Neutrino Mass Squared Differences in the Exact Solution of a 3-3-1 Gauge Model without Exotic Electric Charges

Abstract

The mass splittings for the Majorana neutrinos in the exact solution of a particular 3-3-1 gauge model are computed here in detail. Since both ${\sin }^2{\theta }_{13}\simeq 0$ and the mass splittings ratio $r_{\Delta }\simeq 0.033$ are taken into account, the analytical calculations seem to predict an inverted mass hierarchy and a mixing matrix with a texture based on a very close approximation to the bi-maximal mixing. The resulting formulas for the mass squared differences can naturally accomodate the available data if the unique free parameter ($a$) gets very small values ($\sim 10^{-15}$). Consequently, the smallness of the parameter requires (according to our method) a large breaking scale $<\varphi >\sim 10^6-10^7$ TeV in the model. Hence, the results concerning the neutrino mass splittings may lead to a more precise tuning in the exact solution of the 3-3-1 model of interest, being able - at the same time - to recover all the Standard Model phenomenology and predict the mass spectrum of the new gauge bosons $Z^{\prime },X,Y$ in accordance with the actual data. The minimal absolute mass in the neutrino sector is also obtained - $m_0\simeq 0.0035$ eV - in the case of our suitable approximation for the bi-maxcimal mixing.

Comments: 10 pages, no figures