Q6flavor symmetry model for the extension of the minimal standard model by three right-handed sterile neutrinos

Abstract

The extension of the minimal standard model by three right-handed sterile neutrinos with masses smaller than the electroweak scale ($\ensuremath{\nu}\mathrm{MSM}$) is discussed in a ${Q}_{6}$ flavor symmetry framework. The lightness of the keV sterile neutrino and the near mass degeneracy of two heavier sterile neutrinos are naturally explained by exploiting group properties of ${Q}_{6}$. A normal hierarchical mass spectrum and an approximately $\ensuremath{\mu}\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ symmetric mass matrix are predicted for three active neutrinos. Nonzero ${\ensuremath{\theta}}_{13}$ can be obtained together with a deviation of ${\ensuremath{\theta}}_{23}$ from the maximality, where both mixing angles are consistent with the latest global data including T2K and MINOS results. Furthermore, the tiny active-sterile mixing is related to the mass ratio between the lightest active and lightest sterile neutrinos.