From theory to precision modelling of strong-field QED in the transition regime

The combination of energetic electron beams, delivered from conventional accelerators at a high repetition rate, and ultraintense lasers, makes it possible to perform precision measurements of strong-field QED. The LUXE collaboration aims to perform precision measurements of nonlinear Compton scattering and Breit-Wheeler pair creation in the transition from the perturbative to nonperturbative regimes. Here we present an overview of recent developments in the modelling of strong-field QED processes, which are needed to reach the required precision of a few percent for intensity parameters $0.1 < \xi < 10$. We discuss how to go from plane wave QED results to numerical simulations and present predicted signals and error estimates.