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We analyze the distributions of energy, opening angle and invariant mass inmuonic neutrino trident production processes, $\nu_\mu \to \nu_\mu \mu\overline{\mu}$, in a minimal gauged $U(1)_{L_\mu - L_\tau}$ model, in whichthe discrepancy of anomalous magnetic moment of muon can be solved. It is knownthat the total cross sections of the neutrino trident production are degeneratein new physics parameters, the new gauge coupling and gauge boson mass, andtherefore other observables are needed to determine these parameters. Fromnumerical analyses, we find that the muon energy and invariant massdistributions show the differences among the new physics parameter sets withwhich the total cross sections have the same value, while the anti-muon energyand opening angle distributions are not sensitive to the parameters.

Kinematical distributions of coherent neutrino trident production in gauged $L_\mu-L_\tau$ model