Almost maximally broken permutation symmetry for neutrino mass matrix

Abstract

Assuming three light neutrinos are Majorana particles, we propose mass matrix ansatz for the charged leptons and Majorana neutrinos with family symmetry $S_{3} $ broken into $S_{1}$ and $S_{2}$, respectively. Each matrix has three parameters, which are fixed by measured charged lepton masses, differences of squared neutrino masses relevant to the solar and the atmospheric neutrino puzzles, and the masses of three light Majorana neutrinos as a candidate for hot dark matter with $\sum |m_{\nu}| \sim 6 eV$. The resulting neutrino mixing is compatible with the data for the current upper limit, $ < m_{\nu_e} >_{th} < 0.8 eV$, of neutrino-less double beta decay experiments, and the current data for various types of neutrino oscillation experiments. One solution of our model predicts that $\nu_{\mu} \rightarrow \nu_{\tau}$ oscillation probability is about $< 0.008$ with $\Delta m^{2} \sim 10^{-2} eV^2$, which may not be accessible at CHORUS and other ongoing experiments.