Hajime Ishimori

S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT

We present an S4 flavor model to unify quarks and leptons in the framework of the SU(5) GUT. Three generations of 5-plets in SU(5) are assigned to 31 of S4, while the first and second generations of 10-plets in SU(5) are assigned to 2 of S4, and the third generation of 10-plets is assigned to 11 of S4. Right-handed neutrinos are also assigned to 2 for the first and second generations and to 11 for the third generation. By considering the vacuum alignments of relevant gauge singlet scalars, we predict the quark mixing as well as the tribimaximal mixing of neutrino flavors. In particular, the Cabbibo angle is predicted to be 15 ◦ in the limit of the vacuum alignment. We can improve the model to predict observed CKM mixing angles as well as the nonvanishing Ue3 of the neutrino flavor mixing. Subject Index: 140, 154

D(4) Flavor Symmetry for Neutrino Masses and Mixing

Abstract We present the D 4 × Z 2 flavor symmetry, which is different from the previous work by Grimus and Lavoura. Our model reduces to the standard model in the low energy and there is no FCNC at the tree level. Putting the experimental data, parameters are fixed, and then the implication of our model is discussed. The condition to realize the tri-bimaximal mixing is presented. The possibility for stringy realization of our model is also discussed.

Soft supersymmetry breaking terms from D(4) x Z(2) lepton flavor symmetry

We study the supersymmetric model with D 4 × Z 2 lepton flavor symmetry. We evaluate soft supersymmetry breaking terms, i.e., soft slepton masses and A-terms, which are predicted in the D 4 flavor model. We consider constraints due to experiments of flavor-changing neutral current processes.

An introduction to non-Abelian discrete symmetries for particle physicists

Introduction.- Basics of Finite Groups.- Subgroups and Decompositions of Multiplets.- Anomalies.- Non-Abelian Discrete Symmetry in Quark/Lepton Flavor Models.- Useful Theorems.- Representations of S4 in Different Bases.- Representations of A4 in Different Bases.- Representations of A5 in Different Bases.- Representations of T1 in Different Bases.- Other Smaller Groups.- References.

Lepton flavor model from Δ(54) symmetry

We present the lepton flavor model with ?(54), which appears typically in heterotic string models on the T2/Z3 orbifold. Our model reproduces the tri-bimaximal mixing in the parameter region around degenerate neutrino masses or two massless 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 2?13 is 0.01. There is the strong correlation between ?23 and ?13. Unless ?23 is deviated from the maximal mixing considerably, ?13 remains to be tiny.

Δ(54) flavor model for leptons and sleptons

We study a Δ(54) × Z2 flavor model for leptons and sleptons. The tri-bimaximal mixing can be reproduced for arbitrary neutrino masses if certain vacuum alignments of scalar fields are realized. The deviation from the tri-bimaximal mixing of leptons is predicted. The predicted upper bound for sin θ13 is 0.07. The value of sin θ23 could be deviated from the maximal mixing considerably while sin θ12 is hardly deviated from 1/√3. We also study SUSY breaking terms in the slepton sector. Three families of left-handed and right-handed slepton masses are almost degenerate. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.

CKM matrix and flavor symmetries

Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both

Deviation from tri-bimaximal mixing and flavor symmetry breaking in a seesaw type A(4) model

\theta_{13}

Soft supersymmetry breaking terms from A4 lepton flavor symmetry

and

Lepton flavor models with discrete prediction of theta_{13}

\theta_{23}