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Register a new userQuark mass and mixing in the 3-3-1 model with neutral leptons based on $D_4$ flavor symmetry
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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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We construct a $D_4$ flavor model based on SU(3)_C X SU}(3_L X U(1)_X gauge symmetry responsible for fermion masses and mixings. The neutrinos get small masses from antisextets which are in a singlet and a doublet under $D_4$. If the D_4 symmetry is violated as perturbation by a Higgs triplet under SU(3)_L and lying in {1} of D_4, the corresponding neutrino mass mixing matrix gets the most general form. In this case, the model can fit the experimental data in 2012 on neutrino masses and mixing. Our results show that the neutrino masses are naturally small and a little deviation from the tribimaximal neutrino mixing form can be realized. The quark masses and mixing matrix are also discussed. In the model under consideration, the CKM matrix can be different from the unit matrix. The scalar potential of the model is more simpler than those of the model based on $S_3$ and $S_4$. Assignation of VEVs to antisextets leads to the mixing of the new gauge bosons and those in the Standard Model. The mixing in the charged gauge bosons as well as the neutral gauge boson is considered.
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.
We build the first 3-3-1 model based on the $Delta (27)$ discrete group symmetry, consistent with fermion masses and mixings. In the model under consideration, the neutrino masses are generated from a combination of type-I and type-II seesaw mechanisms mediated by three heavy right-handed Majorana neutrinos and three $SU(3)_{L}$ scalar antisextets, respectively. Furthermore, from the consistency of the leptonic mixing angles with their experimental values, we obtain a non-vanishing leptonic Dirac CP violating phase of $-frac{pi }{2}$. Our model features an effective Majorana neutrino mass parameter of neutrinoless double beta decay, with values $m_{beta beta }=$ 10 and 18 meV for the normal and the inverted neutrino mass hierarchies, respectively.
A new S3 flavor model based on $mathrm{SU}(3)_C otimes mathrm{SU}(3)_L otimes mathrm{U}(1)_X$ gauge symmetry responsible for fermion masses and mixings different from our previous work is constructed. The new feature is a two - dimensional representation of a Higgs anti-sextet under $S_3$ which responsible for neutrino masses and mixings. The neutrinos acquire small masses from only an anti-sextet of $mathrm{SU(3)}$ which is in a doublet under $S_3$. If the difference of components of the anti-sextet is regarded as a small perturbation, S3 is equivalently broken into identity, the corresponding neutrino mass mixing matrix acquires the most general form and the model can fit the latest data on neutrino oscillation. This way of the symmetry breaking helps us to reduce a content in the Higgs sector, only one an anti-sextet instead of two as in our previous work. Our results show that the neutrino masses are naturally small and a small deviation from the tri-bimaximal neutrino mixing form can be realized. The Higgs potential of the model as well as the minimization conditions and gauge boson masses and mixings is also considered.
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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