title page

Abstract

Contents

Chapter 1. Introduction 15

1.1. Review of neutrino mass and oscillation 15

1.2. Calculation of neutrino oscillation probability 16

1.3. Usefulness of atmospheric neutrino for the oscillation study 18

1.4. Detection method of atmospheric neutrino in Super Kamiokande 19

Chapter 2. Super Kamiokande Detector 24

2.1. Detector 25

2.1.1. Tank 25

2.1.2. PMTs 25

2.1.3. PMT support structure and others 28

2.1.4. Inner detector electronics and data acquisition system 30

2.1.5. Outer Detector Electronics and Data Acquisition 32

2.2. Detector Calibration 32

2.2.1. Water Transparency Measurement 32

2.2.2. Relative Gain Calibration 48

2.2.3. Relative Timing Calibration 50

2.2.4. Other calibrations 51

2.3. 2001 accident and Super Kamiokande-II reconstruction 53

Chapter 3. Monte Carlo Simulation 54

3.1. Flux calculation of atmospheric neutrino 54

3.2. Neutrino Interaction 61

3.2.1. Elastic and quasi-elastic scattering 61

3.2.2. Single meson production 62

3.2.3. Deep inelastic scattering 63

3.2.4. Nuclear effects 63

Chapter 4. Atmospheric Neutrino Data Reduction and Reconstruction 66

4.1. Fully Contained Events (FC) 69

4.1.1. FC data reduction 69

4.1.2. FC event reconstruction 71

4.2. Partially Contained Events (PC) 75

4.2.1. PC data reduction 75

4.2.2. PC Event Reconstruction 81

4.3. Upward going muon (UPMU) data 84

4.3.1. UPMU data reduction 84

4.3.2. Upmu Event Reconstruction 88

4.3.3. Upmu Eye-Scanning 89

4.3.4. Background Estimation from Cosmic Ray Muon 90

Chapter 5. Atmospheric Neutrino Data 92

5.1. FC and PC Events 92

5.2. UPMU events 95

Chapter 6. Two Flavor Neutrino Oscillation Analysis 97

6.1. Overview 97

6.2. Oscillation Analysis with New Binning 98

6.2.1. New binning 98

6.2.2. Oscillation analysis method with new binning 98

6.2.3. Systematic uncertainty terms used in the oscillation analysis 101

6.2.4. Study of sensitivity to finer binning with SK-I MC 107

6.2.5. Result with SK-I data and SK-II data separately 107

6.3. Oscillation analysis with SK-I and SK-II combined 111

6.3.1. Combining strategy 111

6.3.2. Result of the combined analysis 111

6.3.3. Oscillation analysis with pseudo data to check the likeliness of the result obtained with real data 117

Chapter 7. Conclusion 119

Appendix Tables 121

Bibliography 130

Abstract 133

Table 4.1. Event rate for each FC reduction step 72

Table 4.2. The efficiency of each reduction step of FC events. 72

Table 4.3. The misidentification probabilities for single-ring e-like and μ-like events estimated with simulated CC quasi-elastic neutrinos 77

Table 4.4. Event rate for each PC reduction step 82

Table 4.5. The detection efficiency of PC events at each reduction step. 83

Table 4.6. Percentage of events saved or rejected at each fitter. 88

Table 4.7. Upmu detection efficiency estimated using Monte Carlo. 89

Table 5.1. The number of observed events in the sub-GeV and multi-GeV samples as well as the expected number of events in the absence of neutrino oscillations. 93

Table 5.2. UP/DOWN ratio of fully-contained events. 94

Table 5.3. The number of observed events in the upward-going muon data sample and Monte Carlo. The numbers in 100 years SK-IMC were normalized to SK-II MC live-time of 60 years. 96

Table 6.1. Summary of the best fit parameters and the allowed range obtained with SK-I data. 110

Table 6.2. Summary of the best fit parameters and the allowed range obtained from the combined analysis. SK-I result are shown for comparison. 112

Table A1. Systematic errors in neutrino flux (1) 122

Table A2. Systematic errors in neutrino flux (2) 123

Table A3. Systematic errors in neutrino interaction 124

Table A4. Systematic errors in event section 125

Table A5. Systematic errors in event reconstruction 126

Table A6. Systematic errors in event section 127

Table A7. Systematic errors in event reconstruction 128

Table A8. Systematic errors in solar activity 129

Figure 1.1. Process of atmospheric neutrino production in the earth's atmosphere. 19

Figure 1.2. A cut away diagram of Super Kamiokande detector. 20

Figure 1.3. Cherenkov radiation is emitted when a particle travels faster than the speed of light in the medium. 21

Figure 1.4. A muon neutrino event forming a ring pattern of Cherenkov light. in the Super Kamiokande detector. 23

Figure 2.1. A cross section view of Super Kamiokande detector. 26

Figure 2.2. Schematic view of a 50 cm PMT used in inner detector of Super Kamiokande. 27

Figure 2.3. Quantum efficiency of the photocathode as a function ofwavelength. 27

Figure 2.4. Schematic view of PMT support structures. 29

Figure 2.5. A block diagram of ATM board used for inner detector data acquisition. 30

Figure 2.6. The data acquisition system for the inner detector. 31

Figure 2.7. OD DAQ block diagram and data flow. 33

Figure 2.8. Relative photo-sensitivity. 34

Figure 2.9. Effective charge observed as a function of the path length. 34

Figure 2.10. Time variation of the water attenuation length measured by through-going cosmic ray muon. 35

Figure 2.11. Laser system for water scattering and absorption parameter measurement and its typical event display. 36

Figure 2.12. The detail view of the arrangement of laser firing setup. 37

Figure 2.13. The upper plot is the photon arrival time distribution of the top PMTs. Dots is data and line is Monte Carlo. The lower plot is the ratio, (MC-DATA)/DATA. 38

Figure 2.14. Comparison of time variation of light attenuation length measure by laser system and cosmic ray muon. 39

Figure 2.15. Positions of light injectors at the detector. 40

Figure 2.16. Diagram of whole light scattering measurement system used in Super Kamiokande-II. 41

Figure 2.17. 'Optical SW (switch)', which distribute laser light into 8 different fibers mechanically by step motor. 42

Figure 2.18. How to calculate Number of hit (Nhit) for each LI for monitoring water quality. 43

Figure 2.19. 'Nhit/Q' as a function of light intensity. Horizontal axis is the ratio of light intensity to normal intensity, which was used in Monte Carlo. 44

Figure 2.20. Upper plot is the spatial distribution of 'number of hit' for 3 different intensity made with Monte Carlo of oldtop LI. Vertical axis is the number of hit PMTs (Nhit) in the top region of the tank normalized by the intensity and horizontal axis is the distance from oldtop LI.... 45

Figure 2.21. 'Nhit/Q' as a function of light intensity without PMTs within 2 m from LI. 46

Figure 2.22. Left plot (a) is the distribution of '0ldtop LI - newtop LI' for '100×DATA(Nhit/Q) / MC(Nhit/Q)' and Right plot (b) the distribution of '(Each wavelength) - (Mean of 4 wavelength)'. 47

Figure 2.23. DATA(Nhit/Q) / MC(Nhit/Q) obtained for each LI for various period of Super Kamiokande-II to investigate position dependence of the water quality. 48

Figure 2.24. The relative gain measurement system. 49

Figure 2.25. The timing calibration system. 51

Figure 2.26. A typical plot of timing vs. pulse height. This plot is referred as 'TQ-map'. 52

Figure 3.1. (a) The atmospheric neutrino energy spectrum calculated by several models. (b) The ratio of the calculated flux models. 56

Figure 3.2. The flux ratio ofvμ + anti-Vμ/Ve + anti-Ve as a function of neutrino energy.(이미지참조) 56

Figure 3.3. The flux ratios of Vμ to anti-Vμ and Ve to anti-Ve versus neutrino energy. Solid, dashed and dotted lines show the prediction by Honda, Bartol and Fluka flux.(이미지참조) 57

Figure 3.4. The flux of atmospheric neutrino versus zenith angle. Solid, dashed and dotted lines show the prediction by Honda, Bartol and Fluka flux. 58

Figure 3.5. The zenith angle distribution of the flux of upward-going atmospheric neutrino observed as upward-going muon event in Super Kamiokande. Solid, dashed and dotted lines show the prediction by Honda, Bartol and Fluka flux. 60

Figure 3.6. The calculated flight length of neutrinos for vertically down-going (0.95＜cosθ＜1.0) and near horizontal-going (0.05＜cosθ＜0.10) directions. 60

Figure 3.7. Cross section for neutrino (upper) and anti-neutrino (lower). Solid line shows the calculated total cross section. The dashed, dot and dash-dotted lines show the calculated quasielastic, single-meson and deep-inelastic scatterings, respectively. Data points are form various experiments.... 65

Figure 4.1. A schematic view of the four event categories of the atmospheric neutrinos observed in Super Kamiokande. 67

Figure 4.2. The number of hits in the largest outer detector cluster, which was used to separate the FC and PC event. The histogram is the MC prediction with neutrino oscillation (solid line) and no oscillation (dashed line). The upper figure is for SK-I MC and data.... 68

Figure 4.3. The distribution of the likelihood difference between a single-ring and multi-ring assumption for sub-GeV (left) and multi-GeV (right) FC events of SK-I. The points show the data and the histograms show the Monte Carlo. 74

Figure 4.4. The distribution of the likelihood difference between a single-ring and multi-ring assumption for sub-GeV (left) and multi-GeV (right) FC events of SK-II. The points show the data and the histograms show the Monte Carlo. 74

Figure 4.5. An event display of an observed single-ring e-like event. 76

Figure 4.6. An event display of an observed single-ring μ-like event. 76

Figure 4.7. The distribution of particle identification likelihood for sub-GeV (left) and multi-GeV (right) FC single-ring events of SK-I. Dots show data and histograms show Monte Carlo. 78

Figure 4.8. The distribution of particle identification likelihood for sub-GeV (top) and multi-GeV (bottom) FC single-ring events of SK-II. Dots show data and histograms show Monte Carlo. 78

Figure 4.9. The procedure to isolate upmu events. 85

Figure 4.10. The zenith angle distribution of upward muon candidates near the horizon for two different regions in azimuth made with SK-I data. The white circles and the black inverted triangle are for thin and thick rock region, respectively. 91

Figure 5.1. Event rate as a function of elapsed days of SK-II data. SK-I event rates were shown as a reference by line. 95

Figure 6.1. The schematic view of the binning. Each bin in this figure is divided further by 10 zenith angle bin. The top is the bins used in the old analysis (180 bins) and the bottom is the new bins (370 bins) used in this analysis. 100

Figure 6.2. Result of sensitivity study to binning effect. 90% C.L allowed region obtained with the virtual data using 180 and 370 bins are shown for various oscillation parameter region and live-time. 108

Figure 6.3. The left plot (a) is the allowed oscillation parameter region corresponding to the 68%, 90% and 99% confidence level (C.L.) obtained with 370 bins. The right plot (b) is the comparison of the results with 180 bins and 370 bins for 90% C.L. 109

Figure 6.4. 90 % C.L allowed region for each sub-sample. The left is the result with 180 bins and the right is 370 bins. 109

Figure 6.5. The allowed oscillation parameter region obtained with SK-II data. The left is the contour obtained with all the samples combined and the right is 90% C.L allowed region for each sub-sample. 110

Figure 6.6. The left plot is the allowed oscillation parameters for Vμ ↔ Vτ with the combined analysis of SK-I and SK-II. Three contours correspond to 68 %, 90 % and 99 % C.L. allowed region. The right Plot is the comparison with the result of SK-I only analysis for 90% C.L.(이미지참조) 113

Figure 6.7. χ²-χ²min distribution projected to sin²2θ and △m² axes resulted from SK-I and SK-II combined analysis.(이미지참조) 113

Figure 6.8. 90 % confidence level allowed oscillation parameter regions of each sub-sample for Vμ ↔ Vτ oscillations with SK-I and SK-II data combined.(이미지참조) 114

Figure 6.9. The zenith angle distribution of fully-contained sub-GeV and multi-GeV sample obtained by the combined analysis of SK-I and SK-II. The points show data, box histograms show the non-oscillated Monte Carlo and the lines show the best fit expectation obtained from... 115

Figure 6.10. The zenith angle distribution of multi-ring, partially-contained and upward-going muon sample obtained by the combined analysis of SK-I and SK-II. The points show data, box histograms show the non-oscillated Monte Carlo and the lines show the best fit expectation... 116

Figure 6.11. The width of △m² region at 90% C.L obtained with 20 set of pseudo data and real data for SK-I (left) and SK-II (right), respectively to check the likeliness of the result of real data. 118