Effective-one-body formalism for leading-order radiative effects in the post-linear framework

TL;DR

This paper develops an effective-one-body formalism for electromagnetic scattering that captures leading-order radiative effects, providing a foundation for future gravitational applications and improving the modeling of unbound orbits.

Contribution

It introduces a six-parameter EOB model for electromagnetic scattering, reduces it to five key parameters, and matches it to known two-body scattering results, advancing the EOB approach for dissipative dynamics.

Findings

Five parameters explicitly computed for the EOB formalism.

Agreement with unbound-to-bound orbit observables.

Conjecture for sub-leading angular momentum loss.

Abstract

In recent years, significant progress has been made in the computation of conservative and dissipative scattering observables using the post-Minkowskian approach to gravitational dynamics. However, for accurate modeling of unbound orbits, an appropriate effective-one-body (EOB) resummation of the post-Minkowski results that also accounts for dissipative dynamics is desirable. As a step in this direction, we consider the electromagnetic analog of this problem here. We show that a six-parameter equation of motion encapsulates the effective-one-body dynamics for the electromagnetic scattering problem appropriate to third-order in the coupling constant. Three of these six parameters describe the conservative part of the dynamics, while the rest correspond to the radiation-reaction effects. Here we show that only two radiation-reaction-related parameters are important at the desired order, making the effective number of parameters in our formalism to be five. We compute the explicit forms of these five parameters by matching EOB scattering observables to that of the original two-body ones computed by [Saketh et al., Phys.Rev.Res. 4 (2022) 1]. Interestingly, our formalism leads to a conjecture for the sub-leading angular momentum loss, for which no precise computations exist. In addition, we demonstrate that the bound-orbit observables computed using our method are in perfect agreement with those calculated using unbound-to-bound analytical continuation techniques. Lastly, we qualitatively discuss the extension of our formalism to gravity.