The H-graph with equal masses in terms of multiple polylogarithms

TL;DR

This paper computes all master integrals for the equal-mass H-graph at third post-Minkowskian order in gravitational wave physics, expressing them via multiple polylogarithms and providing a numerical evaluation tool.

Contribution

It expresses all relevant master integrals for the equal-mass H-graph up to weight four in terms of multiple polylogarithms and offers a numerical program for their evaluation.

Findings

All master integrals up to weight four are expressed in terms of multiple polylogarithms.

A numerical program for evaluating these integrals with arbitrary precision is provided.

The results facilitate precise calculations in gravitational wave modeling at third post-Minkowskian order.

Abstract

The initial phase of the inspiral process of a binary system producing gravitational waves can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph contributes. We consider the case where the two objects making up the binary system have equal masses. We express all master integrals related to the equal-mass H-graph up to weight four in terms of multiple polylogarithms. We provide a numerical program which evaluates all master integrals up to weight four in the physical regions with arbitrary precision.