A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations

TL;DR

This paper introduces a simpler, linear algebra-based algorithm for generating unitarity-compatible integration by parts relations, improving the process of reducing multi-loop Feynman integrals in quantum field theory calculations.

Contribution

It presents a new, conceptually simpler algorithm for generating unitarity-compatible IBP relations, replacing complex computational algebra methods with straightforward linear algebra techniques.

Findings

The new algorithm is easier to implement and understand.

It produces complete sets of IBP relations compatible with unitarity.

The approach is based on recent mathematical results and linear algebra.

Abstract

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower argued that the reduction to master integrals is complicated by the presence of integrals with doubled propagator denominators in the integration by parts relations and they introduced a novel reduction procedure which eliminates all such integrals from the start. Their approach has the advantage that it automatically produces integral bases which mesh well with generalized unitarity. The heart of their procedure is an algorithm which utilizes the weighty machinery of computational commutative algebra to produce complete sets of unitarity-compatible integration by parts relations. In this paper, we propose a conceptually simpler algorithm for the generation of complete sets of unitarity-compatible integration by parts relations based on recent results in the mathematical literature. A striking feature of our algorithm is that it can be described entirely in terms of straightforward linear algebra.