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

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