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.
Highlights
We propose two new simple lepton flavor models in the framework of the S4 flavor symmetry
The lepton flavor structure has been discussed in the framework of the flavor symmetry
Before the reactor experiments reported the non-zero value of θ13, there appears a paradigm of “tri-bimaximal mixing” (TBM) [33, 34], which is a simple mixing pattern for leptons and can be derived from flavor symmetries
Summary
Let us build simple lepton flavor models with the S4 group by the indirect approach of the flavor symmetry. The particle assignments are same in both cases, while the vacuum alignments of flavon for the neutrino sector are different in each model. After inputting charged lepton masses, there remains two independent parameters, which are the mixing angle λ and the CP violating phase ψ. In order to compare our model with the TBM in the neutrino sector, it is useful to write down the mixing angles without the contribution from the charged lepton sector, that is ones in eq (2.11), sin[2] θ1ν2. We can obtain another simple model with the non-vanishing lightest neutrino mass. By using the seesaw mechanism, the left-handed Majorana neutrino mass matrix Mν is written as bb b. We have the same sum rule between θ23 and θ13 in eq (2.25)
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