Generating ${\theta }_{13}$ from sterile neutrinos in $\mu -\tau$ symmetric models

Abstract

The smallness of the ${\theta }_{13}$ mixing angle as observed in neutrino oscillation experiments can be understood through an approximated $\mu -\tau$ exchange symmetry in the neutrino mass matrix. Using recent oscillation neutrino data, but assuming no \textit{CP} violation, we study $\mu -\tau$ breaking parameter space to establish the conditions under which such a breaking could have a perturbative origin. According to the so-obtained conditions, we suggest that a sterile neutrino, matching LSND/MiniBooNE neutrino oscillation results, could provide the necessary ingredients to properly fix atmospheric and ${\theta }_{13}$ mixing angles to observable values, without exceeding the sterile neutrino fraction bound in solar oscillations. In such a scenario, we analyze the general effect of a fourth neutrino on the prediction for the effective $m_{ee}$ majorana mass parameter.

Comments: Version accepted for publication in PRD, 19 pages, 5 figures, references added