Nearly tri-bimaximal mixing in the S_3 flavour symmetry

TL;DR

This paper derives an analytical form of the neutrino mixing matrix within an S_3 flavor symmetry framework, showing it closely approximates the tri-bimaximal form with small, explicit corrections based on lepton mass ratios.

Contribution

It provides an exact analytical expression for the neutrino mixing matrix in an S_3-invariant model, linking mixing parameters directly to lepton mass ratios and a Dirac phase.

Findings

The mixing matrix closely matches the tri-bimaximal form.

Small corrections depend explicitly on lepton mass ratios.

Results are consistent with latest experimental data.

Abstract

We present an analysis of the theoretical neutrino mixing matrix, V_{PMNS}^{th}, previously derived in the framework of the minimal S_3-invariant extension of the Standard Model. All entries in the neutrino mixing matrix, V_{PMNS}^{th}, the mixing angles and the Majorana phases are given as exact, explicit analytical functions of the mass ratios of the charged leptons and neutrinos, and one Dirac phase, in excellent agreement with the the latest experimental data. Here, it will be shown that all entries in V_{PMNS}^{th} are numerically very close to the tri-bimaximal form of the neutrino mixing matrix, so that V_{PMNS}^{th} may be written as V^{tri}+\Delta V_{PMNS}^{tri}. The small correction \Delta V_{PMNS}^{tri} is expressed as a sum of two terms: first, a small correction term proportional to m_{e}/m_{\mu} depending only on the charged lepton mass ratios and, second, a Cabbibo-like, small term, \delta t_{12}, which is a function of both the charged lepton and the neutrino mass ratios.