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Register a new userLepton mass and mixing in a Neutrino Mass Model based on $S_4$ flavor symmetry
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V. V. Vien
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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.
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A multiscalar and nonrenormalizable $B-L$ extension of the standard model (SM) with $S_4$ symmetry which successfully explains the recent observed neutrino oscillation data is proposed. The tiny neutrino masses and their hierarchies are generated via the type-I seesaw mechanism. The model reproduces the recent experiments of neutrino mixing angles and Dirac CP violating phase in which the atmospheric angle $(theta_{23})$ and the reactor angle $(theta_{13})$ get the best-fit values while the solar angle $(theta_{12})$ and Dirac CP violating phase ($delta $) belong to $3, si $ range of the best-fit value for normal hierarchy (NH). For inverted hierarchy (IH), $theta_{13}$ gets the best-fit value and $theta_{23}$ together with $de $ belongs to $1, si $ range while $theta_{12}$ belongs to $3, si $ range of the best-fit value. The effective neutrino masses are predicted to be $langle m_{ee}rangle=6.81 ,, mbox{meV}$ for NH and $langle m_{ee}rangle=48.48,, mbox{meV}$ for IH being in good agreement with the most recent experimental data.
A simple Standard Model Extension based on $T_7$ flavor symmetry which accommodates lepton mass and mixing with non-zero $theta_{13}$ and CP violation phase is proposed. At the tree- level, the realistic lepton mass and mixing pattern is derived through the spontaneous symmetry breaking by just one vacuum expectation value ($v$) which is the same as in the Standard Model. Neutrinos get small masses from one $SU(2)_L$ doublet and two $SU(2)_L$ singlets in which one being in $underline{1}$ and the two others in $underline{3}$ and $underline{3}^*$ under $T_7$ , respectively. The model also gives a remarkable prediction of Dirac CP violation $delta_{CP}=172.598^circ$ in both normal and inverted hierarchies which is still missing in the neutrino mixing matrix.
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 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 construct a low-scale seesaw model to generate the masses of active neutrinos based on $S_4$ flavor symmetry supplemented by the $Z_2 times Z_3 times Z_4 times Z_{14}times U(1)_L$ group, capable of reproducing the low energy Standard model (SM) fermion flavor data. The masses of the SM fermions and the fermionic mixings parameters are generated from a Froggatt-Nielsen mechanism after the spontaneous breaking of the $S_4times Z_2 times Z_3 times Z_4 times Z_{14}times U(1)_L$ group. The obtained values for the physical observables of the quark and lepton sectors are in good agreement with the most recent experimental data. The leptonic Dirac CP violating phase $de _{CP}$ is predicted to be $259.579^circ$ and the predictions for the absolute neutrino masses in the model can also saturate the recent constraints.
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