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 $Δm_{atm}^2 \gg Δm_{\odot}^2$ and $m_τ\gg m_μ\gg m_e$, and a misalignment of the vacuum between neutrino and charged sectors gives large $θ_{atm}$. Explicit models are given which determine $θ_{atm} = 45^\circ$. A similar construction gives vacuum misalignment for the lighter generations and gives a vanishing $ββ_{0 ν}$ 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, $θ_\odot = 45^\circ$.