Hierarchical majorana neutrinos from democratic mass matrices

Abstract

In this paper, we obtain the light neutrino masses and mixings consistent with the experiments, in the democratic texture approach. The essential ansatz is that $\nu_{Ri}$ are assumed to transform as "right-handed fields" $\bf 2_{R} + 1_{R}$ under the $S_{3L} \times S_{3R}$ symmetry. The symmetry breaking terms are assumed to be diagonal and hierarchical. This setup only allows the normal hierarchy of the neutrino mass, and excludes both of inverted hierarchical and degenerated neutrinos. Although the neutrino sector has nine free parameters, several predictions are obtained at the leading order. When we neglect the smallest parameters $\zeta_{\nu}$ and $\zeta_{R}$, all components of the mixing matrix $U_{\rm PMNS}$ are expressed by the masses of light neutrinos and charged leptons. From the consistency between predicted and observed $U_{\rm PMNS}$, we obtain the lightest neutrino masses $m_{1}$ = (1.1 $\to$ 1.4) meV, and the effective mass for the double beta decay $\vev{m_{ee}} \simeq$ 4.5 meV.