Nearly Degenerate Neutrinos and Broken Flavour Symmetry

Abstract

Theories with non-Abelian flavour symmetries lead at zeroth order to neutrino degeneracy and massless charged fermions. The flavour symmetry is spontaneously broken sequentially to give hierarchies $\Delta m_{atm}^2\gg \Delta m_{\odot }^2$ and $m_{\tau }\gg m_{\mu }\gg m_e$, and a misalignment of the vacuum between neutrino and charged sectors gives large ${\theta }_{atm}$. Explicit models are given which determine ${\theta }_{atm}=45^{\circ }$. A similar construction gives vacuum misalignment for the lighter generations and gives a vanishing $\beta {\beta }_{0\nu }$ rate, so that there is no laboratory constraint on the amount of neutrino hot dark matter in the universe, and the solar mixing angle is also maximal, ${\theta }_{\odot }=45^{\circ }$.

10 pages

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