The scalar sector of the $SU(3)_{c}\otimes SU(3)_{L}\otimes U(1)_{X}$ model

A complete study of the Higgs sector of the $SU(3)_{c}\otimes SU(3)_{L}\otimes U(1)_{X}$ model is carried out, obtaining all possible cases of vacuum expectation values that permit the spontaneous symmetry breaking pattern$ SU(3)_{L}\otimes U(1)_{X}\to SU(2)_{L}\otimes U(1)_{Y}\to U(1)_{Q}.$ We find the most general Higgs potentials that contain three triplets of Higgs and one sextet. A detailed study of the scalar sector for different models with three Higgs triplets is done. The models end up in an electroweak two Higgs doublet model after the first symmetry breakdown; we find that the low energy limit depends on a trilinear parameter of the Higgs potential, and that the decoupling limit from the electroweak two Higgs doublet model to the minimal standard model can be obtained quite naturally.
41 pages, no figures, two subsections added. Version to appear in Phys. Rev. D