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

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.