Scattering processes in the massive Schwinger model

TL;DR

This paper develops a resummed mass perturbation theory for the massive Schwinger model, accurately capturing scattering processes, resonances, and particle production thresholds through Dyson-Schwinger equations.

Contribution

It introduces a matrix-valued Feynman rule derivation and applies it to fully incorporate resonances and thresholds in scattering cross sections without additional approximations.

Findings

Resummed mass perturbation theory accurately models scattering processes.

Resonances and particle production thresholds are properly included.

The approach aligns with the complete spectrum of the model.

Abstract

We derive the (matrix-valued) Feynman rules of the mass perturbation theory and use it for the resummation of the $n$-point functions with the help of the Dyson-Schwinger equations. We use these results for a short review of the complete spectrum of the model and for a discussion of scattering processes. We find that in scattering cross sections all the resonances and higher particle production thresholds of the model are properly taken into account by our resummed mass perturbation theory, without the need of further approximations.