Inverted Hierarchy Models of Neutrino Masses

Abstract

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 $ν_e(ν_μ+ν_τ)$ corresponding to two degenerate neutrinos $ν_e$ and $ν_μ+ν_τ$, and one massless neutrino $ν_μ-ν_τ$. Atmospheric neutrino oscillations are accounted for if the degenerate mass term is about $5\times 10^{-2}$ 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 $(1.7-2.0)\times 10^{-4}$ eV for the successful cases. We study the conditions that such models must satisfy in the framework of a U(1) family symmetry broken by vector singlets, 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 $\sin^22θ_{23}\approx 0.93-0.96$ and $\sin^22θ_{12}\approx 0.9-1.0$.