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 propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the asymptotic normali
ty and the asymptotic efficiency. We give a simulation example to illustrate the theory.
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 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.
The like-sign dimuon charge asymmetry of the $B$ meson, which was reported in the D$O$ Collaboration, is studied in the SU(5) SUSY GUT model with $S_4$ flavor symmetry. Additional CP violating effects from the squark sector are discussed in $B_s-bar
B_s$ mixing process. The predicted like-sign charge asymmetry is in the 2$sigma$ range of the combined result of D$O$ and CDF measurements. Since the SUSY contributions in the quark sector affect to the lepton sector because of the SU(5) GUT relation, two predictions are given in the leptonic processes: (i) both ${rm BR}(mu to e gamma)$ and the electron EDM are close to the present upper bound, (ii) the decay ratios of $tau$ decays, $tau to mugamma$ and $tau to e gamma$, are related to each other via the Cabibbo angle $lambda_c$: ${rm BR}(tau to egamma)/{rm BR}(tau to mugamma)sime lambda_c^2$. These are testable at future experiments.
We present a flavor model of quarks and leptons with the non-Abelian discrete symmetry $S_4$ in the framework of the SU(5) SUSY GUT. Three generations of $bar 5$-plets in SU(5) are assigned to ${bf 3}$ of $S_4$ while the first and second generations
of 10-plets in SU(5) are assigned to ${bf 2}$ of $S_4$, and the third generation of 10-plet is assigned to ${bf 1}$ of $S_4$. Right-handed neutrinos are also assigned to ${bf 2}$ for the first and second generations and ${bf 1}$ for the third generation. We predict the Cabibbo angle as well as the tri-bimaximal mixing of neutrino flavors. We also predict the non-vanishing $U_{e3}$ of the neutrino flavor mixing due to higher dimensional mass operators. Our predicted CKM mixing angles and the CP violation are consistent with experimental values. We also study SUSY breaking terms in the slepton sector. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.
We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy
classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for $S_N$, $A_N$, $T$, $D_N$, $Q_N$, $Sigma(2N^2)$, $Delta(3N^2)$, $T_7$, $Sigma(3N^3)$ and $Delta(6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.
We have studied $Delta(54)times Z_2$ flavor model for leptons and sleptons. The tri-bimaximal mixing can be reproduced for arbitrary neutrino masses if vacuum alignments of scalar fields are guaranteed. The deviation from the tri-bimaximal mixing of
leptons is predicted. The predicted upper bound for $sintheta_{13}$ is 0.06. The magnitude of $sintheta_{23}$ could be deviated from the maximal mixing considerably, but $sintheta_{12}$ is hardly deviated from the tri-maximal mixing. We have also studied SUSY breaking terms in the slepton sector. Three families of left-handed and right-handed slepton masses are degenerate. Even although flavor symmetry breaking effects are taken into account, our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.
We present the lepton flavor model with $Delta (54)$, which appears typically in heterotic string models on the $T^2/Z_3$ orbifold. Our model reproduces the tri-bimaximal mixing in the parameter region around degenerate neutrino masses or two massles
s neutrinos. We predict the deviation from the tri-bimaximal mixing by putting the experimental data of neutrino masses in the normal hierarchy of neutrino masses. The upper bound of $sin^2theta_{13}$ is 0.01. There is the strong correlation between $theta_{23}$ and $theta_{13}$. Unless $theta_{23}$ is deviated from the maximal mixing considerably, $theta_{13}$ remains to be tiny.
