$\theta_{13}$ in Neutrino Mass Matrix with the Minimal Texture

Abstract

We show that the neutrino mass matrix with the minimal texture leads to the neutrino mass and mixing that are empirically determined, including $\theta_{13}$ that is measured recently at a high precision. This mass matrix, where the Majorana nature of the neutrino is essential, only allows the normal hierarchy of the neutrino mass, excluding either inverse mass hierarchy or degenerate mass neutrinos, and hence predicts the effective mass of double beta decay to lie within the range $m_{ee}=3.7-5.6$ eV.