A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry

TL;DR

This paper proposes a neutrino mixing model based on an $A_4\times Z_3\times Z_4$ symmetry that slightly deviates from tri-bi-maximal mixing, predicting the CP-violating phase and consistent with current experimental data.

Contribution

It introduces a new neutrino mixing model with specific flavor symmetries and derives a relation between mixing angles and CP violation, predicting observable parameters.

Findings

Predicted CP-violating phase $\delta_{CP}$ within 1$\sigma$ of global fits.

Model yields neutrino masses around 0.1 eV and mixing angle $\theta_{13}$ near $9^\circ$.

Provides a relation allowing prediction of $\delta_{CP}$ and $J_{CP}$.

Abstract

A model of a neutrino mixing with an $A_4\times Z_3\times Z_4$ flavour symmetry is suggested. In addition to the standard model fields, the present model contains six new fields which transform under different representations of $A_4\times Z_3\times Z_4$. The model is constructed to slightly deviate from a tri-bi-maximal model in agreement with the current experimental data, thus, all analysis can be done in the base of the perturbation method. Within this model, as an application, a relation between the mixing angles ($\theta_{12}, \theta_{23}, \theta_{13}$) and the Dirac CP-violation phase ($\delta_{CP}$) is established. This relation allows a prediction of $\delta_{CP}$ and the Jarlskog parameter ($J_{CP}$). The predicted value $\delta_{CP}$ is in the 1$\sigma$ region of the global fit for both the normal- and inverse neutrino mass ordering and gives $J_{CP}$ to be within the bound $|J_{CP}|\leq 0.04$. For an illustration, the model is checked numerically and gives values of the neutrino masses (of the order of 0.1 eV) and the mixing angle $\theta_{13}$ (about $9^\circ$) very close to the current experimental data.