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.
@article{arxiv.2305.08981,
title = {Conservative binary dynamics at order $O(\alpha^5)$ in electrodynamics},
author = {Zvi Bern and Enrico Herrmann and Radu Roiban and Michael S. Ruf and Alexander V. Smirnov and Vladimir A. Smirnov and Mao Zeng},
journal= {arXiv preprint arXiv:2305.08981},
year = {2023}
}