An anomaly-free U(1) gauge here 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 pure energy jeans 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.