Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory

TL;DR

This paper develops an effective field theory framework for analyzing gravitational and electromagnetic interactions in systems with extreme mass ratios, enabling multiloop scattering calculations and verifying known results while presenting new findings.

Contribution

It introduces a novel effective field theory approach for self-force expansions, allowing systematic computation of higher-order corrections in classical scattering processes.

Findings

Verified known two-loop scattering results in electromagnetism and gravity.

Computed new two-loop scattering results for dyons and particles with additional scalar or vector interactions.

Established a formalism that encodes all-order dynamical information from classical backgrounds.

Abstract

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a "recoil operator" that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.