Conserving the lepton number $L_{e}-L_{\mu}-L_{\tau}$ in the exact solution of a 3-3-1 gauge model with right-handed neutrinos

Abstract

In this paper we consider a plausible scenario with conserved lepton number \textbf{$L=L_{e}-L_{\mu}-L_{\tau}$} within the framework of the exact solution of a particular 3-3-1 gauge model. We discuss what are the consequences of conserving this global leptonic symmetry from the viewpoint of the neutrino mass matrix constructed via special Yukawa terms (involving tensor products among Higgs triplets). We prove that the actual experimental data can naturally be reproduced by our scenario since soft breaking terms with respect to this lepton symmetry are properly introduced. As a consequence, our solution predicts for the neutrino sector the correct mass splitting ratio ($\Delta m_{12}^{2}/\Delta m_{23}^{2}\simeq0.033$), the inverted mass hierarchy, the correct values for the observed mixing angles ($\sin^{2}\theta_{23}\simeq0.5$ and $\sin^{2}\theta_{12}=0.31$)and the absolute mass of the lightest neutrino ($m_{0}\sim0.001$eV)independent of the breakung scale of the model.