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 ${\nu }_e({\nu }_{\mu }+{\nu }_{\tau })$ corresponding to two degenerate neutrinos ${\nu }_e$ and ${\nu }_{\mu }+{\nu }_{\tau }$, and one massless neutrino ${\nu }_{\mu }-{\nu }_{\tau }$. 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 ${\sin }^{2}2{\theta }_{23}\approx 0.93-0.96$ and ${\sin }^{2}2{\theta }_{12}\approx 0.9-1.0$.

Typos Corrected and some clarifications added. 22 pages, Latex

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