Classical double copy of worldline quantum field theory

The recently developed worldline quantum field theory (WQFT) formalism for the classical gravitational scattering of massive bodies is extended to massive, charged point particles coupling to biadjoint scalar field theory, Yang-Mills theory, and dilaton-gravity theory. We establish a classical double copy relation in these WQFTs for classical observables (deflection, radiation). The biadjoint scalar field theory fixes the locality structure of the double copy from Yang-Mills to dilaton gravity. Using this, the eikonal scattering phase (or free energy of the WQFT) is computed to next-to-leading order (NLO) in coupling constants using the double copy as well as directly finding full agreement. We clarify the relation of our approach to previous studies in the effective field theory formalism. Finally, the equivalence of the WQFT double copy to the double copy relation of the classical limit of quantum scattering amplitudes is shown explicitly up to NLO.