The criterion of irreducibility of multi-loop Feynman integrals

TL;DR

This paper introduces a new criterion for determining the irreducibility of multi-loop Feynman integrals using integration by parts recurrence relations, clarifying when integrals can be simplified.

Contribution

It presents a novel criterion for irreducibility of Feynman integrals based on recurrence relations, enhancing the understanding of integral reduction possibilities.

Findings

The criterion simplifies the assessment of integral reducibility.

It clarifies the conditions under which integrals can be reduced.

The technique aids in systematic analysis of Feynman integrals.

Abstract

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-product provides with simple criterion of the irreducibility.