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In the 3-3-1 model with right-handed neutrinos (331RHNs), three triplets of scalars engender the correct sequence of symmetry breaking, S U (3) C × S U (3) L × U (1) X → S U (3) C × S U (2) L × U (1) Y → S U (3) C × U (1) EM , generating mass for all fermions, except neutrinos. Tiny neutrino masses may be achieved by implementing the type II seesaw mechanism into the model, requiring the addition of one sextet of scalars to the original scalar content. As consequence, it emerges a very complex scalar sector, involving terms that violate lepton number explicitly, too. The main obstacle to the development of the phenomenology of such scenario is the knowledge of its spectrum of scalars since, now, there are 15 massive scalar particles on it. The proposal of this work is to do an exhaustive analysis of such scalar sector with lepton number being explicitly violated at low, electroweak and high energy scales by means of trilinear terms in the potential. The first case can be addressed analytically and, as a nice result, we have observed that the scalar content of such case is split into two categories: One belonging to the 331 energy scale and the other belonging to the EWSB energy scale, with the last recovering the well know 2THDM + triplet. For the other cases, the scalar sector can be addressed only numerically. Hence, we proposed a very general approach for the numerical study of the potential, avoiding simplifications that can make us reach conclusions without foundation. We show that, in the case of lepton number being explicitly violated at electroweak scale, it is possible to recover the same physics of the 2HDM + triplet, as the previous case. Among all the possibilities, we call the attention to one special case which generates the 3HDM+triplet scenario. For the last case, when lepton number is violated at high energy scale, the sextet becomes very massive and decouples from the original scalar content of the 3-3-1 model. We also discuss, when possible, the phenomenological aspects of each case. [ABSTRACT FROM AUTHOR]

Seesaw mechanisms are the simplest and the most elegant way of generating small masses for the active neutrinos (m ν). In these mechanisms m ν is inversely proportional to the lepton number breaking scale (M) that, in the particular case of the type I seesaw mechanism, is the Majorana mass of the right-handed neutrinos. In the canonical case right-handed neutrinos are supposed to be heavy belonging to the GUT scale. With the advent of the LHC people began to suppose these neutrinos having mass at TeV scale. In this case very tiny Yukawa couplings are required. As far as we know there are no constraints on the energy scales associated to the seesaw mechanisms. In what concern 3-3-1 models, when we trigger the type I seesaw mechanism the lepton number breaking scale that suppresses active neutrino masses contributes to the masses of the standard gauge bosons. Current data on m W demands the mechanism to be performed at GeV scale. As main implication we may have right handed neutrinos with mass varying from few keVs up to hundreds of GeVs. We also investigate the viability of the mechanism and found as interesting result that in the case in which the right-handed neutrino masses belong to the range keV-MeV scale, viability of the mechanism demands that the lightest of the right-handed neutrinos be stable, which makes of it a natural dark matter candidate, and that the lightest of the active neutrinos be ultralight. [ABSTRACT FROM AUTHOR]