Bi-Maximal Mixing of Three Neutrinos

Abstract

We show that if the solar and atmospheric data are both described by maximal vacuum oscillations at the relevant mass scales then there exists a unique mixing matrix for three neutrino flavors. The solution necessarily conserves CP and automatically implies that there is no disappearance of atmospheric $ν_e$, consistent with indications from the Super-Kamiokande experiment. We also investigate the consequences for three-neutrino mixing if the solar and atmospheric oscillations exhibit mixing that is large but not maximal. For non-maximal mixing $ν_e\leftrightarrowν_τ$ and $ν_e\leftrightarrowν_μ$ oscillations are predicted that may be observable in future long-baseline experiments.