Radiation of scalar modes and the classical double copy

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.