Neutrino masses and gauged $U(1)_\ell$ lepton number

We investigate the tree-level neutrino mass generation in the gauged $U(1)_\ell$ lepton model recently proposed by us [arXiv:1805.10382]. With the addition of one Standard Model(SM) singlet, $\phi_1(Y=0, \ell=1)$, and one SM triplet scalar, $T(Y=-1,\ell=0)$, realistic lepton masses can be accommodated. The resulting magnitude of neutrino mass is given by $\sim v_t^3/v_L^2$, where $v_t$ and $v_L$ are the vacuum expectation values of $T$ and $\phi_1$, respectively, and it is automatically of the inverse see-saw type. Since $v_L$ is the lepton number violation scale we take it to be high, i.e. ${\cal O} \gtrsim (\mbox{TeV})$. Moreover, the induced lepton flavor violating processes and the phenomenology of the peculiar triplet are studied. An interesting bound, $0.1\lesssim v_t\lesssim24.1$ GeV, is obtained when taking into account the neutrino mass generation, $Br(\mu\rightarrow e \gamma)$, and the limits from oblique parameters, $\Delta S$ and $\Delta T$. Collider phenomenology of the SM triplets is also discussed.