Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics
Abstract
A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, G, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration via Harmonic Polylogarithms. The analytic expression of the tail contribution to the scattering involve transcendental constants up to weight four.
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