Bound states and the classical double copy

TL;DR

This work extends the classical double copy to bound systems by computing leading-order gluon radiation from interacting color charges on general orbits and mapping the result to dilaton gravity via color-to-kinematics substitutions. The mapped gravitational radiation comprises both graviton and dilaton components, and the approach recovers known bremsstrahlung results in appropriate limits. In the nonrelativistic post-Newtonian regime, the framework reproduces standard PN radiation formulas, including the quadrupole graviton emission and scalar contributions, with a clear mapping from color dipoles to gravitational quadrupoles. The paper also discusses limitations related to dilaton contributions and outlines directions for incorporating higher-order corrections and spin effects to connect more directly with pure GR observations.

Abstract

We extend the perturbative classical double copy to the analysis of bound systems. We first obtain the leading order perturbative gluon radiation field sourced by a system of interacting color charges in arbitrary time dependent orbits, and test its validity by taking relativistic bremsstrahlung and non-relativistic bound state limits. By generalizing the color to kinematic replacement rules recently used in the context of classical bremsstrahlung, we map the gluon emission amplitude to the radiation fields of dilaton gravity sourced by interacting particles in generic (self-consistent) orbits. As an application, we reproduce the leading post-Newtonian radiation fields and energy flux for point masses in non-relativistic orbits from the double copy of gauge theory.

Figures (1)

• Figure 1: Leading order Feynman diagrams for the perturbative expansion of ${\tilde{J}}^\mu_a(k)$.