Tau Neutrino Appearance via Neutrino Oscillations in Atmospheric Neutrinos A Dissertation Presented by Tokufumi Kato to The Graduate School in Partial Ful(cid:12)llment of the Requirements for the Degree of Doctor of Philosophy in Physics Stony Brook University May 2007 Stony Brook University The Graduate School Tokufumi Kato We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of the dissertation. Dr. Chang Kee Jung Advisor Professor of Physics and Astronomy Stony Brook University Dr. Maria Concepcion Gonzalez-Garcia Chairperson of Defense Associate Professor of Physics and Astronomy Stony Brook University Dr. Thomas C. Weinacht Assistant Professor of Physics and Astronomy Stony Brook University Dr. Walter Toki Professor of Physics Colorado State University This dissertation is accepted by the Graduate School. Lawrence Martin Dean of the Graduate School ii Abstract of the Dissertation Tau Neutrino Appearance via Neutrino Oscillations in Atmospheric Neutrinos by Tokufumi Kato Doctor of Philosophy in Physics Stony Brook University 2007 A search for the appearance of tau neutrinos from (cid:23) $ (cid:23) (cid:22) (cid:28) oscillations in the atmospheric neutrinos has been conducted us- ing the atmospheric neutrino data from the Super-Kamiokande-I andtheSuper-Kamiokande-IIexperiment. Atauneutrinoenriched event sample is selected by using the event topologies of the de- cay of tau leptons produced in charged-current weak interactions. An excess of tau neutrino signals is observed, and a best-(cid:12)t tau neutrino appearance signal of 162 (cid:6) 59 (stat.) +21 (sys.), which (cid:0)56 disfavors the no tau neutrino appearance hypothesis by 2.1 sigma. This isconsistent withtheexpected number oftauneutrino events, 121 (cid:6) 39 (sys.) for (cid:1)m2 = 2:4(cid:2)10(cid:0)3eV2, assuming the full mix- ing in (cid:23) $ (cid:23) oscillations. The Super-Kamiokande atmospheric (cid:22) (cid:28) neutrino data are consistent with tau neutrino appearance from (cid:23) $ (cid:23) oscillations. (cid:22) (cid:28) iii Dedicated to my parents. Contents List of Figures viii List of Tables xi Acknowledgements xiii 1 Introduction 1 1.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Neutrinos in the Standard Model . . . . . . . . . . . . . . . . 3 1.3 Neutrino Mass and Neutrino Oscillations . . . . . . . . . . . . 5 1.3.1 Detection of Neutrino Oscillations . . . . . . . . . . . . 7 1.4 Atmospheric Neutrinos and Neutrino Oscillation Experiments 8 1.4.1 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . 8 1.4.2 Neutrino Oscillation Experiments . . . . . . . . . . . . 9 1.5 Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5.1 Super-Kamiokande Collaboration . . . . . . . . . . . . 12 1.6 Motivation of the analysis in this thesis . . . . . . . . . . . . . 12 2 Super-Kamiokande Detector 15 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . 20 2.2 Water Tank: Detector . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 Inner Detector. . . . . . . . . . . . . . . . . . . . . . . 23 2.2.2 Outer Detector . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Photomultiplier Tube (PMT) . . . . . . . . . . . . . . . . . . 24 2.3.1 Inner Detector PMT . . . . . . . . . . . . . . . . . . . 24 2.3.2 Outer Detector PMT . . . . . . . . . . . . . . . . . . . 28 2.4 Water Puri(cid:12)cation System . . . . . . . . . . . . . . . . . . . . 28 2.5 Radon Hut and Air Puri(cid:12)cation System . . . . . . . . . . . . 29 2.6 Electronics and Data Acquisition System (DAQ) . . . . . . . . 32 2.6.1 Inner Detector DAQ . . . . . . . . . . . . . . . . . . . 33 v 2.6.2 Outer Detector DAQ . . . . . . . . . . . . . . . . . . . 34 2.6.3 Trigger System . . . . . . . . . . . . . . . . . . . . . . 37 2.6.4 Flash ADC . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6.5 O(cid:15)ine Data Process . . . . . . . . . . . . . . . . . . . 40 3 Detector Calibration 41 3.1 PMT calibration . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.1 Relative Gain . . . . . . . . . . . . . . . . . . . . . . . 41 3.1.2 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.3 Relative Timing . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Water Transparency Measurement . . . . . . . . . . . . . . . . 46 3.2.1 Light scattering measurement . . . . . . . . . . . . . . 49 3.2.2 Time variation of Water Transparency . . . . . . . . . 49 3.3 Absolute Energy Calibration . . . . . . . . . . . . . . . . . . . 50 3.3.1 Decay electron measurement . . . . . . . . . . . . . . . 54 3.3.2 Neutrino-induced (cid:25)0 measurement . . . . . . . . . . . . 54 3.3.3 Cosmic ray stopping muon measurement . . . . . . . . 57 3.3.4 Time variation of energy scale . . . . . . . . . . . . . . 58 3.4 Calibrations for low energy events . . . . . . . . . . . . . . . . 59 4 Simulation 61 4.1 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . 61 4.2 Neutrino Interactions (Cross Section) . . . . . . . . . . . . . . 68 4.2.1 Elastic and Quasi-elastic Scattering . . . . . . . . . . . 69 4.2.2 Resonant Single-Meson Production . . . . . . . . . . . 70 4.2.3 Deep-inelastic Scattering . . . . . . . . . . . . . . . . . 72 4.2.4 Coherent Pion Production . . . . . . . . . . . . . . . . 75 4.2.5 Nuclear E(cid:11)ect . . . . . . . . . . . . . . . . . . . . . . . 77 4.3 Detector Simulation (Particle Tracking) . . . . . . . . . . . . . 80 4.4 Tau Neutrinos Simulation . . . . . . . . . . . . . . . . . . . . 82 5 Data Reduction 86 5.1 Event Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Reduction for Fully Contained Sample . . . . . . . . . . . . . 88 5.2.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . 88 5.2.2 Second Reduction . . . . . . . . . . . . . . . . . . . . . 90 5.2.3 Third Reduction . . . . . . . . . . . . . . . . . . . . . 90 5.2.4 Fourth Reduction . . . . . . . . . . . . . . . . . . . . . 93 5.2.5 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . . 93 5.2.6 Fully Contained Cut . . . . . . . . . . . . . . . . . . . 94 vi 6 Event Reconstruction 96 6.1 Vertex Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3 Particle Identi(cid:12)cation . . . . . . . . . . . . . . . . . . . . . . . 101 6.4 Precise Vertex Fitting (MS-(cid:12)t) . . . . . . . . . . . . . . . . . . 102 6.5 Momentum Reconstruction . . . . . . . . . . . . . . . . . . . . 106 6.6 Ring Correction . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7 Tau Neutrino Appearance Analysis 107 7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.2 Data and MC set . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.3 Tau Neutrino Events . . . . . . . . . . . . . . . . . . . . . . . 111 7.4 Variables for Distinguishing tau-like events . . . . . . . . . . . 112 7.5 The Likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.6 Zenith Angle Fit . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.7 Zenith angle (cid:12)t with SK-I and SK-II data . . . . . . . . . . . 123 7.8 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 123 7.8.1 Systematic Uncertainties in Atmospheric Neutrino Flux 125 7.8.2 Systematic Uncertainties in Neutrino Interactions . . . 126 7.8.3 Systematic Uncertainties in Event Selection . . . . . . 128 7.8.4 Systematic Uncertainties in Event Reconstruction . . . 128 7.8.5 Systematic Uncertainties in (cid:23) Appearance analysis . . 129 (cid:28) 7.8.6 Systematic Uncertainties in Oscillation Parameters . . 130 7.9 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 8 Conclusions and Future 137 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 8.2 Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 A Super-Kamiokande Accident and SK-II and SK-III 139 A.1 Super-Kamiokande Accident . . . . . . . . . . . . . . . . . . . 139 A.1.1 Cause . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 A.1.2 PMT case . . . . . . . . . . . . . . . . . . . . . . . . . 140 A.2 Super-Kamiokande-II . . . . . . . . . . . . . . . . . . . . . . . 141 A.3 Super-Kamiokande-III . . . . . . . . . . . . . . . . . . . . . . 141 B Energy Flow Analysis 142 B.1 Geodesic binning . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.1.1 Charge Flux . . . . . . . . . . . . . . . . . . . . . . . . 142 B.2 Energy Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 vii B.3 Event Shape Variables . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography 147 viii List of Figures 1.1 Feynman diagrams of weak interactions . . . . . . . . . . . . . 4 1.2 Survival and oscillation probability . . . . . . . . . . . . . . . 7 1.3 Atmospheric neutrino production . . . . . . . . . . . . . . . . 9 1.4 Allowed region of sin22(cid:18) and (cid:1)m2 from SK, K2K and MINOS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 The zenith angle distributions from Super-Kamiokande . . . . 13 1.6 The L/E distribution from Super-Kamiokande . . . . . . . . . 14 2.1 The location of the Super-Kamiokande detector in Japan . . . 16 2.2 The Super-Kamiokande detector . . . . . . . . . . . . . . . . . 18 2.3 A side-view of the Super-Kamiokande detector . . . . . . . . . 19 2.4 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 PMT mounting structure . . . . . . . . . . . . . . . . . . . . . 22 2.6 Inner Detector photomultiplier tube . . . . . . . . . . . . . . . 24 2.7 Chrenkov spectrum and Quantum E(cid:14)ciency of an ID PMT . . 25 2.8 ID PMT: Quantum E(cid:14)ciency . . . . . . . . . . . . . . . . . . 26 2.9 ID PMT: Energy resolution . . . . . . . . . . . . . . . . . . . 26 2.10 ID PMT: Timing resolution . . . . . . . . . . . . . . . . . . . 27 2.11 Water puri(cid:12)cation system . . . . . . . . . . . . . . . . . . . . 30 2.12 Radon levels in the mine air . . . . . . . . . . . . . . . . . . . 31 2.13 Air Puri(cid:12)cation System . . . . . . . . . . . . . . . . . . . . . . 33 2.14 Analog-Timing-Module (ATM) . . . . . . . . . . . . . . . . . 35 2.15 Analog input of the ATM for one channel . . . . . . . . . . . . 35 2.16 Inner Detector DAQ . . . . . . . . . . . . . . . . . . . . . . . 36 2.17 ID trigger scheme . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.18 Outer Detector DAQ . . . . . . . . . . . . . . . . . . . . . . . 38 3.1 Xe calibration system for the ID PMT relative gain measurement 42 3.2 Relative photo-sensitivity of the ID PMTs . . . . . . . . . . . 43 3.3 Relative gain distribution for ID PMTs . . . . . . . . . . . . . 44 3.4 Ni-Cf calibration system . . . . . . . . . . . . . . . . . . . . . 44 ix 3.5 Single photo-electron charge distribution for ID PMT . . . . . 45 3.6 Laser calibration system for relative timing . . . . . . . . . . . 46 3.7 TQ-map: PMT timing response vs charge . . . . . . . . . . . 47 3.8 Timing resolution of the ID PMT . . . . . . . . . . . . . . . . 48 3.9 Laser calibration system for water transparency . . . . . . . . 50 3.10 Time distributions of the hit PMTs. . . . . . . . . . . . . . . . 51 3.11 Attenuation length coe(cid:14)cient . . . . . . . . . . . . . . . . . . 52 3.12 Attenuation length measured by cosmic ray muons . . . . . . 52 3.13 Time variation of water attenuation length . . . . . . . . . . . 53 3.14 Energy spectrum of decay electrons . . . . . . . . . . . . . . . 55 3.15 Distribution of neutrino-induced (cid:25)0 invariant mass . . . . . . . 56 3.16 low energy stopping muons . . . . . . . . . . . . . . . . . . . . 57 3.17 Ratio of the momentum to the range for high energy stopping muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.18 Absolute energy scale calibration . . . . . . . . . . . . . . . . 59 3.19 Time variation of the energy scale . . . . . . . . . . . . . . . . 60 4.1 Primary cosmic ray proton (cid:13)ux . . . . . . . . . . . . . . . . . 63 4.2 The rigidity cuto(cid:11) at the Kamioka site . . . . . . . . . . . . . 64 4.3 The (cid:13)ux of cosmic ray muons . . . . . . . . . . . . . . . . . . 64 4.4 Theabsolute(cid:13)uxandthe(cid:13)avor ratiooftheatmospheric neutrinos 66 4.5 The atmospheric neutrino (cid:13)ux vs zenith angle. . . . . . . . . . 67 4.6 Cross section of quasi-elastic scattering . . . . . . . . . . . . . 71 4.7 Cross section ofcharged current resonant single-meson production 73 4.8 Cross section of neutral current resonant single-meson production 74 4.9 Total charge current cross section divided by E . . . . . . . . 76 (cid:23) 4.10 Cross section of coherent pion production . . . . . . . . . . . . 78 4.11 Cross section of (cid:25)+-16O interactions . . . . . . . . . . . . . . . 79 4.12 Cross section of charged current (cid:23) and (cid:23) interactions . . . . 83 (cid:28) (cid:28) 4.13 Cross section for CC (cid:23) , (cid:23) , (cid:23) and (cid:23) , (cid:23) , (cid:23) interactions . . . 84 (cid:28) (cid:22) e (cid:28) (cid:22) e 5.1 Atmospheric Neutrino Event Classes and their Energy Ranges 87 5.2 Fully contained data reduction . . . . . . . . . . . . . . . . . . 89 6.1 Ring (cid:12)nding algorithm . . . . . . . . . . . . . . . . . . . . . . 98 6.2 Charge map from Hough Transformation algorithm . . . . . . 99 6.3 Ring-counting likelihood distribution . . . . . . . . . . . . . . 100 6.4 Ring-counting likelihood distribution for SK-II . . . . . . . . . 101 6.5 Event display of electron and muon neutrino events . . . . . . 103 6.6 PID likelihood distributions for SK-I . . . . . . . . . . . . . . 104 x