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 that explicitly violate 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 produces 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 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 the effective limit under the standard model symmetry and is naturally heavy. The H-eta relic density and direct detection cross section will have the correct values when the mass of H-eta is in TeV range, as expected. The model predicts the H-eta mass m(H eta) = lambda(5) x 2 TeV and the H-eta-nucleon scattering cross section sigma(H eta-N) = 1: 56 x 10(-44) cm(2), provided that the new neutral Higgs boson is much heavier than the dark matter.