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Register a new userMultiscalar $B-L$ extension based on $S_4$ flavor symmetry for neutrino mass and mixing
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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.
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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 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 present the $D_4times Z_2$ 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.
In a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T_7 in the context of a supersymmetric extension of the Standard Model with gauged U(1)_{B-L}, a correlation was obtained between theta_{13} and theta_{23} in the case where all parameters are real. Here we consider all parameters to be complex, thus allowing for one Dirac CP phase delta_{CP} and two Majorana CP phases alpha_{1,2}. We find a slight modification to this correlation as a function of delta_{CP}. For a given set of input values of Delta m^2_{21}, Delta m^2_{32}, theta_{12}, and theta_{13}, we obtain sin^2 2 theta_{23} and m_{ee} (the effective Majorana neutrino mass in neutrinoless double beta decay) as functions of tan delta_{CP}. We find that the structure of this model always yields small |tan delta_{CP}|.
We argue that neutrino mass and dark matter can arise from an approximate $B-L$ symmetry. This idea can be realized in a minimal setup of the flipped 3-3-1 model, which discriminates lepton families while keeping universal quark families and uses only two scalar triplets in order for symmetry breaking and mass generation. This proposal contains naturally an approximate non-Abelian $B-L$ symmetry which consequently leads to an approximate matter parity. The approximate symmetries produce small neutrino masses in terms of type II and III seesaws and may make dark matter long lived. Additionally, dark matter candidate is either unified with the Higgs doublet by gauge symmetry or acted as an inert multiplet. The Peccei-Quinn symmetry is discussed. The gauge and scalar sectors are exactly diagonalized. The signals of the new physics at colliders are examined.
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