Leptonic CP phases near the $\mu-\tau$ symmetric limit

TL;DR

This paper investigates how small deviations from $$ symmetry in neutrino mass matrices influence CP phases, revealing that such breaking leads to non-zero Majorana phases and correlates them with the Dirac phase, with implications for neutrino mass hierarchy.

Contribution

It demonstrates that small $$ symmetry breaking requires non-zero Majorana phases and establishes their correlation with the Dirac phase, providing predictions based on current experimental data.

Findings

Majorana phases are non-zero and unequal with $$ symmetry breaking.

Small symmetry breaking favors quasi-degenerate neutrino masses.

Majorana and Dirac phases are strongly correlated.

Abstract

The neutrino masses and mixings indicated by current neutrino oscillation experiments suggest that the neutrino mass matrix possesses an approximate $\mu-\tau$ exchange symmetry. In this study, we explore the neutrino parameter space and show that if a small $\mu-\tau$ symmetry breaking is considered, the Majorana $CP$ phases must be unequal and non-zero independently of the neutrino mass scale. Moreover, a small $\mu-\tau$ symmetry breaking favors quasi-degenerate masses. We also show that Majorana phases are strongly correlated with the Dirac $CP$ violating phase. Within this framework, we obtain robust predictions for the values of the Majorana phases when the experimental indications for the Dirac $CP$ phase are used.