Zeros in the magic neutrino mass matrix

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 $\varphi$ and two known parameters $\Delta m_{12}^2$, $r=\Delta m_{12}^2/\Delta m_{23}^2$. 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.

Comments: 9 pages, 3 figures, minor changes as reported in Erratum: Zeros in the magic neutrino mass matrix [Phys. Rev. D 94, 036004 (2016)] (some typographical errors in two equations and a table corrected, results and conclusions unaffected)