Atmospheric and Solar Neutrinos from Single Right-Handed Neutrino Dominance and U(1) Family Symmetry

We argue that in order to provide a natural explanation of both neutrino mass hierarchies and large neutrino mixing angles, as required by the atmospheric neutrino data, a single right-handed neutrino must give the dominant contribution to the 23 block of the light effective neutrino matrix, and illustrate this mechanism in the framework of models with U(1) family symmetries. Sub-dominant contributions from other right-handed neutrinos are required to give small mass splittings appropriate to the small angle MSW solution to the solar neutrino problem. We give general conditions for achieving this in the framework of U(1) family symmetry models containing arbitrary numbers of right-handed neutrinos, and show how the resulting neutrino mass hierarchies and mixing angles may be expanded in terms of the Wolfenstein parameter.