Feynman integrals for binary systems of black holes

TL;DR

This paper computes master integrals for the H-graph in binary black-hole inspiral models at third post-Minkowskian order, expressing them with multiple polylogarithms and addressing mass asymmetry complexities.

Contribution

It provides explicit expressions for master integrals of the H-graph with equal masses and discusses methods for handling unequal masses involving square roots.

Findings

Master integrals expressed up to weight four using multiple polylogarithms.

Techniques developed for unequal mass cases with square root complications.

Enhanced computational tools for gravitational wave physics modeling.

Abstract

The initial phase of the inspiral process of a binary black-hole system can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph, contributes. In this talk we report how all master integrals of the H-graph with equal masses can be expressed up to weight four in terms of multiple polylogarithms. We also discuss techniques for the unequal mass case. The essential complication (and the focus of the talk) is the occurrence of several square roots.