Inverted hierarchy models of neutrino masses

We study models of neutrino masses which naturally give rise to an inverted mass hierarchy and bi-maximal mixing. The models are based on the see-saw mechanism with three right-handed neutrinos, which generates a single mass term of the form νe(νμ+ντ) corresponding to two degenerate neutrinos νe and νμ+ντ, and one massless neutrino νμ-ντ. Atmospheric neutrino oscillations are accounted for if the degenerate mass term is about 5x10-2 eV. Solar neutrino oscillations of the Large Mixing Angle MSW type arise when small perturbations are included leading to a mass splitting between the degenerate pair of about (1.7-2.0)x10-4 eV for the successful cases. We study the conditions that such models must satisfy in the framework of a U(1) chiral family symmetry broken by a pair of scalar singlets with vector-like charges, and catalogue the simplest examples. We then perform a renormalisation group analysis of the neutrino masses and mixing angles, assuming the supersymmetric standard model, and find modest radiative corrections of a few per cent, showing that the model is stable. At low energies we find sin22θ23∼0.93-0.96 and sin22θ12∼0.9-1.0