Consequences of Approximate $S_3$ Symmetry of the Neutrino Mass Matrix

TL;DR

This paper explores how an approximate $S_3$ symmetry in the neutrino mass matrix can explain neutrino data, emphasizing the importance of quasi-degenerate masses and the role of $ au- ext{mu}$ symmetry in achieving tri-bimaximal mixing.

Contribution

It introduces a model where an $S_3$ symmetric dominant term combined with a $ au- ext{mu}$ symmetric sub-dominant term explains neutrino mixing patterns.

Findings

Neutrino masses must be quasi-degenerate under $S_3$ symmetry.

Approximate $ au- ext{mu}$ symmetry leads to tri-bimaximal mixing.

Experimental implications of the symmetry assumptions are discussed.

Abstract

Assuming that the neutrino mass matrix is dominated by a term with the permutation symmetry $S_{\scriptscriptstyle 3}$ it is possible to explain neutrino data only if the masses are quasi-degenerate. A sub-dominant term with an approximate $\mu -\tau$ symmetry leads to an approximate tri-bimaximal form. Experimental consequences are discussed.