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

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.

19 pages, v2: version to be published, v3: boundary value for $J_{25}^{(4)}$ corrected

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• Machine Learning Post-Minkowskian Integrals
• Analytic two-loop master integrals for $tW$ production at hadron colliders. Part II
• Analytic results for two-loop planar master integrals for Bhabha scattering