Relativistic elastic scattering of a muon neutrino by an electron in an elliptically polarized laser field

TL;DR

This paper analyzes how an intense elliptically polarized laser field influences the elastic scattering of a muon neutrino by an electron, providing a generalized analytical expression and revealing polarization-dependent effects on the scattering cross section.

Contribution

It derives a new analytical formula for the differential cross section of neutrino-electron scattering in an elliptically polarized laser field, extending previous results for linear and circular polarizations.

Findings

Cross section is significantly enhanced for linear polarization.

Cross section is reduced for circular and elliptical polarizations.

Provides a generalized analytical expression for the scattering process.

Abstract

Within the framework of electroweak theory, we investigate the elastic scattering process $ e^{-} + \nu_{\mu} \rightarrow e^{-} + \nu_{\mu}$ in the presence of an intense elliptically polarized laser field. We derive an analytical expression for the spin-unpolarized differential cross section using the first Born approximation and the Dirac-Volkov states to describe the incident and scattered electrons. Our results generalize those found for the linearly polarized field by Bai \textit{et al.} [Phys. Rev. A \textbf{85}, 013402 (2012)] and for the circularly polarized field by El Asri \textit{et al.} [Phys. Rev. D \textbf{104}, 113001 (2021)]. We find that the differential cross section is significantly enhanced for linear polarization and reduced for circular and elliptical polarizations.