L/E-flatness of the electron-like event ratio, in Super-Kamiokande and a degeneracy, in neutrino masses

We show that the L/E-flatness of the electron-like event ratio in the Super-Kamiokande atmospheric neutrino data implies the equality of the expectation values for the muon and tau neutrino masses. We establish this result by obtaining a set of three constraints on the neutrino-oscillation mixing matrix as contained in the indicated flatness. The resulting 3×3 neutrino-oscillation matrix depends only on one angle. A remarkable result that follows directly from this matrix is the consistency between the mixing angles observed by LSND and Super-Kamiokande.