Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields

Abstract

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, $\hat{I}»$, of the photon wave packet, and the existence of a critical point $\hat{I}{»}_c$. For $\hat{I}»<\hat{I}{»}_c$ and a field with one peak, the spectrum has one peak where the electron and positron have the same energy. For $\hat{I}»>\hat{I}{»}_c$ this splits into two peaks. We calculate a high-energy ($\hat{I}\text{c◯}\gg 1$) expansion, which to leading order agrees with the results obtained by replacing the space-time field with a plane wave and using the well-known Volkov solutions. We also calculate an expansion for $\hat{I}\text{c◯}\sim a_0\gg 1$, where the field is strong enough to significantly bend the trajectories of the fermions despite $\hat{I}\text{c◯}\gg 1$.

36 pages, 13 figures