Discrete Symmetries and Neutrino Mass Perturbations for \theta_{13}

TL;DR

This paper develops a formalism to analyze how small symmetry-breaking perturbations can explain the observed value of the neutrino mixing angle , and explores implications for CP violation and mixing schemes.

Contribution

It introduces a model-independent approach to perturbations from TBM and GR mixing, linking symmetry structures to observed neutrino mixing parameters.

Findings

Perturbations can fit the observed  angle.

Correlations between  and other mixing angles.

Implications for CP violating phases.

Abstract

The recent measurement of the third lepton mixing angle, \theta_{13}, has shown that, although small compared to \theta_{12} and \theta_{23}, it is much larger than anticipated in schemes that generate Tri-Bi-Maximal (TBM) or Golden Ratio (GR) mixing. We develop a model-independent formalism for perturbations away from exact TBM or GR mixing in the neutrino sector. Each resulting perturbation scheme reflects an underlying symmetry structure and involves a single complex parameter. We show that such perturbations can readily fit the observed value of \theta_{13}, which is then correlated with a change in the other mixing angles. We also determine the implication for the lepton CP violating phases. For comparison we determine the predictions for Bi-Maximal mixing corrected by charged lepton mixing and we discuss the accuracy that will be needed to distinguish between the various schemes.