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

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 $\frac{1}{r}$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multiloop 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).