Neutrinoless double-βdecay in anSU(3)L⊗U(1)Nmodel

We consider a model for the electroweak interactions with the $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\otimes \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_N$ gauge symmetry. We show that the conservation of the quantum number $F=L+B$ forbids the appearance of massive neutrinos and the neutrinoless double-$\beta$ decay ${\left(\beta \beta \right)}_{0\nu }$. Explicit or/and spontaneous breaking of $F$ implies that the neutrinos have an arbitrary mass. In addition the ${\left(\beta \beta \right)}_{0\nu }$ decay also has some channels that do not depend explicitly on the neutrino mass.