Scattering Amplitudes and Conservative Binary Dynamics at $O(G^5)$ without Self-Force Truncation

TL;DR

This paper advances the calculation of gravitational interactions between two non-spinning bodies by computing the complete potential and scattering angle at fifth order in Newton's constant, including second-order self-force effects, using innovative amplitude-based methods.

Contribution

It introduces improved integration algorithms and applies scattering-amplitude techniques to compute high-order conservative dynamics without self-force truncation.

Findings

Complete potential and scattering angle at 5th order in G

Closed-form expression for first self-force sector

Discovery of cancellations related to Calabi-Yau geometry

Abstract

We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order self-force (2SF) effects. The calculation is carried out in the scattering-amplitude framework, combining the double copy, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry.