Neutrino anomalies in an extended Zee model

We discuss an extended SU(2)×U(1) model which naturally leads to mass scales and mixing angles relevant for understanding both the solar and atmospheric neutrino anomalies. No right-handed neutrinos are introduced in the model. The model uses a softly broken Le−Lμ−Lτ symmetry. Neutrino masses arise only at the loop level. The one-loop neutrino masses which arise as in the Zee model solve the atmospheric neutrino anomaly while breaking of Le−Lμ−Lτ generates at two-loop order a mass splitting needed for the vacuum solution of the solar neutrino problem. A somewhat different model is possible which accommodates the large-angle MSW resolution of the solar neutrino problem.