Differential equations for loop integrals without squared propagators

TL;DR

This paper introduces a condition to avoid squared propagators in differential equations for loop integrals, simplifying calculations for many two- and three-loop diagrams using unitarity-compatible reductions.

Contribution

It provides a sufficient condition to prevent squared propagators, enabling more efficient differential equation setups for complex loop diagrams.

Findings

Applicable to a large class of two- and three-loop diagrams

Enables unitarity-compatible IBP reductions

Simplifies the reduction process by avoiding higher-power propagators

Abstract

We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using "unitarity-compatible" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.