On the possibility of search for $L_mu - L_tau$ gauge boson at Belle-II and neutrino beam experiments

We study the possibilities on the search of the light and weakly interacting gauge boson in the gauged $L_mu - L_tau$ model. Introducing the kinetic mixing at the tree-level, the allowed parameter regions for the gauge coupling and kinetic mixing parameter are presented. Then, we analyze one photon plus missing event within the allowed region and show that search for the light gauge boson will be possible at Belle-II experiment. We also analyze neutrino trident production process in neutrino beam experiments.