Is large lepton mixing excluded?

Abstract

The original ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{-}(or{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}\ensuremath{-})$ energy spectrum from the gravitational collapse of a star has a larger average energy than the spectrum for ${\overline{\ensuremath{\nu}}}_{e}$ since the opacity of ${\overline{\ensuremath{\nu}}}_{e}$ exceeds that of ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}(or{\ensuremath{\nu}}_{\ensuremath{\tau}})$. Flavor neutrino conversion ${\overline{\ensuremath{\nu}}}_{e}\ensuremath{\leftrightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ induced by lepton mixing results in partial permutation of the original ${\overline{\ensuremath{\nu}}}_{e}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ spectra. An upper bound on the permutation factor $p\ensuremath{\le}0.35$ (99% C.L.) is derived using the data from SN 1987A and a range of models of the neutrino emission. The relation between the permutation factor and the vacuum mixing angle is established, which leads to the upper bound on this angle. The upper bound ${sin}^{2}2\ensuremath{\theta}>0.7\ensuremath{-}0.9$ excludes the large mixing angle solutions of the solar neutrino problem: "just-so" and, partly, MSW, as well as part of the region of the ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ oscillation space which could be responsible for the atmospheric muon neutrino deficit. These limits are sensitive to the predicted neutrino spectrum and can be strengthened as supernova models improve.