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

TL;DR

This paper introduces new features of the FIRE Mathematica code that, combined with LiteRed, enable efficient reduction of complex Feynman integrals, exemplified by four-loop massless propagator integrals, leading to a four-loop version of MINCER.

Contribution

It presents an integrated approach using FIRE and LiteRed to perform integration by parts reduction for complicated Feynman integral families, including a four-loop variant of MINCER.

Findings

FIRE can be used with LiteRed for complex integral reductions

Achieved reduction of four-loop massless propagator integrals

Developed a four-loop version of the MINCER code

Abstract

New features of the Mathematica code FIRE are presented. In particular, 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 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 well-known three-loop computer code MINCER. We also describe various ways to find additional relations between master integrals for several families of Feynman integrals.