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 ${\nu }_e$, 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 ${\nu }_e\leftrightarrow {\nu }_{\tau }$ and ${\nu }_e\leftrightarrow {\nu }_{\mu }$ oscillations are predicted that may be observable in future long-baseline experiments.

Latex2.09, 12 pages, uses epsf.sty, 1 postscript figure. Minor text corrections (also, title was incorrect in initial listing)

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