Counting master integrals: Integration by parts vs. functional equations

TL;DR

This paper demonstrates how functional equations can effectively relate master integrals, offering an alternative perspective to the traditional integration-by-parts method in multi-loop diagram calculations.

Contribution

It introduces the use of functional equations to establish relationships between master integrals, complementing the integration-by-parts technique.

Findings

Functional equations successfully relate master integrals.

Illustration with a two-loop propagator diagram.

Potential to simplify multi-loop calculations.

Abstract

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.