Laser-assisted scattering of a muon neutrino by an electron within the Electroweak theory

TL;DR

This paper analyzes how a circularly polarized laser field influences the elastic scattering of muon neutrinos by electrons within the electroweak framework, revealing significant modifications to the differential cross-section.

Contribution

It provides a detailed analytical treatment of neutrino-electron scattering in a laser field using Dirac-Volkov wave functions, extending previous Fermi theory results.

Findings

Laser field significantly alters the differential cross-section.

Laser strength and frequency affect photon exchange dynamics.

Results help address unitarity issues in Fermi theory.

Abstract

In accordance with the electroweak theory, we perform, in the first-Born approximation, a detailed analytical treatment of the differential cross-section (DCS) for the elastic scattering process $e^{-}+\nu_{\mu}\longrightarrow e^{-}+\nu_{\mu}$ in both absence and presence of a circularly polarized laser field. This scattering process is examined by using Dirac-Volkov wave functions for charged particles within an external laser field. The theoretical results obtained for the differential cross-section without laser field are compared with other theoretical results within the framework of Fermi theory. These results revealed to us the most important points that contribute to the understanding of the electroweak theory role in solving the problem of unitarity violation of the differential cross-section in Fermi theory. The differential cross section is modified significantly by inserting the electrons into an electromagnetic field. In addition, the influence of the laser strength and its frequency on the photons exchange between the colliding system and the laser field are also included and discussed. These effects are heavily related to the order and argument of the ordinary Bessel functions introduced in the theoretical calculation.