Laser-assisted elastic electron-muon scattering within the framework of electroweak theory

Abstract Within the framework of electroweak theory, we present a detailed analytical calculation of the differential cross section for elastic electron-muon scattering, both in the absence and in the presence of a circularly polarized laser field. Using a perturbative quantum field theoretical approach, we analyze the differential cross section as a function of the incident kinetic energy, the scattering angle, and the laser beam’s intensity and frequency. Our results reveal two distinct regimes: in the subrelativistic domain (MeV scale), the scattering probability is significantly modified by laser-induced dressing and momentum transfer processes, while in the ultra-relativistic domain (GeV scale), the particles’ inertia strongly suppresses the interaction. Furthermore, the differential cross section exhibits a non-monotonic dependence on the field strength, reflecting the underlying nonlinear dynamics of the particle-field interaction. These findings provide new insights into laser-assisted scattering processes, contributing to a deeper understanding of strong-field effects in high-energy particle physics.