Naturally low scale type I seesaw mechanism and its viability in the 3-3-1 model with right-handed neutrinos

Seesaw mechanisms are the simplest and the most elegant way of generating small masses for the active neutrinos $(m_\nu)$. In these mechanisms $m_\nu$ 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 much lighter than the other two active neutrinos.