A prediction for three neutrino masses and mixings and similarity between quark and lepton mixings

Abstract

If neutrinos have mass, we give reasons for a possible pattern of three (squared) mass eigenvalues: $m_1^2\simeq (2.8-5.8)\text{mbox}{(eV)}^2$, $m_2^2\simeq 0.01\text{mbox}{(eV)}^2$, $m_3^2\simeq (1.5-1)\times 10^{-4}\text{mbox}{(eV)}^2$. The flavor states ${\nu }_{\mu }$ and ${\nu }_e$ are mixtures of the eigen\-states with $m_2$ and $m_3$ with a significant mixing, corresponding to an effective mixing angle of about 0.45. The ${\nu }_{\tau }$ is nearly the state with $m_1$; the other two effective mixing angles are about an order of magnitude smaller than 0.45. There is a marked similarity to mixing in the quark sector.