A hidden gauged $U(1)$ addressing radiative neutrino mass, dark matter, $(g-2)_{\mu}$, and $H_0$ tension

Abstract

We propose a radiative seesaw model with a hidden $U(1)$ gauge symmetry. In order to have anomaly cancellations, we need to introduce several new fermions that contribute to muon anomalous magnetic dipole moment $(g-2)_\mu$ as well as explain the neutrino oscillation data. We also consider a fermionic dark matter candidate that correlates with $(g-2)_\mu$ and neutrino mass matrix at the same time. We show allowed regions in our input parameters satisfying several constraints. Finally, we also briefly discuss the possibility of the resolution of the Hubble tension via neutrino self-interactions mediated by a lighter hidden gauge boson without spoiling our model.