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

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.Comment: 16 pages,26 figures, late

A Discrimination Procedure between Muon and Electron in Superkamiokande Experiment Based on the Angular Distribution Function Method

In the previous paper, we construct the angular distribution functions for muon and electron as well as their relative fluctuation functions to find suitable discrimination procedure between muon and electron in Superkamiokande experiment. In the present paper, we are able to discriminate muons from electrons in Fully Contained Events with a probability of error of less than several %. At the same time, our geometrical reconstruction procedure, considering only the ring-like structure of the Cherenkov image, gives an unsatisfactory resolution for 1GeV electron and muon, with a mean vertex position error, delta r, of 5-10 m and a mean directional error, delta theta, of about 6-20 degrees. In contrast, a geometrical reconstruction procedure utilizing the full image and using a detailed approximation of the event angular distribution works much better: for a 1 GeV electron, delta r is about 2 m and delta theta is about 3 degrees; for a 1GeV muon, delta r is about 3 m and delta theta is about 5 degrees. At 5 GeV, the corresponding values are about 1.4 m and about 2 degree for electron and are about 2.9m and about 4.3 degrees for muon. The numerical values depend on a single PMT contribution threshold. The values quoted above are the minima with respect to this threshold. Even the methodologically correct approach we have adopted, based on detailed simulations using closer approximations than those adopted in the SK analysis, cannot reproduce the accuracies for particle discrimination, momentum resolution, interaction vertex location, and angular resolution obtained by the SK simulations, suggesting the assumptions in these may be inadequate.Comment: comments: 141pages, 23 figures,late

Have Superkamiokande Really Measured the Direction of the Atmospheric Neutrinos which Produce Fully Contained Events and Partially Contained Events ?

Quasi Elastic Scattering (QEL) is the dominant source for producing both Fully Contained Events and Partially Contained Events in the Superkamiokande(SK) detector for the atmospheric neutrinos, in the range 0.1 GeV to 10 GeV. In the analysis of SK events, it is assumed that the direction of the incident neutrino is the same as that of the detected charged lepton. In the present letter, we derive the distribution function for the scattering angle of the charged leptons, their averaged scattering angle and their standard deviation due to QEL. Then, it is shown that the SK assumption for the scattering angle of the charged leptons in the QEL is not valid. Further, we examine the influence of the azimuthal angle of the charged leptons over their zenith angle. As the result, we conclude that the zenith angle distribution of the neutrino under the SK assumption does not reflect the real zenith angle distribution of the atmospheric neutrino which produces Fully Contained Events and Partially Contained Events. This result has clear implication for attempts to detect neutrino oscillations from the analyses of Fully Contained Events and Partially Contained Events in Superkamiokande.Comment: Latex, 5 pages, 11 figures, 1 table. Submitted to Physical Review D, Rapid Communicatio

The numerical computer experiment for the neutrino events with the SK neutrino oscillation parameters occurring outside the Superkamiokande detector

Adopting neutrino oscillation parameters obtained by Super-Kamiokande, a numerical computer experiment for neutrino events occurring outside the detector, is carried out in the same SK live days, 1645.9 live days, constructing the virtual Super-Kamiokande detector in the computer. The numerical results by the computer experiment could be directly compared with the real SK experimental data. The comparison shows that it is difficult to obtain convincing conclusion on the existence of the neutrino oscillation with specified neutrino oscillation parameters claimed by SK through analysis for neutrino events occurring outside the detector.Comment: 21 pages, 31 figure

On the Sensitivity of L/E Analysis of Super-Kamiokande Atmospheric Neutrino Data to Neutrino Oscillation Part~2 --- Four Possible L/E Analyses for the Maximum Oscillation by the Numerical Computer Experiment ---

In the previous paper (Part~1), we have verified that the SK assumption on the direction does not hold in the analysis of neutrino events occurred inside the SK detector. We have made four possible L/E analyses, L_nu/E_nu, L_nu/E_mu, L_mu/E_nu and L_mu/E_mu. Among four kinds of L/E analyses, we have shown that only L_nu/E_nu analysis can give the signature of maximum oscillations clearly, while the L_mu/E_mu analysis which are really done by Super-Kamiokande Collaboration cannot give the maximum oscillation at all. It is thus concluded that Super-Kamiokande type experiment cannot find the maximum oscillation from L/E analysis. Therefore, we would suggest Super-Kamiokande Collaboration to re-analyze the zenith angle distribution of the neutrino events which occur inside the detector carefully.Comment: 13 pages with 41 figures, Late

Examination on SK atmospheric neutrino experiment by the computer experiment

We examine neutrino events occurring inside the SuperKamiokande (SK) detector and those occurring outside the same detector using computer simulations. We analyze the zenith angle distribution of Fully Contained Events and show the method for the determination of the incident neutrino by the SK group is unreliable. The analysis of the neutrino events occurring outside the detector shows these events agree with the Monte Carlo simulation without oscillation.Comment: 3 pages, 5 figures, conference of TAUP200

On the Sensitivity of L/E Analysis of Super-Kamiokande Atmospheric Neutrino Data to Neutrino Oscillation Part~1

It is said that the finding of the maximum oscillation in neutrino oscillation by Super-Kamiokande is one of the major achievements of the SK. In present paper, we examine the assumption made by Super-Kamiokande Collaboration that the direction of the incident neutrino is approximately the same as that of the produced lepton, which is the cornerstone in their L/E analysis and we find this approximation does not hold even approximately. In the Part 2 of the subsequent paper, we apply the results from Figures 12, 13 and 14 to L/E analysis and conclude that one cannot obtain the maximum oscillation in L/E analysis which shows strongly the oscillation pattern from the neutrino oscillation.Comment: 12 pages with figures and tables, Late

Comprehensive Analysis of Neutrinos in SK part 3 -- L/E Analysis for Single Ring Muon Events II --

Following the L_nu/E_nu analysis in the preceding paper of the Fully Contained Muon Events resulting from the quasi-elastic scattering obtained from our numerical computer experiment. In the present paper, we carry out the analyses of L_nu/E_mu, L_mu/E_nu and L_mu/E_mu among four possible combinations of L and E. As the result of it, we show that we can not find the characteristis of maximum oscillation for neutrino oscillation among two of three, L_mu/E_mu and L_mu/E_nu. Only the L_nu/E_mu distribution can show something like maximum oscillation, however it cannot be detected owing to the neutral character of L_nu. It is concluded that the Super-Kamiokande Experiment could not have found the existence of the maximum oscillation for neutrino oscillation.Comment: 12 pages with 17 figures, Late

On the Relation between the True Directions of Neutrinos and the Reconstructed Directions of Neutrinos in L/E Analysis Performed by Super-Kamiokande Collaboration Part2

In the previous paper (Part1), we have verified that the SK assumption on the direction does not hold in the analysis of neutrino events occurred inside the SK detector, which is the cornerstone for their analysis of zenith angle distributions of neutrino events. Based on the correlation between L_nu and L_mu (Figures~16 to 18 in Part1) and the correlation between E_nu and E_mu (Figure19 in Part1), we have made four possible L/E analyses, namely L_nu/E_nu, L_nu/E_mu, L_mu/E_mu and L_mu/E_nu. Among four kinds of L/E analyses, we have shown that only L_nu/E_nu analysis can give the signature of maximum oscillations clearly, not only the first maximum oscillation but also the second and third maximum oscillation and etc., as they should be, while the L_mu/E_mu analysis which are really done by Super-Kamiokande Collaboration cannot give any maximum oscillation at all. It is thus concluded from those results that the experiments with the use of the cosmic-ray beam for neutrino oscillation, such as Super-Kamiokande type experiment, are unable to lead the maximum oscillation from their L/E analysis, because the incident neutrino cannot be observed due to its neutrality. Therefore, we would suggest Super-Kamiokande Collaboration to re-analyze the zenith angle distribution of the neutrino events which occur inside the detector carefully, since L_nu and L_mu are alternative expressions of the cosine of the zenith angle for the incident neutrino and that for the emitted muon, respectively.Comment: 17 pages with 47 figures, Latex. arXiv admin note: substantial text overlap with arXiv:1007.492

A Critical Examination on L/E Analysis in the Underground Detectors with a Computer Numerical Experiment Part 1

In the present paper we consider neutrino events due to quasi-elastic scattering (QEL) as the most reliable events among various candidate events to be analyzed, and have carried out the first step of an L/E analysis which aims to confirm the survival probability with a Numerical Computer Experiment. The most important factor in the survival probability is Lnu and Enu, but this cannot be measured for such neutral particles. Instead, Lmu and Emu is utilized in the L/E analysis, where Lnu, Lmu, Enu and Emu denote the flight path lengths of the incident neutrinos, those of the emitted leptons, the energies of the incident neutrinos and those of the emitted leptons, respectively. According to our Computer Numerical Experiment, the relation of Lnu/Enu is nearly equal to Lmu/Emu doesn't hold. In subsequent papers, we show the results on an L/E analysis with the Computer Numerical Experiment based on our results obtained in the present paper.Comment: 20 pages with figures and tables, Latex. arXiv admin note: substantial text overlap with arXiv:1108.1064, arXiv:1007.381