On the Status of Three-Neutrino Mixing

Abstract

All existing solar and atmospheric neutrino oscillation data are described by the standard two-neutrino formulas with neutrino mass squared differences that satisfy the hierarchy relation $\Delta m^{2}_{sol} \ll \Delta m^{2}_{atm}$. We discuss this phenomenon from the point of view of three-neutrino mixing. Possibilities to see effects of three-neutrino mixing and, in particular, effects of CP-violation in the lepton sector depend on the values of $|U_{e3}|^2 $ and $\Delta m^{2}_{sol}$. We present an upper bound of $|U_{e3}|^2 $, which was obtained from a three-neutrino analysis of CHOOZ data in the case if the solar neutrino oscillation parameters lie in the LMA allowed region.