Classical and quantum scattering in post-Minkowskian gravity

TL;DR

This paper explores the structural properties of post-Minkowskian gravity, linking scattering angles to potentials within the effective one body framework, and investigates the relation between quantum amplitudes and classical dynamics.

Contribution

It derives explicit links between scattering angles and potentials up to 4PM order within EOB theory and analyzes the relation between quantum amplitudes and classical scattering.

Findings

Derived explicit links between scattering angle and potentials up to 4PM.

Computed the scattering amplitude from quantized 3PM EOB potential.

Identified tensions between different high-energy and self-force results and proposed resolutions.

Abstract

New structural properties of post-Minkowskian (PM) gravity are derived, notably within its effective one body (EOB) formulation. Our results concern both the mass dependence, and the high-energy behavior, of the classical scattering angle. We generalize our previous work by deriving, up to the fourth post-Minkowskian (4PM) level included, the explicit links between the scattering angle and the two types of potentials entering the Hamiltonian description of PM dynamics within EOB theory. We compute the scattering amplitude derived from quantizing the third post-Minkowskian (3PM) EOB radial potential (including the contributions coming from the Born iterations), and point out various subtleties in the relation between perturbative amplitudes and classical dynamics. We highlight an apparent tension between the classical 3PM dynamics derived by Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)], and previous high-energy self-force results [Phys. Rev. D 86, 104041 (2012)], and propose several possible resolutions of this tension. We point out that linear-in-mass-ratio self-force computations can give access to the exact 3PM and 4PM dynamics.