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FIRE4, LiteRed and accompanying tools to solve integration by parts relations

A.V. Smirnov
V.A. Smirnov
Journal / Anthology

Computer Physics Communications
Year: 2013
Volume: 184
Issue: 12
Page range: 2820-2827

We present the new version of the Mathematica code FIRE and ideas behind it. It can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated families of Feynman integrals. As an example, we consider four-loop massless propagator integrals for which LiteRed provides reduction rules and FIRE assists to apply these rules. So, as a by-product one obtains a four-loop variant of the wellknown algorithm MINCER. The existence of these explicit reduction rules shows that any four-loop massless propagator integral can be reduced to a linear combination of master integrals in the sense of a mathematical theorem. We also describe various algebraic ways to find additional relations between master integrals associated with several families of Feynman integrals.

*Science > Physics