[floriandyduch-bot]

Hello everyone,

I am currently writing my Master thesis on quantum gravity and struggling with the loop integrations over diagrams of 4 graviton interactions. Concretely, I am trying to calculate the diagrams contributing to the flow of the graviton 4-point function. Therefore, I have quite complicated analytical expressions over which I want to perform the integrations. They consist of long (up to a few MB) polynomials in the momenta, a bunch projector terms like SPD[q,p1]*SPD[q,p2]*FAD[q] as well as denominators like

SFAD[{{q, 0},λ1^2, 2}]*SFAD[{{q + p4 - p1 - p3, 0},λ2^2}]*SFAD[{{q - p1, 0}, λ3^2}]

for example. Here, q is the loop momentum, λ1, ..., λ3 are the spectral mass parameters of the gravitons and p1, ..., p4 are the external momenta. My workflow is

TID -> FIREBurn -> TID[ToPaVe -> True] -> PaXEvaluate

which works generally fine. However, the first TID step sometimes takes very long (up to 100 hrs) without giving me a result. I have tried to speed up the TID by evaluating all the terms seperately

terms = List @@ Expand[expr];
resTID = Total[Map[TID[#, {q}] &, terms]];.

However, this only worked in some cases so far and for example not for the denominator mentioned above. I would very much appreciate some advises on how to speed up this first TID calculation or if there is a way to properly parallelise it. Thank you very much for your support!

Best regards

Florian

[vsht]

Hi,

first of all, using FIREBurn is probably the most inefficient way to approach IBP reduction one can think of.
You should switch to FeynHelpers 2.0 and make use of C++ FIRE.

As for TID, you can try parallel evaluation introduced in the recent FeynCalc 10.2, but personally I would
reimplement the whole setup using the new multiloop functionality of FeynCalc 10, e.g. as in

https://feyncalc.github.io/FeynCalcExamples/QCD/TwoLoops/GlGl-H

Since FCLoopTensorReduce does only the minimally needed tensor reduction, most heavy lifting is then
shifted to the IBP reduction tool (FIRE or KIRA) which is more efficient at this task,

I think that this should already help to improve the performance.

The remaining bottleneck might be the tensor reduction of a 4-point function,
where the combinatorics of 3 external momenta
becomes brutal for higher ranks. If this is the case, one might need something like
OPITeR to calculate the decompositions separately.

Cheers,
Vlad