Conservative binary dynamics at order $O(\alpha^5)$ in electrodynamics

TL;DR

This paper calculates the classical scattering angle for two charged bodies in electrodynamics up to fifth order in the coupling, using advanced amplitude and integration techniques, and discusses implications for gravity calculations.

Contribution

It presents a fifth-order computation of the scattering angle in electrodynamics using modern amplitude methods and multi-loop integrals, demonstrating feasibility for gravity theories.

Findings

Potential-photon contributions computed up to $O(\alpha^5)$

Expression involves cyclotomic polylogarithms

Shows methods applicable to gravitational calculations

Abstract

We compute the potential-photon contributions to the classical relativistic scattering angle of two charged non-spinning bodies in electrodynamics through fifth order in the coupling. We use the scattering amplitudes framework, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. At fifth order, the result is expressed in terms of cyclotomic polylogarithms. Our calculation demonstrates the feasibility of the corresponding calculations in general relativity, including the evaluation of the encountered four-loop integrals.