Simple 3-3-1 model and implication for dark matter

We propose a new and realistic 3-3-1 model with the minimal lepton and scalar contents, named the simple 3-3-1 model. The scalar sector contains two new heavy Higgs bosons, one neutral H and another singly-charged H^pm, besides the standard model Higgs boson. There is a mixing between the Z boson and the new neutral gauge boson (Z). The rho parameter constrains the 3-3-1 breaking scale (w) to be w>460 GeV. The quarks get consistent masses via five-dimensional effective interactions while the leptons via interactions up to six dimensions. Particularly, the neutrino small masses are generated as a consequence of the approximate lepton-number symmetry of the model. The proton is stabilized due to the lepton-parity conservation (-1)^L. The hadronic FCNCs are calculated that give a bound w>3.6 TeV and yield that the third quark generation is different from the first two. The correct mass generation for top quark implies that the minimal scalar sector as proposed is unique. By the simple 3-3-1 model, the other scalars beside the minimal ones can behave as inert fields responsible for dark matter. A triplet, doublet and singlet dark matter are respectively recognized. Our proposals provide the solutions for the long-standing dark matter issue in the minimal 3-3-1 model.

The 3-3-1 model with inert scalar triplet

We show that the typical 3-3-1 models are only self-consistent if they contain interactions explicitly violating the lepton number. The 3-3-1 model with right-handed neutrinos can by itself work as an economical 3-3-1 model as a natural recognition of the above criteria while it also results an inert scalar triplet (eta) responsible for dark matter. This is ensured by a Z_2 symmetry (assigned so that only eta is odd while all other multiplets which perform the economical 3-3-1 model are even), which is not broken by the vacuum. The minimal 3-3-1 model can provide a dark matter by a similar realization. Taking the former into account, we show that the dark matter candidate (H_eta) contained in eta transforms as a singlet in effective limit under the standard model symmetry and being naturally heavy. The H_eta relic density and direct detection cross-section will get right values when the H_eta mass is in TeV range as expected. The model predicts the H_eta mass m_{H_eta}=lambda_5times 2 TeV and the H_eta-nucleon scattering cross-section sigma_{H_eta-N}=1.56times 10^{-44} cm^2, provided that the new neutral Higgs boson is heavy enough than the dark matter.

The S_3 flavor symmetry in 3-3-1 models

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 (mathcal{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 rightarrow Z_2 and S_3 rightarrow Z_3 (or equivalently in the sequel S_3 rightarrow Z_2 rightarrow 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 mathcal{L}-violating scalar potential. The TeV seesaw scale can be naturally recognized in the former model. The degenerate masses of fermion pairs (mu, tau), (c, t) and (s, b) are respectively separated due to the S_3 rightarrow Z_3 breaking.

The 3-3-1 model with S_4 flavor symmetry

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.