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Register a new userLepton mass and mixing in a simple extension of the Standard Model based on T7 flavor symmetry
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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.
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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.
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.
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.
We construct a 3-3-1 model based on non-Abelian discrete symmetry $T_7$ responsible for the fermion masses. Neutrinos get masses from only anti-sextets which are in triplets $underline{3}$ and $underline{3}^*$ under $T_7$. The flavor mixing patterns and mass splitting are obtained without perturbation. The tribimaximal form obtained with the breaking $T_7 rightarrow Z_3$ in charged lepton sector and both $T_7 rightarrow Z_3$ and $Z_3 rightarrow {mathrm{Identity}}$ must be taken place in neutrino sector but only apart in breakings $Z_3 rightarrow {mathrm{Identity}}$ (without contribution of $si$), and the upper bound on neutrino mass $sum_{i=1}^3m_i$ at the level is presented. The Dirac CP violation phase $delta$ is predicted to either $frac{pi}{2}$ or $frac{3pi}{2}$ which is maximal CP violation. From the Dirac CP violation phase we obtain the relation between Eulers angles which is consistent with the experimental in PDG 2012. On the other hand, the realistic lepton mixing can be obtained if both the direction for breakings $T_7 rightarrow Z_3$ and $Z_3 rightarrow {mathrm{Identity}}$ are taken place in neutrino sectors. The CKM matrix is the identity matrix at the tree-level.
The $D_4$ flavor model based on $mathrm{SU}(3)_C otimes mathrm{SU}(3)_L otimes mathrm{U}(1)_X$ gauge symmetry that aims at describing quark mass and mixing is updated. After spontaneous breaking of flavor symmetry, with the constraint on the Higgs vacuum expectation values (VEVs) in the Yukawa couplings, all of quarks have consistent masses, and a realistic quark mixing matrix can be realized at the first order of perturbation theory.
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