Discrete symmetries and mixing of Dirac neutrinos

TL;DR

This paper explores how residual symmetries in Dirac neutrinos influence their mixing patterns, deriving new relations that align with current experimental data and predicting specific values for mixing angles and CP violation phases.

Contribution

It generalizes the residual symmetry approach to Dirac neutrinos, identifying new symmetry relations and their implications for neutrino mixing parameters.

Findings

Viable symmetry relations involve charged lepton symmetry G_ell = Z_2.

Predictions include specific ranges for the 2-3 mixing angle.

Corrections of about 10% are needed for larger symmetries to match data.

Abstract

We study mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: $G_\nu=\mathbf{Z}_{n}$ with $n\geq3$. The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them we have found all new relations between mixing parameters and corresponding symmetry assignments which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry $G_{\ell} = \mathbf{Z}_{2}$. The relations involve elements of the rows of the PMNS matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the CP violation phase. For larger symmetries $G_{\ell}$, an agreement with data can be achieved if $\sim10\%$ corrections related to breaking of $G_{\ell}$ and $G_\nu$ are included.