Testing the minimal S₄ model of neutrinos with the Dirac and Majorana phases

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We propose two new simple lepton flavor models in the framework of the S₄ 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 θ₁₃. 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 meV |mee| 49 meV and 34 meV |mee| 59 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 eV ∑ mᵢ 0.101 eV and 0.150 eV ∑ mᵢ 0.160 eV, respectively.