Gauged B−3Lτ and radiative neutrino masses

If the minimal standard model of quarks and leptons is extended to include just a righthanded partner to ντ, then the quantum number B−3Lτ can be added as a gauge symmetry without the appearance of anomalies. A suitable extension of the scalar sector allows one neutrino to have a seesaw mass, and the other two to have radiative masses, with acceptable phenomenological values for neutrino oscillations. The B−3Lτ gauge boson may be light and be observable through its decay into τ+τ−.