Gauged B-3L_tau and Radiative Neutrino Masses

If the minimal standard model of quarks and leptons is extended to include just a righthanded partner to nu_tau, then the quantum number B-3L_tau 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-3L_tau gauge boson may be light and be observable through its decay into tau^+ tau^-.