Counting master integrals: integration by parts vs. differential reduction

TL;DR

This paper compares integration by parts and differential reduction methods for counting master integrals, revealing a new algebraic relation in the two-loop sunset diagram that enhances understanding of integral reduction techniques.

Contribution

It introduces a novel algebraic relation between master integrals in the two-loop sunset diagram not derived from traditional IBP methods.

Findings

Discovered a new algebraic relation among master integrals.

Highlighted differences between IBP and differential reduction techniques.

Enhanced the understanding of master integral counting methods.

Abstract

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the integration-by-parts technique is found.