A Theory of Pattern Recognition for the Discrimination between Muon and Electron in the Super-Kamiokande

Abstract

The standard Super-Kamiokande analysis uses an estimator for particle identification by which it discriminates electrons (electron nutrinos) from muons (muon nutrinos). Use of this estimator has led to the claim of a significant deficiency of muons (muon nutrinos), suggesting the existence of neutrino oscillations. We investigate three areas of concern for the Super-Kamiokande estimator: the separation of the spatial part from the angular part in the probability functions, the neglect of fluctuations in the Cherenkov light in different physical processes due to the charged particles concerned, and the point-like approximation for the emission of Cherenkov light. We show that the first two factors are important for the consideration of stochastic processes in the generation of the Cherenkov light, and that the point-like assumption oversimplifies the estimation of the Cherenkov light quantities. We develop a new discrimination procedure for separating electron neutrinos from muon neutrinos, based on detailed simulations carried out with GEANT~3.21 and with newly derived mean angular distribution functions for the charged particles concerned (muons and electrons/positrons), as well as the corresponding functions for the relative fluctuations. These angular distribution functions are constructed introducing a ``moving point'' approximation. The application of our procedure between the discrimination between electron and muon to the analysis of the experimental data in SK will be made in a subsequent paper.