Integration-by-parts reductions from unitarity cuts and algebraic geometry

TL;DR

This paper introduces a novel method for efficiently deriving integration-by-parts reductions for two-loop integrals by combining unitarity cuts with algebraic geometry techniques, specifically syzygy equations.

Contribution

It presents a new approach that leverages unitarity cuts and algebraic geometry to streamline IBP reductions for complex two-loop integrals.

Findings

Efficient IBP reductions achieved using unitarity cuts.

Polynomial syzygy equations facilitate the reduction process.

Applicable to various two-loop integral topologies.

Abstract

We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.