S4 Flavor Model of Quarks and Leptons

We present an $S_4$ flavor model to unify quarks and leptons in the framework of the SU(5) GUT. Three generations of $\bar 5$-plets in SU(5) are assigned $3_1$ of $S_4$ while the first and the second generations of 10-plets in SU(5) are assigned to be 2 of $S_4$, and the third generation of 10-plet is to be $1_1$ of $S_4$. Right-handed neutrinos are also assigned 2 for the first and second generations and $1_1$ for the third generation, respectively. Taking vacuum alignments of relevant gauge singlet scalars, we predict the quark mixing as well as the tri-bimaximal mixing of neutrino flavors. Especially, the Cabbibo angle is predicted to be $15^{\circ}$ in the limit of the vacuum alignment. We can improve the model to predict observed CKM mixing angles.Comment: 11 pages, talked at the 16th Yukawa International Seminar, Particle Physics beyond the Standard Mode

Predicting CP violation in Deviation from Tri-bimaximal mixing of Neutrinos

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 $\sin ^2\theta _{12}<1/3$, and the CP violating Dirac phase to be $\pm (0.09\pi\sim 0.76\pi)$ for NH ($\pm (0.15\pi\sim 0.73\pi) \ \text{for IH}$) depending on $\sin ^2\theta _{23}$. The rotation of the 1-3 generations of neutrinos in the TBM basis gives $\sin ^2\theta _{12}>1/3$. 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 $\pm(0.35\pi\sim 0.60\pi)$ depending on $\sin ^2\theta _{12}$ for both NH and IH cases. We also discuss the specific case that $\theta_{13}$ is related with the Cabibbo angle $\lambda$ such as $\sin\theta_{13}=\lambda/\sqrt{2}$, in which the maximal CP violation is preferred. The CP violating Dirac phase can distinguish the lepton flavor mixing patterns at T2K and NO$\nu$A experiments in the future.Comment: 18 pages, 22 figures, figures are changed, discussions are adde

Towards the minimal seesaw model via CP violation of neutrinos

We study the minimal seesaw model, where two right-handed Majorana neutrinos are introduced, focusing on the CP violating phase. In addition, we take the trimaximal mixing pattern for the neutrino flavor where the charged lepton mass matrix is diagonal. Thanks to this symmetric framework, the $3\times 2$ Dirac neutrino mass matrix is given in terms of a few parameters. Numerical studies reveal that the observation of the CP violating phase can determine the flavor structure of the Dirac neutrino mass matrix in the minimal seesaw model. In particular, new minimal Dirac neutrino mass matrices are proposed in the case of $\rm TM_1$, which is derived by the additional 2-3 family mixing to the tri-bimaximal mixing basis in the normal hierarchy of neutrino masses. Our analyses include the Littlest seesaw model by King {\it et al.}, which is one of the specific one in our results. Furthermore, it is remarked that our $3\times 2$ Dirac neutrino mass matrix is reproduced by introducing gauge singlet flavons with the specific alignments of the VEV's. These alignments suggest the residual symmetry of $S_4$ group.Comment: 27 pages, 27 figures, final versio

Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model

We discuss the correlation between the CP violating Dirac phase of the lepton mixing matrix and the cosmological baryon asymmetry based on the leptogenesis in the minimal seesaw model with two right-handed Majorana neutrinos and the trimaximal mixing for neutrino flavors. The sign of the CP violating Dirac phase at low energy is fixed by the observed cosmological baryon asymmetry since there is only one phase parameter in the model. According to the recent T2K and NO$\nu$A data of the CP violation, the Dirac neutrino mass matrix of our model is fixed only for the normal hierarchy of neutrino masses.Comment: 19 pages, 4 figures, 1 table. 1 reference is added in this version. arXiv admin note: text overlap with arXiv:1709.0213

Searching for the squark flavor mixing in CP violations of Bs -> K+ K- and K0bar K0 decays

We study CP violations in the B_s-> K+K- and Bs->K0K0 decays in order to find the contribution of the supersymmetry, which comes from the gluino-squark mediated flavor changing current. We obtain the allowed region of the squark flavor mixing parameters by putting the experimental data, the mass difference Delta M_Bs, the CP violating phase phi_s in Bs to J/psi phi decay and the b to s gamma branching ratio. In addition to these data, we take into account the constraint from the asymmetry of B0->K+pi because the Bs->K+K- decay is related with the B0->K+pi- decay by replacing the spectator s with d. Under these constraints, we predict the magnitudes of the CP violation in the Bs->K+K- and Bs->K0K0 decays. The predicted region of the CP violation C_{K+K-} is strongly cut from the direct CP violation of barB0 to K-pi+, therefore, the deviation from the SM prediction of C_{K+K-} is not found. On the other hand, the CP violation S_{K+K-} is possibly deviated from the SM prediction considerably, in the region of 0.1- 0.5. Since the standard model predictions of C_{K0bar K0} and S_{K0bar K0} are very small, the squark contribution can be detectable in C_{K0bar K0} and S_{K0bar K0}. These magnitudes are expected in the region C_{K0bar K0}=-0.06-0.06 and S_{K0bar K0}=-0.5-0.3. More precise data of these CP violations provide us a crucial test for the gluino-squark mediated flavor changing current.Comment: 20 pages, 10 figures, discussions added, references added. arXiv admin note: substantial text overlap with arXiv:1307.037

Like-sign dimuon asymmetry of B0 meson and LFV in SU(5) SUSY GUT with S4 flavor symmetry

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, $\tau \to \mu\gamma$ and $\tau \to e \gamma$, are related to each other via the Cabibbo angle $\lambda_c$: {\rm BR}(\tau \to e\gamma)/{\rm BR}(\tau \to \mu\gamma)\sime \lambda_c^2. These are testable at future experiments.Comment: 33 pages, 4 figures, a footnote and references are adde