A straightforward realization of a quasi-inverse seesaw mechanism at TeV scale

Abstract: In this letter we address the issue of generating appropriate tiny neutrino masses within the framework of a particular $SU(3){c}\otimes SU(3){L}\otimes U(1){X}$ gauge model by adding three singlet exotic Majorana neutrinos to the ones included in the three lepton triplet representations. The theoretical device is the general method of treating gauge models with high symmetries $SU(3){c}\otimes SU(N){L}\otimes U(1){X}$ proposed by Cot\u{a}escu more than a decade ago. When it is worked-out in the 3-3-1 model it supplies a unique free parameter ($a$) to be tuned in order to get a realistic mass spectrum for both the boson and charged-fermion sectors. Its most appealing feature (of special interest here) is that it contains all the needed ingredients to realize the inverse seesaw mechanism for neutrinos. The mandatory couplings leading to the lepton number soft violation in pure Majorana terms result without invoking any element outside the model (such as GUT scales, as one usually does in the literature). The overall breaking scale in this particular model can be set around 1 TeV so its phenomenology is quite testable at present facilities.