Neutrino masses and mixings with an S3 family permutation symmetry

TL;DR

This paper explores how an S3 permutation symmetry in the fermion family sector can naturally explain large neutrino mixing angles and their hierarchy, with symmetry breaking patterns leading to observable mixing phenomena.

Contribution

It introduces a model where S3 symmetry breaking accounts for neutrino mixing angles, linking them to family symmetry and neutrino mass structure.

Findings

Large atmospheric neutrino mixing angle explained by S3->S2 breaking.

U_{e3} is predicted to be zero due to symmetry considerations.

Explicit relation between solar mixing angle and neutrino masses.

Abstract

Large neutrino mixing angles suggest that the Yukawa sector is invariant under permutations of the fermion families. This S_{3} permutation symmetry is broken at a large energy scale but much below the unification scale. Assuming that the lepton mass matrix is approximately diagonal, all neutrino mixing angles naturally come from the breaking of S_{3}-> S_{2}. In the neutrino sector, S_{2} remains (approximately) unbroken. As a consequence, we have a large atmospheric neutrino angle and U_{e3}=0. The S_{3} symmetry at the unification scale can also explain the large solar mixing angle. We give an explicit expression of the solar mixing angle in terms of the left-handed neutrino masses. We observe that this family permutation symmetry comes very naturally from a quantized theory of functionals [1], that is an extension of quantum field theory.