Neutrino masses, mixing, and oscillations in the S4 model of permutation symmetry

Abstract

In the ${\mathrm{S}}_{4}$ model, we work out the simplest possible scheme for neutrino masses. We find that ${\ensuremath{\nu}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ have dominant massless components but not ${\ensuremath{\nu}}_{\ensuremath{\tau}}$. The mixing matrix is completely determined and ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ oscillations are possible with known mixing angles and only one $\ensuremath{\delta}{m}^{2}$.