Radiative Generation of Lepton Masses with the $U(1)$ Gauge Symmetry

We revisit our previous model proposed in Ref. cite{Okada:2013iba}, in which lepton masses except the tauon mass are generated at the one-loop level in a TeV scale physics. Although in the previous work, rather large Yukawa couplings constants; i.e., greater than about 3, are required to reproduce the muon mass, we do not need to introduce such a large but ${cal O}$(1) couplings. In our model, masses for neutrinos (charged-leptons) are generated by a dimension five effective operator with two isospin triplet (singlet and doublet) scalar fields. Thus, the mass hierarchy between neutrinos and charged-leptons can be naturally described by the difference in the number of vacuum expectation values (VEVs) of the triplet fields which must be much smaller than the VEV of the doublet field due to the constraint from the electroweak rho parameter. Furthermore, the discrepancy in the measured muon anomalous magnetic moment ($g-2$) from the prediction in the standard model are explained by one-loop contributions from vector-like extra charged-leptons which are necessary to obtain the radiative generation of the lepton masses. We study the decay property of the extra leptons by taking into account the masses of muon, neutrinos, muon $g-2$ and dark matter physics. We find that the extra leptons can mainly decay into the mono-muon, dark matter with or without $Z$ bosons in the favored parameter regions.