Multiphoton processes in laser-assisted scattering of a muon neutrino by an electron

We study the elastic scattering of a muon neutrino by an electron in the presence of a linearly polarized laser field in the frame of the standard model, and multiphoton processes are observed. The distributions of a multiphoton energy transfer (MPET) spectrum are greatly affected even by the laser fields in a moderate intensity range, while the total differential cross section can be largely changed by several orders of magnitude only in extreme strong laser fields with ultrarelativistic electrons. The method of stationary phase approximation is used for analyzing and elucidating the phenomena of cutoff, oscillation, and shift found in a MPET spectrum. We also analyze the reason giving rise to ``dark windows'' and geometric asymmetry initially noted in the potential scattering. By comparing the results we reach the conclusion that these effects are closely related to the order and arguments of generalized Bessel functions.