New model for the neutrino mass matrix

I suggest a model based on a softly broken symmetry L_e - L_mu - L_tau and on Babu's mechanism for two-loops radiative generation of the neutrino masses. The model predicts that one of the physical neutrinos (nu_3) is massless and that its component along the nu_e direction (U_e3) is zero. Moreover, if the soft-breaking term is assumed to be very small, then the vacuum oscillations of nu_e have almost maximal amplitude and solve the solar-neutrino problem. New scalars are predicted in the 10 TeV energy range, and a breakdown of e-mu-tau universality should not be far from existing experimental bounds.