Conservative binary dynamics beyond order $\alpha^5$ in electrodynamics

TL;DR

This paper advances the calculation of the conservative scattering angle for two charged particles in electrodynamics to sixth order in coupling and fourth order in velocity, surpassing previous results.

Contribution

It introduces a novel computation at higher order in electromagnetic coupling and velocity using the Effective One-Body formalism and classical solutions.

Findings

Achieved sixth order in electromagnetic coupling calculation.

Extended the velocity order to four, beyond previous work.

Utilized classical binary-charge solutions for transfer of information.

Abstract

We compute the conservative scattering angle of two classical charged particles at the sixth order in electromagnetic coupling, and at the fourth order in velocity, thereby going beyond the current state of the art [fifth order in coupling, derived by Bern {\it et al.}, Phys. Rev. Lett. \textbf{132}, 251601 (2024)]. Our result is obtained by using the electromagnetic version of the Effective One-Body formalism to transfer information from the exact circular binary-charge solution of Schild [Phys. Rev. \textbf{131}, 2762 (1963)] to the post-Lorentzian expansion of the scattering angle.