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Register a new userNew $A_4$ lepton flavor model from $S_4$ modular symmetry
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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.
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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 study a neutrino mass model based on $S_4$ flavor symmetry which accommodates lepton mass, mixing with non-zero $theta_{13}$ and CP violation phase. The spontaneous symmetry breaking in the model is imposed to obtain the realistic neutrino mass and mixing pattern at the tree- level with renormalizable interactions. Indeed, the neutrinos get small masses from one $SU(2)_L$ doubplet and two $SU(2)_L$ singlets in which one being in $underline{2}$ and the two others in $underline{3}$ under $S_4$ with both the breakings $S_{4}rightarrow S_3$ and $S_{4}rightarrow Z_3$ are taken place in charged lepton sector and $S_4rightarrow mathcal{K}$ in neutrino sector. The model also gives a remarkable prediction of Dirac CP violation $delta_{CP}=frac{pi}{2}$ or $-frac{pi}{2}$ in the both normal and inverted spectrum which is still missing in the neutrino mixing matrix. The relation between lepton mixing angles is also represented.
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 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 $sin^2theta_{13}$ 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.
We discuss an inverse seesaw model based on right-handed fermion specific $U(1)$ gauge symmetry and $A_4$-modular symmetry. These symmetries forbid unnecessary terms and restrict structures of Yukawa interactions which are relevant to inverse seesaw mechanism. Then we can obtain some predictions in neutrino sector such as Dirac-CP phase and sum of neutrino mass, which are shown by our numerical analysis. Besides the relation among masses of heavy pseudo-Dirac neutrino can be obtained since it is also restricted by the modular symmetry. We also discuss implications to lepton flavor violation and collider physics in our model.
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.
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