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

Abstract

In accordance with the electroweak theory, we perform a detailed analytical treatment of the differential cross-section (DCS) for the elastic scattering process e − + ν μ ⟶ e − + ν μ in both absence and presence of a circularly polarized laser field. This scattering process is examined, in the first-Born approximation, by using Dirac–Volkov wave functions for charged particles within an external laser field. The theoretical results obtained for the differential cross-section without a laser field are compared with other theoretical results within the framework of Fermi theory. These results revealed to us the importance of using electroweak theory instead of Fermi approximation for studying high energy electroweak interactions. 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 is also included and discussed. These effects are heavily related to the order and argument of the ordinary Bessel functions introduced in the theoretical calculation.