博士論文
Indications of Muon Neutrino Oscillation
in a 250km Long Baseline Experiment(250km 長基線実験におけるミューオンニュートリノ振動の示唆)

平成 15 年 1 月
神戸大学大学院自然科学研究科
岩下 大器
Taiki IWASHITA

Abstract
K2K is a long-baseline neutrino oscillation experiment extending from KEK, thehigh energy accelerator research organization in Ibaraki prefecture, to Kamioka.
K2K is the rst long-baseline neutrino oscillation experiment in the world to usean accelerator. It was designed to con rm the presence of muon neutrino oscillation observed in the Super-Kamiokande collaboration. It also aims to quantitatively measure the oscillation parameters 1m2 and sin2 2 . In this thesis, therst result of spectrum analysis of neutrino oscillation three years into the K2K
experiment is reported.
The K2K neutrino beam is produced with a 12 GeV proton synchrotron.
Numerous beam monitors along the beam line measure beam intensity and direction. Near and far detectors along the beam are used to compare neutrino
ux at two points. The near detector is 300m downstream from the target.
It measures the neutrino spectrum and the number of neutrino events directly
after neutrino production. It consists of the 1kt water C erenkov detector andthe ne grain detector (FGD) system. We have constructed a scintillating ber(SciFi) detector as the main component of the FGD. The far detector, SuperKamiokande (SK), is 250km downstream from the target. Neutrino oscillation isobserved as a reduction of muon neutrino ux and the distortion of the energy
spectrum at far detector. K2K's sensitive region is sin2 2  1, 1m2  1002 to
1003eV 2 for  !  . Analysis of atmospheric neutrinos at SK (1144 day exposure) suggests the allowed region is sin2 2  1 and 1m2  1003  5 2 1003eV 2
for  !  mode.
The analysis and results in this thesis were obtained using the SciFi detector,
one of the most important components of the near detector. The SciFi detector
is a tracker made of scintillating bers, consisting of 20 layers of ber sheets interspersed with 19 layers of water target. IITs (image intensi er tubes) intensify
the track information on secondary charged particles from neutrino interaction.
CCD cameras record this information. This thesis develops and describes analiii

iv
ysis techniques to reconstruct tracks from CCD camera images. With the track
information from the SciFi detector and downstream detectors, 12317 neutrino
events captured by the K2K SciFi detector over a three year period were reconstructed. Combining the SciFi data with the 1kt water C erenkov detector data,a view of the neutrino energy spectrum at the near detector was obtained.
Fifty six beam neutrino events at SK were observed. With an expectation of:2
80:1+605:4 events at the near detector assuming no oscillation, the result indicatesthe probability of no oscillation is less than one percent. Additionally, a maximum
likelihood analysis using spectrum shape was performed. Twenty-nine one-ringmuon type events were used to reconstruct neutrino energy. In a two- avor
oscillation framework, the allowed region of 1m2 is between 1:5 2 1003 and 3:9 21003 eV2 at 90% C.L. at sin2 2 = 1.0, which is consistent with the results of the
SK collaboration using atmospheric neutrinos.

Acknowledgements
First I would like to express my deepest appreciation to the initiators of thisK2K experiment, Professor Koichiro Nishikawa at Kyoto University and Professor
Kenzo Nakamura at KEK. Thank you for allowing me to participate.
I am also grateful to Prof. T. Hara, Prof. S. Aoki, and Dr. A. C. Suzuki,
who o ered guidance to me as an undergraduate at Kobe University. I would nothave been able to undertake this project without their help.
I was fortunate to work alongside Prof. M. Sakuda and Dr. T. Ishida at
KEK during the construction, operation and analysis phases of the SciFi detector
project. I am grateful for the opportunity to share their challenges, their concerns,
and their aspirations. The body of this thesis comes from work undertaken incooperation with them.
I give special thanks to Dr. Y. Hayato at KEK. His work on the electronics
at SciFi is indispensable.
Dr. H. Park and Dr. S. Boyd, and Dr. H. Ishino as PostDoc at KEK,
Dr. B.J. Kim from Seoul National University, and Ms. H. Yokoyama from Tokyo
University of Science (SUT) all made great contribution for the analysis software.
Acknowledgements go out to Mr. S. Echigo, Mr. K. Tashiro and Mr. M.
Kitamura at Kobe University for preparing me to take on the challenge of thiswork. I must mention the SciFi construction and maintenance work carried out
by Mr. M. Onchi, Mr. K. Sato, Mr. G. Kume, Mr. K. Takenaka, Mr. K. Fujii
and Mr. Y. Tanaka, all from Kobe University, Dr. T. Kadowaki and Mr. S. Kishi
from SUT, and Dr. S. Matsuno from the University of Hawaii. I will never forget
the time we spent together.
Ms. E. J. Jeon from the Graduate University for Advanced Studies, Ms. U.
Golebiewska from Warsaw University, Prof. C. W. Walter and Prof. E. Kearns
from Boston University, Dr. E. Sharkey from Stony Brook University New York(SUNY) all worked alongside me on the SciFi detector.
Numerous people made my stay at KEK a happy and pleasant one. I givev

vi
special thanks to Dr. A. Sakai at KEK (now with Fujitsu Ltd.), Dr. T. Maruyama
from Tohoku University (now at Chicago University.), Dr. M. Kohama from Kobe
University (now with Riken), Dr. M. Yoshida at KEK, Dr. T. Inagaki from Kyoto
University (now at SPring-8), Mr. J. H. Choi from Chonnam National University,
Mr. M. Nakamura from Niigata University, Mr. H. Maesaka, Mr. S. Mukai, and
Mr. A. Shima from Kyoto University.
If this thesis is a good one, it is due to the help of the following people: Dr.
T. Hasegawa from Tohoku University and Dr. J. Hill from SUNY, who worked
hard to provide a stable neutrino beam; Prof. T. Kobayashi, Dr. Y. Oyama, andDr. T. Ishii at KEK, who operated and led analysis at the near detector; Prof.
T. Nakaya, Mr. I. Kato from Kyoto University, Dr. S. Mine from the Universityof California, and Dr. C. Mauger from SUNY, who kindly allowed me to use datafrom the 1kton C erenkov detector; Prof. Y. Totsuka, Prof. Y. Suzuki, Prof. T.
Kajita, Prof. K. Kaneyuki, Prof. M. Nakahata, Prof. Y. Itow, Dr. J. Kameda,
Dr. M. Miura, Mr. S. Nakayama, Mr. S. Yamada, and Dr. Y. Obayashi at
Super-Kamiokande , who graciously allowed me to conduct a neutrino oscillation
analysis. Thank you all so much.
I also thank Ms. T. Otaki, Ms. M. Takatsuki, Mr. S. Nishiyama, Mr. S.
Noda, Mr. Y. Suga, Mr. F. Nakata, and Ms. M. Sekiguchi, all from Kobe
University.
My deepest gratitude goes out to Prof. H. Takeda, and Prof. M. Nozaki at
Kobe University, who introduced me to the beautiful world of the elementary
particle.
Finally, I wish to thank my family for their support over the past three years.

Thank you all so very much.

Contents
1 Introduction

1.1 The Neutrino in the Last Century . . . . . . . . . . . . . . . . . .
1.1.1 Neutrino Mass . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . .
1.1.3 The Atmospheric Neutrino Anomaly . . . . . . . . . . . .
1.1.4 Observation of Atmospheric Neutrino Oscillation by the SK
Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The K2K Experiment . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Overview of this thesis . . . . . . . . . . . . . . . . . . . . . . . .

2 Setup of the K2K Experiment

3

3
3
4
5

6
7
8
11

2.1 12 GeV Proton Synchrotron . . . . . . . . . . . . . . . . . . . . . 11
2.2 Proton Beam Line . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Beam Line Monitors . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Target and Magnetic Horns . . . . . . . . . . . . . . . . . . . . . 13
2.4 Secondary Particle Monitors . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Pion Monitor . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Muon Monitors . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3 Beam Line DAQ . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Near Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 1kton Water C erenkov Detector (1kt Detector) . . . . . . 18
2.5.2 Scintillating Fiber (SciFi) Detector . . . . . . . . . . . . . 19
2.5.3 Trigger/Veto Counters, Lead Glass Counter, Muon Range
Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.4 Data Aquisition (DAQ) System of Near Detectors . . . . . 20
2.6 Far Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.1 Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.2 Water Puri cation System . . . . . . . . . . . . . . . . . . 22
vii

viii

CONTENTS

2.6.3 DAQ System . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Global Positioning System (GPS) . . . . . . . . . . . . . . . . . . 22
3 SciFi Detector

29

4 Simulations

47

5 Analysis Procedure of the SciFi Detector

61

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Scintillating Fiber . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Scintillating Fiber Sheets . . . . . . . . . . . . . . . . . . 32
3.2.3 Water Target . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Readout System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Data Aquisition (DAQ) . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Calibration System . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 EL Calibration . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1 Neutrino Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Neutrino Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Elastic Scattering o Electron . . . . . . . . . . . . . . . 49
4.2.2 Quasi-Elastic Scattering o Nucleon . . . . . . . . . . . . . 50
4.2.3 Single Meson Production via Baryon Resonances . . . . . 52
4.2.4 Coherent Pion Production o 16O . . . . . . . . . . . . . . 53
4.2.5 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . 53
4.2.6 Nuclear E ects . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.7 Rescattering of Proton . . . . . . . . . . . . . . . . . . . . 56
4.3 Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 FGSIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Water C erenkov Detectors . . . . . . . . . . . . . . . . . . 57
5.1 Hit Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.1 First Track Finding . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Track Matching with TRG Counter . . . . . . . . . . . . 64
5.2.3 Track Matching Veto with VETO Counter . . . . . . . . . 64
5.2.4 Track Matching with LG . . . . . . . . . . . . . . . . . . . 64
5.2.5 Track/Hit Matching with MRD . . . . . . . . . . . . . . . 64
5.2.6 Second Track and Vertex Finding . . . . . . . . . . . . . . 64

CONTENTS

ix

5.2.7 Muon Energy Reconstruction . . . . . . . . . . . . . . . . 66
5.3 Event Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 Performance of SciFi Detector . . . . . . . . . . . . . . . . . . . . 67
5.4.1 Hit Finding Eciency . . . . . . . . . . . . . . . . . . . . 67
5.4.2 Track Finding Eciency . . . . . . . . . . . . . . . . . . . 68
5.4.3 Hit Position Resolution . . . . . . . . . . . . . . . . . . . 69
5.4.4 Noise Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6 Expected Number of Neutrino Events at SK73

7 Neutrino Energy Spectrum at Near Detector

87

8 Neutrino Events at SK

101

9 Oscillation Analysis

109

6.1 Total Number of Protons on Target (POT) . . . . . . . . . . . . . 73
6.1.1 POTSK and POTSciFi . . . . . . . . . . . . . . . . . . . . . 73
6.2 Neutrino Beam Aiming and Targeting . . . . . . . . . . . . . . . . 75
6.3 Neutrino Event Rate at SciFi . . . . . . . . . . . . . . . . . . . . . 75
6.4 NSK Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4.1 Neutrino Flux Ratio of Far and Near Detectors . . . . . . 76
6.4.2 SciFi/SK Eciency . . . . . . . . . . . . . . . . . . . . . 76
6.5 Source of NSK Systematic Error . . . . . . . . . . . . . . . . . . . 76
6.5.1 Error Terms from FGD . . . . . . . . . . . . . . . . . . . . 76
6.5.2 Error Terms from Extrapolation to Far Detector . . . . . . 77
6.6 NSK from the SciFi Detector . . . . . . . . . . . . . . . . . . . . . 79
7.1 Basic Plots from the SciFi Detector . . . . . . . . . . . . . . . . . 87
7.2 Neutrino Energy Reconstruction . . . . . . . . . . . . . . . . . . . 87
7.3 Neutrino Energy Spectrum at the Near Detector . . . . . . . . . 91
7.3.1 Neutrino Event Selection at the 1kt Detector . . . . . . . . 92
7.3.2 2 tting . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 E ect of Neutrino Interaction Models on Spectrum Analysis . . . 97
8.1 Event Selection at Super-Kamiokande . . . . . . . . . . . . . . . 101
8.2 One-ring  event . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8.3 Observed SK Events . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.1 Statistical Signi cance of No Oscillation . . . . . . . . . . . . . . . 109
9.1.1 KS Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

x

CONTENTS

9.2 Maximum-Likelihood Analysis . . . . . . . . . . . . . . . . . . . 110
10 Conclusion

117

List of Figures
1.1 The zenith angle distribution of -like and e-like events. . . . . . . 7
1.2 Neutrino energy spectrum distortion in K2K. . . . . . . . . . . . . 9
1.3 Sensitive region of the K2K experiment for  !  mode. . . . . 10
2.1 Schematic overview of K2K experiment. . . . . . . . . . . . . . . . 12
2.2 KEK-12GeV proton synchrotron. . . . . . . . . . . . . . . . . . . . 13
2.3 Proton beam line. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Schematic view of a SPIC. . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Target and magnetic horn. . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Estimated neutrino ux with horn current 0kA and 250kA. . . . . 17
2.7 Pion monitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Pion monitor measures the angle and momentum of pions. . . . . 19
2.9 Muon monitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.10 Beam line DAQ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.11 K2K near detectors. . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.12 DAQ system of the near detector. . . . . . . . . . . . . . . . . . . 25
2.13 Far detector Super Kamiokande. . . . . . . . . . . . . . . . . . . . 26
2.14 SK water puri cation system. . . . . . . . . . . . . . . . . . . . . 26
2.15 The data acquisition system for the inner detector. . . . . . . . . 27
2.16 Overview of GPS system at SK. . . . . . . . . . . . . . . . . . . . 27
3.1 Overview of the SciFi detector. . . . . . . . . . . . . . . . . . . . . 30
3.2 Scintillating ber. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 SCSF-78M (version 11) light wavelength . . . . . . . . . . . . . . 32
3.4 Aging of SciFi SCSF78M . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 SciFi SCSF-78M attenuation measurement . . . . . . . . . . . . . 34
3.6 SciFi sheet spooling machine. . . . . . . . . . . . . . . . . . . . . 35
3.7 SciFi sheet spooling process. . . . . . . . . . . . . . . . . . . . . 36
3.8 Top view (left) and cross section (right) of SciFi sheet. . . . . . . . 36
xi

xii

LIST OF FIGURES

3.9 Six SciFi sheets are glued to each side of a honeycomb panel. . . 38
3.10 How SciFi sheets are bundled. . . . . . . . . . . . . . . . . . . . . 40
3.11 Picture of a ber bundle. . . . . . . . . . . . . . . . . . . . . . . 41
3.12 IIT-CCD chain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.13 Sensitivity of photocathode. . . . . . . . . . . . . . . . . . . . . . 42
3.14 Lifetime of phosphor screen. . . . . . . . . . . . . . . . . . . . . . 43
3.15 HV supplier for 24 IITs. . . . . . . . . . . . . . . . . . . . . . . . 44
3.16 DAQ setup of the SciFi detector. . . . . . . . . . . . . . . . . . . 45
3.17 Picture of ber bundle illuminated by the EL. . . . . . . . . . . . 46
4.1 Neutrino ux calculated by beam simulation. . . . . . . . . . . . . 49
4.2 Scattering angle distributions for e MC with and without nal
state interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3 Setup of LED calibration. . . . . . . . . . . . . . . . . . . . . . . 59
5.1 A typical CCD image of a cosmic-ray event . . . . . . . . . . . . 62
5.2 Example of SciFi two-track MRD event. . . . . . . . . . . . . . . 65
5.3 Hit nding eciency of 24IITs. . . . . . . . . . . . . . . . . . . . . 67
5.4 Stability of hit nding eciency from Nov '99 to Jul '01. . . . . . 68
5.5 Track nding eciency as a function of the track length. Eciency
is 70% (87%) in a track length of the three (four) SciFi layers
and approaches 100% in longer tracks. . . . . . . . . . . . . . . . 69
5.6 Hit residual distributions using neutrino beam data. The curve isa single Gaussian t to the data with  = 0.73mm (0.61mm) formuon energy E < 1GeV ( E > 1GeV). . . . . . . . . . . . . . . 70
6.1 Top gure shows integrated number of protons on target from 1999
to 2001. Bottom one shows number of protons per pulse in same
period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.2 Neutrino beam direction stability measured by the muon monitor(ionization chamber). . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3 Neutrino beam ux around SK in MC (at 10 2 20 POT). Neutrino
ux reduction 1km from axis (4mrad) is within 3%. . . . . . . . . 83
6.4 SciFi LG stopping event rate per month . . . . . . . . . . . . . . . 84
6.5 Neutrino Spectrum and Ratios of SK (far) and KEK (near) Estimated by Pion Monitor. (November con g.) . . . . . . . . . . . . 84
6.6 SK and SciFi detection eciency . . . . . . . . . . . . . . . . . . . 85

LIST OF FIGURES

xiii

7.1 P distribution of MRD events. . . . . . . . . . . . . . . . . . . . 88
7.2  distribution of MRD events. . . . . . . . . . . . . . . . . . . . 89
7.3 Reconstructed MRD-event vertices distribution for X and Y. . . . 90
7.4 Reconstructed event vertices distribution (Z) and distribution of
number of tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.5 P distribution of LG events. . . . . . . . . . . . . . . . . . . . . . 92
7.6  distribution of LG events. . . . . . . . . . . . . . . . . . . . . . 93
7.7 Reconstructed LG-event vertices distribution for X and Y. . . . . . 94
7.8 Reconstructed LG-event vertices distribution (Z) and distributionof number of tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.9 cos 1 distribution for all two-track MRD events. . . . . . . . . . 96
7.10 De nition of the 25-ton ducial volume at the 1kt C erenkov detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.11 P- distribution of the 1kt detector . . . . . . . . . . . . . . . . 98
7.12 1kt and SciFi distribution after 2 tting. . . . . . . . . . . . . . 99
7.13 Measured neutrino spectrum at near detector. . . . . . . . . . . . 100
8.1 Time di erence distribution of selected events . . . . . . . . . . . 104
8.2 Typical neutrino event at SK. . . . . . . . . . . . . . . . . . . . . 105
8.3 Visible energy distribution of SK events. . . . . . . . . . . . . . . 106
8.4 Muon momentum distribution of SK events. . . . . . . . . . . . . . 106
8.5 Reconstructed neutrino energy distribution of SK events. . . . . . 107
8.6 Reconstructed vertex distribution of SK events. . . . . . . . . . . 108
9.1 A poisson distribution smeared by Gaussian. . . . . . . . . . . . . 110
9.2 Reconstructed E distribution at SK. . . . . . . . . . . . . . . . . 113
9.3 Allowed regions of oscillation parameters. . . . . . . . . . . . . . 114
9.4 Allowed regions (68% C.L.) of oscillation parameters (number or
shape only). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

List of Tables
1.1 Current mass limits for three types of neutrino by PDG [11] . . .
1.2 R of atmospheric neutrino for neutrino observatories around theworld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
6

3.1 Refraction indices of SciFi SCSF-78M media. . . . . . . . . . . . . 31
3.2 IIT V5502UX applied high voltage. . . . . . . . . . . . . . . . . . 37
3.3 IIT V1366GX applied high voltage. . . . . . . . . . . . . . . . . . 37
5.1 SciFi event summary table. Common selection of FGD requires atleast one FGD component has activity. . . . . . . . . . . . . . . . 66
6.1 Numbers used in NSK calculation. . . . . . . . . . . . . . . . . . . 79
6.2 Systematic error terms table of NSK for MRD events. (November
Con g.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3 Systematic error terms table of NSK for LG events. (November
con g.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.4 Systematic error terms table of NSK for MRD events. (June con g.) 81
7.1 Best t results from spectrum t of near detector. . . . . . . . . 98
8.1 Reduced number of events in SK after cuts. . . . . . . . . . . . . 103
9.1 Percentage of energy dependent systematic errors on the predicted
neutrino spectrum at SK. . . . . . . . . . . . . . . . . . . . . . . . 111
9.2 Best t points from the maximum-likelihood analysis. . . . . . . 112

1

Chapter 1
Introduction
1.1

The Neutrino in the Last Century

1.1.1 Neutrino Mass

The neutrino is one of the most remarkable particles in current high energy
physics. It is a neutral lepton of zero or very small mass.
In 1930, W. Pauli [1] postulated the existence of a very light neutral particle
with spin 1/2 as a solution to the problem of the continuous energy spectrum of
the electron from -decay n ! p + e0 . In 1956, F. Reines and C. Cowan [2]showed direct evidence of neutrino existence from the inverse -decay, e + p !
e+ + n. Neutrinos have the same generations as the charged leptons: the electron,
the muon, and the tauon. These are called electron-neutrino (e ), muon-neutrino( ), and tau-neutrino( ), respectively.
Neutrino mass has been a mystery for a long time. The modern standard
model [3, 4, 5] assumes that neutrinos have no mass, given that even if they
did it would be very small. Though there is no basis for this assumption, thisstandard model explains observations very well.
Meanwhile, the investigation into neutrino mass has continued. The mostsensitive experiment for e mass uses -decay of Tritium [6]:31

H ! 32 He + e0 + e(1.1)

If e has a nite mass, the end point of the electron energy spectrum shifts fromthat calculated, assuming e mass is 0. The current upper limit on the mass of
e adopted by Particle Data Group (PDG) [12] is 3 eV.
34

CHAPTER 1. INTRODUCTION

Table 1.1: Current mass limits for three types of neutrino by PDG [11]Flavore

Mass limit
Experiment
3 eV
Tritium decay
190 keV(90% C.L.)
Pion decay at rest18.2 MeV(95% C.L.) Tau decay in e+e0 collider

For , momentum measurements of muon from pion decay at rest
 !  + 
(1.2)
give the best mass limit [7]. PDG's value is 190keV.
For  , the best limit is 18.2 MeV, which is obtained from kinematics of tauon
decay in ALEPH [8]:
 ! 20+
(1.3)
 ! 302+0 :(1.4)
The current mass limits for the three types of neutrino are summarized in Table 1.1.
1.1.2 Neutrino Oscillation

Neutrino oscillation is a means of studying the small mass of neutrinos and theirmixing [9, 10]. Here is an example of two- avor neutrino oscillation.
We assume e and  have nite and di erent masses and mix with angle 
between weak and mass eigenstates. We can get
0 1 0
10 1

cos

sin

e
@ A=@
A @ 1 A ;(1.5)

0 sin  cos 
2where l = (e ;), i = (1 ;2) are the weak and mass eigenstates, respectively.
This can be written simply:jl >= Uli ji >;
(1.6)
where
0
1
cos

sin

U  @ 0 sin  cos  A :
(1.7)

5

1.1. THE NEUTRINO IN THE LAST CENTURY

The neutrino beam generated as a weak eigenstate, jl >, is evolved in time asXXXjl (t) >= Uli e0iE tji >; =UliUl ie0iE tjl >
(1.8)
i

0

i

i

i

0

l0

after time t. We use the approximation2m
Ei = p + 2pi :(1.9)
Oscillation probability of l to l after t becomes
P (l ! l ) = j < l jl(t) > j2 = X X UliUl iUli Ul i 2 cos [(Ei 0 Ei ) t] : (1.10)
0

0

0

0

i

0

0 0

0

i0

Using distance L (L = t)!
2
1m
P (l ! l ) = sin 2 sin 4E L ;(1.11)

1m2 = m22 0 m21 :(1.12)

0

2

2

where
When we use eV2, GeV and km as units for 1m2 , E , and L, the mixing probability is
!
2
2
1
m
[
eV
]
1
L
[
km
]
2
2
:
(1.13)P (l ! l ) = sin 2 sin 1:27 1 E [GeV ]0

In a neutrino oscillation experiment, we can measure 1m2 , and not theneutrino mass directly.
1.1.3 The Atmospheric Neutrino Anomaly

Primary cosmic rays dominated by protons and particles interact with nuclei
in the atmosphere of the earth to produce  mesons and K mesons.  decays like

 !  + 
 ! e + e + :(1.14)

Neutrinos generated in the atmosphere are called \atmospheric neutrinos." Theratio  / e should be 2/1 from the reactions in 1.14. Systematic error due tothe uncertainty of ux of primary cosmic rays can be reduced from  30% to6

CHAPTER 1. INTRODUCTION

Table 1.2: R of atmospheric neutrino for neutrino observatories around the world.
"Sub-GeV (Multi-GeV)" indicates events with visible energy less (more) than 1:33
GeV.
ExperimentR(Eqn.1.15)
Citation:06
Kamiokande(Sub-GeV)
0:60+0[13]
00:05 6 0:05
+0:08
Kamiokande(Multi-GeV) 0:5700:07 6 0:07
[13]
IMB
0:54 6 0:05 6 0:07
[14]
Frejus
1:00 6 0:15 6 0:08
[15]
+0:35
0:9900:25
[16]
NUSEX
+0:05
Soudan2
0:5100:07 6 0:14
[17]
SK(Sub-GeV)
0:635 6 0:033 6 0:053 [18]:065SK(Multi-GeV)
0:604+0[18]
00:58 6 0:087
5% by by taking the double ratio of the number of observed neutrino and thesimulated one:=N (e + e)data
R  NN((++))=N(1.15)(e + e )simulation
Kamiokande found that R was 0.6, meaning that the observed data showed ade cit of  40% [13]. IMB [14], Soudan2 [17], and Super-Kamiokande (SK)[18] also show results consistent with Kamiokande. This de cit is called the\atmospheric neutrino anomaly." Results from neutrino observatories aroundthe world are summarized in Table 1.2. These results suggest that the numberof  is smaller than expected and/or the number of e is larger than expected.
1.1.4 Observation of Atmospheric Neutrino Oscillation by
the SK Collaboration

The SK collaboration also observed clear asymmetry between upward-going anddownward-going  s [18]. Distance from the production point to the SK detector
varies from  10km to  104 km, depending on the zenith angle of the ight
direction of the neutrinos. If atmospheric  s oscillate into another type of as in Eq. 1.13, the number of events will change along with the zenith angle.
Figure 1.1 shows the zenith angle distribution of neutrino events observed in SK,
shown with simulation results assuming oscillation and no oscillation.

1.2. THE K2K EXPERIMENT

7

The distribution was well explained by  !  neutrino oscillation where
the parameters are 1m2 = 3.2 21003eV2 and sin2 2 = 1. The SK collaboration
concluded that they had observed neutrino oscillation.

Figure 1.1: The zenith angle distribution of -like and e-like events. Observed
neutrino events in SK (cross) and simulation assuming oscillation (line) and no
oscillation (hatched box). The distribution is well explained by  !  neutrino
oscillation where the parameter is 1m2 = 3.2 21003eV2, sin2 2 = 1. "Sub-GeV(Multi-GeV)" indicates events in which visible energy is less (more) than 1:33
GeV.

1.2

The K2K Experiment

The KEK E362 experiment is colloquially known as K2K (KEK to Kamioka). It
is the rst long-baseline neutrino oscillation experiment in the world that uses
an accelerator. It was approved in 1994. We produce an arti cial muon neutrino beam at the KEK 12 GeV proton synchrotron and observe it using the SK
neutrino detector at a distance of 250km.
The main purpose of the K2K experiment is to con rm the SK collaboration
observation of muon neutrino oscillation. It also aims to quantitatively measure
the oscillation parameters, 1m2 and sin2 2 . The method is as follows: If neutrino oscillation occurs, the number of muon events at the far site will

8

CHAPTER 1. INTRODUCTION

be fewer then the number of events expected in a null-oscillation model.

 In addition, we will observe some distortion of the neutrino energy spectrum
because the probability of neutrino oscillation varies according to its energy.
Figure 1.2 shows distorted E spectrums at K2K in one 1m2 case. (1m2 =0.005eV2 , sin2 2 = 1)
 For every parameter set (1m2 , sin2 2 ), the energy spectrum is calculated
and compared with the observed one.
 From the likelihood analysis, we determine the allowed region of parameters.
In the K2K experiment, the mean neutrino energy < E > is 1.4GeV and the
distance L is 250km. The sensitive region is 1m2  2 2 1003eV2, and sin2 2 
1 (Figure 1.3) for  !  mode.

1.3

Overview of this thesis

After three years of work on the K2K experiment, this thesis details the rst
result of spectrum analysis.
An overview of the K2K experiment is described in Chapter 2. The scintillating ber (SciFi) detector was built to measure the neutrino energy spectrumat the near site.
The construction of the SciFi detector and its hardware setup is discussed in
Chapter 3. Chapter 4 explains the neutrino simulation procedure, undertaken topredetermine detector performance and detect systematic errors of measurement
prior to an actual run. The analysis technique, as well as neutrino event selection,
is described in Chapter 5. Event counting, a summary of error estimation, anda comparison between observation at the far site and the expectations at thenear site are described in Chapter 6. Matching simulated data to observed data,
we measure the neutrino energy spectrum with the near detectors (including the
1kton detector) in Chapter 7. Chapter 8 details event selection at the far site.
Finally in Chapter 9, using information on the number of events and spectrum
shape, we perform a neutrino oscillation analysis.

91.3. OVERVIEW OF THIS THESIS

2

2

probability

Neutrino Oscillation (∆m =0.005eV )
1
0.75
0.5
0.25
0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

number of neutrinos/cm2

Eν(GeV)
80000
60000
40000
20000
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

number of neutrino interactions

Eν(GeV)

15
10
5
0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Eν(GeV)

Figure 1.2: Neutrino energy spectrum distortion in K2K in the case of the oscillation at (1m2 = 0.005eV2, sin2 2 = 1). The top gure shows the probability ofneutrino oscillation as a function of energy. The middle gure shows the neutrino
ux at SK. The histogram shows the expected neutrino ux by MC [units are\number of neutrinos/cm2 /1020POT(Protons On Target)"]. The hatched areais the expected ux times the oscillation probability. The bottom gure shows
the neutrino ux times the total cross section of neutrino interaction with water,which corresponds to the expected number of events at SK.

10

CHAPTER 1. INTRODUCTION

K2K νµ↔ντ oscillation sensitivity-1

1022.5ktonFC
1 ringµ-like-2

recEν >500MeV2

2∆m (eV )

10

-3

10
90%CL
99%CL
99.9%CL
-4

10
0

0.2

0.4

2

0.6

0.8

1

sin 2θ

Figure 1.3: Sensitive region of the K2K experiment for  !  mode. The
right side of three lines correspond 90%, 99%, and 99.9% C.L. Allowed regions ofoscillation parameters in Kamiokande and Super-Kamiokande are overlaid.

Chapter 2
Setup of the K2K Experiment
A schematic overview of the K2K experiment is shown in Figure 2.1. The neutrino beam produced by the 12GeV proton synchrotron (PS) (a) travels throughthe neutrino beam line (b). There are several monitors along the beam line:
proton beam line monitors, a pion monitor, and muon monitors. The proton
beam line monitors normalize the live time of the detectors and predict neutrino
ux. The pion monitor estimates ux ratio at the near and far detectors. The
muon monitors measure the direction of the neutrino beam. The neutrino ux atthe near detector (c) is measured and compared with that at Super-Kamiokande,
the far detector (d). The 12GeV PS, the beam line, and the near detector wereconstructed on-site at KEK. A GPS system (e) controls targeting and time synchronization between KEK and the far detector.
This chapter describes the components used to conduct the K2K experiment,from upstream to downstream.

2.1

12 GeV Proton Synchrotron

The 12 GeV proton synchrotron (PS) is located at KEK (High Energy Accelerator
Research Organization) in Ibaraki Prefecture, Japan. The accelerator consists ofa 750keV Cockcroft Walton accelerator, a 40 MeV linac injector, a 500 MeV
booster, and the main ring, a 12 GeV synchrotron.
Proton beams are extracted from the \EP1" beam channel in the main ring
every 2.2 seconds. This is known as "fast extraction" as all of the protons are
kicked out in 1.1 sec. The typical number of protons per pulse (PPP) is 5:621012.
There are nine rf packets in the main ring and therefore protons are transported
11

12

CHAPTER 2. SETUP OF THE K2K EXPERIMENT(e)GPS Sattelites
(a)
12GeV
PS
(b)Neutrino Beamline(d) Super-Kamiokande(c)Front Detectors

Pion
Muon
MonitorMonitor
0000001111111100
0100000011111100000011111100
110
1000000111111000000111111
00
11
π 10
µ
P
000000ν 11111100
1110µ
000000111111
π
0000
000
111
000000111111SPIC 1111
Decay Pipe
1111
0000
0000
1111
CT
000
111
111111000000(200m)
1010
0000
1111
Magnetic
Iono0000
1111
Focusing Copter
0000
1111
Fine-Grained
HORNs
1kt waterC
Al
Targetν11111110000000
0000000
1111111000000111111000000111111000000111111

Detector(FGD)

0 m

300 m

250km

Figure 2.1: Schematic overview of K2K experiment.
to the beam line in nine bunches.

2.2

Proton Beam LineIn 1994, with approval granted for the K2K experiment, the proton beam line
was built to extract and bend the primary proton beam in the direction of the
far detector.
The arc section of the beam line consists of 18 bending magnets and 18
quadrupoles. The transport eciency of the beam line is approximately 85%.
2.2.1 Beam Line Monitors

The proton beam line has 13 CTs (current transformers) and 28 SPICs (segmented plates ionization chambers). The CTs are coils sensitive to the beam
current. They are used as beam intensity monitors and they determine the absolute number of protons to within 10%. SPICs obtain pro les of the proton
beams. A SPIC consists of three 28 m thick copper sheets. The middle sheet isa cathode plane (-HV). The other two are horizontal and vertical readout (GND)
planes. Figure 2.4 shows a schematic view of a SPIC. The readout planes have
32 channels giving x and y readouts. For more detail on the K2K SPICs, pleasesee reference [19].

2.3. TARGET AND MAGNETIC HORNS

13

Figure 2.2: KEK-12GeV proton synchrotron consists of a 750keV Cockcroft Walton accelerator, a 40 MeV linac injector, a 500 MeV booster, and a 12GeV main
ring.

2.3

Target and Magnetic Horns

The target is made of aluminum. It was 20mm in diameter in June 1999 and30mm from November 1999. The 66cm length corresponds to a 1.5 interaction
length.
The two magnetic horns which focus the pions are also made of aluminum.
The horns are driven every 2.2 seconds with a 2 msec. long 250 kA pulsed
current. They need to be synchronized with the fast extracted beam (1.1 sec.
bunch width) to generate toroidal magnetic elds.
Figure 2.5 is a schematic view of the target and magnetic horns. The rst
horn is 2.5 meters long and 0.60 meters in diameter. The second horn is 2.8
meters long and 1.7 meters in diameter. It is located eight meters downstream

14

CHAPTER 2. SETUP OF THE K2K EXPERIMENTTo Super-Kamiokande

protonFigure 2.3: Proton beam line.
of the rst horn.
The strength of the magnetic eld B (kGauss) at R(cm) distance from thebeam center is given by;

B = 5:0I1 R ;(2.1)

where I is the current supplied to the horn magnets (kA). According to thecalculation, we have 50 kGauss at R = 1cm. Simulated neutrino ux above 0.5
GeV with magnetic horns supplied at 250 kA current is approximately 22 times
greater than at 0 kA (Figure 2.6).
Not only the diameter of the target was changed; the current supplied to themagnetic horns was increased from 200 kA to 250 kA. This will be taken into
consideration when we analyze the neutrino data.

15

2.4. SECONDARY PARTICLE MONITORS
to ADC

to ADC

Protonbeam

Protonbeam-HV

Figure 2.4: Schematic view of a SPIC.

2.4

Secondary Particle Monitors

The pion monitor and muon monitors monitor secondary particles after they pass
the target [24]. The pion monitor measures the momentum and the angle of pions
immediately after they pass the second horn. The muon monitors measure theintensity and position distribution of muons produced by pion decay.
2.4.1 Pion Monitor

The pion monitor is a gas C erenkov detector. Charged particles traveling ina medium at a velocity faster than the velocity of light in that medium emitC erenkov radiation. Photons are emitted in a cone with respect to the directionof the particle. See subsection 4.3.2 for more detail on C erenkov radiation.
The pion monitor consists of a gas vessel, a pie-shape spherical mirror, andphoto detectors (Figure 2.7). C erenkov radiation emitted in gas re ects o thespherical mirror and is detected by photo detectors. The gas vessel is lledwith Freon gas. Increasing the gas pressure from 0.34atm to 1.70atm changes
the refractive index of the gas from 1.00047 to 1.00236, which corresponds to aC erenkov threshold of pions at 4.6GeV/c to 2.0GeV/c. The photo detector is a
20 photomultiplier tube (PMT) array.

16

CHAPTER 2. SETUP OF THE K2K EXPERIMENT
2.8m
2.5m

π+

1.7m

p
π+
0.6m

π

1stHORN−

2ndHORN

Figure 2.5: Target and magnetic horn. The target is an aluminum rod. Bothhorns only focus positive pions.
The pion production angle can be measured by detecting C erenkov light (Figure 2.8). Changing the refractive index of gas, this measurement is taken inseveral gas refractive index values, from which pion momentum distribution is
obtained. With this distribution of pions in P -  space, we can estimate neutrino ux in the neutrino beam at the near and far detectors [24]. Using thiscalculated ux ratio, the expected number of events at the far detector can bederived from the number of events at the near detector. (Chapter 6).
Measurements were taken with the pion monitor in June and November 1999.
(The pion monitor is not on the beam line during normal neutrino beam runs.)

2.4.2 Muon Monitors

Muon monitors monitor beam direction and stability on a spill-by-spill basis.
Since we monitor muons from the reaction  + ! + + , the pro le center ofmuons is the same as of muon neutrinos.
The muon monitors are 200m downstream of a decay volume lled with Hegas. They consist of a silicon pad detector (SPD) and a ionization chamber(Figure 2.9). The SPD has 25 silicon pads. The ionization chamber has 36 and32 channels for the X and Y readout electrodes, respectively.

17

Arbitrary unit of neutrino flux

2.5. NEAR DETECTORS

withHORN current

without
HORN current
0

1

2

3

4

5

Neutrino energy (GeV)

Figure 2.6: Estimated neutrino ux with horn current 0kA and 250kA (simulation). The hatched and white areas correspond to 0kA and 250kA, respectively.
250kA horn current focuses neutrinos 22 times greater than at 0kA.
2.4.3 Beam Line DAQCAMAC ADCs convert the data from the beam line monitors into a digital signal,
which is then processed by six IBM-PC compatible machines (PCs) connected
via a PC-CCP bus interface system [20].
Figure 2.10 shows the beam line DAQ system.

2.5

Near Detectors

The near detectors are located 300m downstream of the target. Figure 2.11
is an overview of the near detectors. The near detector hall is 16m in depth
and 24m in diameter. From upstream to downstream, it houses the 1kt waterC erenkov detector, veto counters, the scintillating ber detector (SciFi detector),
trigger counters, lead glass counters (LG), and the muon range detector (MRD).
The near detectors aside from the 1kt are collectively called the ne grain
detector (FGD). The 1kt has a high eciency for muons below 1 GeV/c, andfull 4 solid angle coverage, but a low eciency for muons above 1.5 GeV/csince the muon exits the detector. FGD (which includes SciFi and MRD) has a

18

CHAPTER 2. SETUP OF THE K2K EXPERIMENT~ Design on May 11,’98 ~Spherical
mirror15

0

230

Top view
mm

64

34
le

Blind

48

24

470

th

ng

al

c

Fo

900

Pion monitor
Gas volume

200

To decay
volume

2750

190

2100

Beam window

910

From
2nd Horn
527

Beam view
2

200

33

110

600

910

Photo detector
20 PMTs

Figure 2.7: Pion monitor.
high eciency for muons above 1GeV/c, and it has higher resolution of position,
providing rich track information around the interaction vertex.
 erenkov Detector (1kt Detector)
2.5.1 1kton Water C

The ring image water C erenkov detector is the most upstream of the near detectors. C erenkov detectors detect C erenkov radiation emitted by charged particles
traveling in water at a velocity faster than the velocity of light in the water. They
are emitted in a cone with respect to particle direction. The analysis techniqueused for this detector is the same used for the far detector.
The detector is a cylindrical tank 10.8m tall and 10.8m in diameter. It islled with 1000 tons of pure water, from which it derives the name \1kt". The
inner detector (ID) is 8.6m in diameter and 8.6m tall. It surrounded by the outerdetector (OD). The ID and the OD are optically separated.
The ID has 680 20-inch PMTs to detect charged particles produced by neutrino interaction. The photo cathode coverage is 40%. The OD vetoes incoming
particles; it has 68 eight-inch PMTs.
The 1kt detector measures ux normalization in order to estimate the ex-192.5. NEAR DETECTORSSide viewθparticle =0

particles
Cherenkov photons

θparticle beam

x=0
focal plane(x=r/2)spherical mirror(radius r)ring image@focal planeθparticle > 0

particles
Cherenkov photons

x=0
focal plane(x=r/2)spherical mirror(radius r)ring image@focal plane

Figure 2.8: Pion monitor measures the angle and momentum of pions.
pected number of events at SK. Little systematic error is expected as the target
material (water) and analysis technique are same at the far detector, SuperKamiokande (Section 2.6).
The 1kt detector has water puri cation system to remove small dust, bacteria
and metal ions from the water. Water purity is continually monitored throughthe measurement of electrical resistance. The temperature of water is around10C.
2.5.2 Scintillating Fiber (SciFi) Detector

The SciFi detector is a tracking detector made up of scintillating ber (SciFi)
sheets interspersed with water target tanks [25]. Where other components of thenear/far detectors were used in earlier experiments, this SciFi detector was newly
developed for K2K. The SciFi detector will be fully described in Chapter 3).
2.5.3 Trigger/Veto Counters, Lead Glass Counter, Muon
Range Detector

Sixty four-meter long trigger and veto scintillation counters lie downstream andupstream of the SciFi detector respectively.
A lead glass counter (LG) triggers counters downstream of the SciFi detector.

20

CHAPTER 2. SETUP OF THE K2K EXPERIMENT

Figure 2.9: Muon monitors.
Attached to each of the six hundred cylindrical lead glass cells is a light guidewhich carries light to the PMT. The LG measures the contamination of e in a beam. This contamination is reported to be 2%, which is consistent with our
prediction based on the Monte Carlo simulation [21].
The muon range detector (MRD) is the biggest of the near detectors. It is
made up of an iron target and drift chambers.
All of these components were used in the Tristan experiment and recycled forK2K.
2.5.4 Data Aquisition (DAQ) System of Near Detectors

Figure 2.12 shows the DAQ system of the near detector. Two types of front-end
computer collect data from the detectors. The 1kt C erenkov detector runs Sun
Bit3 on a VME crate. FGD runs HP-RT on a VME crate. We have 3 HP-RT,
one of which handles trigger/veto counters, LG, and MRD. The other two are for
the SciFi detector. Section 3.4 describes the SciFi DAQ in detail.
The trigger signal for FGD of each spill is given by the kicker magnet in the
proton beam-line.

21

2.6. FAR DETECTOR
Host
PC
100Mbyte/sec Ethernet

PC

PC

PC

PC

PC

PC

TKO
ADC

CAMAC
ADC

CAMAC
FBUS
ADC

CAMAC
FBUS
ADC

CAMAC
FBUS
ADC

VME

Muon
monitor

Pion
monitor

CT
SPIC

CT
SPIC

CT
SPIC

GPS

Arc

North Counter Hall

Muon pit

T-Station

Figure 2.10: Beam line DAQ.

2.6

Far Detector

2.6.1 Super-Kamiokande

Super-Kamiokande (SK) was developed in 1996 as a successor to KamiokaNDE(Kamioka Neutrino Detector). It was constructed in a Kamioka mine in Mozumicho, Gifu Prefecture, Japan.
SK is huge, with a ducial volume of 25ktons, yet because it is 1000m underground, the number of cosmic ray background events is smaller ( 1005 ) than if
it were at ground level.
The detector consists of a 50kton pure water cylindrical tank, a water and air
puri cation system, and photo multiplier tubes (PMTs). Like the 1kt detector,
SK is a ring image water C erenkov detector.
The tank is optically separated into two parts: an inner detector (ID) and anouter detector (OD). The ID is a cylinder 36.2m tall and 33.8m in diameter. The
OD encases the ID. The gap between the ID and OD walls is 2m at the barrel, and2.2m at the top and bottom. The ID has 11460 20-inch PMTs. Photo cathodecoverage is 40%. The insensitive section of ID is covered with a black sheet so as
not to re ect light. The OD has 1885 eight-inch PMTs. The insensitive part of
OD is covered with a re ective Tyvek sheet to collect additional light.

22

CHAPTER 2. SETUP OF THE K2K EXPERIMENT

2.6.2 Water Puri cation System

The pure water in the SK tank comes from a spring in the Kamioka mine. We
have a water puri cation system in order to lter radioactive materials and tomaintain good transparency (Figure 2.14. It supplies approximately 50 tons ofultra-pure water per hour. The water temperature is kept at 13 C to kill bacteria.
2.6.3 DAQ System

The inner detector DAQ system is shown in Figure 2.15. Analog-to-digital conversion is performed by 946 TKO modules known as ATM (analog timing modules) [26]. Timing (TDC) and charge (ADC) data from each PMT are read byeight online computers through the SMP (super memory partner) modules of
VME. These electronics and computers are housed in ve huts at the top of the
SK tank.

2.7

Global Positioning System (GPS)The K2K experiment requires precise information on the position of both theneutrino beam line and SK. Additionally, time synchronization between KEK
and SK is necessary to perform event selection against continuous background
events. Clocks at both sites need to be synchronized to within an accuracy of s.
For these reasons, K2K uses Global Positioning System (GPS) [23].
GPS consists of 27 satellites maintained by the US Department of Defense.
Each satellite has an atomic clock. The clock time and the position of the satellite
is regularly calibrated with the others in the system. Four to six satellites supply
the GPS receiver with position and time information. The KEK GPS receiver isin the north counter hall. It calculates its precise latitude, longitude, and altitude,
as well as the calibrated time in the form a Coordinated Universal Time (UTC)time stamp. It has an average resolution is 40 ns and a maximum uctuation of
150 nsec.
Figure 2.16 shows the time synchronization system. Two GPS clocks run inparallel at each site, providing hardware backup as well as a check on data quality.
At KEK, the two receivers are in the beam line control room and the antennae areon the room roof. At SK, the GPS receiver is in a building near the mine entrance
and it is connected to a VME receiver at the central electronics hut by 2km opticalber. It sends one UTC time stamp signal every second, which the VME receiver2.7. GLOBAL POSITIONING SYSTEM (GPS)23converts into UTC time. The VME receiver sends calibration trigger signals to an
LTC module. The LTC module has a 50 MHz clock synchronized to these trigger
signals. The LTC module receives timing signals either of beam extraction at
KEK or an event trigger at SK. A computer records the LTC count of the event
triggered time, the calibration triggered time, and the UTC time from the VME
module. The UTC time of the triggered events is calculated by interpolation of
the calibrated UTC time in o -line analysis, as shown in Figure 2.16.

24

CHAPTER 2. SETUP OF THE K2K EXPERIMENT

Veto/Trigger
counter

Muon Range Detector
Lead Glass
SciFi

1kt
Water Cherenkov
Detector
Neutrino Beam

Figure 2.11: K2K near detectors.

25

2.7. GLOBAL POSITIONING SYSTEM (GPS)Front detector DAQ
online WS

Analog signal

monitor PC

Digital signal

DATA server
Ethernet

ADC

Fastbus

MemoryModuleFrontend
Board

ADC

Sun Bit3

FIFO

FADC
(NIM)

ATM

ADC TDC

DORAE
module

TDC

MP

F-I/F

TMC

Input
Register

MP
TKO

HPRT

MP

HPRT

Discri.

Muon Range
Detector

TGC
PMTs

LG
PMTs

IIT,CCDSCIFI

1kt detector
PMTs

Figure 2.12: DAQ system of the near detector.

26

CHAPTER 2. SETUP OF THE K2K EXPERIMENT

Figure 2.13: Far detector Super Kamiokande.

Figure 2.14: SK water puri cation system.

27

2.7. GLOBAL POSITIONING SYSTEM (GPS)

Inner DAQ
×6

20-inch PMT´ 8· PMT ´ 11146

SCH
ATM

· ATM ´ 946

´ 20

´ 240

ATM
GONG

TKO

· SMP ´ 48

SUN classic
interfaceSMP´ 6· online computer
server ´ 9host ´ 1

onlinecomputer(server)

SUN sparc10

trigger signal(to ATMs)HITSUM(from ATMs)

VME

trigger logic

onlinecomputer(host)

VME
interface
TRG

SUN classic

FDDI

onlinecomputer(server)

NIM

Figure 2.15: The data acquisition system for the inner detector.

GPS receiverTime stamp(every 1 s)

Event trigger

VME receiver
decode to UTC
Synchronization
LTC(50MHz clock)

LTC count

OnlineComputerevery 1 s

GPS receiver
VME receiver

UTC = Tn-1

UTC = Tn

LTC = N n-1

LTC = N n

LTC (50MHz)
LTC = N ev

SK event trig.
recorded DATA

LTC & UTC

LTC & UTCLTC

SK event time = Tn + (Nev -N n ) x UTC
LTC

Figure 2.16: Overview of GPS system at SK. Block diagram (upper) and thetiming chart (lower) are shown.

Chapter 3
SciFi Detector
3.1

Overview

SciFi (scintillating ber) is a variety of optical ber made from a scintillator.
Nowadays SciFis are used in numerous components of particle detectors. One ofK2K's ne grain detectors (FGD) is a SciFi detector. It consists of ber tracking
layers interspersed with water target tanks.
Figure 3.1 shows an overview of the SciFi detector. The SciFi detector has
20 240cm-wide tracking layers. Each layer consists of an X-tracking layer and a
Y-tracking layer [the X, Y axes are perpendicular to the beam direction (Z axis)].
X and Y layers are glued onto each side of a 260cm2260cm honeycomb board
1.6cm in thickness. The distance between two tracking layers is 9cm. Between
the 20 tracking layers are 19 water- lled aluminum tanks. The aluminum wall is
0.18cm thick. The water target eliminates a common Super-Kamiokande detector
systematic error.

3.2

Construction

3.2.1 Scintillating Fiber

Charged particles excite and ionize atoms when passing through a medium. With
scintillator material, the excitation energy re-emerges as visible light during deexcitation.
Fiber made out of scintillator material is used as opt ber and is wrappedwith clad, which has a smaller refraction index. This is called \Scintillating Fiber(SciFi)". Our SciFi, Kuraray SCSF-78M, has a polystyrene scintillator core and29

30

CHAPTER 3. SCIFI DETECTOR

17

3c

cm
260

m

Water filled
aluminum tube

260cm

Fiber module(Honeycomb panel+
Fiber sheet)νμ beamImage intensifier
Micro-Channel-Plate
CCD camera

Figure 3.1: Overview of the SciFi detector.
a polymethyl methacrylate (PMMA) inner clad. These have refraction indicesof 1.59 and 1.49, respectively. Light emitted from the scintillator core can passthrough SciFi only when the re ection angle  satis es the relation:cos   nn2(3.1)
1

where n1 and n2 are the core and clad refraction indices.
SciFis are classi ed by the number of layers (clads) that cover the scintillator
core, (e.g. single/multi-cladding bers). SCSF-78M is multi-cladding ber withan outer clad of uoropolymer. Figure 3.2 is a drawing of SCSF-78M. The thickness of the clad in our SciFi is approximately two percent of the radius. Table 3.1
shows the media and refraction indices of the parts.

31

3.2. CONSTRUCTION

0.7mm

charged particle

photoncore (polystyrene) : n = 1.59
clad (polymethylmethacrylate) : n = 1.49
clad (fluorinated polymer) : n = 1.42

Figure 3.2: Scintillating ber SCSF-78M (multi-cladding type).

Table 3.1: Refraction indices of SciFi SCSF-78M media.
Part
Media
Refraction index
Core
Polystyrene
1.59
Inner Clad
PMMA
1.49
Outer Clad Fluoropolymer
1.42
The IIT (Image Intensi er Tube) photocathode shows the best sensitivity to300500nm wavelength light (Figure 3.13), requiring us to use the SciFi, whichemits light of approximately 450nm wavelength. The light originally emitted
from the core polystyrene is 340nm wavelength yet a wavelength shifter (WLS) is
doped in the core and transports it eciently. The SCSF-78M WLS shifts lightfrom the core to light of 430nm wavelength. (Figure 3.3).
We examined the light yield, attenuation length, and aging e ect on SciFi ofseveral scintillators from private companies. SCSF-78M (improved version 11)
at less than 20C showed sucient life time for our several-year experiment [27](Figure 3.4). The wavelength of SCSF-78M is shown in Figure 3.3. We measured
its attenuation length using a radio isotope electron source (90Sr) at 320cm [27, 28](Figure 3.5).

32

CHAPTER 3. SCIFI DETECTOR
2.0

Arbitrary Unit

1.5

1.0

0.5

0.0

350

400

450

500

550

600

650

700

Wavelength (nm)Figure 3.3: SCSF-78M (version 11) light wavelength. The eight lines correspondto measurement at 20cm, 40cm,... 160cm from the entrance point of the light.
3.2.2 Scintillating Fiber Sheets

Tracking layers need SciFi sheets with no space between bers. The Nagoya
University group [29] developed a method of making suitable SciFi sheets. First,
ber is wound around a grooved metal drum, then glued together with siliconpaint. The painted SciFi sheets have a suitably long life time [27]. After the paintdries, the ber is cut and opened. Figure 3.6 and 3.7 show the sheet spoolingprocess.
The SciFi sheet has dimensions of 40cm 2 370cm (on the left in Figure 3.8).
One sheet is composed of two ber layers. Figure 3.8 shows the cross section ofa sheet on the right. Six SciFi sheets are glued to each side of the honeycomb
panel (Figure 3.9), forming one unit of readout module.
An epoxy resin (Araldite CY221/HY2967) is used to glue the SciFi sheets tothe honeycomb panels. When the usual glue was found to damage and age SciFi,
the SciFi light yield was carefully tested with di erent glues. Evaporating a gas
dominated by toluene in the glue for approximately ve minutes proved to be thebest solution. [30].

33

10

5

10

4

10

3

10

2

9353.5days(93535)

55°C

10

6

(210315)521031.5 days 10
10

4

10

3

10

2

1/e lifetime [days]

90%(10% loss) lifetime [days]

3.2. CONSTRUCTION

40°C

70°C
10

10

-1

10
90 80 70

60 50

40

30

20 15 10

Temperature [°C]

Figure 3.4: Aging of SciFi SCSF-78M. The life times of the product under 40,
50, and 70 C are plotted. We can estimate the life time light yield falls 10% at
under 20  C.
Both ends of the sheet are polished. To collect more light, the side that is
not read out is coated with aluminum. Sheets are cut and bundled as in Figure
3.10 because the photocathode of IIT is circular [31]. A polishing machine for
the SciFi bundles was developed by a group from the University of Washington.
One of the polished bundles is shown in Figure 3.11.
3.2.3 Water Target

The Boston University group developed the aluminum water tanks. Their sizeis 240cm 2 16cm 2 6cm. The wall is 0.18cm thick. There are 19 layers oftarget, each layer consisting of 15 tanks. Before installation, they were checked34# of photoelectrons

CHAPTER 3. SCIFI DETECTOR

20

SCSF-78M (700µmφ)
normalwith painting
with Al coating

10
9
8
7
6
5
4
3

2

1

0

50

100

150

200

250

300

Distance from PMT [cm]Figure 3.5: SciFi SCSF-78M attenuation measurement. The star and the whitecircle correspond to measurement with white paint and Al-coated bers, respectively. An Al-coated ber has a tted attenuation length of 320cm.
for leakage with an air compressor. 1

3.3

Readout System

The SciFi detector readout system consists of serial coupling to IITs (image
intensi er tubes) and a CCD (charge coupled device) camera [32].
The IIT is a photo detector which accelerates photo electrons with a highvoltage electric eld. After the photo electrons are emitted from the photocathAfter installation, 21 out of 285 water tanks leaked and were subsequently emptied. The
decrease of ducial mass was taken into account in our detector simulation.
1

35

3.3. READOUT SYSTEMAC SERVOMOTORROTARYENCODERPERSONALCOMPUTERSTEPPING
MOTOR

BOBBINGUIDEPULLEYLASER DIAMETERLINEAR GUIDE MONITOR
HONEYCOMB DRUM
(φ= 1.2m, width=55cm)
WITH 0.7mm PITCH GROOVEDRAWINGSYSTEMTENSIONCONTROLLER

Figure 3.6: SciFi sheet spooling machine.
ode, a phosphor screen converts them into light. The IIT can amplify the lightwhile retaining information about the image.
Our system utilizes two kinds of IIT (Figure 3.12). The front IIT is a Hamamatsu Photonics V5502UX, the rear is a V1366GX. They are coupled by bers.
The front IIT is an electrostatic IIT. The sensitive surface of its photocathodeis 100mm  and typical quantum eciency is 22% at wavelength 430nm (seeFigure 3.13). The rear IIT is a micro channel plate (MCP) IIT that accelerates
photo electrons. Applying the gate signal turns on the MCP high voltage. The
gate is controlled by TTL positive logic and can open from 200nsec. to DC, ata maximum frequency of 100Hz. For K2K, we opened the gate 100 sec. every
2.2 seconds, synchronizing to neutrino beam timing, because the life time of thephosphor screen is 100 sec. (Figure 3.14).
Hamamatsu made a 24-channel high voltage supplier for the IITs (Figure /refFig.SFHV). It supplies power to both front and rear IITs. Table 3.2 and 3.3 summarize their applied high voltage. Typical total gain of the IIT chain is 7 2 106,
calculated:

Total Gain = =eF 2 QEB 2 =eB 2 MCP Gain 2 

(3.2)

36

CHAPTER 3. SCIFI DETECTOR(1) 1st spooling(3) 2nd spooling(2) 1st painting(4) 2nd painting(5) cutting(6) opposite side paintin

Figure 3.7: SciFi sheet spooling process.
Bundle part

Detector part
Light guide part
0.7 mm

40 cm

40 cm (571 fibers / layer)
30 cm 80 cm

260 cm370 cmFigure 3.8: Top view (left) and cross section (right) of SciFi sheet.
where suces F and B correspond to the front and rear IITs. =e is the gain of
the phosphor screen, 530 for the front IIT and 20 for the rear. QEB is typically
14. MCP gain is 6 2 103 at applied voltage 900kV.  is 0.8. An image of 100mm
 at the photocathode is reduced to 23mm  after output to the phosphor screen.
A CCD camera is a well-known electric appliance. An NTSC Hamamatsu
was used. It shoots 8.8mm26.6mm(2/3 in.) with 768(H)2493(V) pixels. The
relay lens has a reduction rate of 3.09:1.

3.4

Data Aquisition (DAQ)The CCD camera outputs a composite video signal through a BNC cable. Twelve
ash ADCs (analog to digital converters) convert each pixel of the video signal
from 24 CCD cameras into an 8-bit of brightness. The VME threshold modulein each IIT sets the threshold values of ADC brightness. Twenty four FIFO
( rst in rst out) memories (VME) store information on pixels with brightness
greater than the threshold and coordinate information from the CCG (clock andcoordinate generator). The CCG also sends a 14MHz pixel clock signal to the3.4. DATA AQUISITION (DAQ)

Table 3.2: IIT V5502UX applied high voltage.
Part
Voltage Current(max.)
Photocathode0V
1st Grid
110V
1A
2nd Grid 12001400V
1A
3rd Grid
3.4kV
1 A
Anode
20kV
3 A
for Pump
2.5kV
20A

Table 3.3: IIT V1366GX applied high voltage.
Part
Voltage
Photocathode
0V
Anode
2.7kV
Collimator
700V
MCP in1.7kV
MCP out 2.22.7kV
Screen7.37.8kV37

38

CHAPTER 3. SCIFI DETECTOR
fiber sheet

honeycomb board

260cm

Figure 3.9: Six SciFi sheets are glued to each side of a honeycomb panel.
ADC modules. The size of the data is one word per pixel at this stage. The total
data size of a typical beam spill is approximately 2.5kbites. Figure 3.16 shows
the DAQ setup of the SciFi detector.

3.5

Calibration System

The analysis procedure will be described in Chapter 5. To reconstruct tracks
in SciFi at the analysis stage, we need one-to-one correspondence between theidenti cation of bers and their position in the CCD camera view. We call thisan "EL table" as we developed the technique of position calibration using an EL(electro-luminescent) plate.
Additionally, the IIT light yield was calibrated principally in order to build
a simulation of the SciFi detector. Calibrated LED light was used to determine
operational high voltage and to understand the response of IIT-CCD system. A
detailed description is in Section 4.3.

3.5. CALIBRATION SYSTEM

39

3.5.1 EL Calibration

An EL (electro-luminescent) plate is a device that emits light when applied voltage is changed. It is thin and easy to cut.
We made 240 EL plate strips. Figure 3.10 shows how the EL plates are placed
over the back of the SciFi sheets with the readout at the front. Every 20th or
40th bers is selected (we call them ducial bers) and illuminated as shown in
Figure 3.17. We ash the EL plates periodically and take data. To take data,
the MCP gate must be delayed approximately 300 seconds. This procedure iscalled EL calibration. Identi cation the ducial bers in the CCD view enables
calculation the positions of the non-illuminated bers. The position resolution of
an EL map is approximately 100m [33, 34].
We carry out EL calibration prior to a neutrino beam run and make an EL
table for the coming run period. One run period lasts approximately six months,
from January to July of each year. The drift of IITs during those six months iswithin 100m [33].

40

CHAPTER 3. SCIFI DETECTOR

Electroluminescenceplate(EL)

A
B
C
D
E

Divided into
5 parts

Fiber sheet
Epoxy glue
Acrylic film separator
12 cm

Fiber block

E
D
C
B
A

Acrylic frame

Half bundle

Figure 3.10: How SciFi sheets are bundled.

3.5. CALIBRATION SYSTEM

Figure 3.11: Picture of a ber bundle.

Figure 3.12: IIT-CCD chain.

41

42

CHAPTER 3. SCIFI DETECTOR

Figure 3.13: Sensitivity of front IIT (V5502UX) photocathode. The most sensitive region is 400nm600nm. The dashed line shows quantum eciency of aphotocathode.

43

3.5. CALIBRATION SYSTEM

相対輝度

100

10-1

10-2

10-3
0.1

1

10

時間（μs）

100

1000

Figure 3.14: Lifetime of phosphor screen. X-axis is time (sec.), Y-axis is relative
brightness.

44

CHAPTER 3. SCIFI DETECTOR

630mm

570mm

1200mmMCP Dial

Front
DC out(V1366GX,3pin)
VG1G2G3(V5502UX,6pin)

VSCREEN(V5502UX,1pin)

CCD camera 12pin
MCP gate NIM

X 24
IIT

Rear

Figure 3.15: HV supplier for 24 IITs.

V G1G 2G3
DC OUT

Figure 3.16: DAQ setup of the SciFi detector.

IIT (MCP) lens CCD
10Hz
C. G.

1Hz
TRIGGER
VETO

VETO

C. G.

GROBAL
SPILL

8bit
interrupt
register

VME
TRG

WIDTH
100 µsec

3.5. CALIBRATION SYSTEM

H.V. BOXV SCREEN

MONITORVIDEO IN

TRIGER
OUT

FAN

1

COIN.

1

0

FAN

FAN

G. G.

G. G.
CAMERA
BOX

WIDTH
100nsec

VIDEO
OUT

CLOCK AND
COORDINATOR
GENERATOR

COIN.

2

FLASH ADC

VIDEO

CCD
CAMERA

1

75Ω

TRIG.

[THRESHOLD]EXT SYNC

3

FAN

COIN.

2
N

V. SYNC

VD

H. SYNC

HD

T

C. SYNC
OUT

4

COIN.

I

3

8

G. G.

T

PIXEL
CLOCK
M

8

MONIT
T
T

N
I

L

M

DELAY

N
I

T
T

M

L

WIDTH LATCH
DELAY 100nsec

11nsec

75Ω
TRANS
GATE

G.G. : GATE GENERATOR
C.G. : CLOCK GENERATOR
COIN. : COINCIDENCE
FAN : FAN IN / FAN OUTVMEP CLOCK

WS

FIFO

L

BLANK

VETO

VME

BLANK

X

BRIGHTNESS

Y

TRANS

V. coordinator

V

H. coordinator

H

45

TRANS

46

CHAPTER 3. SCIFI DETECTOR

Figure 3.17: Picture of ducial bers in a ber bundle illuminated by the EL.

Chapter 4
Simulations
Simulations are an important aspect of high energy physics. They enable us toestimate detector feasibility and performance prior to construction. Additionally,
simulations are used to estimate the uncertainty of measurements at the analysis
stage. Various computer programs have been developed that simulate physicalprocesses and/or detector response. These commonly utilize the Monte Carlo(MC) method Bib.PDG2000. For this reason, the simulation or simulation result
is often referred to as \MC".
K2K runs three simulations:
1. Neutrino beam simulation
This simulates proton injection to the aluminum target, pion production,
pion focusing by magnetic horn, and the tracking of pions until their decay
to neutrinos. It delivers a neutrino ux at near and far detectors.
2. Neutrino interaction simulation
This simulates neutrino interaction on target nuclei. It provides information
on daughter particles of neutrinos.
3. Detector response simulation
This simulates the transportation of daughter particles through the detector
and detector response. The input for this simulation is the four-vectors of
secondary particles from the neutrino interaction simulation.

4.1

Neutrino Beam

For neutrino beam simulation, the following is taken into account:47

48

CHAPTER 4. SIMULATIONS

1. Proton pro le at the target,
2. Production of secondary particles,
3. Magnetic horn focusing,
4. Particle decay.
Two SPICs (silicon pad ionization chambers) measure proton beam emittance
between the last beam line magnet and the target horn. The SPICs are V39SPIC
and TGTSPIC, respectively. The measurements are the input for beam simulation.
The hadron interaction is one of the largest ambiguities of the simulation.
Pion production simulation adopts the Cho model [38], with Sanford-Wang parameterization [39] determined experimentally. In this model, the di erential
yield of the secondary particle is as follows;
d2n = C1 1 pC2 1 0 p ! 1 exp 0 C3 1 pC4 0 C6 1 (p 0 C7 1 pB cosC8 )!
ddp
pB 0 1
pCB5(4.1)
where p, pB are the momentum of the secondary particle and the beam momentum, respectively.  is the angle between the secondary particle and the beamaxis. C1 , C2 ,...C8 are the tted parameters for + according to Cho.
The GEANT package developed by CERN [37] is used to simulate the transportation of particles in the magnetic eld of the horn. GEANT also simulates
the decay of pions in the gas decay volume. The simulation is expected to deliver
a 98% pure  beam with an average energy < E > 1.3GeV. Contributions fromkaons etc. are expected to be quite small.
The resulting neutrino ux at KEK and SK is shown in Figure 4.1. From thebeam MC, e / is estimated to be 1.3%,  / to be 0.5%, and e / to be 2 2 1004.

4.2

Neutrino Interaction

Neutrino interactions in the energy region of the K2K experiment are categorized
into the following types:
1. Charged current (CC) and neutral current (NC) elastic scattering o electron ( + e0 !  + e)

49

4.2. NEUTRINO INTERACTION
2

Neutrino flux at Super-Kamiokande
number of neutrinos/cm

number of neutrinos/cm2

Neutrino flux at Near Detector (KEK)
10 11

νµ
10 10

10

5

10 4

νµ

10 3

10 9

νe

–

–

10 8

νµ

10 2

νe

νµ
–

νe
–

10

νe

10 7

1
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0

0.5

1

1.5

2

2.5

3

3.5

Eν(GeV)4

4.5

5Eν(GeV)

Figure 4.1: Neutrino ux calculated by beam simulation. The hadron production
model selected is the Cho model. Left gure: Neutrino ux at KEK. Right gure:
Neutrino ux at SK.
2. CC quasi-elastic scattering o nucleon ( + N ! l + N 0 )3. NC elastic scattering o nucleon ( + N !  + N )4. CC single meson production ( + N ! l + N 0 + meson)
5. NC single meson production ( + N !  + N 0 + meson)
6. CC deep inelastic scattering ( + N ! l + N 0 + hadrons)
7. NC deep inelastic scattering ( + N !  + N 0 + hadrons)
8. CC coherent pion production ( +16 O ! l +16 O + )
9. NC coherent pion production ( +16 O !  +16 O + )
where l represents a charged lepton and N and N 0 represent nucleons.
4.2.1 Elastic Scattering o Electron

The cross section of this interaction is approximately three orders of magnitude
smaller than the other modes ( 10041cm2 at E =1.0GeV) and therefore it issimply omitted from the simulation.

50

CHAPTER 4. SIMULATIONS

4.2.2 Quasi-Elastic Scattering o Nucleon

This reaction is the dominant mode in the K2K neutrino beam energy region.
Our simulation of the interaction is based on Llewellyn Smith's formula [40]. The
amplitude is described as a product of hadronic and leptonic weak currents:

T = GpF2 u(k2) (1 0 5)u (k1) < N 0(p2)jJhadronjN (p1) >(4.2)
where GF is the Fermi coupling constant, p1 (p2 ) is the initial ( nal) nucleon 4momentum, and k1(k2) is the initial ( nal) lepton 4-momentum. The hadronic
weak current is expressed as:

#

2 2
i
 q FV (q )2
+  5 FA (q ) uN (p1 )c N (p2 )  FV (q ) +M< N 0jJ hadronjN >= cos u


"

0

1

2

(4.3)
where FV (q ) and FV (q ) are the vector form factor, FA(q ) is the axial vector
form factors, q  k1 0 k2 is the 4-momentum transfer, M is the target nucleon
mass, and c is the Cabbibo angle. If we assume the conserved vector current
hypothesis, FV1 (q 2) and FV2 (q2 ) are written in terms of the electric and magnetic
form factors, GE and GM :
1

2

2

2

2

!01 "
#
2
2
q
q
2
2
FV (q ) = 1 0 4M 2 GE (q ) 0 0 4M 2 GM (q )
!01 h
2
i
q
2 2
(4.4)
FV (q ) = 1 0 4M 2 GE (q2) 0 GM (q2)where   p 0 n = 3:71.  is the anomalous magnetic dipole moment of
nucleon. GE and GM have dipole forms which have been determined by electron
1

2

scattering experiments:

GE (q2) = (1 +  )01GM (q2) =  1 q (4.5)
1 0 M22
where MV is vector mass which is set at 0.84 GeV/c2 in our simulation.
By analogy with the vector form factor, we assume the axial vector form factor
FA has a dipole form:(4.6)
FA (q2) = 0  1:23q2 2
1 0 M2VA

4.2. NEUTRINO INTERACTION

51

where MA is the axial vector mass. Several experiments suggested that 0.9
GeV/c2  MA 1.1 GeV/c2 [41]. We adopt 1.01 GeV/c2 in our simulation.
The constant value 1.23 came from neutron decay experiments [42].
The di erential cross section is expressed as follows:d() = M 2G2F cos2 c "A(q2) 7 B(q 2) s 0 u + C (q2) (s 0 u)2 #
(4.7)
dq2
8E2
M2
M4
where s and u are Mandelstam variables, E is a neutrino energy, and m is an
outgoing lepton mass. A(q2 ), B (q2), and C (q 2 ) are written as follows:
"
!
!
!
2
2
2
2
2
2
m
0
q
q
q
q
q
2
1 2
2 2
A(q ) = 4M 2 4 0 M 2 jFA j 0 4 + M 2 jFV j 0 M 2 jFV j 1 + 4M 2
#
2 1
2
2 

4
q
F
F
m
V
V
0 M 2 0 M 2 (FV1 + FV2 )2 + jFAj22 
B (q2) = Mq 2 FA (FV1 + FV2 )
!
2
1
q
2
2
1 2
2 2
C (q ) = 4 jFAj + jFV j 0 4M 2 jFV j(4.8)
2

For the nucleons in oxygen nuclear, we also consider both the Fermi motionof the target nucleon and the Pauli blocking e ect. We use the Fermi momentum
distribution in 16O estimated by the electron scattering experiment on 12 C target [43]. The Pauli blocking e ect is reproduced in this simulation. It gives theoutgoing nucleon's momentum, which must be larger than the Fermi surface momentum. This sets a limit of 217MeV/c for 16O [43]. In other cases quasi-elastic
interaction is forbidden.
Neutral current (NC) QE cross-sections are derived by multiplying factors
and charged current (CC) QE cross-sections. The factors come from neutrino
experiments [44, 45]:(p ! p) = 0:153 2 (n ! e0p)( p ! p) = 0:218 2 (p ! e+n)
(n ! n) = 1:5 2 (p ! p)(n ! n) = 1:0 2 (p ! p)

(4.9)

52

CHAPTER 4. SIMULATIONS

4.2.3 Single Meson Production via Baryon Resonances

Single meson production via resonance is the dominant hadron process in theregion where the invariant mass of the hadron system is less than approximately
2.0 GeV/c2 .
The simulation of single meson production via resonance is based on Rein and
Sehgal's model [46]. This model was originally developed for single pion productions. We extend their method to encompass  and the K meson productions.
In this model, single meson production is considered in two steps:

 + N ! l( ) + N 3
Resonance production
30
N ! N + (; K )Resonance decay
where N 3 is baryon resonance, N and N 0 are nucleons, and l is an outgoing

charged lepton. The amplitude of the baryon excitation is:(4.10)T (N ! lN 3) = GpF2 ul (1 0 5)u < N 3jJhjN >where < N 3 jJhjN > is the weak hadronic current for this process. The matrix

element of the hadronic current is calculated by the FKR (Feynman, Kislinger,
Ravndal) model [47], which describes the baryon as a relativistic three-bodysystem.
The amplitude of resonance decay is expressed by Breit-Wigner formula withan experimentally measured decay width and a branching ratio of each resonance. These interactions are characterized by q2 and W , and the di erential
cross section can be written:s2d2 = 1 1 1 X T (N ! lN 3)1pE 1sign(Nj ) 0j 1
1
jdq2dW 32ME2 2 j;spin2 W 0 Mj + i 02
j

(4.11)

where Nj3 is j's baryon resonance, E is the neutrino energy, pE is thebranching ration of Nj3 to N'+meson, Mj is Nj3's mass, 0j is the total decay widthof Nj3 , and sign(Nj ) is the sign of the decay amplitude of Nj3. The sign(Nj3 )is the sign of decay amplitude of N 3 which is lost when the decay width isjexperimentally measured. in order to consider the interference e ects of theneighboring resonances correctly. Summation in Eq.4.11 is done over all relevant
resonances and their spin, In our simulation, a region where W2.0 GeV/c2 wascovered and 18 resonances were taken into account.

4.2. NEUTRINO INTERACTION

53

In Rein and Sehgal's method, the nal kinematics of the hadron system aredetermined so that the e ects of the polarization of the produced resonances andthe interference are properly considered. In our simulation, we employ their detailed calculations only for 1(1232). We simply assume that mesons are emitted
isotropically in the resonance rest frame for other resonances.
It is known that a baryon resonance in a nucleus can sometimes be absorbedwith no mesons being generated via the following interaction:

N 3 + N ! N 0 + N 00

(4.12)
where N 3 is a baryon resonance and N, N', N" are nucleons. The rate of theirinteractions is estimated by theoretical calculation [48]. We assume that 20% of
the resonances in 16O disappear without meson emissions.
Fermi momentum of nucleons is considered as in the case of quasi-elastic interaction. The Pauli blocking e ect on the nucleon from the baryon resonances
decay is also taken into account by correcting pion momentum so that the momentum of the nucleon may be larger than 217MeV/c.
4.2.4 Coherent Pion Production o 16 O

Coherent pion production is a neutrino interaction with a nucleus as a whole.
The di erential cross-section of coherent pion production is calculated by Rein
and Sehgal [50] as:d3 = G2F M f 2A2E (1 0 y) 1 h0N (E y)i2 1 + Re(fN (0)) !2!
dxdydjtj 22 
16 totIm(fN (0))
!
2


2
M
1
A
2=3
2 M 2 + Q2 exp 0 3 R jtj Fabs(4.13)
A
where x and y are the Bjorken parameters, t is the square of three-momentum
transfer, f is the pion decay constant(=0.93m ), fN is the pion-nucleon scattering amplitude, A is the atomic number of oxygen, MA is the axial vector mass,
M is the nucleon mass, R is the radius of the oxygen nucleus, tot0N is the averaged cross-section of pion-nucleon scattering, and Fabs is the t-independent factor
representing the e ect of pion absorption in the nucleus.
4.2.5 Deep Inelastic Scattering

The di erential cross section for the process is described as follows:

54

CHAPTER 4. SIMULATIONS

d2() = G2F ME 1 0 y + y2 + C1F2(x;q2) 6 y 1 0 y + C2 xF3(x;q2) ;
dxdy

2
2
2
2
ym 0 xyM 0 m ;C1 = 4ME
2E 0 4mE 2ME x
xm2(4.14)
C2 = 0 4ME
xwhere x, y are Bjorken parameters, F2 (x;q2 ) and xF3 (x;q2 ) are the nucleon structure functions, M and m are the target nucleon and the outgoing lepton mass,22


respectively. We adopt the GRV94 parton distribution function [51, 52] for the
calculation of F2 and xF3 .
To remain consistent with the other interaction modes, this interaction isconsidered in the region where 1.3GeV/c2 < W . The number of produced pions
is required to be greater than one a region where 1.3GeV/c2 < W < 2.0GeV/c2.
The nal kinematics of the hadron system is obtained in two di erent ways.
For a region where 1.3GeV/c2 < W < 2.0GeV/c2 , the produced mesons are
assumed to be pions. We determine the pion multiplicity from a measurementfrom the FNL seven-foot hydrogen bubble chamber experiment [54]:< n >= (0:06 6 0:06) + (1:22 6 0:03) ln(W 2)(4.15)
where < n > is the mean multiplicity of charged pions. Assuming < n+ >=<n >=< n0 >, the mean multiplicity of pion < n > is described as:
660< n >= 0:09 + 1:83 ln(W 2)(4.16)For individual Monte Carlo events, the pion multiplicity is determined using
KNO (Koba-Nielsen-Olesen) scaling, which describes pion multiplicity distribution with mean multiplicity < n >. We also consider the forward-backward
asymmetry of pion multiplicity (nF )=(nB ) in the hadronic center of the mass
system [55]:nF = 0:35 + 0:41 ln(W 2)nB 0:5 + 0:09 ln(W 2)(4.17)
where forward is the direction of the hadronic system in the laboratory frame.
For the region where W > 2.0GeV/c2, the nal kinematics of hadrons is determined by the JETSET7.4 package [53], commonly used in high energy physics.
The package considers other particle production (K, ;; etc.).

55

4.2. NEUTRINO INTERACTION

For NC deep inelastic scattering, di erential cross-sections are calculated bymultiplying factors and CC cross sections estimated from the experimental results
shown in Ref. [56, 57]:
8(E  3GeV )(N ! X ) = >< 00::26
E03+ 0:04 2 3 (3 GeV< E < 6GeV)(N ! 0X ) >: 0:26
30
(E  6GeV)
8(E  3GeV )(N ! X ) = >< 00::39
E0
3
0 0:02 2 3 (3 GeV< E < 6GeV)(N ! +X ) >: 0:39
37
(E  6GeV)

4.2.6 Nuclear E ects

Particles produced in neutrino interaction undergo secondary interaction before
leaving the 16O nucleus. Our simulation considers interactions of , K,  mesons.
For pions, inelastic scattering, charge exchange, and absorption are considered. The mean free paths are calculated using a model by L. Salcedo et al. [58]The momentum and angular distribution of the scattered pions are determinedby phase shift analysis using the experimental results on -N scattering [59]. The
density of the nucleon inside 16O is assumed to be in the form of the Saxon-Woods
potential [60]:(r) = AZ 0 1 +1e(4.18)
where r is the distance from the center of 16 O. 0 = 0.48m3 , a = 0.41fm, c =2.69fm, Z = 8 and A = 16, respectively.
Pauli blocking e ects in -N scattering are also considered. Assuming the
Fermi gas model, Fermi surface momentum is calculated as follows:
3
 13
2
Pf (r) = 2  (r) :(4.19)For kaons, elastic scattering and charge exchange are considered. The crosssection of the scattering is based on K6 N scattering measurement [11].
For , interactions via baryon resonance:
 + N ! N3 ! N + X(4.20)are considered. Where X is either , , or , N3 is either N(1535) or N(1650) [11].
Cross section of interactions are given by Bright-Wigner form:(4.21)
(k) = k2 (W 0 M0N)02X+ 02 =4
r 0c
a

N3

tot

56

CHAPTER 4. SIMULATIONS

where k is the momentum of , 0N is a partial decay width of the interaction
N3 ! N + , and 0X is a partial decay width of N3 ! N + X, respectively.
4.2.7 Rescattering of Proton

The recoil proton in charged current interaction can be rescattered by the nucleon
inside the nucleus. The probability of this nucleon-nucleon nal state interaction
is estimated from the measurement of a scattered angle of protons in electron
scattering on 12C target [61];e +12 C ! e0 + p + X:

(4.22)The proton at scatter angle  at 66 and 120 was measured at their experiment. The ratio between the two angles is:R(120 6 8)=(66 6 8) = 0:019 6 0:0001(4.23)

We tuned the probability of the nal state interaction in our e simulation byobserving the proton scattering angle. Figure 4.2 shows the scattering angle
distributions for e MC with and without nal state interaction. R(12068 )=(6668 ) is 0:023 6 0:002(stat:) for our MC.

4.3

Detector Response

4.3.1 FGSIM

Our detector simulation utilizes GEANT 3.21, developed by CERN [37]. GEANT
is fed detector geometry input and then simulates the passage of elementary particles through matter. In K2K, GEANT transports particles through the FGD.
The simulation of detector response obtained graphically represents both the
FGD and particle trajectories. This is known as FGSIM. The GEANT package
includes a variety of materials. When the exact material used in the detector
is unavailable, GEANT can create a similar compound from atoms inside theprogram.
We set up the program to describe the response of the SciFi detector under
FGSIM. It is divided into two parts: the calculation of the light yield of SciFi
and pixel simulation.

57

4.3. DETECTOR RESPONSE

We made a conversion table of the deposit energy
inside SciFi calculated by GEANT and the light yield (the number of photoelectrons measured by the PMT). The light yield of SciFi is calibrated using a
cosmic ray muon or 90 Sr source [28]. Attenuation in the SciFi and re ection fromthe aluminum coating at the edges is also considered.
Light Yield of SciFi

To construct a reliable MC detector simulation, data of
the response of the IIT-CCD part is taken using a calibrated LED. The data isparameterized and reproduced by the MC [62]. The set up of the calibrationis shown in Figure 4.3. We can analyze simulated CCD pixels and reconstructneutrino events with this data as if it were raw data from a neutrino beam run.
(The analysis procedure is described in Chapter 5.)
Pixel Simulation

 erenkov Detectors
4.3.2 Water C

The detector simulation programs of 1kt and SK water C erenkov detectors use
the same technique.
Transportation of particles

GEANT package used on the FGD.

The simulation program is based on the same

 erenkov light
Emission and propagation of C

A water C erenkov detector observes relativistic charged particles via their emission of C erenkov light.
C erenkov radiation is a shock wave created by a relativistic charged particle witha velocity greater than the light velocity in the medium:v  nc(4.24)

where v is the particle velocity and n is the refractive index of the medium. Generated photons propagate in water with a group velocity c=n. Rayleigh scattering,
Mie scattering, and the absorption of the photon are considered. The parametersof their interactions are tuned with cosmic ray muon data.
 erenkov light
Detection of C

The number of photons arriving at the surface of the PMT is converted to the number of photoelectrons, with consideration
to the quantum eciency of PMTs.

58

CHAPTER 4. SIMULATIONS

w/o rescatterwith rescatter

0

60

120

Scattering Angle

Figure 4.2: Scattering angle distributions for e MC with and without nal stateinteraction. Alanakyan et, al. measured proton number ratio between the scattered angle 120 6 8 and 66 6 8 .

59

4.3. DETECTOR RESPONSE

Fiber-2300V

Black tube

HV

PMT
LED

PULSEROUT PUT 1
EXT input

WIDTH=50nsec

C. G.
G. G.

100Hz

WIDTH=100nsec
DELAY=50nsec

GONG ADCTKO

G.G. : GATE GENERATOR
C.G. : CLOCK GENERATOR

Figure 4.3: Setup of LED calibration.

WSChapter 5
Analysis Procedure of the SciFi
Detector
This chapter describes neutrino event reconstruction. Analysis begins with thesearch for ber hits in CCD pixel information. SciFi tracks are then reconstructed. Hits are connected hits using straight tting. Additionally, we match
tracks between the SciFi and downstream FGD components. Our goal is toreconstruct muon energy and track multiplicity for neutrinos events inside the
SciFi.

5.1

Hit Finding

Hits in the SciFi detector are reconstructed from CCD pixel images. Figure 5.1(a) shows a typical CCD image of a cosmic-ray event from an IIT. Figure 5.1 (b)is an expanded view of (a). The circles in the gures represent the coordinatesof the SciFi in an expanded view of (a). The gures illustrate a typical SciFi hit
where a cosmic-ray muon passes through the ber sheet.
There are four steps to hit reconstruction:
1. Hit Pixels in CCD Camera View
As explained in Chapter 3.4, raw data from the SciFi detector consists ofhit pixels in CCD coordinates (x, y) in 8-bits of ADC brightness. Theseare encoded one word per pixel. There are typically 3500 hit pixels in aneutrino event.
2. Pixel Clustering61

62

CHAPTER 5. ANALYSIS PROCEDURE OF THE SCIFI DETECTOR

Figure 5.1: (a) A typical CCD image of a cosmic-ray event. (b) This expanded
view of (a) shows a typical SciFi hit. Circles inside the gures represent thecoordinates of the SciFi in the CCD view. The size of hit pixel is proportional
to the brightness in the ADC. Hit bers are represented by the thick circles. A
SciFi hit is de ned as a cluster of neighboring hit bers.
A pixel cluster is a group of neighboring hit pixels. Isolated single-pixel
hits from random electrical noise in the CCD are rejected here.
3. Identifying Hit Fibers
Identi cation of a hit ber requires a cluster of pixels at the ber positions.
The CCD coordinates of the hit ber position is determined with a mappingtable obtained from EL calibration.
4. Hit Fiber Clustering
A ber cluster is de ned as a group of neighboring hit bers. We de ne
ber clusters as hits in the SciFi detector.
We apply two kinds of ltering algorithms to the ber clusters to improve thesignal-to-noise ratio: A ber cluster is required to consist of hit bers in both the upper andlower layers of a ber sheet (See Figure 3.8). This eliminates the small
pixel clusters caused by dark current in the IIT.

5.2. EVENT RECONSTRUCTION

63

 When a big pixel cluster lies on an adjacent ber sheet and forms multiple
ber clusters, only ber clusters with peak ADC brightness are chosen,
which eliminates fake ber clusters formed by the dense bundle arrangementof ber sheets.
Every hit in SciFi detector must pass these lters. The hit position is de ned
as the centroid of a ber cluster, weighted by the ADC value of the hit pixel.
The hit position CCD coordinates are then converted into detector coordinates(x;z or y;z) in our experimental hall.

5.2

Event Reconstruction

After nding the hits, we look for neutrino events in the SciFi detector. Tracks
are used for event reconstruction. These tracks are then classi ed and matchedwith the FGD components and their track information.
Tracks in the SciFi detector are classi ed as either rst or second tracks.
The rst track is for muons generated in charged current (CC) interaction. The
second tracks are for other particles such as protons or pions. When two or more
tracks are found, we de ne the vertex of the tracks as the interaction point of theincoming neutrino.
5.2.1 First Track Finding

The rst track- nding algorithm in the SciFi detector is optimized for charged
current interactions which contain one muon in the nal state [35, 36]. There arethree steps to the track- nding algorithm, which is designed to remove combinatorial background or noise tracks.
Firstly, the track nder searches for two-dimensional (2D) track candidates
on the (x;z ) or (y;z) planes which traverse at least three layers of SciFi detector.
A three-dimensional track is reconstructed from the best combination of two 2D
tracks. In order to eliminate combinatorial fake tracks, the start and end of hit
layers must not di er by more than one layer and the two 2D tracks must overlap
at least two layers.
Secondly, a track candidate must reach the edge of the SciFi detector. It
cannot be a contained event.
Finally, a track candidate must match a hit in the downstream trigger counter.
This will be described in the next subsection, 5.2.2.

64

CHAPTER 5. ANALYSIS PROCEDURE OF THE SCIFI DETECTOR

5.2.2 Track Matching with TRG Counter

If a muon produced via the charged current interaction inside of SciFi detector
goes forward, it will register as a hit in downstream TRG counters. Hits mustregister in TRG counters on the extrapolated line of SciFi tracks. The matching
criteria is 610cm for the x and 650cm for the y direction. Only events with atleast one track matching TRG counters are classi ed as "TRG matching" andused in further analysis.
5.2.3 Track Matching Veto with VETO CounterTo avoid incoming muons from neutrino interactions inside 1kt or the beam dump,
SciFi tracks with VETO counter hits along the extrapolated line to the upstream
detector are eliminated. The matching criteria is 620cm and 650cm in directions
x and y, respectively.
5.2.4 Track Matching with LG

SciFi tracks that match with TRG counters are extrapolated to the position of
the downstream LG. If the extrapolated track lines and LG blocks intersect, theLG hit cluster requires an energy deposit greater than 100MeV for the event tobe considered an "LG matching sample".
5.2.5 Track/Hit Matching with MRD

If an LG matching sample has an MRD track or a hit in the rst layer of MRD, its
track or hit is examined. As low-energy muons can scatter multiple times, a rangeof positions and angles between the SciFi track and MRD tracks is permitted.
Events which pass MRD matching are known as "MRD events". Events which fail
MRD matching are known as "LG stopping events", or in the following chapters,"LG events". Only these event samples were used in our analysis.
5.2.6 Second Track and Vertex Finding

Once a good, energetic rst track is found, the most upstream hit position is dened as the neutrino interaction point. The second track nder begins searchingfor extra tracks near this point. These tracks are mostly short tracks with two or
more SciFi hits. Many of them come from protons or pions from the interaction.

5.2. EVENT RECONSTRUCTION

65

If no short tracks are found near the starting point of the rst track, the event
is considered a one-track event. If an event has one short track, it considered a
two-track event. If the second track nder identi es more than two tracks, theevent is a three-track event (or more).
A vertex is de ned as the intersection of the rst and second tracks. For onetrack events, the vertex is taken from the middle point of the closest upstream
water tube to the track.
After locating the second track, we can classify an event by track multiplicity.
Figure 5.2 is an example of a two-track MRD event.

Figure 5.2: Example of a SciFi two-track MRD event. The upper gure is the
top view, the lower gure the side view.

66

CHAPTER 5. ANALYSIS PROCEDURE OF THE SCIFI DETECTOR

Table 5.1: SciFi event summary table. Common selection of FGD requires atleast one FGD component has activity.
Selection
Jun 1999 Nov 1999-Jun 2000 Jan 2001-Jul 2001
Common selection of FGD 156747
11359831633558
SciFi has track
7035
102081148284
TRG match
2192
14762
22266
Bad run cut
1582
12588
19417
VETO match veto
1118
8923
13734
MRD match
295
3261
5132
LG stopping
1473
2156
5.2.7 Muon Energy Reconstruction

Muon energy is calculated from its range. For the SciFi, LG, and Veto, a GEANT
table is used to calculate deposit energy from path lengths in the detectors. For
MRD, a conversion table of range in iron and muon energy is used. The di erence
between the GEANT table and table used for the MRD was con rmed as at most
1.7%. We sum up the deposit energy for all FGD hits or tracks related to the
rst track muon. Finally, muon mass (=105.658389MeV) is added.

5.3

Event Summary

K2K ran in June 1999, in November 1999, from January to July in 2000, andfrom January to July in 2001. We collected 8688 MRD events and 3629 LG
events in total over two years. The summary table 5.3 shows the reduction of thedata at each step of analysis. Common selection of a FGD event requires that atleast one of the FGD components has activity. The bad run cut is described insubsection 6.1.1. In total, 12317 SciFi events were obtained.
In June 1999, MRD events with tracks in MRD were counted and LG eventsand MRD events with hits in rst layer of the MRD were discarded. This wasdone because systematic errors for these samples were not estimated during thisperiod. Until June 1999, a di erent magnetic horn current and target size wereused.

5.4. PERFORMANCE OF SCIFI DETECTOR

5.4

67

Performance of SciFi Detector

5.4.1 Hit Finding Eciency

Hit nding eciency for all 24 IITs is estimated from cosmic ray data samples.
FGD cosmic ray samples are triggered by coincidence of veto/trigger scintillators.
For each event, a cosmic ray muon is required to penetrate more than 15 layersof the SciFi detector to be accepted as a SciFi cosmic ray data sample.
The de nition of the hit nding eciency is as follows:

Number of layers with hits
Hit finding efficiency  Numberof penetrated SciFi layers:(5.1)

The results are shown in Figure 5.3. Estimated eciency for 24 IITs in MC
detector simulation are shown. MC data agrees remarkably well.

Figure 5.3: Hit nding eciency of 24IITs.
The stability of the eciency is also studied. For K2K runs, our acceleratorgroup had machine study time for a few hours on Monday mornings. We obtained
cosmic ray data during this time and checked its eciency over the long term.
Figure 5.4 shows the eciency for this period. It is stable to within 2%.

01JanFeb

Track finding efficiency  Number of events with track between scintillators
Numberofcosmicray0
triggered
events:(5.2)
In order to understand the dependence of the track nding eciency on track
length, hits on the upstream side of the track are arti cially eliminated. For
example, to estimate the eciency of ten SciFi hit layers using a 19-layer track,
the rst nine hit layers are eliminated before applying a track- nding algorithm.
Figure 5.5 shows track nding eciency as a function of track length in SciFi
layers with cosmic ray data.
Track nding ineciencies are the result of hit nding failures and imperfections in the track reconstruction.

Figure 5.5 shows track nding eciency in the SciFi detector as a function of
track length, or number of layers. Track nding eciency is de ned as:

July

CHAPTER 5. ANALYSIS PROCEDURE OF THE SCIFI DETECTOR

june

68

May

1.1

Mar

1.05

Feb

1

00Jan

0.95

May

0.9

June

Beam

Apr

Cosmic-ray

mar

0.85

0.8
Nov

Figure 5.4: Stability of hit nding eciency from Nov '99 to Jul '01.

99Oct

5.4.2 Track Finding Eciency<Efficiency>

69

Efficiency

5.4. PERFORMANCE OF SCIFI DETECTOR

1999 cosmic data
2000 cosmic data
2001 cosmic data

Track Length

Figure 5.5: Track nding eciency as a function of the track length. Eciency
is 70% (87%) in a track length of the three (four) SciFi layers and approaches
100% in longer tracks.
5.4.3 Hit Position Resolution

The geometry of the SciFi and its support structure was measured after installation. According to this survey, ber alignment is estimated to be within 5mm.
Closer alignment was obtained by minimizing the sum of the squared hit-residuals
using a global t on cosmic ray tracks [36].
Slight curvature of the ber sheets occurred as they were glued to the ber
modules. This caused displacement from the aligned ber-position and resulted
in rotational misalignment. The curvature of each ber sheet was measured after
ber module assembly. By tting the measured points to a forth-order polynomial, the curvature of the sheets was accounted for in corrections of rotational
misalignment.
For position resolution, the muon tracks from the neutrino data are used to

70

CHAPTER 5. ANALYSIS PROCEDURE OF THE SCIFI DETECTOR

obtain the best estimation. Figure 5.6 shows the hit residual distribution of theneutrino data. The position resolution is 0.73mm (0.61mm) for muon energy E
< 1GeV ( E > 1GeV). The overall position resolution is 0.6460.07mm.

Figure 5.6: Hit residual distributions using neutrino beam data. The curve is asingle Gaussian t to the data with  = 0.73mm (0.61mm) for muon energy E
< 1GeV ( E > 1GeV).
5.4.4 Noise Rate

Noise hits in the SciFi detector were tracked to the following sources:
1. Contamination from cosmic rays or penetrating muons
2. Dark current of IIT
3. Fake hits made by large pixel clusters5.4. PERFORMANCE OF SCIFI DETECTOR

71

4. Electrical noise in the CCD
These hits were reproduced in our detector simulation by histograming each noiseusing cosmic ray or random triggered data. The averaged number of noise hits is
56 per one data event.

Chapter 6
Expected Number of Neutrino
Events at SK
In this chapter, we assume a null-oscillation case and calculate the estimatednumber of neutrino events at SK (NSK ) from the number of SciFi detector
events. As shown in Chapter 1,  de cit will be observed if neutrinos oscillate.
The probability of no oscillation is derived from the NSK statistical estimation in
Chapter 9.

6.1

Total Number of Protons on Target (POT)

Figure 6.1 shows the integrated number of protons injected to the target from1999 to 2001. Following an engineering run from March 1999, our physics run
started in June. The number of protons delivered to the target (POT) from
June 1999 to July 2001 totaled 5:6 2 1019. In the June 1999 run, the target
was 2cm in diameter and the horn current was 200kA. This is known as \theJune con guration". In November 1999, a 3cm diameter target and 250kA horncurrent were adopted. This is known as \the November con guration". Data
from both con gurations were used to calculate NSK .
6.1.1 POTSK and POTSciFi

The observed number of events at the near and far detectors must be normalized
to take into account beam condition and detector live time. \Bad run" periods
were due to the following reasons:7374 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK

Delivered Protons on Target (POT)
1999
2001
2000
60

Protons/Pulse (1012)

Accumulated POT (1018)

70

50
40
30
20

5.6x1019POT(July 12,2001)

10
0
6
4
2
0 Jan

Apr

Jul

Oct

Jan

Apr

Jul

Oct

Jan

Apr

Jul

Date

Figure 6.1: Top gure shows integrated number of protons on target from 1999
to 2001. Bottom one shows number of protons per pulse in same period.

 Bad beam conditions or unexpected beam downs (at least 1:0 2 1012 protons
per pulse were required) Maintenance work on the detectors during beam time Calibration runs of the SK detector during beam time DAQ failure of the beam line and/or detectors
These periods were subtracted from the delivered POT. POTSK and POTSciFi are
the integrated POTs for the far and near detectors. They are 4:79 2 1019 and4:20 2 1019 , respectively.

6.2. NEUTRINO BEAM AIMING AND TARGETING

6.2

75

Neutrino Beam Aiming and Targeting

Neutrino beam direction is monitored by the muon monitor (subsection 2.4.2).
Figure 6.2 shows aiming stability. The solid line points in the direction of the far
detector. The broken lines correspond to 61mrad. di erence from this direction.
From this we can conclude that the neutrino beam is aimed to within 61mrad.
of SK. [24, 63].
The pion monitor and the beam MC simulation are utilized to study the SK
neutrino beam pro le. Figure 6.3 shows neutrino beam ux around SK in MC(at 10 2 20 POT). Neutrino ux reduction at 1km from the axis (4mrad) is within
3%. The muon monitor guaranteed 61mrad accuracy to the beam direction.

6.3

Neutrino Event Rate at SciFi

Figure 6.4 shows the rate of MRD and LG stopping events per month. Afternormalization by POTSciFi, this rate can be considered reasonably stable andwe can conclude that a constant neutrino beam was delivered to SK during thisperiod.

NSK Calculation

6.4

The number of neutrino events at SK(NSK ) is calculated with the following
formula:
POTSK ;
NSK = NSciFi SK_ 1 RSK=Near 1 POT
(6.1)

where

SciFi

SK 1 NtSK
RSK=Near = 88Near
1 NtSciFi ;SciFi

NSciFi is the number of observed events at the SciFi detector,(6.2)

8SK is neutrino ux at SK,
8Near is the neutrino ux at the SciFi detector,
NtSK is the number of water target in the SK ducial volume (25kton),
NtSciFi is the number of water target in the SciFi ducial volume (5.9kton),SK is the SK detection eciency, andSciFi is the SciFi detection eciency.

76 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK
6.4.1 Neutrino Flux Ratio of Far and Near Detectors

We estimate 8SK and 8Near from the pion monitor measurement of neutrinos
with energy  1GeV (Subsection 2.4.1). To estimate below 1GeV, we use theMC simulation of models of pion production [49]. Error caused by the uncertaintyof the estimated neutrino ux can be reduced by taking the ratio RSK=Near :SK
RSK=Near  88Near
:

(6.3)

Figure 6.5 shows the neutrino spectrum at KEK and SK with RSK=Near the November con guration. Measured and MC estimations are in agreement for neutrinos
with energy above 1GeV. We conclude that the MC model utilized is reasonable
and RSK=Near from MC is therefore used in the calculation in the next section.
6.4.2 SciFi/SK Eciency

Figure 6.6 shows SK and SciFi detection eciency, or MRD events, of neutrinos
as functions of neutrino energy. This is de ned as (observed neutrino events)/ (generated neutrino events in the ducial volume) for both detectors and isestimated by MC simulation. Where SK is sensitive to approximately half ofNC (neutral current) events, the SciFi detector is insensitive to most (NC isestimated to be 0.5% of total reconstructed MRD events). The SciFi detector has
a low eciency for neutrinos with an energy of less than 1 GeV as SciFi requires
muons from interactions to either have tracks or register as hits in downstream
detector (Chapter 5).

6.5

Source of NSK Systematic Error

Summary tables of systematic error terms for NSK are shown in Tables 6.2, 6.3,
6.4. Each term is explained below.
6.5.1 Error Terms from FGD

This is examined using a cosmic ray data sample. We
masked part of the penetrating cosmic ray track to test that the software nds
vertices correctly. We assigned an error of 61%.
Fiducial Volume

6.5. SOURCE OF NSK SYSTEMATIC ERROR

77

We take the di erence between the data and MCof the SciFi detector rst track nding eciency as an error. Using cosmic raydata, it is examined and an error of 63% is assigned. Track connection eciency
between a SciFi track and the downstream detectors hit is counted as an error
term. The di erence between the data and MC eciencies is taken. These are61%, 61%, and 62% for TRG counters, LG, and MRD respectively. A quadratic
sum of all numbers is also taken: 63.9%.
Event Reconstruction

SciFi detector target water is in 2mm thickaluminum tanks. Each layer of the tank is 4mm of aluminum and 6cm of water.
15% of the total weight is aluminum. Assuming that neutrino cross sections
in aluminum di er 620% from the same weight of water, the SciFi event rate
therefore has a 63% error (20% 2 15%).
Aluminum Cross Section

6.5.2 Error Terms from Extrapolation to Far Detector

Di erence between the eciencies of SciFi(SciFi) andSK(SciFi) are shown in Figure 6.6. Shape di erence can contribute to an NSK error. The Eqn. 6.1 can be rewritten as follows: SK 
(6.4)
NSK = NSciFi 1 NNSciFi
MC
where NSK and NSciFi in the MC square parenthesis are
NSK = SK 1 8SK 1 NtSK 1 POTSK;(6.5)
NSciFi = SciFi 1 8SciFi 1 NtSciFi 1 POTSciFi:
0 will be:
If the neutrino ux at near site has an error of 18, NSK2
P  18  1 nSK 3
N+
NSK0 = NSciFi 1 4 SK Pi  188 i iSciFi 5(6.6)
NSciFi + i 8 i 1 ni MC
where i shows energy bin 1  6,
6X
ni = N:(6.7)
Neutrino Spectrum

NSK0 can be transformed

i=1

2
P  18  nSK 3
1
+
SK
SK 7
NSK0 = NSciFi 64 NNSciFi
1 P i 188  i nNSciFi
5
1 + i 8 i NSciFi MC
i

i

(6.8)

78 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK" X
 nSK X nSciFi #
6 
6 
18
18
i
i
0
 NSK 1 +
8
N
8
N
i SK
i SciFi
i=1
i=1
and so the error term is
!
6 
SciFi
X
18  1 nSKi 0 ni8 i NSK NSciFi MC :
i=1

(6.9)

The result for MRD events is 62:7%.
Ratio of charged current interaction and neutral current interaction(CC/NC ratio) Although SK is sensitive to approximately half of NC events,

the SciFi detector is insensitive to most, and therefore the CC/NC ratio gives
an error of event numbers. The uncertainty of the CC/NC ratio in water isapproximately 30%. We estimate the error from the CC/NC ratio by changing
it 630% inside the MC simulation. This gives an overall change of 64:1%
This term also comes from the uncertainty of the interaction. We estimated the error from the inelastic/elastic:6%
interaction ratio by changing it 620% in MC simulation. The result is +5
07:1% .
620% is given by the result of spectrum tting described in Chapter 7.
Inelastic/Elastic Interaction Ratio

Far/Near ux ratio is given by the pion monitor.
:6%
The error comes primarily from tting and is +5
07:1%
Far/Near Flux Ratio

The near detector monitors the event rate. The deadtime of the near detector and SK is corrected by POT. The error is estimatedfrom RMS of (neutrino interactions=CT ) 2 dead time, 61%.
CT Normalization

Vertices in SK events must be inside the 22.5 kt ducial
volume. The vertex is reconstructed using \TDC t". We checked the vertex
position of the selected SK events against an alternative tting method. In MC
simulation, the two results show a 62% di erence. This is taken as an SK
event error term. Additionally, the statistical error of the MC event sample isapproximately 61%.
SK Eciency

6.6. NSK FROM THE SCIFI DETECTOR

79

Table 6.1: Numbers used in NSK calculation.
Terms
NtSK (kton)
NtSciFi (ton)Jun.99 Nov.99-Jun.00 Jan.01-Jul.01
25000
25000
25000
8.624
8.624
8.624
SK
0.78100.78470.7847
SciFi0.165
0.25570.2557
19
POTSK(210 ) 0.3099
1.985
2.500
19
POTSciFi(210 ) 0.2273
1.589
2.381
NSciFi
295
4734
7288
NSK
5.25
35.10
45.55

6.6

NSK from the SciFi Detector

NSK from the SciFi Detector is calculated by Formula 6.2 and the numbers listed

in Table 6.1.

NSK = 85:9 6 1:0(stat:)0+78::85(sys:):(6.10)
Note: The ocial number given by the K2K collaboration refers to NSK from:2
the 1kton water C erenkov detector, 80:6 6 1:0(stat:)+6
05:4 (sys:).

80 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK

Table 6.2: Systematic error terms table of NSK for MRD events. (November
Con g.)
Error Source (November con g.) +Fiducial Volume
1.0% 1.0%
Event Reconstruction
3.9% 3.9%
Aluminum Cross Section
3.0% 3.0%
Neutrino Spectrum
3.0% 3.0%
Inelastic/Elastic Ratio
3.3% 4.0%
CC/NC Ratio
4.1% 4.1%
Far/Near Flux Ratio
5.6% 7.1%
CT Normalization
1.0% 1.0%
SK Eciency
3.0% 3.0%
Total
10.2% 11.4%

Table 6.3: Systematic error terms table of NSK for LG events. (November con g.)
Error Source (November con g.) +Fiducial Volume
1.0% 1.0%
Event Reconstruction
3.7% 3.7%
Aluminum Cross Section
3.0% 3.0%
Neutrino Spectrum
2.0% 2.0%
Inelastic/Elastic Ratio
1.0% 1.0%
CC/NC Ratio
3.0% 3.0%
Far/Near Flux Ratio
5.6% 7.1%
CT Normalization
1.0% 1.0%
SK Eciency
3.0% 3.0%
Total
8.5% 9.6%

6.6. NSK FROM THE SCIFI DETECTOR

81

Table 6.4: Systematic error terms table of NSK for MRD events. (June con g.)
Error Source (June con g.) +Fiducial Volume
1.0% 1.0%
Event Reconstruction
3.9% 3.9%
Aluminum Cross Section 3.0% 3.0%
Neutrino Spectrum
4.4% 4.4%
CC/NC Ratio
4.3% 4.3%
Inelastic/Elastic Ratio 5.6% 7.2%
Far/Near Flux Ratio
13.6% 9.6%
CT Normalization
1.0% 1.0%
SK Eciency
3.0% 3.0%
Total
17.0% 14.9%

profile center x (ch)82 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK

35
30
25
20
15
10
5

S

N

profile center y (ch)99Jun Nov 00JanFeb Mar May Jun 01JanFeb Mar Apr May Jun Jul

35
30

U

25
20
15
10
5

D
99Jun Nov 00JanFeb Mar May Jun 01JanFeb Mar Apr May Jun Jul

Figure 6.2: Neutrino beam direction stability measured by the muon monitor(ionization chamber). The top gure shows the horizontal pro le, the bottom
gure the vertical. The X-axis is months; The Y-axis is the readout channel. The
solid line points in the direction of the far detector. The broken lines correspondto within 61mrad. di erence from this direction.

6.6. NSK FROM THE SCIFI DETECTOR

83

neutrino flux vs radius (at super-Kamiokande)

number of neutrinos/ cm

2

x 10 3
1400

1200

1000

800

600

400

200

0

0

0.5

1

1.5

2

2.5

3

3.5

radius (km)Figure 6.3: Neutrino beam ux around SK in MC (at 10 2 20 POT). Neutrino
ux reduction 1km from axis (4mrad) is within 3%.

84 CHAPTER 6. EXPECTED NUMBER OF NEUTRINO EVENTS AT SK

EVrate

01Jly

01Jun

01Apr

01May

01Mar

01Feb

01Jan

00Jun

00Mar

00May

00Jan

01Jul

01Jun

01Apr

01May

0

01Mar

0

01Feb

20

01Jan

50

00Jun

40

00Mar

100

00May

60

00Jan

150

00Feb

80

99Nov

200

00Feb

LG Event rate at SciFi (2002.04.12)
100

99Nov

MRD Event rate at SciFi (2002.04.12)
250

EVrateFigure 6.4: SciFi MRD and LG stopping event rate per month normalized by
POTSciFi.

x 10 8KEK flux

6000

MC

Integrated
Pion monitor above 2.5GeV

5000
4000

far/near

x 10

-5

0.3
Pion monitor

0.25

MC

3000
2000
0.2

1000
0
x 10 2
4500
4000
3500
3000
2500
2000
1500
1000
500

0.5

1

1.5

2

2.5

3
0.15

SK flux

MC
Integrated
Pion monitor above 2.5GeV

0.1
Integrated
above 2.5
GeV

0.05

0

0.5

1

1.5

2

2.5

3

Eν(GeV)

0

0

0.5

1

1.5

2

2.5

3

Eν(GeV)

Figure 6.5: Neutrino spectrum (left) and RSK=Near (right) estimated by pion monitor. MC results (the Cho model) are overlaid. (November con guration)efficiency

6.6. NSK FROM THE SCIFI DETECTOR

85

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

0.5

1

1.5

2

2.5
efficiency

3

3.5

4

4.5
5
Eν (GeV)Figure 6.6: SK/SciFi detection eciency as a function of neutrino energy (GeV).

Chapter 7
Neutrino Energy Spectrum at
Near Detector
Oscillation parameters can be determined not only from SK event data but also
via spectrum analysis. Spectrum analysis requires the neutrino energy spectrumat the near detector be reconstructed.

7.1

Basic Plots from the SciFi Detector

The muon momentum, the muon production angle with respect to the beam,
the number of tracks, and the distribution of vertices are shown for MRD eventsin Figure 7.1, 7.2, 7.3, and 7.4. The corresponding distributions for LG events
are shown in Figure 7.5, 7.6, 7.7, and 7.8. For all plots, dots are data andthe histogram is MC. The hatched areas of the histograms represent charged
current quasi-elastic (CCQE) interactions in MC. The plots show good MC/dataagreement, which suggests we understand the detector and neutrino interaction
well.

7.2

Neutrino Energy Reconstruction

For the neutrino spectrum analysis, we need to reconstruct the energy of a mother from a daughter muon in our MRD sample. Considering the kinematics, we
can reconstruct E in case of a charged current quasi-elastic (CCQE) event

+N !+p87(7.1)

88CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

Figure 7.1: P distribution of MRD events.
without regard to proton momentum. The calculation is as follows:

P1 + P2 = P3 + P4
(P1 + P2 0 P3 )2 = P42(7.2)

where P1 ;P2 ;P3 and P4 are 4-vectors of the incident neutrino, the target neutron,
the produced muon, and the recoil proton. Equation 7.2 can be written in theform:(P1 0 P3 )2 + 2P2 1 (P1 0 P3 ) + P22 = P42(7.3)
The right hand side of this:

R:H:S: = P12 + P32 0 2P1 1 P3 + 2(P2 1 P1 0 P2 1 P3) + P22

(7.4)

89

7.2. NEUTRINO ENERGY RECONSTRUCTION

Figure 7.2:  distribution of MRD events.
= M2 0 2(E 1 E 0 E jP~j cos ) + 2(MnE 0 MnE ) + Mn2= 2E (0E + jP~j cos  + Mn) 0 2Mn E + 2MnE + Mn2 + M22
M
n E 0 M =2
E = Mn 0 E + P cos l :

(7.5)

Mn , E, P, M,  are the mass of nucleon, the muon energy, the muon momen-tum, the mass of muon, and the production angle of muon, respectively.
Because a QE (quasi-elastic) event is a two-body interaction, the daughter
muon and the proton are emitted on one plane. From the momentum balance,
we can anticipate the direction of the proton. When we observe the second track,
we can distinguish if the track comes from the proton or not by comparing thedirection of the expected and observed tracks. The expected proton direction is

90CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

Figure 7.3: Reconstructed MRD-event vertices distribution for X (left), Y (right).
calculated:

P~p = (0Px; 0Py ;P 0 P cos )(7.6)
For the observed second track, we can measure the projected angles XZ and Y Z
for the XZ and YZ planes respectively. The unit vectors of their direction are:
(7.7)
P~ = ( tanLXZ ; tanLY Z ; L1 )q
L = tan2 XZ + tan2 Y Z + 1(7.8)
1 can be calculated from 7.6 and 7.8:
cos 1 = 0 tan x 1 Px 0 tan x~1 Px + P 0 P cos (7.9)
L 1 jPpj
1 will be smaller for QE events than other interaction modes. We can enhance
the QE interaction with kinematics information. cos 1 distribution for all twotrack events is shown in Figure 7.9. The dots and the histogram correspond to
the data and MC, respectively. The hatched area of the histogram shows QEinteractions in MC. In the small 1 region there are more QE events than we
expected. In contrast, the large 1 region is dominated by non-QE interaction
modes.

7.3. NEUTRINO ENERGY SPECTRUM AT THE NEAR DETECTOR

91

Figure 7.4: Reconstructed event vertices distribution for Z direction (left) anddistribution of number of tracks (right). Both plots show MRD sample.
In following analysis, two-track events are divided into two groups: 1  25
and 1  30 . We call these QE samples and non-QE samples. QE samples are
60% CCQE in MC. 85.7% of events in non-QE samples come from interactions
other than CCQE. (ex. single meson production mode, see Chapter 4.)
Now we have one-track, two-track QE, and two-track non-QE samples. These
three event categories are used to measure the neutrino spectrum and the ratioof the cross section between QE and non-QE interactions.

7.3

Neutrino Energy Spectrum at the Near Detector

The energy spectrum is measured by analyzing muon momentum and angular
distributions both in the 1kt water C erenkov detector (1kt detector) and the SciFi
detector. The 1kt detector has a high eciency for muons with momentum below
1GeV/c and full 4 coverage in solid angle, yet little eciency for reconstructing
muons with momentum above 1.5GeV/c, since the muon exits the detector. The
SciFi detector has a high eciency for measuring muons above 1GeV/c. The

92CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

Figure 7.5: P distribution of LG events.
two complementary detectors are thus able to cover the relevant energy range
completely.
7.3.1 Neutrino Event Selection at the 1kt Detector

For 1kt detector analysis, the ducial volume is a 25-ton cylindrical volume thatsits lengthwise in the upstream part of the detector. The selection criteria forux normalization are as follows: Good beam selection
As is described in Subsection 6.1.1. Beam spills in good condition are
selected.
 Selection using beam time window

7.3. NEUTRINO ENERGY SPECTRUM AT THE NEAR DETECTOR

93

Figure 7.6:  distribution of LG events.
The 1kt detector is triggered when more than 40 inner PMTs have hits
within a 200nsec time window. The triggered events occurring within a
1.1sec. beam spill are recorded.
 Pre-activity cut
To avoid fake in-time events caused by re ections o the cables, events withpre-activity within 1.2sec. of the beam spill are cut.
 Total photo electron cut
To obtain the sum of all ID PMT, one thousand photoelectrons are required at ash ADC (FADC). This cut is equivalent to an energy depositof 100MeV.
 Single event selection

94CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

Figure 7.7: Reconstructed LG-event vertices distribution for X (left), Y (right).
Sometimes more than one 1kt event occurs in a 1.1sec. beam spill (multipleevents). It's dicult to reconstruct the vertex of the multiple events. We
rejected events with more than one FADC peak.

 Fiducial volume cut
The ducial volume of the 1kt detector used for spectrum analysis is shownin Figure 7.10. The ducial mass is 25ton for this de nition.
The measurement has a 5% systematic uncertainty [67]. The largest contribution is from vertex reconstruction.
For spectrum measurement, events with a one-ring  are selected from all of
events which passed the selection criteria for the ux normalization. The sample
is dominated by QE events, as was the case with one-track events in the SciFi
detector. Furthermore, to calculate its energy, the muon must be fully contained
inside the detector (an FC sample). Muons which meet these criteria are known
as \one-ring FC samples". The dominant systematic uncertainty of this spectrum
measurement is uncertainty about the energy scale of the detector. The energy
scale in the 1kt detector is understood to within +2
03 %, which has been con rmed
by energy calibration using cosmic rays.

7.3. NEUTRINO ENERGY SPECTRUM AT THE NEAR DETECTOR

95

Figure 7.8: Reconstructed LG-event vertices distribution for Z direction (left)and distribution of number of tracks (right). Both plots show LG sample.
7.3.2 2 tting

The two-dimensional distributions of the muon momentum versus the production
angle with respect to the beam of four-event categories (1kt one-ring  samples,
SciFi one-tracks, two-track QEs, and two-track non-QE samples) are used tomeasure the neutrino energy spectrum. Figure 7.11 shows the distribution of the
1kt detector data.
We use the 2 tting method to compare this data to the MC expectation.
The neutrino spectrum is divided into eight energy bins (0-0.5GeV, 0.5-0.75GeV,
0.75-1.0GeV, 1.0-1.5GeV, 1.5-2.0GeV, 2.0-2.5GeV, 2.5-3.0GeV, 3.0GeV-). During the t, the ux in each energy bin is re-weighted relative to the values in the
beam MC. The parameter Rnqe is also used to re-weight the ratio between the
QE and non-QE cross sections relative to the MC simulation. The systematic uncertainties of the near detectors are also incorporated into the tting parameter.
These are energy scales, track- nding eciencies, and the detector thresholds. In
addition, the spectrum measurement by the pion monitor is used as a constraint
on the re-weighting factors.
The value of 2 is 227.2/197 D.O.F (degrees of freedom) at the best t point.
Best t results are summarized in Table 7.1. Measured neutrino energy spectrum

96CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

SciFi 2 track cos(∆ΘP) distribution
600

µ
500

ν
P
∆Θ exp.

400

Data
MC

200

.
bs

Po

300

P

(CCQE)

>30

100
0

-1

-0.8 -0.6 -0.4 -0.2

0

o

<25

o

0.2 0.4 0.6 0.8 1cos(∆ΘP)

Figure 7.9: cos 1 distribution for all two-track MRD events. The hatched areashows MC CCQE events. The diagram shows the de nition of 1 .

at the near detector is shown in Figure 7.13. All parameters including the detector
systematics were found to lie within their expected errors, except Rnqe .
Although the t result for Rnqe is 0:93 6 0:06, the Rnqe from the 1kt detector t
alone is 40% lower (Rnqe = 0.73) than the SciFi detector t alone (Rnqe = 1.09).
This di erence can be attributed to our incomplete knowledge of neutrino-nucleon
cross sections. The error on Rnqe from the t is increased to 620% in order totake this uncertainty into account.
The muon momentum and angular distributions of the one-ring  samples
in the 1kt detector, and the muon momentum distributions of the two-track QE
and non-QE samples in the SciFi detector are overlaid with the tted MC in
Figure 7.12. The t result agrees well with the data.

7.4. EFFECT OF NEUTRINO INTERACTION MODELS ON SPECTRUM ANALYSIS97

4m

Y

X

2m

Z

Fiducial Volume

Figure 7.10: De nition of the 25-ton ducial volume at the 1kt C erenkov detector.

7.4

E ect of Neutrino Interaction Models on
Spectrum Analysis

Changing some parameters, the uncertainty from the neutrino interaction models
was studied.
In QE interaction, the axial vector mass MA (Subsection 4.2.2) was set to acentral value of 1.1 GeV=c2 and varied 610% in tests. The MA for single pion
production was set at a central value of 1.2 GeV=c2 and varied 620%. Thisa ected both the q2 dependence of the cross section and the total cross section.
For coherent pion production, two di erent models were used: one the Rein and
Sehgal model [50] and the other a model by Marteau [64]. For deep inelastic
scattering, GRV94 [65] and the corrected structure function by Bodek and Yang[66] were studied. The choice of models did not a ect the spectrum measurement
beyond the size of the tted errors except for the value of Rnqe . The systematic
error on Rnqe was increased to 620 % to take this di erence into account.

98CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

1kt DATA: Pµ vs θµ Distributionθµ (deg.)

100

integreted
90
80
70
60
50
40
30
20
10
0

200

400

600

800

1000

1200

1400 1600
Pµ (MeV/c)

Figure 7.11: Two-dimensional distributions of muon momentum vs. production
angle with respect to the beam direction in the 1kt detector.
Table 7.1: Best t results from spectrum t of near detector.

E

Fitted ux (Rnqe ) relative to MC
0.0-0.5
1.360.5
0.5-0.75
1.0260.12
0.75-1.0
1.0160.09
1.0-1.5
1 ( xed)1.5-2.0
0.9560.07
2.0-2.5
0.9660.08
2.5-3.0
1.1860.19
3.01.0760.20
Rnqe
0.9360.20

7.4. EFFECT OF NEUTRINO INTERACTION MODELS ON SPECTRUM ANALYSIS99

events / 0.25 GeV/cevents / 0.1 GeV/c

250

(a)

Data

3000

MC

Data

150

CC-QE(MC)2000∆θp < 25o

(c)

200

MC

100

1000
0
0

0.5

1

1.5

CC-QE(MC)

50
0
0

2

1

2

(b)

Data

4000

MC

3000

CC-QE(MC)events / 0.25 GeV/cevents / 10o

5000

400

∆θp > 30o

(d)

300

Data
MC

200

2000

CC-QE(MC)

100

1000
0
0

3

Pµ [GeV/c]

Pµ [GeV/c]

50

100

150

θµ [deg.]

0
0

1

2

3

Pµ [GeV/c]

Figure 7.12: (a) The muon momentum distribution of the 1kt detector one-ring samples, (b) the angular distribution of the 1kt one-ring  samples, (c) themuon momentum distribution of the SciFi QE samples, and (d) of the SciFi nonQE samples, The dots are data and the boxes are MC simulation with best t
parameters. The hatched histograms are the CCQE events estimated by the MC
simulation.

100CHAPTER 7. NEUTRINO ENERGY SPECTRUM AT NEAR DETECTOR

80000
70000
60000
50000
40000
30000
20000
10000
0

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5
5
Eν (GeV)Figure 7.13: Measured neutrino spectrum at near detector.

Chapter 8
Neutrino Events at SK
8.1

Event Selection at Super-KamiokandeThis section describes event selection at SK.
 Rough timing cut
SK events are selected using timing information from GPS (See Section 2.7).
K2K neutrino event selection occurs in a 6 500 sec. timing window atbeam time. Time di erence is de ned as follows:
1T  TSK 0 TKEK 0 TOF(8.1)
where TSK is the arrival time at SK, TKEK the start time of the beam spillat KEK, and TOF the time of ight from KEK to SK, 833sec.
 Good beam selection
As mentioned in subsection 6.1.1, beam spills in good condition are selected.
 Decay electron cut
If a muon stops in the tank, it decays into an electron and neutrinos: ! e +  + e
(8.2)
To avoid this being misidenti ed as a neutrino event, SK events with activity 30sec. prior to an event are cut. Dead time factor is less than
1/1000.
 HE (High Energy) trigger
Hits in the inner detector of more than 31PMTs (corresponds to 50100
photoelectrons) in a 200nsec. timing window are triggered.
101

102

CHAPTER 8. NEUTRINO EVENTS AT SK

 Total photo electron cut
After gain correction of PMTs, The light yield of SK events must be greaterthan 200 photoelectrons in a 300nsec. timing window (corresponding to adeposit energy of 20MeV).
 OD (outer detector) cut
SK events must have no activity in the OD to avoid either incoming oroutgoing muons. This sample is referred to as the fully-contained (FC)sample.
 30MeV cut
We calculate muon energy (or visible energy, Evis ) of the FC samples. We
require Evis to be greater than 30MeV.
 D-Wall (distance from wall) cut
Every vertex must be inside the 22.5kton ducial mass at a distance of 2mor more from the ID wall.
 GPS precise timing cut
SK events from the K2K neutrino beam must occur within an arrival time
window of 1.5 sec.
The selection eciency of CC (charged current) interactions is 93%. With the
GPS timing cut, approximately 1003 background events caused by atmospheric
neutrinos are expected per neutrino event. The procedure is illustrated in Figure 8.1. After reduction, a clear peak can be seen within 1.1  sec. of beam spill
width and 6 0.2  sec. of GPS precision. Table 8.1 shows the number of events
after each cut.

8.2

One-ring  event

Observed SK events after the above selection are classi ed by the number ofC erenkov rings in each event. Additionally, particle identi cation (PID) utilizesC erenkov ring patterns. Electrons produce electro-magnetic showers. In particular, low-energy electrons exhibit much multiple scattering and produce rather
di use C erenkov rings. In contrast to this, muons produce sharp C erenkov edges,
as shown in Figure 8.2.

8.3. OBSERVED SK EVENTS

103

Table 8.1: Reduced number of events in SK after cuts.
Cut
Number of events
6500sec. cut, Decay-e cut
107892
HE Trigger
36560
Total p.e cut
18902
Fully contained
108
Evis > 30MeV
100
00:2sec. 1T  1:3sec.
91
DW all  2m
56

8.3

Observed SK Events

From June 1999 to July 2001, 56 FC events were observed after selection. Of
these, 30 were one-ring  events. Figure 8.2 shows a typical one-ring  SK event.
Figure 8.3, 8.4, 8.5 show visible energy, muon momentum, and reconstructed
neutrino energy distribution in SK, respectively.
Reconstructed vertices distributions of SK events are shown in Figure 8.6.
The gure includes OD events near the wall. The left gure shows the topview and the right gure the side view with respect to beam direction. The
outer circle and box represent the inner detector wall. The inner circle and box
represent the ducial volume boundary. Each circle point shows a reconstructedvertex position. Its line shows the reconstructed particle momentum along theC erenkov ring. Open circles are events whose vertices fall outside the ducial
volume. Closed circles are events whose vertices lie inside the ducial volume(FC 56 events, after DW all cut).

104

CHAPTER 8. NEUTRINO EVENTS AT SK

events

FC
10

3

10

2

10
1
-500

-250

0

500
∆(T) µs

events

20

250

15
10
5
0
-5

0

5
∆(T) µs

Figure 8.1: Time di erence distribution of HE (High Energy) triggered events
after decay electron cut (solid line), total photo-electron cut (light hatch), andselected events inside ducial volume (dark hatch). The upper gure is at 6500
sec., the lower gure at 65 sec. A clear peak can be seen within 1.1 sec. ofbeam spill width and 60.2 sec. of GPS precision.

105

8.3. OBSERVED SK EVENTS

Super-Kamiokande
Run 8356 Event 11385639
100-02-19:18:35:49
Inner: 2296 hits, 10885 pE
Outer: 1 hits, 0 pE (in-time)
Trigger ID: 0x07
D wall: 512.3 cm
FC mu-like, p = 1298.2 MeV/c

Charge(pe)>26.7
23.3-26.7
20.2-23.3
17.3-20.2
14.7-17.3
12.2-14.7
10.0-12.2
8.0-10.0
6.2- 8.0
4.7- 6.2
3.3- 4.7
2.2- 3.3
1.3- 2.2
0.7- 1.3
0.2- 0.7
< 0.2

460

KEK Beam
direction marked
by diamond

368
276
184
92
0
0

500

1000

1500

2000

Times (ns)Figure 8.2: Typical neutrino event at SK. The observed charge for each PMT isindicated by the color scale. The black map shows the ID PMTs. The upper whitegure shows the OD PMTs. The lower right gure shows the timing distribution
in nsec.

106

CHAPTER 8. NEUTRINO EVENTS AT SK

Evis F.C. 22.5kt
30

20

10

0

0

1

2

3
GeV

Figure 8.3: Visible energy distribution of SK events.

Pµ F.C. 22.5kt 1-ring µ-like

20

15

10

5

0

0

1

2

3
GeV

Figure 8.4: Muon momentum distribution of SK events.

107

8.3. OBSERVED SK EVENTS

Eν F.C. 22.5kt 1-ring µ-like

20

15

10

5

0

0

1

2

3
EνGeV

Figure 8.5: Reconstructed neutrino energy distribution of SK events.

108

CHAPTER 8. NEUTRINO EVENTS AT SK

vertex positionyvertex position

beam direction

beam direction

0

0

2 GeV

2 GeV

z

x

x

Figure 8.6: Reconstructed vertex distribution of SK events. The left gure shows
the top view and the right gure shows the side view with respect to beam direction. The outer circle and box represent the inner detector wall. The inner circle
and box represents the ducial volume boundary. Each circle point shows a reconstructed vertex position. Its line shows the reconstructed particle momentum
along the C erenkov ring. Open circles are events whose vertices fall outside the
ducial volume. Closed circles are events whose vertices fall inside the ducial
volume (FC 56 events after DWall cut).

Chapter 9
Oscillation Analysis
9.1

Statistical Signi cance of No Oscillation

Comparing the observed and expected number of fully-contained (FC) events at
SK, we can estimate the probability of no oscillation statistically.
:9
With fty-six FC events observed at SK, we expect 85:9+7
08:5 events at SciFi,
assuming no oscillation (Chapter 6). In order to judge this number, the following
purely statistical Monte Carlo test is performed.
Poisson distributions are generated repeatedly, which smear the average around85.9 by a Gaussian function and attach to it an error of 68.5 (8.5 is conservative). The probability of this observation is calculated as the integration of theprobability of less than or equal to 56 events. The de nition of the probability isexpressed as follows:
R 1 Pn e  1 e ( 21 0 )2 d
P (x  n; 0 6 1) = 0 x=0 px2! 1
(9.1)
where n, 0 , and 1 are the number of observed events, the center value of thenumber of expected events, and its error, respectively. In our case, n = 56, 0 =85.9, and 1 = 8.5.
By a 106 times test, the obtained probability is 0.7% for this observation of
56 events (Figure 9.1). The null-oscillation hypothesis is excluded with a morethan 99% C.L. (con dence level).
This result is very consistent with the 1kt C erenkov detector and the null:2
oscillation hypothesis is excluded with a more than 99% C.L. for 80:6+6
05:4 events
expected.
0

109

x

0 0



110

CHAPTER 9. OSCILLATION ANALYSIS

Figure 9.1: A poisson distribution (0 = 85.9, and 1 = 8.5) smeared by Gaussian. By a 106 times test, the probability is 0.7% for the observation of 56 events.
9.1.1 KS Test

A Kolgomorov-Smirnov(KS) test of arrival times compared to a random arrival
distribution for the FC sample obtains a 43% probability, consistent with constantarrival of neutrinos.

9.2

Maximum-Likelihood Analysis

We also performed a maximum-likelihood analysis to search for the oscillation
parameters. The number of FC events and the energy spectrum shape of onering  events are used in the analysis.
The likelihood function is de ned as:
L = Lnorm 2 Lshape:(9.2)
The normalization term Lnorm (Nobs; Nexp) is the Poisson probability used to observe Nobs events when the expected number of events is Nexp(1m2 ; sin2 2;f ).
The symbol f represents the set of parameters with varied systematic errors during the t. f consists of the re-weighted neutrino spectrum measured at the neardetector (8near ), the F/N ratio, the reconstruction eciency (SK ) of SK for onering  events, the re-weighting factor for the CC-QE/non-QE ratio Rnqe , the SK9.2. MAXIMUM-LIKELIHOOD ANALYSIS

111

Table 9.1: Percentage of energy dependent systematic errors on the predicted
neutrino spectrum at SK.
E GeV 8near RSK=Near SK
0 - 0.5 37
2.6 8.7
0.5 - 0.75 12
4.3 4.3
0.75 - 1.0 6.7
4.3 4.3
1.0 - 1.5 3.1
6.5 8.9
1.5 - 2.0 4.7
1010
2.0 - 2.5 8.2
11
9.8
2.5 - 3.0 15
12
9.9
3.0 1712
9.9energy scale, and the overall normalization. The errors on the rst three items
are energy dependent and correlated. The diagonal parts of their error matrices
are summarized in Table 9.1. The f parameters are treated as tting parameterswith an additional constraint term in the likelihood.
The shape term of likelihood is written as:

Lshape =Y

N1ring
i=1

P (Ei; 1m2; sin2 2;f ):(9.3)

This is the product of the probabilities of each one-ring  event to be observed at
the bin of Ei. The reconstructed neutrino energy (Erec ) is Ei, P is the normalizedErec distribution estimated by MC, and N1ring is the number of one-ring  events.
We used the whole data sample for the normalization term, i.e. Nobs =56.
Data taken in June 1999 is discarded for the shape term. This is because inthis period the target radius and the horn current were altered and therefore theneutrino spectrum was di erent; the estimation of correlation in the near detector
spectrum and the far/near ratio RSK=Near have not been completed for the June
1999 data. The data in June 1999 correspond to 3:1 2 1018 POT (6.5% of total
POT). The number of one-ring  events from the entire running period is 30.
Excluding the June 1999 data, N10ring= 29.
The error on Rnqe is set to 20%, taking the di erence between the 1kt andSciFi detector t results (subsection 7.3.2). The error on the SK energy scale
is 3% [67]. The errors on the normalizations for the June 1999 and subsequent

112

CHAPTER 9. OSCILLATION ANALYSIS:00
period data take +1
00:85 % and 5.3%, respectively. Normalization errors do not a ect
shape part of the likelihood.
The likelihood is calculated at each point in the 1m2 and sin2 2 space tond the point where it is maximized. The best t point in the physical regionof the oscillation parameter space is found to be at (sin2 2 , 1m2 )=(1:0; 2:8 21003 eV 2). At the best- t point, the total number of predicted events is 54.2,
which agrees within statistical error with the observation of 56. The observed Erec
distribution of the one-ring  sample at SK is shown in Figure 9.2. The expecteddistribution of the best t oscillation parameters and the expected spectrum
without oscillations are also shown. Consistency between the observed and bestt Erec spectrum is checked in a KS test, from which a KS probability of 79% is
obtained. Both the best t number of events and the spectrum shape agree withobservations.
The allowed regions of oscillation parameters are drawn in Figure 9.3. The
90% C.L. contour crosses the sin2 2 = 1 axis at 1:5 and 3:9 2 1003 eV2 for 1m2 .
The allowed regions using only Lnorm or Lshape are shown in Figure 9.4. The
oscillations parameters preferred by the total ux reduction and the distortion of
the energy spectrum agree well.
The best t oscillation parameters are summarized in Table 9.2.

Table 9.2: Best t points from the maximum-likelihood analysis. The unit of
1m2 is 1003 eV2 . Results are shown for the both entire parameter space and forthe case where the parameters are constrained to the physical.
Likelihood
Constraint
sin2 2 1m2
Shape only
1.0
3.0
(allowing unphysical) 1.09
3.0
Norm + Shape
1.0
2.8(allowing unphysical) 1.03
2.8
The probability of the observations being due to a statistical uctuation instead of neutrino oscillation is estimated by computing the likelihood ratio of
the best t point to the null-oscillation case. The null-oscillation probability is

113

9.2. MAXIMUM-LIKELIHOOD ANALYSIS

20

Events

15
10
5
0
0

1

2

3

Eνrec (GeV)

45

Figure 9.2: The reconstructed E distribution. Dots are observations, the box
histogram is the expected spectrum without oscillations. The height of the boxes
are the systematic error sizes. The open histogram is the best t spectrum. The
area of both histograms is normalized to the observations.

114

2

2

∆m (eV )CHAPTER 9. OSCILLATION ANALYSIS

-2

10

-3

10

-4

10

68%
90%
99%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
sin 2θ
Figure 9.3: Allowed regions of oscillation parameters. The insides of the two solidlines are 99% C.L. The right side of dashed line and the insides of the distorted
circles of dashed line are the 90% C.L. The right side of dotted line is 68% C.L.

115

∆m2(eV2)

9.2. MAXIMUM-LIKELIHOOD ANALYSIS

10

10

10

10

-1

-2

-3

-4

0

0.2

0.4

0.6

0.8

sin22θ

Figure 9.4: Allowed regions (68% C.L.) of oscillation parameters given by normalization only (solid) and shape only (dashed). The inside of the two solid lines
and the right side of the dashed curve are the allowed regions.

1

116

CHAPTER 9. OSCILLATION ANALYSIS

calculated to be 0.7%. When only normalization (shape) information is used,
the probabilities are 1.3% (16%). With the current statistics, the null-oscillation
probability is strongly constrained by the normalization part of the likelihood.
The analysis of atmospheric neutrinos at SK (1144day exposure) suggests anallowed region of sin2 2  1 and 1m2  1003  5 2 1003eV 2 for  !  mode.
Our results are consistent with it.
Finally, study of the uncertainties of neutrino interactions uses the same procedure as spectrum measurement at the near detector. It is found that the e ectof interaction model di erence on all results is negligible due to cancellation
caused by using the same models at both the near detector and SK.

Chapter 10
Conclusion
The SciFi detector, a tracker made of scintillating ber, was developed as a main
component of the near detector for the K2K long baseline experiment. Analysis
techniques were also developed for the SciFi detector. The performance of thedetector was studied extensively using Monte Carlo simulation.
With the track information from the SciFi detector and the downstream muonchamber, 12317 neutrino events that occurred in the SciFi detector during thethree-year K2K run were reconstructed. Combining this with data from the 1kt
water C erenkov detector, we reconstructed the neutrino energy spectrum at thenear detector. Fifty-six beam neutrino events were observed at the far detector
Super-Kamiokande (SK). The number of events expected at the near detector:2(the 1kt water C erenkov detector) is 80:1+6
05:4 without oscillation. Expectationfrom the SciFi detector data is very consistent with the 1kt detector. Statisticalanalysis proves the probability of no oscillation is less than 1%.
Additionally, a maximum likelihood analysis of the neutrino energy spectrum
was performed. We de ned the likelihood function in normalization and spectrum
shape terms. All of the 56 neutrino events were used for the normalization terms.
The 29 one-ring muon samples were used for the shape terms. Assuming a twoavor oscillation case, the allowed region of 1m2 is between 1:5 2 1003 and3:9 2 1003 eV2 at 90% C.L. at sin2 2 = 1.0, which is consistent with the resultsof the Super-Kamiokande collaboration using atmospheric neutrinos.

117

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