Classical double copy from color kinematics duality: A proof in the soft limit

Classical double copy is an intriguing relationship between classical solutions to a gravity theory and solutions to classical Yang-Mills equations. Although formally inspired by the double copy relation between (quantum) scattering amplitudes in Yang-Mills and perturbative gravity, a direct proof of the former from the latter continues to be under investigation. In this paper, we attempt to prove classical double copy from the color-kinematics duality symmetry of scalar QCD amplitudes in a restricted setting. That is, we consider radiative solutions with classical scattering sources in Yang-Mills theory and perturbative gravity in D>4 spacetime dimensions. We show that when the frequency of radiation is much smaller than the characteristic frequency of the process, then at the subleading order in frequency, the classical double copy relating radiative gluon field to radiative gravitational field can be proved from the color-kinematics duality of scalar QCD amplitudes.