The (Z_2)^3 symmetry of the non-tri-bimaximal pattern for the neutrino mass matrix

TL;DR

This paper explores a specific flavor symmetry, (Z_2)^3, to explain non-zero neutrino mixing angles and mass hierarchies, proposing models compatible with observed data and discussing implications for leptogenesis.

Contribution

It explicitly derives realizations of the (Z_2)^3 flavor symmetry for non-tri-bimaximal neutrino mixing, incorporating charged lepton hierarchies and leptogenesis within different seesaw mechanisms.

Findings

(Z_2)^3 symmetry can accommodate non-zero θ_z

Models can explain charged lepton mass hierarchy

Type-II seesaw with symmetry may generate baryon asymmetry

Abstract

In view of the recent neutrino oscillation data pointing to a non-vanishing value for the smallest mixing angle ($\theta_z$), we derive and find explicit realizations of the $(Z_2)^3$ flavor symmetry which characterizes, for the neutrino mass matrix, uniquely a variant of the tripartite form, originally conceived to lead to the tri-bimaximal mixing with $\theta_z=0$, so that to allow now for a non-tri-bimaximal pattern with non-zero $\theta_z$. We impose this flavor symmetry in a setting including the charged leptons and we see that it can make room, through higher order terms involving new SM-singlet scalars, for the mass hierarchy of charged leptons. Moreover, within type-I seesaw mechanism augmented with the flavor symmetry, certain patterns occurring in both the Dirac and the Majorana neutrino mass matrices can accommodate all types of mass hierarchies in the effective neutrino mass matrix, but no lepton/baryon asymmetry can be generated. Finally, we discuss how type-II seesaw mechanism, when supplemented with the flavor symmetry, could be used to interpret the observed baryon asymmetry through leptogenesis.