  In view of the great contribution of neutrino-electron scattering to the deep
understanding of electroweak interactions, we focus in this paper on the study
of elastic scattering of a muon neutrino by an electron
$(e^{-}\nu_{\mu}\rightarrow e^{-}\nu_{\mu})$ in the presence of a circularly
polarized electromagnetic field. We perform our theoretical calculation within
the framework of Fermi theory using the exact wave functions of charged
particles in an electromagnetic field. The expression of the differential cross
section (DCS) for this process is obtained analytically in the absence and
presence of the laser field. The effect of the field strength and frequency on
the exchange of photons as well as on the DCS is presented and analyzed.
Massive neutrino effects are also included and discussed. This study, added to
the previous ones, will significantly enrich our knowledge in fundamental
physics.
