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

Within the framework of electroweak theory, we investigate the elastic scattering process $e^{-}+{\nu }_{\mu }\to e^{-}+{\nu }_{\mu }$ 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 $\mathit{\text{et}}\mathit{\text{al.}}$ [Phys. Rev. A $\mathbf{\text{85}}$, 013402 (2012)] and for the circularly polarized field by El Asri $\mathit{\text{et}}\mathit{\text{al.}}$ [Phys. Rev. D $\mathbf{\text{104}}$, 113001 (2021)]. We find that the differential cross section is significantly enhanced for linear polarization and reduced for circular and elliptical polarizations.