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

摘要

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 solutionof a particular 3-3-1 gauge model. We discuss what are the consequences ofconserving this global leptonic symmetry from the viewpoint of the neutrinomass matrix constructed via special Yukawa terms (involving tensor productsamong Higgs triplets). We prove that the actual experimental data can naturallybe reproduced by our scenario since soft breaking terms with respect to thislepton symmetry are properly introduced. As a consequence, our solutionpredicts for the neutrino sector the correct mass splitting ratio ($\Deltam_{12}^{2}/\Delta m_{23}^{2}\simeq0.033$), the inverted mass hierarchy, thecorrect 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.