An anomaly-free U(1) gauge extension of the standard model (SM) is presented. Only one Higgs doublet with a nonzero vacuum expectation is required as in the SM. New fermions and scalars as well as all SM particles transform nontrivially under this U(1), resulting in a model of three active neutrinos and one sterile neutrino, all acquiring radiative masses. Charged-lepton masses are also radiative as well as the mixing between active and sterile neutrinos. At the same time, a residual Z2 symmetry of the U(1) gauge symmetry remains exact, allowing for the existence of dark matter.
Adhikari, R., Borah, D., & Ma, E. (2016). New U(1) gauge model of radiative lepton masses with sterile neutrino and dark matter. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 755, 414–417. https://doi.org/10.1016/j.physletb.2016.02.039