Connecting real-time properties of the massless Schwinger model to the massive case

Quantum electrodynamics in $1 + 1$ space-time dimensions is analytically solvable for massless fermions, while no solution is known for massive fermions. Employing the classical-statistical approach, we simulate the real-time dynamics on a lattice using Wilson fermions with mass $m$ at gauge coupling $g$. It is shown that quantitative properties of the massless Schwinger model are emerging in the limit of large $g/m$. We investigate two scenarios corresponding to opposite charges which are either held fixed or moving back-to-back along the light cone, as employed in effective descriptions for jet energy loss and photon production in the context of heavy-ion collisions. Remarkably, we find that the dynamics is rather well described by the massless limit for a wide range of mass values at fixed coupling. Moreover, our study shows that previous approximate scenarios with external charges on the light cone rather accurately capture the self-consistent dynamics of the energy conserving simulation.