A flavor dependent gauge symmetry, Predictive radiative seesaw and LHCb anomalies

Abstract

We propose a predictive radiative seesaw model at one-loop level with a flavor dependent gauge symmetry $U(1)_{xB_3-xe-\mu+\tau}$ and Majorana fermion dark matter. For the neutrino mass matrix, we obtain an $A_1$ type texture (with two zeros) that provides us several predictions such as the normal ordering for the neutrino masses. We analyze the constraints from lepton flavor violations, relic density of dark matter, and collider physics for the new $U(1)_{xB_3-xe-\mu+\tau}$ gauge boson. Within the allowed region, the LHCb anomalies in $B\rightarrow K^* \mu^+ \mu^-$ and $B\rightarrow K \ell^+ \ell^-$ with $\ell=e$ or $\mu$ can be resolved, and such $Z'$ could be also observed at the LHC.