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 lepto
n 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 $0.0952~text{eV}lesssim sum m_ilesssim 0.101~text{eV}$ and $0.150~text{eV}lesssim sum m_ilesssim 0.160~text{eV}$, respectively.
We study the CP violation in the deviation from the tri-bimaximal mixing (TBM) of neutrinos. We examine non-trivial relations among the mixing angles and the CP violating Dirac phase in the typical four cases of the deviation from the TBM. The first
two cases are derived by the additional rotation of the 2-3 or 1-3 generations of neutrinos in the TBM basis. The other two cases are given by the additional rotation of the 1-3 or 1-2 generations of charged leptons with the TBM neutrinos. These four cases predict different relations among three mixing angles and the CP violating Dirac phase. The rotation of the 2-3 generations of neutrinos in the TBM basis predicts $sin ^2theta _{12}<1/3$, and the CP violating Dirac phase to be $pm (0.09pisim 0.76pi)$ for NH ($pm (0.15pisim 0.73pi) text{for IH}$) depending on $sin ^2theta _{23}$. The rotation of the 1-3 generations of neutrinos in the TBM basis gives $sin ^2theta _{12}>1/3$. The CP violating Dirac phase is not constrained by the input of the present experimental data. For the case of the 1-3 and 1-2 rotations of charged leptons in the TBM basis, the CP violating Dirac phase is predicted in $pm(0.35pisim 0.60pi)$ depending on $sin ^2theta _{12}$ for both NH and IH cases. We also discuss the specific case that $theta_{13}$ is related with the Cabibbo angle $lambda$ such as $sintheta_{13}=lambda/sqrt{2}$, in which the maximal CP violation is preferred. The CP violating Dirac phase can distinguish the lepton flavor mixing patterns at T2K and NO$ u$A experiments in the future.
We study the sensitivity of the squark flavor mixing to the CP violating phenomena of $K$, $B^0$ and $B_s$ mesons in the framework of the split-family scenario, where the first and second family squarks are very heavy, ${cal O}(10)$TeV, on the other
hand, the third family squark masses are at ${cal O}(1)$TeV. In order to constrain the gluino-sbottom-quark mixing parameters, we input the experimental data of the CP violations of $K$, $B^0$, and $B_s$ mesons, that is $epsilon_K$, $phi_d$, and $phi_s$. The experimental upper bound of the chromo-EDM of the strange quark is also input. In addition, we take account of the observed values $Delta M_{B^0}$, $Delta M_{B_s}$, the CKM mixing $|V_{ub}|$, and the branching ratio of $bto sgamma$. The allowed region of the mixing parameters are obtained as $|delta_{13}^{dL(dR)}|=0sim 0.01$ and $|delta_{23}^{dL(dR)}|=0sim 0.04$. By using these values, the deviations from the SM are estimated in the CP violations of the $B^0$ and $B_s$ decays. The deviation from the SM one is tiny in the CP asymmetries of $B^0to phi K_S$ and $B^0to eta K^0$ due to the chromo-EDM of the strange quark. On the other hand, the CP asymmetries $B_s to phi phi$ and $B_s to phi eta $ could be largely deviated from the SM predictions. We also predict the time dependent CP asymmetry of $B^0to K^0bar K^0$ and the semi-leptonic CP asymmetries of $B^0 to mu ^-X$ and $B_s to mu ^-X$. We expect those precise measurements at Belle II, which will provide us interesting tests for the squark flavor mixing.
We study the contribution of the gluino-squark mediated flavor changing process for the CP violation in $bto s$ and $bto d$ transitions facing on recent experimental data. The mass insertion parameters of squarks are constrained by the branching rati
os of $bto sgamma $ and $bto dgamma $ decays. In addition, the time dependent CP asymmetries of $B^0to phi K_S$ and $B^0to eta K^0$ decays severely restrict the allowed region of the mass insertion parameter for the $bto s$ transition. By using these constraints with squark and gluino masses of 1.5 TeV, we predict the CP asymmetries of $B_sto phi phi $, $B_sto eta phi $, and $B^0to K^0bar K^0$ decays, as well as the CP asymmetries in $bto sgamma $ and $bto dgamma $ decays. The CP violation in the $B_sto phi phi$ decay is expected to be large owing to the squark flavor mixing, which will be tested at LHCb soon.
We discuss slepton mass matrices in the $S_4$ flavor model with SUSY SU(5) GUT. By considering the gravity mediation within the framework of supergravity theory, we estimate the SUSY breaking terms in the slepton mass matrices, which contribute to th
e $mu rightarrow e + gamma$ decay. We obtain a lower bound for the ratio of $murightarrow egamma$ as $10^{-13}$ if $m_{text{SUSY}}$ and $m_{1/2}$ are below 500GeV. The off diagonal terms of slepton mass matrices also contribute to EDM of leptons. The predicted electron EDM is around $10^{-29}-10^{-28}$cm. Our predictions are expected to be tested in the near future experiment.
We discuss a neutrino mass model based on the S4 discrete symmetry where the symmetry breaking is triggered by the boundary conditions of the bulk right-handed neutrino in the fifth spacial dimension. While the symmetry restricts bare mass parameters
to flavor-diagonal forms, the viable mixing angles emerge from the wave functions of the Kaluza-Klein modes which carry symmetry breaking effect. The magnitudes of the lepton mixing angles, especially the reactor angle is related to the neutrino mass patterns and the model will be tested in future neutrino experiments, e.g., an early (late) discovery of the reactor angle favors the normal (inverted) hierarchy. The size of extra dimension has a connection to the possible mass spectrum; a small (large) volume corresponds to the normal (inverted) mass hierarchy.
