Nearly Degenerate Neutrinos and Broken Flavour Symmetry

TL;DR

This paper explores how broken non-Abelian flavour symmetries can produce nearly degenerate neutrinos with large mixing angles, hierarchical charged fermion masses, and implications for neutrino mass observables and dark matter.

Contribution

It presents explicit models demonstrating how sequential symmetry breaking and vacuum misalignment yield realistic neutrino mixing angles and mass hierarchies, with implications for neutrino observables.

Findings

Neutrino degeneracy and massless charged fermions at zeroth order.

Hierarchies in neutrino mass-squared differences and charged fermion masses.

Maximal solar and atmospheric mixing angles with no laboratory constraints on neutrino dark matter.

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, $\theta_\odot = 45^\circ$.