Doubly perturbedS3neutrinos and thes13mixing parameter

Abstract

We further study a predictive model for the masses and mixing matrix of three Majorana neutrinos. At zeroth order the model yielded degenerate neutrinos and a generalized tribimaximal mixing matrix. At first order the mass splitting was incorporated and the tribimaximal mixing matrix emerged with very small corrections but with a zero value for the parameter ${s}_{13}$. In the present paper a different, assumed weaker, perturbation is included which gives a nonzero value for ${s}_{13}$ and further corrections to other quantities. These corrections are worked out and their consequences discussed under the simplifying assumption that the conventional $CP$ violation phase vanishes. It is shown that the existing measurements of the parameter ${s}_{23}$ provide strong bounds on ${s}_{13}$ in this model.