Simplest neutrino mixing from S4 symmetry

In 2004, two us proposed a texture, the “Simplest” neutrino mass matrix, which predicted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sin {\theta_{13 }}=\sqrt{{{{{2\varDelta m_{{^{sol}}}^2}} \left/ {{3\varDelta m_{{^{atm}}}^2}} \right.}}} $\end{document} and δCP = 90°. Using today’s measured values for neutrino mass-squared differences, this prediction gives \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {\sin^2}2{\theta_{13 }}\simeq 0.086_{-0.006}^{+0.003 } $\end{document}, compared with a measured value, found by averaging the results of the Daya Bay and RENO experiments, of sin22θ13 = 0.093 ± 0.010. Here we present a specific model based on S4 symmetry leading to this successful texture in the context of the type-1 see-saw mechanism, assuming Majorana neutrinos. In this case, slightly different predictions are obtained relating θ13 to the light neutrino masses, which are in accord with current experimental limits and testable at future experiments. Large CP asymmetries remain a generic prediction of the texture.