L/E-Flatness of the Electron-Like Event Ratio in Super-Kamiokande and a Degeneracy in Neutrino Masses

TL;DR

This paper demonstrates that the flatness of the electron-like event ratio in Super-Kamiokande implies equal muon and tau neutrino masses and derives a simplified neutrino mixing matrix consistent with LSND and Super-Kamiokande observations.

Contribution

It establishes a novel connection between event ratio flatness and neutrino mass degeneracy, deriving a simplified mixing matrix with only one angle.

Findings

Electron-like event ratio flatness implies muon and tau neutrino mass equality.

Derived a 3x3 neutrino mixing matrix depending on a single angle.

Found consistency between LSND and Super-Kamiokande mixing angles.

Abstract

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 3x3 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.