Trouble when integrating Feynman parameters

[MeissnerAndre]

Hi,

at the moment, I have to evaluate an integral of the form

FCFeynmanParametrize[(SPD[p, p]^4 ) SFAD[{p, -k^2,
2}] SFAD[{p + q, -[Lambda]^2}] SFAD[{p + q, 0, 2}], {p},
Names -> x, "Euclidean" -> True, FeynmanIntegralPrefactor -> "Unity",
FCReplaceD -> {D -> 4 - 2 [Epsilon]}],

which should translate to

p^8/((p^2+k^2)^2((p+q)^2 + lambda^2)(p+q)^4)

if I did everything correctly. When trying to integrate the resulting Feynman parameters, my computer breaks down (probably due to an exhausted RAM). Since I'm new to FeynCalc, I wanted to ask if there is a better alternative in how to calculate this integral with FeynCalc or if there are any other ways to make the calculate this with the Feynman parameters.

FeynCalc 10.1.0 (stable version).
Mathematica 14.0

Thanks a lot for the great package and thanks in advance for any responses :)

[vsht]

Hi, in general, not every Feynman parametric integral can be integrated directly in a straight forward fashion. Otherwise, one would not need other techniques such as differential equations, Mellin-Barnes etc. In your case the integral still can be simplified using partial fractioning and tesnor reduction / IBPs. This should provide a list of simpler master integrals to calculate. Apart from that, Erik Panzer's HyperInt package is probably the most powerful tool for calculating Feynman parametric integrals directly https://bitbucket.org/PanzerErik/hyperint/src Am 11.01.25 um 01:26 schrieb MeissnerAndre:

…

Hi, at the moment, I have to evaluate an integral of the form FCFeynmanParametrize[(SPD[p, p]^4 ) SFAD[{p, -k^2, 2}] SFAD[{p + q, -[Lambda]^2}] SFAD[{p + q, 0, 2}], {p}, Names -> x, "Euclidean" -> True, FeynmanIntegralPrefactor -> "Unity", FCReplaceD -> {D -> 4 - 2 [Epsilon]}], which should translate to p^8/((p^2+k^2)^2((p+q)^2 + lambda^2)(p+q)^4) if I did everything correctly. When trying to integrate the resulting Feynman parameters, my computer breaks down (probably due to an exhausted RAM). Since I'm new to FeynCalc, I wanted to ask if there is a better alternative in how to calculate this integral with FeynCalc or if there are any other ways to make the calculate this with the Feynman parameters. FeynCalc 10.1.0 (stable version). Mathematica 14.0 Thanks a lot for the great package and thanks in advance for any responses :) — Reply to this email directly, view it on GitHub <https://github.com/ FeynCalc/feyncalc#295>, or unsubscribe <https://github.com/ notifications/unsubscribe-auth/ ABXSD5ETZHRZ4QZFV5BLPND2KBQLVAVCNFSM6AAAAABU7MLAAWVHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZXHAYDONBYGE>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>