We build a complete supersymmetric version of a 3-3-1 gauge model using the superfield formalism. We point out that a discrete symmetry, similar to R symmetry in the minimal supersymmetric standard model, is possible to be defined in this model. Hence we have both R-conserving and R-violating possibilities. Analysis of the mass spectrum of the neutral real scalar fields show that in this model the lightest scalar Higgs boson has a mass upper limit, and at the tree level it is 124.5 GeV for a given illustrative set of parameters.

We recall the many obstacles which seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. We also present their solutions, leading to the construction of the supersymmetric extensions of the Standard Model. Finally we discuss briefly the early experimental searches for Supersymmetry.

The R-symmetry formalism is applied for the supersymmetric SU(3) C ⊗ SU(3) L ⊗ U(1) X (3-3-1) model with right-handed neutrinos. For this kind of models, we study generalization of the MSSM relation among R-parity, spin and matter-parity. Discrete symmetries for the proton stable in this model are imposed, and we show that in such a case it is able to give leptons masses at only the tree level contributions required. A simple mechanism for the mass generation of the neutrinos is explored. We show that at the low-energy effective theory, neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the energy-level where the mixing among them with neutralinos turned on, neutrinos obtain Majorana masses and correct the lowenergy effective result which naturally gives rise to an inverted hierarchy mass pattern. This mass spectrum can fit the current data with minor fine-tuning. Consistent values for masses of the charged leptons are also given. In this model, the MSSM neutralinos and charginos can be explicitly identified in terms of the new constraints on masses which is not as in a supersymmetric version of the minimal 3-3-1 model.

Several left-right parity violating asymmetries in lepton-lepton scattering in fixed target and collider experiments are considered as signals for doubly charged vector bosons (bileptons).

We consider the minimal supersymmetric extension of the 3-3-1 model. We study the mass spectrum of this model in the fermionic and gauge bosons sectors without the antisextet. We also present some phenomenological consequences of this model at colliders such as Large Hadron Collider (LHC) and International Linear Collider (ILC)