Radiation of scalar modes and the classical double copy

TL;DR

This paper extends the classical double copy framework to scalar theories, showing how pion radiation relates to special Galileons and mapping bi-adjoint scalar radiation to non-linear sigma models.

Contribution

It generalizes the classical double copy to scalar theories, establishing a correspondence between pion and Galileon radiation and constructing the single copy via color-kinematics replacements.

Findings

Classical perturbative double copy relates pion and Galileon radiation.

Mapping bi-adjoint scalar radiation to non-linear sigma models.

Leading and next-to-leading order radiation amplitudes computed.

Abstract

The double copy procedure relates gauge and gravity theories through color-kinematics replacements and holds for both scattering amplitudes and in classical contexts. Moreover, it has been shown that there is a web of theories whose scattering amplitudes are related through operations that exchange color and kinematic factors. In this paper, we generalize and extend this procedure by showing that the classical perturbative double copy of pions corresponds to special Galileons. We consider point-particles coupled to the relevant scalar fields, and find the leading and next to leading order radiation amplitudes. By considering couplings motivated by those that would arise from extracting the longitudinal modes of the gauge and gravity theories, we are able to map the non-linear sigma model radiation to that of the special Galileon. We also construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements.