Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy

TL;DR

This paper analytically computes complex integrals related to gravitational scattering at the seventh order in G, advancing the understanding of binary system dynamics at high post-Newtonian accuracy using multi-loop integral techniques.

Contribution

It introduces a novel analytical method to evaluate multi-loop integrals in gravitational scattering at sixth post-Newtonian order, previously resistant to such analysis.

Findings

Successfully computed all integrals for nonlocal-in-time contributions at 6PN accuracy.

Achieved analytical expressions for the classical scattering angle at seventh order in G.

Enhanced computational techniques for multi-loop Feynman integrals in gravitational physics.

Abstract

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated $\frac1r$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multi-loop Feynman integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).