Direct Solution of Integration-by-Parts Systems

TL;DR

This paper introduces a novel method for directly solving integration-by-parts systems in quantum field theory, enabling efficient reduction of complex Feynman integrals to master integrals.

Contribution

The paper presents a new approach that derives direct reduction equations for numerator terms, including arbitrary powers of irreducible invariants, improving integral simplification.

Findings

Able to obtain reduction equations for arbitrary powers of invariants

Demonstrates effectiveness on complex Feynman integrals

Simplifies the process of integral reduction in quantum field theory

Abstract

Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products of irreducible invariants to a small set of master integrals. I present a new approach to solving these systems that finds direct reduction equations for numerator terms of a given Feynman integral. As a particular example of its power, I show how to obtain reduction equations for arbitrary powers of irreducible invariants, along with their solutions.