Low scale seesaw models for low scale $U(1)_{L_\mu-L_\tau}$ symmetry

We propose models for neutrino masses and mixing in the framework of low scale $U(1)_{L_\mu-L_\tau}$ gauge extension of the standard model. The models are designed to spontaneously break $U(1)_{L_\mu-L_\tau}$ so that the $U(1)_{L_\mu-L_\tau}$ gauge boson acquires an MeV scale mass, which is required to solve the long-standing problem of muon anomalous magnetic moment. Tiny neutrino masses are obtained by simultaneously invoking the linear and the inverse seesaw mechanism, and we succeed in realizing two types of one-zero textures in the active neutrino mass matrix. Both of the obtained textures favor inverted neutrino mass ordering and are testable in next generation experiments of neutrinoless double beta decay. We also show that some of extra scalar bosons can have MeV scale masses and would have significant impacts on observations of high energy cosmic neutrinos.