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

TL;DR

This paper introduces two simple $S_4$ flavor symmetry models predicting neutrino mass hierarchies, phases, and effective masses, with testable predictions for upcoming experiments.

Contribution

The paper proposes two novel $S_4$-based lepton flavor models that predict specific neutrino phases and mass parameters, aligning with experimental sensitivities.

Findings

Predicted effective neutrino mass for double beta decay: 32-49 meV and 34-59 meV.

Total neutrino mass sum predictions: 0.0952-0.101 eV and 0.150-0.160 eV.

Models are consistent with inverted hierarchy and future experimental tests.

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.