Momentum spectrum of nonlinear Breit-Wheeler pair production in spacetime fields

We show how to use a worldline-instanton formalism to calculate, to leading order in the weak-field expansion, the momentum spectrum of nonlinear Breit-Wheeler pair production in fields that depend on time and one spatial coordinate. We find a nontrivial dependence on the width, lambda, of the photon wave packet, and the existence of a critical point lambda(c). For lambda < lambda(c) and a field with one peak, the spectrum has one peak where the electron and positron have the same energy. For lambda > lambda(c) c this splits into two peaks. We calculate a high-energy (Omega >> 1 ) expansion, which to leading order agrees with the results obtained by replacing the spacetime field with a plane wave and using the well-known Volkov solutions. We also calculate an expansion for Omega similar to a(0) >> 1 , where the field is strong enough to significantly bend the trajectories of the fermions despite Omega >> 1 .