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We have studied $Delta(54)times Z_2$ flavor model for leptons and sleptons. The tri-bimaximal mixing can be reproduced for arbitrary neutrino masses if vacuum alignments of scalar fields are guaranteed. The deviation from the tri-bimaximal mixing of leptons is predicted. The predicted upper bound for $sintheta_{13}$ is 0.06. The magnitude of $sintheta_{23}$ could be deviated from the maximal mixing considerably, but $sintheta_{12}$ is hardly deviated from the tri-maximal mixing. We have also studied SUSY breaking terms in the slepton sector. Three families of left-handed and right-handed slepton masses are degenerate. Even although flavor symmetry breaking effects are taken into account, our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.
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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 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.
We study extensions of the standard model by one generation of vector-like leptons with non-standard hypercharges, which allow for a sizable modification of the h -> gamma gamma decay rate for new lepton masses in the 300 GeV - 1 TeV range. We analyze vaccum stability implications for different hypercharges. Effects in h -> Z gamma are typically much smaller than in h -> gamma gamma, but distinct among the considered hypercharge assignments. Non-standard hypercharges constrain or entirely forbid possible mixing operators with standard model leptons. As a consequence, the leading contributions to the experimentally strongly constrained electric dipole moments of standard model fermions are only generated at the two loop level by the new CP violating sources of the considered setups. We derive the bounds from dipole moments, electro-weak precision observables and lepton flavor violating processes, and discuss their implications. Finally, we examine the production and decay channels of the vector-like leptons at the LHC, and find that signatures with multiple light leptons or taus are already probing interesting regions of parameter space.
To include the quark sector, the $A_{5}equiv I$ (icosahedron) four generation lepton model is extended to a binary icosahedral symmetry $I$ flavor model. We find the masses of fermions, including the heavy sectors, can be accommodated. At leading order the CKM matrix is the identity and the PMNS matrix, resulting from same set of vacua, corresponds to tribimaximal mixings.
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.
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