Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders

TL;DR

This paper derives nonlocal tail effects in gravitational scattering at high orders using advanced integration techniques, providing essential insights for modeling binary inspirals.

Contribution

It introduces a novel integration-by-parts algorithm, SpideR, to compute tail effects at 5PM and 10SF orders, advancing the precision of gravitational dynamics calculations.

Findings

Agreement with existing literature up to sixth post-Newtonian order

Development of the Sparse Integral Reducer (SpideR) algorithm

Derivation of tail effects involving polylogarithms of weight three

Abstract

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to fifth Post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight three. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the Sparse Integral Reducer (SpideR). We find perfect agreement in the overlap with all existing literature through sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order.