Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries

TL;DR

This paper explores how combining generalized Z_2 x Z_2 and CP symmetries constrains neutrino mass matrices, predicting non-zero θ13, maximal atmospheric mixing, and linking the neutrino mass scale to θ13.

Contribution

It introduces a minimal extension of tri-bimaximal mixing using generalized Z_2 x Z_2 symmetries derived from A_4, providing a predictive framework with only four parameters.

Findings

Predicts non-zero θ13 and maximal atmospheric mixing.

Links neutrino mass scale to the reactor angle θ13.

Shows how symmetries constrain the neutrino mass matrix.

Abstract

We discuss consequences of combining the effective $Z_2\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $\theta_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle $\theta_{13}$.