Classical and quantum scattering in post-Minkowskian gravity

TL;DR

This work develops a detailed PM/EOB framework for two-body gravitational dynamics, deriving how the classical scattering angle χ decomposes across PM orders and how it depends on energy, angular momentum, and mass ratio.It clarifies the links between two PM descriptions (the Q mass-shell potential and an energy-dependent radial potential W) and the two kinds of potentials used in PM/EFT formalisms, and shows how χ at 2PM–4PM is determined by a small set of γ-dependent functions, notably a single function at each PM order beyond 2PM.The authors extend the classical-to-quantum map by computing the 3PM quantum amplitude from the 3PM EOB potential, including IR/UV structures from Born iterations, and discuss the subtleties of translating quantum scattering amplitudes into classical dynamics, with Bohr’s cautionary view on overlapping domains of validity.A central tension is highlighted between the high-energy behavior inferred from Bern et al.’s 3PM calculation and the high-energy self-force results, which motivates conjectures about HE behavior and possible noncommutativity of limits, as well as radiative (tail) corrections that could mediate these discrepancies.Overall, the paper provides a coherent structural understanding of PM dynamics, offers pathways to obtain exact 3PM/4PM results via SF data, and outlines multiple avenues—including higher-PM calculations and refined quantum-classical maps—to resolve current tensions.

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.