Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases

Abstract

We propose two new simple lepton flavor models in the framework of the $S_4$ flavor symmetry. The neutrino mass matrices, which are given by two complex parameters, lead to the inverted mass hierarchy. The charged lepton mass matrix has the 1-2 lepton flavor mixing, which gives the non-vanishing reactor angle ${\theta }_{13}$. These models predict the Dirac phase and the Majorana phases, which are testable in the future experiments. The predicted magnitudes of the effective neutrino mass for the neutrino-less double beta decay are in the regions as $32\text{meV}\lesssim |m_{ee}|\lesssim 49\text{meV}$ and $34\text{meV}\lesssim |m_{ee}|\lesssim 59\text{meV}$, respectively. These values are close to the expected reaches of the coming experiments. The total sum of the neutrino masses are predicted in both models as $0.0952\text{eV}\lesssim \sum m_i\lesssim 0.101\text{eV}$ and $0.150\text{eV}\lesssim \sum m_i\lesssim 0.160\text{eV}$, respectively.

Comments: 27 pages, 14 figures, final version