Zeros in the magic neutrino mass matrix

TL;DR

This paper investigates the phenomenological consequences of two-zero textures in a magic neutrino mass matrix, identifying only two viable patterns and deriving relations among neutrino observables.

Contribution

It identifies the only two experimentally acceptable two-zero patterns in a magic neutrino mass matrix and provides a model based on A4 symmetry for these textures.

Findings

Only two two-zero textures are experimentally viable.

Derived a relation for  in terms of known parameters.

Presented an A4-based mass model for the textures.

Abstract

We study the phenomenological implications of the presence of two zeros in a magic neutrino mass matrix. We find that only two such patterns of the neutrino mass matrix are experimentally acceptable. We express all the neutrino observables as functions of one unknown phase $\phi$ and two known parameters $\Delta m^{2}_{12}$, $r=\Delta m^{2}_{12}/\Delta m^{2}_{23}$. In particular, we find $\sin^2 \theta_{13}=(2/3)r/(1+r)$. We also present a mass model for the allowed textures based upon the group $A_{4}$ using type I+II see-saw mechanism.