Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory

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.

77 pages, 10 figures (corrected minor typos and added minor clarifications)

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Cited by in corpus (7)

• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Frequency-domain self-force calculations using Gegenbauer reconstruction