The SU(3)C ⊗ SU(3)L ⊗ U(1)X gauge model with the minimal scalar sector (two Higgs triplets) is studied in detail. One of the vacuum expectation values u is a source of lepton-number violations and a reason for the mixing among the charged gauge bosons -the standard model W and the bilepton (with L = 2) gauge bosons as well as among neutral non-Hermitian X 0 and neutral gauge bosons: the photon, the Z and the new Z ′ . Because of these mixings, the lepton-number violating interactions exist in both charged and neutral gauge boson sectors. An exact diagonalization of the neutral gauge boson sector is derived and bilepton mass splitting is also given. The lepton-number violation happens only in the neutrino but not in the charged lepton sector. In this model, leptonnumber changing (∆L = ±2) processes exist but only in the neutrino sector. Constraints on VEVs of the model are estimated and u ≃ O(1) GeV, v ≃ v weak = 246 GeV and ω ≃ O(1) TeV.

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We show that, in frameworks of the economical 3-3-1 model, all fermions get masses. At the tree level, one up-quark and two down-quarks are massless, but the one-loop corrections give all quarks the consistent masses. This conclusion is in contradiction to the previous analysis in which, the third scalar triplet has been introduced. This result is based on the key properties of the model: First, there are three quite different scales of vacuum expectation values: $\om \sim {\cal O}(1) \mathrm{TeV}, v \approx 246 \mathrm{GeV}$ and $ u \sim {\cal O}(1) \mathrm{GeV}$. Second, there exist two types of Yukawa couplings with different strengths: the lepton-number conserving couplings $h$'s and the lepton-number violating ones $s$'s satisfying the condition in which the second are much smaller than the first ones: $ s \ll h$. With the acceptable set of parameters, numerical evaluation shows that in this model, masses of the exotic quarks also have different scales, namely, the $U$ exotic quark ($q_U = 2/3$) gains mass $m_U \approx 700 $ GeV, while the $D_\al$ exotic quarks ($q_{D_\al} = -1/3$) have masses in the TeV scale: $m_{D_\al} \in 10 \div 80$ TeV.Comment: 20 pages, 8 figure

We propose two 3-3-1 models (with either neutral fermions or right-handed neutrinos) based on S 3 flavor symmetry responsible for fermion masses and mixings. The models can be distinguished upon the new charge embedding (L) relevant to lepton number. The neutrino small masses can be given via a cooperation of type I and type II seesaw mechanisms.The latest data on neutrino oscillation can be fitted provided that the flavor symmetry is broken via two different directions S 3 → Z 2 and S 3 → Z 3 (or equivalently in the sequel S 3 → Z 2 → {Identity}), in which the second direction is due to a scalar triplet and another antisextet as small perturbation. In addition, breaking of either lepton parity in the model with neutral fermions or lepton number in the model with right-handed neutrinos must be happened due to the L-violating scalar potential. The TeV seesaw scale can be naturally recognized in the former model. The degenerate masses of fermion pairs (µ, τ ), (c, t) and (s, b) are respectively separated due to the S 3 → Z 3 breaking.

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 L related to the ordinary lepton charge L and a SU (3) charge by L = 2 √ 3 T 8 + 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 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.

In this paper we compute all contributions to the muon magnetic moment stemming from several 3-3-1 models, namely, minimal 331, 331 with right-handed neutrinos, 331 with heavy neutral leptons, 331 with charged exotic leptons, 331 economical and 331 with two Higgs triplets. Further, we exploit the complementarity among current electroweak, dark matter and collider constraints to outline the relevant parameter space of the models capable of explaining the anomaly. Lastly, assuming that the experimental anomaly has been otherwise resolved, we derive robust 1σ bounds using the current and projected measurements.

We show that, in frameworks of the economical 3-3-1 model, the suitable pattern of neutrino masses arises from the three quite different sources -the lepton-number conserving, the spontaneous lepton-number breaking and the explicit lepton-number violating, widely ranging over the mass scales including the GUT one:At the tree-level, the model contains three Dirac neutrinos: one massless, two large with degenerate masses in the order of the electron mass. At the one-loop level, the left-handed and right-handed neutrinos obtain Majorana masses ML,R in orders of 10 −2 −10 −3 eV and degenerate in MR = −ML, while the Dirac masses get a large reduction down to eV scale through a finite mass renormalization. In this model, the contributions of new physics are strongly signified, the degenerations in the masses and the last hierarchy between the Majorana and Dirac masses can be completely removed by heavy particles. All the neutrinos get mass and can fit the data.

The supersymmetric extension of the economical 3-3-1 model is presented. The constraint equations and the gauge boson identification establish a relation between the vacuum expectation values (VEVs) at the top and bottom elements of the Higgs triplet χ and its supersymmetric counterpart χ ′ . Because of this relation, the exact diagonalization of neutral gauge boson sector has been performed. The gauge bosons and their associated Goldstone ones mix in the same way as in non-supersymmetric version. This is also correct in the case of gauginos. The eigenvalues and eigenstates in the Higgs sector are derived. The model contains a heavy neutral Higgs boson with mass equal to those of the neutral non-Hermitian gauge boson X 0 and a charged scalar with mass equal to those of the W boson in the standard model, i. e. m ̺ 1 = m W . This result is in good agreement with the present estimation: m H ± > 79.3 GeV, CL= 95 %. We also show that the boson sector and the fermion sector gain masses in the same way as in the non-supersymmetric case.