(Ultra-)High Energy Muon Neutrino Propagation through the Earth and Induced Muon Energy Distribution near the One Cubic Kilometer Detector

We calculate high and (ultra-)high energy upward-going muon neutrino propagation through the Earth and the induced muon energy distribution near the one cubic kilometer detector using the Monte Carlo simulation, due to both charged current interaction and neutral one. The initiated neutrino energies on the surface of the Earth are 1PeV, 1EeV and 1ZeV. The mean free paths of (ultra-)high energy neutrino events generated by the deep inelastic scattering may be comparable with the diameter of the Earth or less than it. Therefore, the induced muon production distribution is influenced by the change of the densities interior to the Earth. Furthermore, in such situation, the contribution from the neutral current neutrino interaction to the induced muon production distribution cannot be neglected. We report several examples of the deep inelastic scattered depth of muon neutrino in the Earth and the induced muon energy distribution near the detector.Comment: Poster presented at the XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010), Batavia, IL, USA, 28 June - 2 July 2010. 4 pages, 11 figure

Fluctuation of TeV to EeV Energy Muons and Induced Muon Showers in Water

By using the integral method in the muon propagation through water, we calculate the range fluctuation of high and ultra high energy muons. Many authors divide all radiative processes into two parts, namely, the continuous part and radiative part in their Monte Carlo simulation in order to consider the fluctuation in the both ranges and energies of the muons, while we treat all stochastic processes as exactly as possible, without the introduction of the continuous parts in all stochastic processes. The validity of our Monte Carlo method is checked by the corresponding analytical method which is methodologically independent on the Monte Carlo procedure. Accompanied cascade showers are generated by the direct electron pair production, bremsstrahlung and photo-nuclear interaction. These showers are calculated by the exact Monte Carlo Method in one dimensional way. We report survival probabilities, range distributions and examples of individual muon behavior.Comment: Poster presented at the XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010), Batavia, IL, USA, 28 June - 2 July 2010. 4 pages, 11 figure

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

Comparison of big event with calculations of the air shower development

The incidence of high energy hadrons and electron-photons in air showers at various stages of development is calculated. Numerical calculation is used to solve the diffusion equation for a nuclear cascade and analytical calculation for cascade shower induced gamma rays. From these calculations, one can get the longitudinal development of the high energy hadron and electron-photon components, and the energy spectra of these components at various depths of air shower development. The total number of hadrons (N sub H) and electron-photon components (N sub gamma) are related according to stages of the air shower development and primary energy. The relation of the total energy of hadron and electron-photon component above the threshold energy is given. The energy balance between both components is also a useful parameter to study high energy events accompanying air showers. The relation of N sub H and fractional hadronic energy E (sum E sub H sup gamma/sum E sub H sup gamma + Sum E sub gamma) is calculated. This relation is helpful to understand the stage of air shower development(t) and primary energy (E sub p)

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

Muon's Behaviors under Bremsstrahlung with both the LPM effect and the Ter-Mikaelian effect and Direct Pair Production with the LPM effect

Differential and integral cross sections of the muon are calculated in the materials: water, standard rock, iron and lead with and without the LPM effect. The corresponding cross sections are also calculated with dielectric supression effect (Ter-Mikaelian effect), in addition to the LPM effect. To demonstrate the importance of the LPM effect in the bremsstrahlung process, depth intensity relation of muon, energy spectrum, range distribution and survival probability are calculated taking into account bremsstrahlung spectrum.Comment: 17 pages,Latex, 32 postscript figure

Atmospheric muon fluxes underwater as a tool to probe the small-x gluon distribution

We compute deep-sea energy spectra and zenith-angle distributions of the atmospheric muons, both conventional and prompt. The prompt muon contribution to the muon flux underwater is calculated taking into consideration predictions of recent charm production models in which probed is the small-x behavior of the gluon distribution inside of a nucleon. We argue for a possibility to discriminate the PQCD models of the charm production differing in the slope of the gluon distribution, in measurements with neutrino telescopes of the muon flux at energies 10-100 TeV.Comment: 4 pages, 4 figures, uses icrc.cls, talk to be presented at the 27th International Cosmic Ray Conference, Hamburg, Germany, August 7-15, 200

Hybrid TLC-pair meter for the Sphinx Project

The chief aims in THE SPHINX PROJECT are research of super lepton physics and new detector experiments. At the second phase of THE SPHINX PROJECT, a hybrid TLC-PAIR METER was designed for measuring high energy neutrino sources (E upsilon * TeV), searching high energy muon sources (E mu TeV) and measuring muon group (E mu 1 TeV). The principle of PAIR METER has been already proposed. In this TLC-PAIR METER, electromagnetic shower induced by cosmic ray muons are detected using TL (Thermoluminescence) sheets with position counters

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