Scalar QED as a toy model for higher-order effects in classical gravitational scattering

TL;DR

This paper uses scalar QED as a simplified model to study higher-order classical scattering effects, employing advanced amplitude techniques to extract observables at two-loop order, providing insights relevant to gravitational physics.

Contribution

It introduces a novel application of scalar QED at two-loop order to analyze classical scattering, utilizing modern amplitude methods and simplifying the extraction of the radial action.

Findings

Successful extraction of classical scattering observables at two-loop order

Demonstration of scalar QED as an effective toy model for gravitational effects

Development of a simplified method for radial action extraction

Abstract

Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth order in the charges (two-loop order) in a classical regime analogous to the post-Minkowskian expansion in General Relativity. We employ modern scattering amplitude tools and extract classical observables by both eikonal methods and the formalism of Kosower, Maybee, and O'Connell (KMOC). In addition, we provide a simplified approach to extracting the radial action beyond the conservative sector.