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Register a new userS_4 x Z_2 Flavor Symmetry in Supersymmetric Extra U(1) Model
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We propose a E_6 inspired supersymmetric model with a non-Abelian discrete flavor symmetry (S_4 group); that is, SU(3)_c x SU(2)_W x U(1)_Y x U(1)_X x S_4 x Z_2. In our scenario, the additional abelian gauge symmetry; U(1)_X, not only solves the mu-problem in the minimal Supersymmetric Standard Model(MSSM), but also requires new exotic fields which play an important role in solving flavor puzzles. If our exotic quarks can be embedded into a S_4 triplet, which corresponds to the number of the generation, one finds that dangerous proton decay can be well-suppressed. Hence, it might be expected that the generation structure for lepton and quark in the SM(Standard Model) can be understood as a new system in order to stabilize the proton in a supersymemtric standard model (SUSY). Moreover, due to the nature of the discrete non-Abelian symmetry itself, Yukawa coupling constants of our model are drastically reduced. In our paper, we show two predictive examples of the models for quark sector and lepton sector, respectively.
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We construct a 3-3-1 model based on family symmetry S_4 responsible for the neutrino and quark masses. The tribimaximal neutrino mixing and the diagonal quark mixing have been obtained. The new lepton charge mathcal{L} related to the ordinary lepton charge L and a SU(3) charge by L=2/sqrt{3} T_8+mathcal{L} and the lepton parity P_l=(-)^L known as a residual symmetry of L have been introduced which provide insights in this kind of model. The expected vacuum alignments resulting in potential minimization can origin from appropriate violation terms of S_4 and mathcal{L}. The smallness of seesaw contributions can be explained from the existence of such terms too. If P_l is not broken by the vacuum values of the scalar fields, there is no mixing between the exotic and the ordinary quarks at the tree level.
We study a flavor model with $A_4$ symmetry which originates from $S_4$ modular group. In $S_4$ symmetry, $Z_2$ subgroup can be anomalous, and then $S_4$ can be violated to $A_4$. Starting with a $S_4$ symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only $A_4$ symmetry when $Z_2$ in $S_4$ is anomalous. We obtain modular forms of two singlets and a triplet representations of $A_4$ by decomposing $S_4$ modular forms into $A_4$ representations. We propose a new $A_4$ flavor model of leptons by using those $A_4$ modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase $delta_{CP}$ and the mixing $sin^2theta_{23}$ depend on the sum of neutrino masses for NH.
We study a simple extension of the Zee model, in which a discrete $Z_2$ symmetry imposed in the original model is replaced by a global $U(1)$ symmetry retaining the same particle content. Due to the $U(1)$ symmetry with flavor dependent charge assignments, the lepton sector has an additional source of flavor violating Yukawa interactions with a controllable structure, while the quark sector does not at tree level. We show that current neutrino oscillation data can be explained under constraints from lepton flavor violating decays of charged leptons in a successful charge assignment of the $U(1)$ symmetry. In such scenario, we find a characteristic pattern of lepton flavor violating decays of additional Higgs bosons, which can be a smoking gun signature at collider experiments.
We study the modulus stabilization in an $A_4$ model whose $A_4$ flavor symmetry is originated from the $S_4$ modular symmetry. We can stabilize the modulus so that the $A_4$ invariant superpotential leads to the realistic lepton masses and mixing angles. We also discuss the phenomenological aspect of the present model as a consequence of the modulus stabilization.
We show that in a large class of models based on anomalous U(1) symmetry which addresses the fermion mass hierarchy problem, leptonic flavor changing processes are induced that are in the experimentally interesting range. The flavor violation occurs through the renormalization group evolution of the soft SUSY breaking parameters between the string scale and the U(1)_A breaking scale. We derive general expressions for the evolution of these parameters in the presence of higher dimensional operators. Several sources for the flavor violation are identified: flavor-dependent contributions to the soft masses from the U(1)_A gaugino, scalar mass corrections proportional to the trace of U(1)_A charge, non-proportional A-terms from vertex corrections, and the U(1)_A D-term. Quantitative estimates for the decays mu -> e gamma and tau -> mu gamma are presented in supergravity models which accommodate the relic abundance of neutralino dark matter.
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