Indications of Neutrino Oscillationin K2K Experiment

A Dissertation
By

Issei Kato

UNI VE

KY O

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ITY
RS

T

July 2004

ND

8
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97

JAPAN

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KYOTO

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Department of Physics, Graduate School of Science
Kyoto University

A Dissertation Submitted
to
The Graduate School of Science,
Kyoto Universityon
28 July 2004
inPartial Fulfillment of The Requirements
for The Degree of Doctor of Philosophy
inPhysicsbyIssei Kato
Department of Physics, Graduate School of Science, Kyoto University
Kitashirakawa-oiwake-cho, Sakyo-ku, Kyoto 606–8502, JAPANissei@scphys.kyoto-u.ac.jp

Abstract
This thesis presents the first results of analysis dedicated to neutrino oscillation with the disappearance of muon neutrino in a long baseline neutrino experiment, the K2K experiment. The
analysis is based on the data taken June 1999 to July 2001, in correspondence to total numberof protons on target of 4.79 × 1019 . In the analysis, the neutrino flux and energy spectrum measurements in the detectors at near site, the beam extrapolation from near to far site validated bya pion monitor measurements, and the observation in far site are all in use with the correlation
between energies and interaction cross-sections taken into account. The results indicate theexistence of neutrino oscillation νµ 6→ νµ : a reduction of νµ flux together with a distortion of theenergy spectrum. Fifty-six beam neutrino events are observed in Super-Kamiokande, 250 km
from the neutrino production point, with an expectation of 80.1+6.2−5.4 in the case of no neutrino
oscillation. Twenty-nine one ring µ-like events are used to reconstruct the neutrino energy spectrum, which is better matched to the expected spectrum with neutrino oscillation than without.
The probability that the observed flux at Super-Kamiokande is explained by statistical fluctuation without neutrino oscillation is less than 1%. The oscillation parameters at the best-fit
point are obtained to be (sin2 2θ, ∆m2 ) = (1.0, 2.8 × 10−3 eV2 ) for the two flavor oscillation.
The 90% C.L. region for the mass squared difference, ∆m2 , at sin2 2θ = 1 is estimated to be(1.5−3.9) × 10−3 eV2 . These results are consistent with the results of the atmospheric neutrino
observations.

Acknowledgements
This thesis could not be achieved without any supports. First of all, I would like to express myappreciation to Prof. Koichiro Nishikawa, the supervisor of this thesis and the spokesperson of
K2K experiment. He involved me with the most exciting experiments in high energy physics,
K2K and Super-Kamiokande, and gave me a great chance to study the most important partsof neutrino physics and high energy physics in the world. It has been an extraordinary time inphysics and for me. He has guided me through thick and thin to become a physicist. I would also
like to make an appreciation to Prof. Tsuyoshi Nakaya. He has also been one of advisers for thisthesis. He has been giving me a number of things interesting about high energy physics. I could
learn a lot of things from basic knowledges to technical issues. I thank Prof. Takashi Kobayashi
for his many advices all the time since the very beginning of my graduate school life. He has
encouraged me to join the HARP experiment at CERN and gave me very precious experiences
to enjoy physics abroad and to make discussions with the overseas physicists. I wish to extend
my appreciation to Prof. Y. Totsuka, Prof. K. Nakamura, Prof. Y. Suzuki, Prof. C. K. Jung,
Prof. R. J. Wilkes, and Prof. M. Sakuda. They have been managed the K2K experiment toaccomplish my research.
My study strongly depends on the hard works of many collaborators. For 1KT part, Prof.
Y. Itow gave me a lot of instruction about the detector, the analysis software, and the physics
issues. I also want to thank Dr. M. Miura, Dr. S. Mine, Dr. S. Nakayama, Ms. J. Zalipska,
Dr. A. K. Ichikawa, Dr. C. Mauger, and other 1KT group members for their supports for the
stable data taking and analysis. For the beam monitoring, I was supported by Beam Monitor
Group, especially Dr. T. Hasegawa, Dr. T. Maruyama, and Dr. J. Hill. I also thank the SciFi
and MRD Groups, particularly Prof. M. Sakuda, Dr. T. Ishii, Dr. T. Ishida, Dr. T. Inagaki,
Dr. T. Iwashita, and Ms. H. Yokoyama for their instructions on the system and the analysis.
The analysis for Super-Kamiokande data is supported by Prof. K. Kaneyuki, Dr. S. Yamada,and all of Super-Kamiokande collaborators. I express my gratitude for their great works on
the detector calibrations and data analysis. The complete works for the data taking have been
performed by Prof. T. Kobayashi, Dr. Y. Hayato, Dr. M. Yoshida, and many other people, andhere I want to thank them. I also give another thank to Dr. Y. Hayato for his supports in thesimulation works. I really thank Mr. H. Maesaka, Mr. M. Hasegawa, and Mr. S. Yamamoto forsupporting me in my research as collaborating students from Kyoto University. K2K is madepossible by the inventiveness and the diligent efforts of the KEK-PS machine and beam channelgroups. I would like to give my special thanks to them for their perfect beam operation. Thanks
to all of the kind collaborators, I could spend very precious, fruitful, and happy time in the K2K
experiment.
For the HARP experiment, which unfortunately could not be included in this thesis, I would
like to thank Prof. J. J. Gomez Cadenas who has taken care of me about the data analysis andmy stay in CERN as a analysis coordinator and also as a K2K collaborator. I also express myappreciation to Dr. A. Cervera Villanueva who has also co-worked with me on the analysis. I’mvery gratitude to Prof. J. Panman and Prof. F. Dydak, spokespersons of HARP experiment,
for their kindly inviting us to the experiment. I also want to give thanks to all the other HARP
collaborators for their kindness during my stay in HARP. I could have very precious and valuable
time and experience there.
I am deeply grateful to all the members of my laboratory in Kyoto University; To Prof.
N. Sasao for giving me the first educations on the high energy physics. To Prof. H. Sakamoto,
Dr. R. Kikuchi, Dr. T. Nomura, and Dr. M. Yokoyama for encouraging me in my research
life and giving me great advices. To Mr. Y. Honda, Mr. A. Shima, and Mr. E. Shin’ya as
colleagues at my laboratory. To Mr. M. Suehiro, Dr. Y. Takeuchi, Dr. K. Murakami, Dr.
iii

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Acknowledgements

Y. Ushiroda, Dr. H. R. Sakai, Dr. T. Inagaki, Mr. T. Fujiwara, Mr. and Ms. Nakamura, Dr.
S. Nishida, Mr. H. Yokoyama, Mr. H. Yumura, and Mr. S. Mukai for their advices and helps.
To Mr. H. Maesaka, Mr. K. Mizouchi, Ms. K. Uchida, Mr. M. Hasegawa, Mr. S. Yamamoto,
Mr. T. Sumida, Mr. S. Tsuji, Mr. T. Sasaki, Mr. K. Hayashi, Mr. T. Morita, Mr. S. Ueda,
Mr. K. Hiraide, Mr. J. Kubota, Mr. T. Shirai, Ms. N. Taniguchi, Ms. K. Takezawa, andall the other members for making my life in laboratory very interesting, exciting, and happy.
I also want to give my thanks to my friends for cheering me up all the time. Here, I would
like to make a lot of appreciations to Ms. A. Nakao and Ms. T. Kiyosawa, secretaries of ourlaboratory, for their appropriate works and kindness, and to Ms. K. Nakagawa, Ms. E. Hirai,
Ms. A. Saito, and all the members in the secretariat of the department for their taking care ofevery official/private bissinesses.
I thank the KEK and ICRR Directorates for their strong support and encouragement. I
gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. This
work has been supported by the Ministry of Education, Culture, Sports, Science and Technology,
Government of Japan and its grants for Scientific Research, by the Japan Society for Promotionof Science (JSPS), by the U.S. Department of Energy, by the Korea Research Foundation, andby the Korea Science and Engineering Foundation. Personally, I have been supported by JSPS
Research Fellowship for Young Scientists for the financial support and the promotion of thisresearch. I gratefully acknowledge Prof. Y. Totsuka for his financial support to give me a
precious opportunity to attend and give a talk at an authoritative conference of “Recontres deMoriond”. I have also been supported by a Grant-in-Aid for the 21 century COE of “Center for
Diversity and Universality in Physics”.
Finally, I would like to express the special appreciation to my parents, to my family, especiallyto my grandfather, for a number of physical, mental, and financial supports throughout my life,
and to Aya Bamba for her loving helps and encouragements, and giving me a happy life.
Issei Katoat Kyoto
5 July 2004

Ph.D. Thesis by Issei Kato, July 2004

The K2K Collaboration
E. Kearns, S. Likhoded, J. L. Stone, L. R. Sulak, C. Walter, W. Wang
Boston University
R. Helmer, P. Kitching, A. Konaka
Canada’s National Laboratory for Particle and Nuclear Physics (TRIUMF)
J. H. Choi, H. I. Jang, J. S. Jang, E. M. Jeong, J. Y. Kim, H. K. Lee, M. J. Lee, I. T. Lim,S. H. Lim, K. J. Ma, S. Y. You
Chonnam National University
M. Y. Pac
Dongshin University
I. Endo, M. Iinuma, S. Nawang, T. Takahashi
Hiroshima University
R. Ashie, S. Fukuda, Y. Fukuda, J. Hosaka, K. Ishihara, M. Ishitsuka, Y. Itow, T. Kajita,
K. Kaneyuki, Y. Kobayashi, Y. Koshio, A. Minamino, M. Miura, S. Moriyama, M. Nakahata,
S. Nakayama, T. Namba, R. Nambu, Y. Obayashi, A. Okada, K. Okumura, T. Ooyabu,
C. Saji, N. Sakurai, M. Shiozawa, Y. Suzuki, Y. Takenaga, H. Takeuchi, Y. Takeuchi, K. Taki,
T. Toshito, S. Yamada
Institute for Cosmic Ray Research, University of Tokyo
A. Butkevich, M. Khabibullin, A. Khotjantsev, Y. Kudenko, V. Matveev, S. Mikheyev,
O. Mineev, N. Yershov
Institute for Nuclear Research, Moscow
T. Chikamatsu, Y. Hayato, A. K. Ichikawa, T. Ichida, T. Ishii, H. Ishino, T. Iwashita,
J. Kameda, T. Kobayashi, S. B. Lee, T. Maruyama, K. Nakamura, K. Nakayoshi, K. Nitta,
Y. Oyama, H. S. Park, A. Sakai, M. Sakuda, K. Shiino, M. Tanaka, K. Tauchi, Y. Totsuka
Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization
S. Aoki, K. Asakura, S. Echigo, K. Fujii, T. Hara, M. Kitamura, M. Kohama, G. Kume,
Y. Moriguchi, F. Nakata, S. Nishiyama, S. Noda, M. Onchi, T. Otaki, K. Satoh, M. Sekiguchi,
Y. Suga, A. Suzuki, M. Takatsuki, K. Kakenaka, Y. Tanaka, K. Tashiro
Kobe University
S. H. Ahn, S. An, S. J. Hong, C. O. Kim, T. J. Kim, D. K. Koo, J. W. Lee, J. K. Oh,
S. H. Park, S. K. Park
Korea University
M. Hasegawa, K. Hayashi, K. Hiraide, T. Inagaki, I. Kato, J. Kubota, H. Maesaka, T. Morita,
S. Mukai, T. Nakadaira, T. Nakaya, K. Nishikawa, T. Sasaki, N. Sasao, A. Shima, S. Ueda,
S. Yamamoto, M. Yokoyama
Kyoto University
K. McConnel, K. Scholberg
Massachusetts Institute of Technology
S. Kenmochi, K. Miyano, K. Nakamura, N. Tamura
Niigata Universityv

vi

The K2K Collaboration
A. Ikeda, I. Nakano, T. Umeda, T. Yamaguchi
Okayama University
Y. Kuno, Y. Takubo, M. Yoshida
Osaka University
J. Argyriades, J. Bouchez, C. Cavata, M. Fechner, J. Mallet, F. Pierre, S. T’Jampens
Saclay (DSM-DAPNIA)
M. H. Ahn, H. C. Bhang, E. J. Jeon, K. Joo, B. Kang, B. Kim, H. I. Kim, J. H. Kim,
S. B. Kim, E. Seo, H. So, J. Yoo
Seoul National University

J. Hill, C. K. Jung, D. Kerr, K. Kobayashi, K. Martens, C. Mouger, C. McGrew, A. Sarrat,
E. Sharkey, C.Yanagisawa
SUNY at Stony Brook
M. Etoh, T. Hasegawa
Tohoku University
T. Inada, T. Kadowaki, S. Kishi, H. Yokoyama
Tokyo University of Science
E. Aliu, X. Espinal, E. Fernandez, F. Sanchez, A. Rodriguez
University of Barcelona
F. Berghaus, T. Kutter, S. Oser, J. Wendland
University of British Columbia
D. Casper, W. Gajewski, W. R. Kropp, S. Mine, M. Smy, H. W. Sobel, V. Tumakov, M. Vagins
University of California, Irvine
A. Blondel, S. Borghi, A. Cervera
University of Geneva
A. Kibayashi, J. G. Learned, S. Matsuno
University of Hawaii
U. Dore, P. F. Loverre, L. Ludovici
University of Rome “La Sapienza”
S. Miyamoto
University of Tokyo
H. G. Berns, S. B. Boyd, R. Gran, K. K. Shiraishi, A. Stachyra, R. J. Wilkes
University of Washington
J. Burguet Castell, J. J. Gomez Cadenas, A. T. Lopez, V. G. Sitjes
University of Valencia
U. Golebiewska, D. Kielczewska, J. Zalipska
Warsaw University

Ph.D. Thesis by Issei Kato, July 2004

Contents
1 Introduction
1.1 A brief history of neutrinos and their masses . . . . . . . . . . . . . . . . . . . .
1.2 Phenomenology of neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Experimental sensitivity to oscillation parameters . . . . . . . . . . . . . . . . . .
1.4 Summary of neutrino oscillation measurements . . . . . . . . . . . . . . . . . . .
1.5 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
2
5
6
8

2 The K2K Experiment
2.1 Conceptual description of the K2K experiment . . . . . . . . . . . . . . . . . . .
2.2 Design of the K2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Comparison between the measurements in ND and SK . . . . . . . . . . .
2.2.2 Neutrino interaction studies in ND . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Extrapolation of the neutrino flux and spectrum from ND to SK . . . . .
2.2.4 Neutrino beam pointing to SK . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Time synchronization between KEK-PS and SK . . . . . . . . . . . . . .
2.3 Sensitivity of the K2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 History of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9
9
11
11
12
13
13
14
15
15

3 Experimental Components and Their Performances
17
3.1 Accelerator and neutrino beam line . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Proton accelerator and primary beam transportation line . . . . . . . . . 17
3.1.2 Production target and focusing horn magnets . . . . . . . . . . . . . . . . 19
3.1.3 Decay volume and beam dump . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Primary beam monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Intensity monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Profile and position monitors . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Secondary beam monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.1 Pion monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.2 Muon monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Data acquisition system of beam line monitors . . . . . . . . . . . . . . . . . . . 32
3.5 Near neutrino detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.1 1 kt water Cherenkov detector . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.2 Trigger/veto counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.3 Scintilating fiber tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.4 Lead glass Cherenkov calorimeter . . . . . . . . . . . . . . . . . . . . . . . 48
3.5.5 Muon range detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5.6 Data acquisition system in ND . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Far neutrino detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.6.1 Detector structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
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Contents

3.7

3.6.2 Water purification system and water transparency . . . . . . . . . . . . .
3.6.3 Data acquisition system in SK . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 ATM, PMT gain, and timing calibrations . . . . . . . . . . . . . . . . . .
3.6.5 Calibration of the absolute energy scale . . . . . . . . . . . . . . . . . . .
Global positioning system for the time synchronization . . . . . . . . . . . . . . .
3.7.1 Overview of GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.2 Time synchronization between KEK and SK . . . . . . . . . . . . . . . .
3.7.3 Stability of GPS system . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53
54
55
56
57
57
57
59

4 Monte Carlo Simulations
61
4.1 Neutrino beam simulation: Beam-MC . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.1 Proton injection onto the production target . . . . . . . . . . . . . . . . . 61
4.1.2 Production of secondary particles in the target . . . . . . . . . . . . . . . 62
4.1.3 Particle tracking through the horn magnets and decay volume . . . . . . 63
4.1.4 Particle decays into neutrino . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.5 Monte Carlo prediction of neutrino properties at ND and SK . . . . . . . 66
4.2 Neutrino interaction simulation: Neut-MC . . . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Neutrino interactions in a few GeV region . . . . . . . . . . . . . . . . . . 69
4.2.2 CC quasi-elastic and NC elastic scattering . . . . . . . . . . . . . . . . . . 70
4.2.3 Single-meson production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.4 Deep inelastic scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.5 Coherent pion production . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.6 Nuclear effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.7 Summary of modifications in Neut-MC . . . . . . . . . . . . . . . . . . . . 75
4.3 Detector simulation: DetSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.1 Simulation of water Cherenkov detector, 1KT and SK . . . . . . . . . . . 76
4.3.2 Simulation of fine-grained detector . . . . . . . . . . . . . . . . . . . . . . 78
5 Analysis Strategy and Data Set for Analysis
79
5.1 Overview of the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Data set for analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1 Good beam condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.2 Good GPS status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.3 Status of data taking in ND and SK . . . . . . . . . . . . . . . . . . . . . 81
5.2.4 Total number of POT used in the analysis . . . . . . . . . . . . . . . . . . 82
5.3 Beam stability during the data taking . . . . . . . . . . . . . . . . . . . . . . . . 83
6 Far-to-near Neutrino Spectrum Ratio
87
6.1 Measurements of pion monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Extraction of pion momentum and angular distribution . . . . . . . . . . . . . . 88
6.3 Neutrino energy spectra at ND and SK and their ratio . . . . . . . . . . . . . . . 89
6.4 Systematic errors on the PIMON measurements . . . . . . . . . . . . . . . . . . . 90
6.5 Error matrix for the far-to-near ratio . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5.1 The form of error matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5.2 Error matrix below 1 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5.3 Error matrix above 1 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.5.4 Resulting error matrix of far-to-near ratio . . . . . . . . . . . . . . . . . . 93
Ph.D. Thesis by Issei Kato, July 2004

Contentsix

7 Analysis in Near Detector
95
7.1 Analysis flow in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.1.1 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.1.2 Event reconstruction in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.1.3 Fiducial volume in 1KT analysis . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Number of neutrino interactions in 1KT . . . . . . . . . . . . . . . . . . . . . . . 104
7.2.1 Outline to obtain the number of neutrino interactions in 1KT . . . . . . . 104
7.2.2 Event selection for neutrino interaction in the fiducial volume . . . . . . . 104
7.2.3 Event selection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.2.4 Background rate in the selected events . . . . . . . . . . . . . . . . . . . . 105
7.2.5 Multi-event correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.6 Correction from 7 to 9-bunch for data in May and June 2000 . . . . . . . 107
7.2.7 Total number of interactions in 1KT . . . . . . . . . . . . . . . . . . . . . 108
7.2.8 Systematic errors on the number of neutrino interaction in 1KT . . . . . 108
7.3 Expected number of neutrino events in Super-Kamiokande . . . . . . . . . . . . . 112
7.3.1 Extrapolation of the number of interactions in 1KT to SK . . . . . . . . . 112
7.3.2 Systematic errors on the expected number of neutrino events in SK . . . . 113
7.4 Measurement of neutrino spectrum in near detectors . . . . . . . . . . . . . . . . 116
7.4.1 Further event selections in 1KT . . . . . . . . . . . . . . . . . . . . . . . . 117
7.4.2 Neutrino event selection in FGD . . . . . . . . . . . . . . . . . . . . . . . 119
7.4.3 Basic distributions of FC1Rµ and SciFi-MRD samples . . . . . . . . . . . 123
7.4.4 Choice of neutrino interaction models . . . . . . . . . . . . . . . . . . . . 123
7.4.5 χ2 -fitting to derive the neutrino spectrum at ND . . . . . . . . . . . . . . 129
7.4.6 Dependence of fitting results on interaction models . . . . . . . . . . . . . 141
7.5 Summary of ND analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8 Observation in Far Detector
145
8.1 Event selection for beam originated neutrino candidates . . . . . . . . . . . . . . 145
8.2 The number of observed neutrino events in SK . . . . . . . . . . . . . . . . . . . 151
8.3 Systematic uncertainty in the event selection . . . . . . . . . . . . . . . . . . . . 155
8.4 Error matrix of selection efficiency for 1Rµ events . . . . . . . . . . . . . . . . . . 157
9 Analysis for Neutrino Oscillation
159
9.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
9.2 Likelihood function for the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 160
9.2.1 Definition of likelihood function . . . . . . . . . . . . . . . . . . . . . . . . 160
9.2.2 Input values for systematic parameters . . . . . . . . . . . . . . . . . . . . 162
9.3 Re-estimation of expected number of neutrino events and spectrum at SK in thecase of no oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.4 Best-fit point for neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.5 Null oscillation probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9.6 Constraint on the neutrino oscillation parameters . . . . . . . . . . . . . . . . . . 167
9.7 Dependence of results on neutrino interaction models . . . . . . . . . . . . . . . . 167
9.8 Comparison with the results from atmospheric neutrino observation . . . . . . . 170
10 Discussions and Prospects

171

11 Conclusion

173
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x

Contents

A Neutrino oscillation measurements before K2K experiment175
A.1 Atmospheric neutrino observations . . . . . . . . . . . . . . . . . . . . . . . . . . 175
A.2 Solar neutrino observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
A.3 Reactor neutrino experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
A.4 Accelerator neutrino experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
B Event Reconstruction in Water Cherenkov Detectors
187
B.1 Vertex finding (auto-fit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
B.1.1 Point-fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
B.1.2 Ring edge search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.1.3 TDC-fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
B.2 Ring counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
B.2.1 Ring candidate search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
B.2.2 Ring candidate test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
B.3 Particle identification (PID) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
B.3.1 Expected charge distribution . . . . . . . . . . . . . . . . . . . . . . . . . 193
B.3.2 Estimation of the particle type . . . . . . . . . . . . . . . . . . . . . . . . 194
B.4 Precise vertex finding (MS-fit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
B.5 Momentum determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
B.6 Correction to the number of rings (ring correction) . . . . . . . . . . . . . . . . . 197
B.7 Correction to the number of rings for the events in 1KT (ring correction II) . . . 197
C Systematic Uncertainties in PIMON Analysis

199

References

205

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List of Figures
1.1
1.2

The behavior of experimental sensitivity to oscillation parameters . . . . . . . . .
Allowed/excluded regions for νe ↔ νµ , νe ↔ ντ , and νµ ↔ ντ oscillation parameters

6
7

2.1
2.2

Overview of K2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The expected neutrino energy spectra with and without neutrino oscillation at
Super-Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Correlation between true and reconstructed neutrino energy in Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The profile and the energy spectra of neutrino at 250 km distance . . . . . . . .
Sensitivity to the νµ → νx oscillation in K2K experiment . . . . . . . . . . . . . .

10

Schematic view of K2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of KEK-PS and neutrino beam line and location of beam line
components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Schematic view of the two horn magnets . . . . . . . . . . . . . . . . . . . . . . .
3.4 Comparison of the neutrino energy spectrum at SK between with and withouthorn current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Schematic views of the beam dump and the muon-pit . . . . . . . . . . . . . . .
3.6 An oscilloscope image of a typical CT signal . . . . . . . . . . . . . . . . . . . . .
3.7 A schematic view of the segmented plate ionization chamber, SPIC, (left) andtypical profiles of the proton beam measured by the V39out- and TGT-SPICs(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 A schematic view of the pion monitor (PIMON) . . . . . . . . . . . . . . . . . .
3.9 Distributions of β for protons, pions, muons, and electrons/positrons after the
2nd horn magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 The principle of spherical mirror . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 The momentum distributions of muons, pions, and neutrinos at muon-pit . . . .
3.12 A schematic view inside the muon-pit . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Typical muon profiles measured by ionization chamber (ICH) and silicon pad
detector arrays (SPD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 A schematic view of near detectors . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 A schematic view of 1KT detector . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 A schematic view of 20-inch photo-multiplier tube used in 1KT and SK . . . . .
3.17 A schematic diagram of the water purification system in 1KT . . . . . . . . . . .
3.18 A schematic diagram of the data acquisition system in 1KT . . . . . . . . . . . .
3.19 Charge-to-counts and Time-to-count responses of ADC and TDC in ATM module
3.20 A schematic view of the laser calibration system in 1KT . . . . . . . . . . . . . .
3.21 A typical plot of the detected charge versus timing in a PMT, “T-Q map” . . . .
3.22 Position of the pre-calibrated PMTs in 1KT . . . . . . . . . . . . . . . . . . . . .
3.23 A schematic view of the Xenon calibration system in 1KT . . . . . . . . . . . . .

18

2.3
2.4
2.5
3.1
3.2

xi

11
12
14
15

18
20
21
22
24

24
26
27
28
29
30
31
33
34
35
36
38
40
41
42
42
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List of Figures
3.24 Typical event displays of vertical (left) and horizontal (right) cosmic-ray muons .
3.25 The comparison between data and Monte Carlo simulation in the charge scale
distribution of vertical-µ and horizontal-µ events, and the distribution of reconstructed π 0 invariant mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.26 The summary of various measurements on the energy scale in 1KT . . . . . . . .
3.27 The distribution of the total number of photoelectrons for single ring µ-like eventswith the particle fully contained in the inner detector of 1KT . . . . . . . . . . .
3.28 Stability of the energy scale in 1KT during K2K-I period . . . . . . . . . . . . .
3.29 A schematic view of SciFi detector . . . . . . . . . . . . . . . . . . . . . . . . . .
3.30 The track finding efficiency in SciFi as a function of the length of track . . . . .
3.31 Schematic views of a cell (upper) and a module (lower) of lead glass Cherenkov
calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.32 A schematic view of the muon range detector (MRD) . . . . . . . . . . . . . . . .
3.33 The tracking efficiency as a function of the track length in MRD . . . . . . . . .
3.34 A schematic diagram of the data acquisition system in ND . . . . . . . . . . . . .
3.35 A schematic view of Super-Kamiokande detector . . . . . . . . . . . . . . . . . .
3.36 Schematic diagrams of the data acquisition system for the inner (upper) and outer(lower) detectors in SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.37 The results of the measurements of absolute energy scale with several calibration
sources in SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.38 A schematic view of GPS system in the K2K experiment . . . . . . . . . . . . . .
3.39 The stability of LTC in SK site . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A schematic view of the measurements of the profile and the divergence of the
primary proton beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 The differential cross-section of positive pion production in past experiments andfitted curves of Cho-CERN model . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 The energy spectrum for each type of neutrinos at ND (left) and SK (right)
estimated by Beam-MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Contributions of each decay mode to each type of neutrino . . . . . . . . . . . .
4.5 The energy spectra of muon neutrino at ND (most left) and SK (middle), andtheir ratio (most right) predicted by several hadron production models . . . . . .
4.6 The difference of the neutrino energy spectra at SK between the configurations
in June 1999 (K2K-Ia) and since Nov. 1999 (K2K-Ib) . . . . . . . . . . . . . . .
4.7 Cross-section of each neutrino interaction channel with water as a function ofincident neutrino energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Cross-section of CC-qe interaction on a free neutron in our simulation, together
with the results of the measurements by bubble chamber experiments . . . . . .
4.9 Cross-section of CC-1π production calculated by our simulator, together with theexperimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Cross-section of the coherent pion production calculated in our simulation, as afunction of incident neutrino energy . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 The cross-section of π + -16 O interactions . . . . . . . . . . . . . . . . . . . . . . .

45

45
46
46
46
47
48
49
50
50
51
52
54
56
58
58

4.1

5.1
5.2

The number of protons delivered onto the production target in the period of from
June 1999 to July 2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability of muon yield measured by the silicon pad detector array (SPD) in
MUMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ph.D. Thesis by Issei Kato, July 2004

61
64
67
67
68
68
69
70
72
74
75
80
84

List of Figures
5.3
5.4
5.5
5.6
5.7
6.1
6.2
6.3
6.4

xiii

Stability of the center of muon profile measured by the ionization chamber (ICH)in MUMON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Profile of the vertex of neutrino events measured in MRD . . . . . . . . . . . . .
Stability of the center of neutrino beam profile measured in MRD . . . . . . . . .
Stability of the neutrino event rate measured in MRD . . . . . . . . . . . . . . .
Stability of the energy (left) and angular (right) distribution of muons scatteredby the neutrino interaction in MRD . . . . . . . . . . . . . . . . . . . . . . . . .
A typical Cherenkov light distribution observed by the PMT array in PIMON
measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cherenkov light distributions for various refractive indices measured in Nov. 1999
The fitting results of pion (pπ , θπ ) distribution in Nov. 1999 run . . . . . . . . . .
The neutrino energy spectrum at ND and SK and F/N ratio for June 1999 andNov. 1999 runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84
85
85
86
86
88
89
90
91

7.1
7.2
7.3

A typical neutrino event observed in 1KT . . . . . . . . . . . . . . . . . . . . . . 96
A flow chart of data reduction and event selection in the 1KT analysis . . . . . . 97
A typical event display (left), the distributions of PMT hit timing recorded by
ATM (right upper) and its PMTSUM signal recorded by FADC (right lower) fora multiple event in a beam spill . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4 The efficiency curve for the FADC peak search as a function of the total numberof photoelectrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.5 The number of PMTSUM peaks per spill counted using FADC data (left) andtheir peak timing distribution (right) . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.6 A flow chart of data reduction and event selection in the 1KT analysis . . . . . . 100
7.7 The distribution of PID estimator for the CC-qe events of muon and electron
neutrino in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.8 The resolution of the vertex reconstruction for fully contained (FC) and partiallycontained (PC) single-ring and multi-ring events in 1KT . . . . . . . . . . . . . . 102
7.9 The resolution of the ring direction reconstruction for fully (FC) and partially(PC) contained single-ring events in 1KT . . . . . . . . . . . . . . . . . . . . . . 102
7.10 Momentum resolution for single-ring µ-like FC events in 1KT as a function ofmuon momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.11 Definition of the fiducial volumes used in 1KT analysis . . . . . . . . . . . . . . . 103
7.12 The distributions of the reconstructed vertex in the radius direction (left) and thebeam directions (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.13 Event selection efficiency for Fiducial-C as a function of R, z, and the incident
neutrino energy Eν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.14 The distribution of FADC peak timing for each event spill observed from May
2000 to June 2000 (left) and the correction factors for 7 to 9 bunches obtained in
January to March 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.15 Long term stability of the neutrino event rate measured in 1KT . . . . . . . . . . 109
7.16 Reconstructed vertex profiles in horizontal (leftmost), vertical (middle), and longitudinal (rightmost) directions in 1KT . . . . . . . . . . . . . . . . . . . . . . . 110
7.17 Categories of neutrino events in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.18 The distribution of pomax20deg in 1KT . . . . . . . . . . . . . . . . . . . . . . . 118
7.19 Distributions of the ring counting likelihood for single and multiple ring separation(left) and the number of ring distribution (right) in 1KT . . . . . . . . . . . . . . 119
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List of Figures
7.20 The distribution of the likelihood for particle identification, for FC 1-ring sample
in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.21 The distribution of the total number of photoelectron for the FC1Rµ sample in
1KT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.22 Event display of a typical SciFi-MRD 2-track events . . . . . . . . . . . . . . . . 121
7.23 The distribution of cosine of the angular difference between the expected and theobserved second track directions, cos ∆θp , in SciFi-MRD 2-track events . . . . . . 122
7.24 The momentum (upper left) and angular (upper right) distributions of scatteredmuons in FC1Rµ sample, and the distributions of the reconstructed neutrinoenergy (lower left) and the reconstructed 4-momentum transfer squared (lower
right) for FC1Rµ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.25 The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 1-track sample, and the distributions of the reconstructed
neutrino energy (lower left) and the reconstructed 4-momentum transfer squared(lower right) for SciFi-MRD 1-track sample . . . . . . . . . . . . . . . . . . . . . 125
7.26 The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 2-track QE sample, and the distributions of the reconstructed neutrino energy (lower left) and the reconstructed 4-momentum transfer
squared (lower right) for SciFi-MRD 2-track QE sample . . . . . . . . . . . . . . 126
7.27 The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 2-track non-QE sample, and the distributions of the reconstructed neutrino energy (lower left) and the reconstructed 4-momentum transfer
squared (lower right) for SciFi-MRD 2-track non-QE sample . . . . . . . . . . . . 127
7.28 Systematic studies on the effect of the uncertainty in the energy scale on the momentum (left) and reconstructed neutrino energy (right) distributions in FC1Rµsample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.29 Systematic studies on the effect of the angular biases in the reconstruction on the
angular (left) and reconstructed 4-momentum transfer squared (right) distributions in FC1Rµ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.30 Comparison of the muon momentum and angular distributions between NEUT0000 and NEUT-1211 for FC1Rµ sample . . . . . . . . . . . . . . . . . . . . . . . 129
7.31 Two-dimensional distributions of the muon momentum versus scattering angle
for data (red plot) and for the Monte Carlo simulation for each energy bin andeach interaction mode (blue plots) . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.32 Contributions of various uncertainties to the momentum and angular distributionsin FC1Rµ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.33 Distributions of the muon momentum (upper left), the muon angle (upper right),
the reconstructed neutrino energy (lower left), and the reconstructed Q2 (lower
right) after the fitting for FC1Rµ sample . . . . . . . . . . . . . . . . . . . . . . . 138
7.34 Distributions of the muon momentum (upper left three figures), the muon angle(upper right three figures), the reconstructed neutrino energy (lower left threefigures), and the reconstructed Q2 (lower right three figures), after the fitting for
SciFi-MRD samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.35 Behavior of ∆χ2 around the best fit point as a function of each fitting parametervalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.36 Comparison of the fitting results between 1KT only fitting and FGD only fitting,
together with the 1KT+FGD merged fitting . . . . . . . . . . . . . . . . . . . . . 140
7.37 Error size of the fitting parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 141

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List of Figuresxv

7.38 Dependence of fitted Rnqe values on neutrino interaction models (top) and χ2 /d.o.f.
values at the best-fit points (bottom) . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.39 The neutrino energy spectrum measured at ND . . . . . . . . . . . . . . . . . . . 143
8.1

Event display for one of the K2K beam neutrino candidates with FC 1-ring µ-like
Cherenkov ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
8.2 A flow chart of the data reduction and the event selection in the Super-Kamiokande
analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.3 Distribution of the total number of photoelectrons in 300 nsec time window(PE300 ) for the events after high energy trigger cut . . . . . . . . . . . . . . . . . 148
8.4 Distributions of PEmax /PE300 for the events after total photoelectron cut (left)
and the goodness of vertex fitter for flasher cut for the events with the numberof hit ID-PMTs less than 500 (right) . . . . . . . . . . . . . . . . . . . . . . . . . 149
8.5 Distributions of the number of hit PMTs in the largest OD hit cluster (Nhitac)
for the events after flasher cut (left) and the number of hit OD-PMTs within
800 nsec time window (Nhita800 ) for the events after Nhitac cut (right) . . . . . 150
8.6 Distribution of the goodness of vertex fitting (TDC-fit) for the events after OD cut151
8.7 Distribution of the visible energy (Evis ) for the events after fitting goodness cut . 151
8.8 Distribution of the time difference between two UTC time stamps (∆T ) . . . . . 152
8.9 Distribution of the distance from the vertex point to the nearest wall of innertank (Dwall ) for the events after visible energy cut for the atmospheric neutrino
sample in SK (left) and for the K2K event candidates (right) . . . . . . . . . . . 152
8.10 Selection efficiency in SK as a function of incident neutrino energy, estimated by
a Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.11 Relation between the accumulated number of protons on target (POT) and thenumber of observed events in SK . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.12 Distribution of the reconstructed vertex points (circles) and momentum of eachring in an event (lines) observed in SK . . . . . . . . . . . . . . . . . . . . . . . . 154
8.13 The Momentum and angular distributions for FC1Rµ events in SK . . . . . . . . 156
8.14 The distribution of the reconstructed neutrino energy for FC1Rµ events in SK . 156
9.1

9.2
9.3
9.4
9.5

9.6

9.7
9.8

The distribution of expected numbers of neutrino events (left) and the reconstructed neutrino energy (right) in SK for many trial of random number generation without neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Contribution of various uncertainties to the reconstructed neutrino energy spectrum165
The reconstructed neutrino energy distribution for 1Rµ sample . . . . . . . . . . 166
Allowed region of oscillation parameter constrained by K2K experiment . . . . . 168
Behaviors of the log-likelihood difference −∆ ln L as a function of ∆m2 along theaxis of sin2 2θ = 1 (left) and as a function of sin2 2θ along ∆m2 = 2.8 × 10−3 eV2(right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
The 68% allowed regions of oscillation parameter space in the case of using normalization term only or spectrum shape term only (left) and their behavior of
the log-likelihood difference, −∆ ln L, as a function of ∆m2 along the axis ofsin2 2θ = 1 (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Comparison of different neutrino interaction models for the reconstructed neutrinoenergy and allowed parameter region . . . . . . . . . . . . . . . . . . . . . . . . . 169
The allowed region of oscillation parameters constrained by K2K experiment together with that constrained by the atmospheric neutrino observation in SK . . . 170
Ph.D. Thesis by Issei Kato, July 2004

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List of Figures
A.1
A.2
A.3
A.4
A.5

The zenith angle dependence of the µ-like and e-like events in Super-Kamiokande 177
Allowed regions of the oscillation parameters for νµ → νx mode . . . . . . . . . . 178
The solar neutrino spectrum predicted by the standard solar model . . . . . . . . 179
The fluxes of 8 B solar neutrino, φ(νe ) and φ(νµ,τ ), deduced from SNO experiment. 181
The allowed/excluded regions for νe ↔ νµ , νe ↔ ντ , and νµ ↔ ντ oscillation
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

B.1 A typical distribution of PE(θ) (upper figure) and its second derivative (lower
figure) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
B.2 The basic idea of the ring candidate search (left) and a typical charge of Cherenkov
rings derived by Hough transformation . . . . . . . . . . . . . . . . . . . . . . . . 190
B.3 Typical Cherenkov ring images for an electron event (left) and a muon event (right)192
B.4 A schematic view of the Cherenkov radiation from a muon . . . . . . . . . . . . . 194
B.5 The distribution of the PID estimator for fully-contained (FC) single-ring events 195
B.6 A typical event in which the ring correction II is done and the fake ring is removed
in 1KT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Ph.D. Thesis by Issei Kato, July 2004

List of Tables
1.1

The summary of current upper limit on each neutrino mass . . . . . . . . . . . .

2

2.1

The precise positions of the production target at KEK and the center of SK watertank measured by GPS survey . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The history of the K2K experiment . . . . . . . . . . . . . . . . . . . . . . . . . .

14
16

2.2
3.1
3.2

Specifications of KEK-PS components and its operations for K2K experiment . .
Specifications of 20 inch photo-multiplier tube, R3600 made by Hamamatsu Photonics Corporation, used in 1KT and SK . . . . . . . . . . . . . . . . . . . . . . .

19

62

4.4
4.5

Summary of the beam parameters for the runs in K2K-Ia and K2K-Ib . . . . . .
The fitted parameters of the Sanford-Wang formula for the positive pion production in Sanford-Wang, Cho-ANL, and Cho-CERN compilations . . . . . . . . . .
The kaon decay modes taken into account for the contribution to neutrino beamin Beam-MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The list of the correspondence of abbrebiations to models . . . . . . . . . . . . .
The list of the processes considered in our detector simulation . . . . . . . . . . .

5.1
5.2

Chart of the definition of beam spills in use . . . . . . . . . . . . . . . . . . . . .
Summary of the number of protons on target used in the analysis for each month

82
82

6.1

Summary of the operation of the PIMON measurements in June 1999 and Nov.
1999 runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Components of error matrices contributing to the error matrix of F/N ratio below
hadron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 GeV, MF/N
Error matrices of each uncertainty in the PIMON measurements . . . . . . . . .

4.1
4.2
4.3

6.2
6.3
7.1
7.2
7.3
7.4
7.5

36

63
65
77
78

87
94
94

Summary of the number of interactions measured in 1KT . . . . . . . . . . . . . 106
Summary of systematic errors on the number of interactions measured in 1KT . 109
Comparison of event rate in various fiducial volume in 1KT . . . . . . . . . . . . 111
Summary of the expected number of neutrino events in SK . . . . . . . . . . . . 114
Summary of the systematic errors on the expected number of neutrino events in
SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.6 Summary of the event selections for FC1Rµ sample in data and a Monte Carlosimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.7 The central values and the uncertainties of systematic parameters incorporated
in the χ2 function of FGD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.8 Summary of the numbers used in the constraint term of PIMON in the χ2 function136
7.9 Summary of the χ2 fitting results . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.10 Error matrix for fiφ and Rnqe obtained in the χ2 fitting . . . . . . . . . . . . . . 137
xvii

xviii

List of Tables

7.11 The central values, errors, and error matrix for fiφ and Rnqe used in the oscillation
analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.1
8.2

Summary of the number of selected events in each reduction step in SK . . . . . 146
Summary of observed events in SK . . . . . . . . . . . . . . . . . . . . . . . . . . 153

9.1

Summary of contribution of each systematic uncertainty to the expected numberof neutrino events in SK in the case of no oscillation . . . . . . . . . . . . . . . . 164
The Best-fit points for several conditions . . . . . . . . . . . . . . . . . . . . . . . 166
Effect of each systematic uncertainty on the null oscillation probability . . . . . . 167

9.2
9.3

A.1 Summary of the observed R values in atmospheric neutrino experiments . . . . . 176
A.2 Summary of the results from solar neutrino experiments and a comparison with
the SSM predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
A.3 Summary of the results from reactor neutrino experiments . . . . . . . . . . . . . 182
A.4 Summary of the results from accelerator neutrino experiments . . . . . . . . . . . 183
C.1 Summary of systematic errors of the PIMON measurements on the spectra at ND
and SK in June 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
C.2 Summary of systematic errors of the PIMON measurements on the spectra at ND
and SK in Nov. 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
C.3 Summary of systematic errors of the PIMON measurements on the far-to-near
spectrum ratio in June 1999 and Nov. 1999 . . . . . . . . . . . . . . . . . . . . . 204

Ph.D. Thesis by Issei Kato, July 2004

Chapter 1
Introduction
Neutrinos, which are identified as elementary particles constructing the universe today, arebelieved that they have been played important roles in the evolution of the Universe since thevery beginning of the Universe. However, detailed properties of neutrinos are still in mystery,
because of their weakness of interaction with materials. In particular, the existence of theirfinite masses and their flavor mixing had been unknown until quite recent, and it is one of
the hot topics in present high energy physics, elementary particle physics and astrophysics.
Neutrino oscillation is one of the phenomena which directly proves non-vanishing neutrino massand flavor mixing in the lepton sector. In this chapter, a brief history of neutrino physics
and phenomenology of neutrino oscillation are described. In addition, current knowledges fromexperiments on neutrino oscillation and the motivation of K2K experiment are also referred to.
Finally, an outline of this thesis is provided in the last section.

1.1

A brief history of neutrinos and their masses

The history of neutrino physics began with W. Pauli’s letter written in 1930 [1], in which hepostulated the existence of a new particle, neutrino, in order to explain the observed continuous
electron spectrum accompanying nuclear β-decay. In his hypothesis, neutrino was required to
be a neutral particle with spin 1/2 and a very tiny mass. Learning of Pauli’s idea, E. Fermi
proposed his theory of β-decay in 1934 [2]. The first experimental evidence of a neutrino induced interaction was brought by F. Reines and C. L. Cowan in search for the inverse β-decay,
ν e p → e+ n [3]. In 1962, muon neutrino was discovered by L. M. Lederman, M. Schwartz,
J. Steinberger et al. [4], and it was proved that muon neutrino is distinguishable from electron
neutrino. In addition to these two neutrinos, the existence of tau neutrino was inferred by
M. L. Perl et al. in 1975 [5], and finally discovered by DONUT experiment in 2000 [6].
As more and more experimental evidence became available, our understanding of weak interaction and neutrino physics was greatly developed. Along the experimental and theoreticalprogresses, S. L. Glashow [7], S. Weinberg [8], and A. Salam [9] advocated the modern weakinteraction theories which became a part of the framework of the “standard model”. This modelis capable of describing almost all the known physics of weak and electromagnetic interactions,
incorporating almost all the experimental results in energy range available at present accelerators. In the standard model of elementary particles, neutrino is assumed to be a massless lepton,
and the number of types of neutrino is believed to be three, which is strongly favored by the
results of LEP experiments [10]. These three types of neutrino are distinguished as electron
neutrino (νe ), muon neutrino (νµ ), and tau neutrino (ντ ) in the correspondence to electron (e),muon (µ), and tau (τ ) charged leptons, respectively, in the weak interaction. The masslessnessof neutrino requires that the neutrinos can be expressed only in the flavor eigenstates of weak1

2

Chapter 1. Introduction

Table 1.1: The summary of current upper limit on each neutrino mass. For upper
three items, the values are evaluated by Particle Data Group [20]. Several upper limits
are derived in the analyses of Supernova SN1987A, typically a few 10 eV. The last itemis the result from the WMAP observation.
Flavor of Neutrinos
νe
νµ
ντ
νe
X
νl

Experimental Technique3
1 H β-decay kinematics
π decay kinematics
τ decay kinematics
Supernova SN1987A
Cosmic Microwave Background

Upper Limit
3 eV (95% C.L.)
170 keV (90% C.L.)
18.2 MeV (95% C.L.)
14 ∼ 23 eV [15, 16, 17, 18]
0.69 eV (95% C.L.) [19]interaction like νe , νµ , and ντ .
Although it is assumed that all the neutrinos are massless in the standard model, theirmasses are not necessarily vanishing theoretically. If the neutrinos indeed have finite masses,
they can also be expressed in the eigenstates of masses as well as in the flavor eigenstates, andthen a number of questions are coming up: Whether are the neutrino masses of Dirac type orof Majorana type? Whether are the massive neutrinos stable or not? Does the flavor mixing
in lepton sector exist? If exists, how does it differ from what observed in quark sector? Howabout the CP violation in the lepton sector? And so on. Therefore, observation of non-zeroneutrino mass and flavor mixing in the lepton sector will make great impact on the current
particle physics and will give important keys to explore the physics beyond the standard model.
Up to now, in spite of a number of experimental efforts to measure the masses of neutrinos
directly using decay kinematics of parent particles, no experiment has found a finite mass overthe experimental errors because of their very tiny masses.
The most sensitive experiment to measure the mass of the electron neutrino was that measures the energy spectrum of electron emitted in the β-decay of tritium: 31 H → 32 He e− ν e , inwhich the end-point of spectrum shifts if neutrino is massive. Although various experiments
have been analyzed, they give only upper limits of several eV [11, 12].
The best limit on the mass of muon neutrino have been obtained from the measurement ofmuon momentum in pion decay at PSI to be 170 keV with the confidence level of 90% [13].
The current limit on the tau neutrino mass was derived by ALEPH detector in LEP experiments from the kinematics of the tau decay into three or five pions plus a tau neutrino. It set
the upper limit of mντ < 18.2 MeV/c2 with the confidence level of 95% [14]. The upper limits
on neutrino masses are summarized in Table 1.1.
In addition to these experimental limits, astronomical and cosmological limits on neutrinomass also exist. The observations of the arrival time spread of the neutrinos from Supernova
SN1987A provided upper limits on mνe around a few 10 eV [15, 16, 17, 18]. Recently, WMAP
collaboration have derived a most stringent limit on the neutrino mass to be less than 0.23 eV
for three degenerate neutrino species by observing the anisotropy cosmic microwave backgroundradiation [19]. However all the observations result in just setting upper limits up to now.

1.2

Phenomenology of neutrino oscillation

There exists another experimental method of search for finite masses of neutrinos via a phenomenon known as “neutrino oscillation”. The highlights of the phenomenology of neutrino
oscillation are described in this section. With the phenomenon of neutrino oscillation, lepPh.D. Thesis by Issei Kato, July 2004

1.2. Phenomenology of neutrino oscillation3

ton number conservation is violated in a subtle way, because the neutrino mass terms are notdiagonal when expressed in terms of flavor eigenstates.
A flavor eigenstate of neutrino, |να i (α = e, µ, τ ), can generally be expressed by superpositions of mass eigenstates, |νi i (i = 1, 2, 3):|να i =

X∗
Uαi
|νi i ,

(1.1)

iwhere Uαi is a element of a unitary matrix referred as MNS matrix, which was first proposed by
Z. Maki, M. Nakagawa, and S. Sakata [21], and is in correspondence to the CKM matrix [22] inquark sector. In the case of that lepton sector consists of 3 flavors, the matrix U is 3 × 3 withfour independent parameters: three mixing angles, θ12 , θ23 , and θ13 , and one CP phase, δ;




1
0
0
c13
0 s13 e−iδ
c12 s12 0  −s12 c12 0 
010
U =  0 c23 s23  
0 −s23 c23−s13 eiδ 0
c13
0
0 1


c12 c13s12 c13s13 e−iδs23 c13  ,(1.2)=  −s12 c23 − c12 s23 s13 eiδ c12 c23 − s12 s23 s13 eiδ
iδiδs12 s23 − c12 c23 s13 e−c12 s23 − s12 c23 s13 e
c23 c13
where cij = cos θij and sij = sin θij .
Neutrino is generated and interacts as a flavor eigenstate in weak interaction, whereas thestate of neutrino evolutes in time as mass eigenstates following the Schrödinger’s equation.
Applying Schrödinger’s equation to the νi component of να in the rest frame of that component,
we obtain|νi (τi )i = e−imi τi |νi (0)i ,(1.3)
where mi is the mass of νi , and τi is time in the νi frame. The Lorentz-invariant phase factor in
Eq. (1.3) is written in terms of the time t and position L in the laboratory frame;e−imi τi = e−i(Ei t−pi L)

.

(1.4)

Here, Ei and pi are respectively the energy and momentum of νi in the laboratory frame. In
practice, neutrino is extremely relativistic due to the tininess of the mass, so we can makefollowing replacements in Eq. (1.4);t ≈ L ,qm2
Ei = p2i + m2i ≈ pi + i
2pi

(1.5)
.

(1.6)

All of να ’s mass eigenstates have a common momentum, since να should have been producedwith a definite momentum p. Therefore, we can use this p for all νi components instead of pi .
With all the replacements above, the phase factor is approximately2e−i(mi /2p)L

.

(1.7)

From this expression and Eq. (1.1), the state of να after a neutrino produced as να has propagateda distance L has becomeX∗ −i(m2i /2E)L
|να (L)i ≈Uαie|νi (0)i ,(1.8)
i

Ph.D. Thesis by Issei Kato, July 2004

4

Chapter 1. Introduction

where E ' p is the average energy of the various mass eigenstate components of the neutrino.
Using the unitarity of matrix U to invert Eq. (1.1), and inserting the result in Eq. (1.8), we find
that
"
#
X X
2
∗ −i(mi /2E)LUαie
Uβi |νβ i .
(1.9)|να (L)i ≈βi

We see that να has turned into a superposition of all the flavors in traveling the distance L.
This phenomenon is called “neutrino oscillation”. The probability P (να → νβ ) that the flavor
β is observed after να travels the distance L is
P (να → νβ ) = |hνβ |να (L)i|2X∆m2ij L∗∗= δαβ − 4Re(UαiUβi Uαj Uβj) sin2
4E
i>j

−2

X

∗
∗
Im(UαiUβi Uαj Uβj
) sin

i>j

∆m2ij L2E,

(1.10)

where ∆m2ij ≡ m2i − m2j , the mass squared difference between νi and νj . The sign of the lastterm in Eq. (1.10) is + instead of − in the case of the expression for anti-neutrinos.
From Eq. (1.10), the conditions where neutrino oscillation can take place are found as following:
1. At least one of three ∆m2 ’s should be non-zero, or neutrino masses should not completelydegenerate.
2. At least one of three mixing angles should be non-zero, or flavor eigenstates should notcompletely identical with mass eigenstates.
When the previously omitted factors, ~ and c, are included in Eq. (1.10), and ∆m2ij , L, andE are expressed in the unit of eV2 , km, and GeV, respectively, the oscillation phase can be
written as∆m2ij LL [km]∼
Φij ≡,(1.11)= 1.2669328 · ∆m2ij [eV2 ] ·4E
E [GeV]
which gives the oscillation probability to be dependent on the neutrino flight distance L and theneutrino energy E. (We usually use the number 1.2669328 in Eq. (1.11) with a significance of
three-digit, i.e. 1.27.)
Because of the condition ∆m12 + ∆m23 + ∆m31 = 0 to be imposed, the independent parameters for neutrino oscillation are in total six in the case of three lepton generations: three
mixing angles, (θ12 , θ23 , θ13 ), one CP phase, δ, and any two out of three mass squared differences,∆m2 ’s.
We usually take two ∆m2 values as are suggested by solar and atmospheric neutrino observations;∆m212 = ∆m2sol ∼ O(10−4 −10−5 ) eV2
∆m223

=

∆m2atm−2∼ O(10

−10

−3

) eV

,
2

(1.12).

(1.13)

An overview of these observations is described in Appendix A. For an oscillation with E ∼∆m223 · L, which is the case of the K2K experiment, the subject of this thesis, the contribution
Ph.D. Thesis by Issei Kato, July 2004

1.3. Experimental sensitivity to oscillation parameters

5of ∆m212 terms are negligibly small, and the oscillation probabilities can be expressed by two
mixing angles [23];P (νµ → νµ ) ' 1 − cos4 θ13 · sin2 2θ23 · sin2 Φ23≡ 1 − sin2 2θµτ · sin2 Φ23
2

2,(1.14)2

P (νµ → νe ) ' sin θ23 · sin 2θ13 · sin Φ23≡ sin2 2θµe · sin2 Φ2322,

P (νe → νe ) ' 1 − sin 2θ13 · sin Φ23(1.15).

(1.16)

Here, sin2 2θµτ ≡ cos4 θ13 · sin2 2θ23 and sin2 2θµe ≡ sin2 θ23 · sin2 2θ13 . These expressions can be
regarded as the case of two flavor oscillations with their effective mixing angles of θµτ and θµe .
According to the mechanism of neutrino oscillation described above, if neutrino oscillation is
actually observed, it proves the both facts that neutrino has non-vanishing mass and that there
exists the flavor mixing in the lepton sector, giving the constraint on the parameter space of(sin2 2θ, ∆m2 ).

1.3

Experimental sensitivity to oscillation parameters

In this section, it is discussed that how experimental sensitivity to oscillation parameters behaves.
For simplification, the case of two flavor oscillation is considered. The oscillation probability in
two flavor case is
¶
µ
2
2
2L
.
(1.17)P (να → νβ ) = sin 2θ · sin 1.27∆m
E
In real experiment, E and L have spread due to various effects. However, there is a welldefined hL/Ei, average of L/E, about which events distribute. If a toy model in which b ≡1.27L/E has a Gaussian distribution with standard deviation of σb about the central value ofb0 , then the convolution of this Gaussian with P as given in Eq. (1.17) results in [20]hP i =

£
¡
¢
©
ª¤
1
sin2 2θ 1 − cos 2b0 ∆m2 · exp −2σb2 (∆m2 )22.

(1.18)The value of hP i is set by the experiment, for example, as an upper limit on oscillation
probability, and so on. With this fixed hP i, sin2 2θ can be found as a function of ∆m2 . A
schematic drawing of this function is shown in Fig. 1.1. The contour line in the figure, which insome cases is the boundary of allowed/excluded region by a measurement and in other cases isthe boundary of the sensitivity region of the experiment, has the following features:
1. For large ∆m2 , oscillation is fast and is completely washed out by the experimental resolution. The boundary is sin2 2θ = 2hP i.
2. The maximum sensitivity to sin2 2θ occurs at ∆m2 =if the resolution is good.

πwith the value of sin2 2θ = hP i,
2b0

3. Forplarge sin2 2θ, the nearly straight-line segment at the bottomp
is described by ∆m2 ≈
hP i
hP i
√
.
, which intercepts the axis of sin2 2θ = 1 at ∆m2 =2
1.27hL/Ei
b0 sin 2θ
The wiggles depends on the experimental features such as the size of the neutrino source, theneutrino energy distribution, detector resolution, and analysis details.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 1. Introduction

10

2

2

∆m (eV )

6

10

3

2hP i

2

10

1

π/2
1.27hL/Ei

−1

10

√

−2

∆m2 ≈

10

hP i
√
1.27hL/Ei sin2 2θ

≥ hP i
−3

10 −3
10

−2

10

−1

10

1
2
sin 2θ

Figure 1.1: The behavior of experimental sensitivity to oscillation parameters. The red contour
line shows how the experimental limit on oscillation parameters behaves when the observed oscillation probability is hP i with a certain confidence
level.

As a summary of the discussion above, aside from the details, the experimental sensitivityπ
to ∆m2 is determined by hL/Ei of the experiment to be around ∆m2 =, while that to2hL/Eisin2 2θ by hP i, which mainly depends on the statistics of the experiment in the usual case.

1.4

Summary of neutrino oscillation measurements

Up to now, a number of experiments and observations to search for neutrino oscillation havebeen performed around the world. They are categorized into four types according to theirsource of neutrinos; atmospheric neutrino observations, solar neutrino observations, reactor
neutrino experiments, and accelerator neutrino experiments. Detailed descriptions on them areprovided in Appendix A. Allowed/excluded regions from their results are also shown in Fig. 1.2
In summary, there are three possible regions remaining for neutrino oscillation parameters.
1. Atmospheric region:
2. Solar region:
3. LSND region:∆m2 = (1.5−5) × 10−3 eV2∆m2 = (3−19) × 10−5 eV2∆m2 = 0.2−1 eV2(sin2 2θ ∼ 0.88−1)(sin2 2θ ∼ 0.64−0.97)(sin2 2θ ∼ 0.003−0.04)

As mentioned in Sec. 1.2, only two ∆m2 ’s can independently exist and three ∆m2 ’s should
satisfy the relation ∆m212 + ∆m223 + ∆m231 = 0 in the framework of three neutrino scenario,
whereas these results do not. If there results are true, introduction of some new framework,
such as the fourth generation, sterile neutrinos, or other exotic reduction scenarios, may beneeded to the current Standard Model in order to explain all the experimental results. However,before that, these results should be investigated by systematically different experiments so thatthey are surely confirmed or rejected.
The KamLAND experiment [24], a reactor neutrino experiment in Japan with long baselineof about 180 km, has been performed since early in 2002 to explore small ∆m2 region down to∼ 10−5 −10−6 eV2 including the “solar region”. In the case of that neutrino oscillation exists, it
Ph.D. Thesis by Issei Kato, July 2004

1.5. Outline of this thesis

7

100

KARMEN2

CDHSWCHORUS( )*,+.-!#"$&%' NOMAD

90/
99%

/0132546467

Bu

ge

y

SuperK 90/99%  10

8:9<;>=:?,@

-3

RUS

CHO



Z

KamLAND95%

Cl 95%∆m2 [eV2]

SNO 95%10-6
SuperK 95%

10-9



νe↔ νXνµ↔ ντ
νe↔ ντ
νe↔ νµAll limits at 90% CL
unless otherwise noted

10-12
-4
10

10

-2
2

tan θ

10

0

10

2

Figure 1.2: Allowed/excluded regions for νe ↔
νµ , νe ↔ ντ , and νµ ↔ ντ oscillation parameters. Filled regions are the allowed ones derived from positive results, while blank regions
are excluded by measurements with negative results. Only the results of experiments which provided the most stringent limits are figured. The
CPT invariance is assumed and neutrinos andanti-neutrinos are both shown together. There
are three regions remaining to be allowed; atmospheric region: ∆m2 = (1.5 − 5) × 10−3 eV2(sin2 2θ ∼ 0.88 − 1), solar-LMA region: ∆m2 =(3−19) × 10−5 eV2 (sin2 2θ ∼ 0.64−0.97), LSND
retion: ∆m2 = 0.2−1 eV2 (sin2 2θ ∼ 0.003−0.04).
This figure is taken from [28].

can see the reduced number of events with the observed energy spectrum distorted∗ .
For the “LSND region”, a short baseline accelerator neutrino experiment, the MiniBooNE
experiment [26], at Fermi National Accelerator Laboratory in U.S. has been in operation since thesummer in 2002. The energy of muon neutrino beam and the length of baseline are 1−1.5 GeV
and ∼ 500 m, respectively. MiniBooNE will analyze in the νµ → νe appearance mode. The
sensitivity to ∆m2 and sin2 2θ is down to 2 × 10−2 eV2 at sin2 2θ = 1 and 10−3 for large ∆m2 ,respectively, which completely covers the whole allowed region of LSND.
In order to investigate the “atmospheric region”, the K2K experiment [27] have been done
since June 1999. The K2K experiment is the first long baseline experiment in the world, andit uses accelerator-produced muon neutrino beam with a baseline of 250 km. K2K can explore
down to ∼ 10−3 eV2 by looking at the reduction in the number of events and the distortionof energy spectrum in comparison of the measurements at near and far sites. Therefore, if theoscillation parameters really exist in the “atmospheric region”, K2K will provide a firm evidence
for the neutrino oscillation.
Understanding of the entire picture of neutrino oscillation will play an important role tounderstand the structure of mass hierarchy of elementary particles and the mixing between
generations, which bring us some crucial clues to go beyond the Standard Model.
∗

Recently, KamLAND experiment has confirmed the ν e disappearance with a set of oscillation parameters to
be around the “solar region” [25].

Ph.D. Thesis by Issei Kato, July 2004

8

1.5

Chapter 1. Introduction

Outline of this thesis

After the first two years of the K2K experiment, we analyzed the data using both flux and spectrum information for the first time, and we obtained strong indications for neutrino oscillation.
This thesis details the first analysis and results on neutrino oscillation in the K2K experimentwith the use of the data taken in the period from June 1999 to July 2001.
First, an overview of the K2K experiment are briefly described in Chapter 2. Then thedescription on experimental components and their calibrations and stabilities are detailed in
Chapter 3. Some Monte Carlo simulations are used for neutrino beam to be extrapolated fromnear to far site, and for detector response and interaction models to be compared with data, andso on. Chapter 4 explains these simulations. Following chapters from Chapter 5 to Chapter 9,
are dedicated to describe the method and the results of the analysis for neutrino oscillation indetail. Finally, the discussions and the prospects of the future analysis are given in Chapter 10,
and the conclusion of this thesis are mentioned in Chapter 11.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 2
The K2K Experiment
A long baseline neutrino oscillation experiment, “K2K experiment” (KEK-PS-E362), using
accelerator-produced neutrinos was proposed in 1995 [27]. In K2K experiment, neutrinos areproduced by 12 GeV proton synchrotron in High Energy Accelerator Research Organization(KEK) in Tsukuba, Ibaraki, travel the distance of 250 km in the earth, and are detected at
Super-Kamiokande detector located in Kamioka, Gifu (Fig. 2.1). The main purpose of the K2K
experiment is to investigate in detail the neutrino oscillation indicated by the atmospheric neutrino observations. K2K started its physics data taking in June 1999, and have been in operation
about six months per year until July 2001. In this chapter, an overview of the K2K experimentis described.

2.1

Conceptual description of the K2K experiment

K2K experiment uses an accelerator-produced neutrino beam to probe the same ∆m2 region
as that explored with atmospheric neutrinos. The neutrino beam is produced using 12 GeV
proton synchrotron (KEK-PS) accelerator in KEK. After protons hit an aluminum target, theproduced positively charged particles, mainly pions, are focused by a pair of magnetic horns[29, 30]. Then neutrinos are produced via mainly the decay of pions in flight:
π + → µ + νµ

.

(2.1)

The neutrino beam consists of 98% pure muon neutrinos, and has a mean energy of 1.3 GeV.
Generated neutrinos travel in the earth a distance of 250 km to Super-Kamiokande, the far
detector of K2K experiment. A set of detectors is located 300 m downstream the proton target
as near detectors (ND). Properties of neutrino beam, such as the flux, the energy spectrum, andthe purity of muon neutrino, before neutrinos travel the 250 km distance are measured in ND.
Simultaneously, they are measured also in Super-Kamiokande (SK). Finally, the measurements
at near and far sites are compared with each other in order for neutrino oscillations to beinvestigated, and in order for the oscillation parameters to be determined in the case of thatneutrino oscillation exists.
The main characteristics of K2K experiment are as follows: Accelerator-produced neutrinos
are controlled and monitored by measuring the primary protons, secondary pions, and muons sothat the uncertainties in the neutrino source become as small as possible. Concerning the sensitive region to the oscillation parameter ∆m2 , the neutrino beam with a mean energy of 1.3 GeV
and the neutrino flight distance of 250 km make the region of ∆m2 around 10−2 −10−3 eV2 to beaccessible, as is calculated using Eq. (1.14). This region is corresponding to the region exploredby atmospheric neutrino observations. The simultaneous measurements at near and far sites
910

Chapter 2. The K2K Experiment

Kamioka
Super−Kamiokande

250 kmTsukuba
KEK

Figure 2.1: An overview of K2K experiment. The neutrino beam is produced in KEK at
Tsukuba, Ibaraki, and detected in Super-Kamiokande at Kamioka, Gifu, after neutrinos
travel a distance of 250 km.

and their comparison enable us to cancel out most of uncertainties of systematics such as theflux and the spectrum shape of the neutrino beam, cross-section of neutrino interactions, andso on. To use Super-Kamiokande, the most massive neutrino detector in the world, is also oneof the features of K2K experiment. Since the cross-section of neutrino interactions with matteris very tiny, and since the geometrical acceptance is small due to the distance of 250 km fromthe neutrino source, the number of neutrino events in far detector becomes small. However, theuse of SK gains enough number of events to be analyzed. In K2K experiment, expected event
rate at SK in the case of no neutrino oscillation is typically 0.4 events per day.
Taking the advantages mentioned above, detailed studies on neutrino oscillation bocome
possible. The oscillation modes which can be studied in K2K experiment are as follows.
Disappearance of muon neutrino: If the neutrino oscillation indicated by the observation of
atmospheric neutrinos takes place, muon neutrinos oscillate into mainly tau neutrinos. In K2K
case, the energy of neutrino is mostly below the threshold of tau production, oscillated neutrinos
can not react via charged-current interaction. Therefore the reduction of the number of neutrino
events, “disappearance of muon neutrino”, is expected in the far detector. Furthermore, because
the flight distance of neutrino is fixed to be 250 km, the reduction factor have a dependence on
the energy of neutrino as expressed in Eq. (1.14), and hence the neutrino energy spectrum is
distorted like Fig. 2.2 in the case of that neutrino oscillation exists. The oscillation parameters(sin2 2θ, ∆m2 ) are determined by studying these two characteristics. This mode is referred toas νµ → νx mode, or νµ 6→ νµ mode, and is the main subject of K2K experiment.
Appearance of electron neutrino: If the mixing angle θ13 in Eq. (1.2) is not vanishing, anotheroscillation, νµ → νe , may also take place. In the K2K experiment, the neutrino beam consist ofalmost pure muon neutrinos and the contamination of electron neutrino is estimated to be as
small as about 1%. Therefore, when the νµ → νe oscillation exists, electron events are observed
Ph.D. Thesis by Issei Kato, July 2004

11

8

-2

7
6

6

-1

ΦνSK (×10 cm GeV )2.2. Design of the K2K experiment

5
4
3
2

Ratio (oscillated/expected)

1
0
1
0.8
0.6
0.4
0.2
0

0

1

2

3

4

5
Eν (GeV)Figure 2.2: The expected neutrino energy spectra with and without neutrino oscillation at SuperKamiokande. The Blank and hatched histograms in
the upper figure respectively shows the expected neutrino energy spectrum without and with neutrino oscillation, and their ratio is plotted in the lower figure. In these figures, a set of oscillation parameters of(sin2 2θ, ∆m2 ) = (1.0, 3 × 10−3 eV2 ) is assumed in theoscillated case.

in the far detector, while only muon events are expected to be observed in the case of no νµ → νeoscillation.
Search for sterile neutrino: Even if the disappearance of muon neutrino is observed, there still
remains a possibility that the oscillation is induced by sterile mode, νµ → νs . Sterile neutrino
is a neutrino which does not react with matter, therefore when neutrino is detected by muon
producing interaction, its oscillation signal may behave as similar to the oscillation into tau
neutrino in the energy region of K2K. However the difference of sterile neutrino from normal
ones can be seen in the neutral-current interaction; sterile neutrino does not react with mattereven via neutral-current interaction, while normal ones do. Therefore the number of neutralcurrent interaction in SK is also expected to be reduced when the oscillation occurs with νµ → νsmode, whereas the reduction is not observed in the case of νµ → ντ mode.
This thesis is devoted to the studies on the disappearance of muon neutrinos by looking at
the reduction in number of neutrino events and the distortion in energy spectrum of neutrino.

2.2

Design of the K2K experiment

In order to investigate neutrino oscillation in detail, the knowledge of the neutrino flux and theenergy spectrum at both near and far sites is indispensable. In addition, the study of crosssection of neutrino interactions is also important because its ambiguity does not completely
cancel out in comparison of measurements in the near and the far detectors, especially in oscillated case. For these purposes, a number of experimental components are equipped in the K2K
experiment. The design and the construction of the components have been done so that thefollowing key issues are satisfied. Further detailed descriptions for each components are provided
in Chapter 3.

2.2.1

Comparison between the measurements in ND and SK

Super-Kamiokande is a water-Cherenkov type detector, in which neutrino interacts with water(H2 O) and the scattered charged particles are detected as Cherenkov rings when its momentum
Ph.D. Thesis by Issei Kato, July 2004

Reconstructed Eν (GeV)

12

Chapter 2. The K2K Experiment

5

4.5
4

3.5
3

2.5
2
1.5
1
0.5
0

0

0.5

1

1.5

2

2.5

3

3.5 4 4.5 5
True Eν (GeV)

Figure 2.3: Correlation between true and reconstructed neutrino energy in Monte Carlo simulation.
Blue and red dots are charged-current quasi-elastic(CC-qe) and charged-current non-quasi-elastic (nonqe) events, respectively. Energy of neutrino can be wellreconstructed in CC-qe events, while that in non-qe
events cannot due to that additional invisible particles
are emitted in the interaction.

is greater than its Cherenkov threshold in the water. If measurements were done only in SK, theuncertainties in the neutrino interactions cross-section and the detection efficiency for neutrino
events fully come into the systematic errors on the measurements of the number of neutrino
events and energy spectrum. In order to avoid these “additional” systematic errors to be quoted,
a similar detector to SK, 1 kiloton water-Cherenkov detector (1KT), is installed in the neardetector system. The target of neutrino in 1KT is also water, and its detection technique issame as SK. Therefore, by comparing the measurements between in 1KT and in SK, the largepart of the uncertainties in the neutrino cross-section and the detection efficiency can be canceled
out.

2.2.2

Neutrino interaction studies in ND

As mentioned above, the ambiguity of cross section of neutrino interactions can be almost canceled out in comparing the measurements in ND and SK. However, when the spectral distortionis studied, the situation becomes a bit different.
To measure the energy spectrum of neutrino in SK, events which have only one muon-like
Cherenkov ring (1Rµ) are selected in order to enhance the fraction of charged-current quasielastic interactions, νµ n → µ− p, where only the muon is visible since the proton is typicallybelow Cherenkov threshold. In 1Rµ events, the energy of the parent neutrino can be calculated
by using the observed muon momentum, assuming CC-qe interactions, and neglecting Fermi
momentum of nucleons;Eνrec =

1 m2p − m2n − m2µ + 2mn Eµ·2
mn − Eµ + pµ cos θµ

,

(2.2)

where mp , mn , mµ , Eµ , pµ , and θµ are the proton mass, the neutron mass, the muon mass, themuon energy, the muon momentum, and the scattering angle of muon relative to the neutrino
beam direction, respectively. The neutrino mass is ignored.
Correlation between the true neutrino energy and the reconstructed neutrino energy calculated by Eq. (2.2) for 1Rµ sample in Monte Carlo simulation is shown in Fig. 2.3. For CC-qe
events, the reconstructed energy reproduces well the true one as plotted by blue dots. However,in K2K beam, about 50% of 1Rµ events are from interactions other than CC-qe. In these non-qe
Ph.D. Thesis by Issei Kato, July 2004

2.2. Design of the K2K experiment

13

events, particles other than muon or proton are also emitted but invisible due to that they havelower momentum than Cherenkov threshold. Therefore non-qe events have missing energy andthe energy of parent neutrino is calculated to be lower than true one, as shown in Fig. 2.3 by
red dots.
Non-qe events become a source of background in the study of spectral distortion, and hence
they should be understood well. In order to study the neutrino interactions as well as the flux
and the energy spectrum of neutrino, a fine-grained detector system (FGD) is installed in ND. It
is able to track charged particles even with lower momenta. With the use of the measurements
in FGD together with those in 1KT, the fraction of non-qe events with respect to CC-qe eventsis studied in order to feed it back into the study of spectral distortion in SK.

2.2.3

Extrapolation of the neutrino flux and spectrum from ND to SK

Since the acceptances of neutrinos entering ND and SK are different, the measurements in ND
can not be easily extrapolated only by multiplying a factor of L2ND /L2SK , where LND = 300 m
and LSK = 250 km. The difference of acceptances for ND and SK is caused by the finite size of
decay volume, the dependence of pion decay point on its energy, and the dependence of spacial
spread of neutrinos on the angular spread of pion and its Lorentz boost.
Since the neutrino energy is determined only by the kinematics of pion decay, we can know
the energy spectrum of neutrinos at any distance from the production target once the momentum
and angular distributions of pions and the geometry of decay volume are provided. However
since there has been large uncertainty in the hadron production processes in a thich target
around the energy region of K2K, the simulation of pion production is not reliable enough topredict the flux and energy spectrum of neutrino beam.
Our simulation of hadron production processes is validated by measurements of a pion monitor (PIMON), which is installed just downstream the focusing horn magnets and occasionallymeasures the energy and angular distribution of pions. The flux and the spectrum of neutrino in
SK is estimated by multiplying the far-to-near ratio (F/N ) to the measurements in ND, where
the F/N ratio is the ratio of fluxes at SK to that at ND which is estimated by a beam simulation.
By using the simulation in the form of F/N , large part of uncertainties in the hadron production
process and its measurements is canceled out.

2.2.4

Neutrino beam pointing to SK

The direction of neutrino beam must always aim the SK within a certain accuracy since theflux and the energy spectrum of neutrino at SK changes as the beam direction changes. Fig. 2.4
shows the profile and the energy spectra of neutrino at the distance of 250 km estimated by aMonte Carlo simulation. According to these figures, both the flux and spectrum do not change
more than 1% as long as the neutrino beam is pointing to SK within the accuracy of 3 mrad.
Hence the neutrino beam at SK is stable enough when the beam direction is controlled with anaccuracy of better than 1 mrad.
The direction of neutrino beam is defined by the direction of pions which is determined by
the incident position and angle of proton beam onto the target and by the alignment of the two
focusing magnets, called “horn magnets”. In order to monitor the incident position and angleof the proton beam, a number of monitors are installed along the proton beam line, and theymeasure the profile of the beam on spill by spill basis. The direction of the pion is monitored
also on spill by spill basis by measuring the profile of muons emitted from the pion decay using
muon monitor (MUMON), which is installed just downstream the beam dump. The directionof neutrino beam itself is measured by muon range detector (MRD) which is installed in ND.
Ph.D. Thesis by Issei Kato, July 2004

1.6

SK size
1mrad
3mrad

1.4

-2

ΦνSK [ ×10 cm (1020-1ΦνSK [×104 cm-2 (0.1 GeV)-1 (1020 POT)-1]

Chapter 2. The K2K Experiment

POT) ]

14

6

1.2
1

0.8
0.6

9
8
7
6
5
4
3

0.4

2

0.2

1

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 5
R [km]

on beam axis
4 mrad off
8 mrad off
12 mrad off

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 5
Eν (GeV)Figure 2.4: The profile and the energy spectra of neutrino at 250 km distance. The left figure shows
the profile of neutrino, and the right one shows energy spectra of neutrino on beam axis (black),
4 mrad off (red), 8 mrad off (green), and 12 mrad off (blue) the beam axis, which provide that boththe flux and energy spectrum does not change over 1% even if the beam direction changes within
3 mrad. These distributions are estimated by a beam Monte Carlo simulation without neutrino
oscillation.

Table 2.1: The precise positions of the production target at KEK and the center of SK watertank measured by GPS survey. The precise distance from the production target to SK and the
downward tilt of the beam are also shown in the table.
Survey point
Latitude
Production target in KEK 36◦ 090 14.953100 N.
Center of SK water tank 36◦ 250 32.586200 N.
Distance from KEK to SK
Downward tilt of the beamLongitude140◦ 040 16.330300 E.
137◦ 180 37.121400 E.
249.83 km
1◦ 040 3000

Altitude above sea
70.218 m
371.839 m

The MRD has a transverse area of 7.6 m × 7.6 m, and hence it can measures the spatial profile
over ±10 mrad range.
In order to align these components with sufficient accuracy, Global Positioning System (GPS)was utilized. The positions of the production target at KEK and the center of water tank of SK
were measured by GPS survey with a precision of within 0.01 mrad [31], which are summarizedin Table 2.1. By referring to the GPS survey points, all the experimental components were
carefully aligned with the precision of within 0.1 mrad.

2.2.5

Time synchronization between KEK-PS and SK

An expected rate of K2K signal in SK is estimated to be about 0.4 event per day in the caseof no oscillation, while the event rate of fully-contained atmospheric neutrino events, a main
background events in K2K, is about 8 events/day. Therefore, K2K observation in SK might bedominated by background events if no constraint is imposed. The most effective way to identify
Ph.D. Thesis by Issei Kato, July 2004

2.4. History of the experiment

νµ

1

νx

15

90%C.L.

CHARM
CDHS

-1

(99 %)

102∆m (eV )Kamiokande
sub-GeV + multi-GeV

2

K2K
-2

10

MINOS
-3

10
Super-Kamiokande
700 days, F.C.+ P.C. with

µ

-4

10

0

0.2

0.4

0.6

0.8

2

sin (2θ)

1

Figure 2.5: Sensitivity to the νµ → νx oscillationin K2K experiment. The vertical and the horizontal axes are ∆m2 [eV2 ] and sin2 2θ, respectively.
The red lines show the sensitivity contours of
K2K experiment with the confidence levels of 90%(solid line) and 99% (dotted line). The results ofKamiokande, Super-Kamiokande, CHARM, andCDHS are also shown in this figure. The hatchedresults are positive ones, therefore show the allowed regions. These contours are of the confidence level of 90%. In addition, the sensitivity
region of the future long baseline neutrino experiment in U.S., MINOS, is also drawn with light
blue line.

the neutrino events associated to the K2K beam is to make a time synchronization between
KEK-PS beam and SK events.
For this purpose, GPS receivers are set at each site. By receiving the GPS signal at bothsites simultaneously, time synchronization with the precision of about 100 nsec is realized. The
proton beam is provided every 2.2 sec by fast extraction mode with the extracting duration of
1.1 µsec. A time window of 1.5 µsec is set to select the beam associated neutrino events in the
SK analysis. In this way, the background rate is reduced by the order of 10−5 .

2.3

Sensitivity of the K2K experiment

The K2K experiment is designed to be sensitive to the parameter region constrained by theatmospheric observations. Fig. 2.5 shows the region of sensitivity to the νµ → νx oscillation inK2K experiment, together with the results from several experiments. As shown in this figure,K2K has the sensitivity to the region of ∆m2 & 10−3 eV2 on the axis of sin2 2θ = 1.0.

2.4

History of the experiment

A brief history of the K2K experiment is summarized in Table 2.2. Civil construction anddetector installation had been done by the end of 1998, test operations of the beam extraction and
Ph.D. Thesis by Issei Kato, July 2004

16

Chapter 2. The K2K Experiment

Table 2.2: The history of the K2K experiment. The runs from June 1999 to July 2001
are referred to as K2K-I, and runs after Dec. 2002 are referred to as K2K-II.
Year
1995

Month

1996
1998
1999
1999

2000
2001
2001
2002

Feb.
Mar.
June
Oct.–Nov.
Jan.–June
Jan.–July
Nov.
Mar.–Oct.
Dec.

Events
Proposal of K2K [27] was approved by KEK.
Components design was started.
Civil construction was started.
Detector components were installed.
Civil construction had been finished.
Proton beam with the fast-extraction mode was succeeded.
Horn magnets has been operated.
Physics run was started. (K2K-I)
RUN-I with 200 kA horn current (K2K-Ia)
RUN-IIa with 250 kA horn current (K2K-Ib, until July 2001)
RUN-IIb with 250 kA horm current
RUN-III with 250 kA horn current
SK accident.
SK reconstruction.
Data taking was restarted. (K2K-II)

horn magnets had been done early in 1999. Stable data taking for physics has been performed
since June 1999. From June 1999 to July 2001 (K2K-I), we had four periods of data taking;
RUN-I, IIa, IIb, and III as shown in Table 2.2. During RUN-I, horn magnets was operated with200 kA current for safety reason, while the target current is 250 kA and they were operated with
250 kA current after RUN-II. For convenience, we refer to the run in June 1999 as “K2K-Ia”,
and the rest of runs in K2K-I as “K2K-Ib”.
In this thesis, whole the data of K2K-I are analyzed, which is corresponding to the accumulated number of protons on target (POT) for physics analysis of 4.793 × 1019 ; 0.310 × 1019 POT
in K2K-Ia and 4.483 × 1019 POT in K2K-Ib.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 3
Experimental Components and Their
Performances
K2K experiment consists of the accelerator, neutrino beam line, near detector system, SuperKamiokande, and time synchronization system. The schematic view of arrangement of thesecomponents are shown in Fig. 3.1. In this chapter, the description on each component and its
performance is provided in the order from the upstream of the beam line. First, the descriptions
on the accelerator and the neutrino beam line are given in Sec. 3.1. Second, the monitors forprimary proton beam and secondary pions and muons are explained in Sec. 3.2 and Sec. 3.3,
respectively. Then, the explanations for the near detector system are provided in Sec. 3.5 and thedescription on the far detector is given in Sec. 3.6. Finally, the method for time synchronization
between KEK and SK is described in Sec. 3.7.

3.1

Accelerator and neutrino beam line

The accelerator and the neutrino beam line are consist of KEK 12 GeV proton synchrotron,
primary proton transportation line to the production target, the production target, a set of
focusing horn magnets for secondary particles, decay volume, and beam dump. They are briefly
explained in this section.

3.1.1

Proton accelerator and primary beam transportation line

In order to produce neutrino beam, a 12 GeV proton synchrotron accelerator in KEK (KEK-PS)
is used. A schematic view of KEK-PS is shown in Fig. 3.2 and its specifications are summarizedin Table 3.1.
First, protons are accelerated step-by-step by 750 keV pre-injector, 40 MeV LINAC, and
500 MeV rapid-cycle booster synchrotron, and then they are injected into the main ring of
KEK-PS. In the main ring, more than 7 × 1012 protons are accelerated up to the kinetic energyof 12 GeV in one cycle. The number of bunches in the main ring is 9, which is corresponding
to the harmonic number of the main ring. After acceleration finished, all the 9 bunches are
extracted just in single turn to the EP1 neutrino beam line by kicker magnet system at EP1-A
section (shown in Fig. 3.2). The duration of an extraction, or “a spill”, is 1.1 µsec. This is called“fast extraction mode”.
The extracted beam is collimated and led to EP1 neutrino beam line. Typical beam intensity
just after the extraction is about 6×1012 protons in a spill. The EP1 neutrino beam line consistsof 61 quadrupole and 44 dipole magnets to leads proton beam to the production target through17

18

Chapter 3. Experimental Components and Their PerformancesGPS

12GeV−PS
Beam Dump

PIMON

SciFi

Decay Pipe
Target/Horn

p

π

µ

π

µ

1KT

MRD
LG

SK

ν
ν

MUMON

300 m

Near Detectors

250 kmFigure 3.1: Schematic view of K2K experiment.

80m





































































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 
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12GeV-PS

 
 




Target Station

Figure 3.2: A schematic view of KEK-PS and neutrino beam line and the location of beam line components. The EP1 neutrino beam line leads protons through a distance of 400 m from EP1-A extraction
point to the target station via the straight and arc sections. The characters “C” and “S” in the figure
show the location where CT and SPIC are installed, respectively. The lower-left inset is a magnified viewof the target area.

Ph.D. Thesis by Issei Kato, July 2004

3.1. Accelerator and neutrino beam line

19

Table 3.1: Specifications of KEK-PS components and its operations for K2K
experiment.
Components/Parameters
Accelerator components:
Pre-injector
LINAC
BOOSTER
Main Ring
Accelerator operations:Operation mode for K2K
Typical intensity in main ring
Typical intensity at EP1
Typical intensity at target
Number of bunches
Bunch repetition
Spill duration
Repetition cycle

Values
750 keV (Cockroft-Walton acc.)
40 MeV
500 MeV
12 GeV (in kinetic energy)
fast extraction (single turn) to EP1-A
7 × 1012 protons/spill
6 × 1012 protons/spill
5 × 1012 protons/spill
9 bunches
about 120 nsec
1.1 µsec
2.2 seca distance of 400 m. As shown in Fig. 3.2, the beam extracted toward the north direction isbent by about 90 degrees toward the direction of SK at the arc section.
The target station is built after the arc section. The proton beam is finally focused onto the
production target at target station. Just before the target, a steering magnet is placed, which
directs the beam to SK by about 1 degree downward from the horizontal level. Then protons
are going to hit the target and produce a number of secondaries.
The efficiency to transport the proton beam from EP1-A to the target is about 85%, andthe beam intensity just before the target is about 5 × 1012 protons in a spill.
In order to monitor the intensity, 13 current transformers (CTs) are installed in the neutrino
beam line. Furthermore, 28 segmented plate ionization chambers (SPICs) are also placed in
the beam line to monitor the position and profile of the beam. These properties of the beam
are monitored on spill-by-spill basis. More detailed descriptions for the beam monitoring areprovided in Sec. 3.2.

3.1.2

Production target and focusing horn magnets

Secondary particles, mainly pions, are generated by hadron interactions of 12 GeV protons insidea production target. Two toroidal magnetic horns are used in order to focus pions toward SK.
A schematic view of the horn magnets is shown in Fig. 3.3. The dimensions of the 1st horn are
0.70 m in diameter and 2.37 m in length, while those of the 2nd horn are 1.65 m in diameter and2.76 m in length. Both horns is cylindrically symmetric in shape. The production target, a rod ofa length of 66 cm and a diameter of 3 cm which is made of aluminum alloy 6061-T, is embedded
inside the 1st horn. This length of aluminum is corresponding to 1.67 interaction length. The
target also plays a role of inner conductor of the 1st horn, making a strong magnetic field inside
the horn to achieve high focusing efficiency. The 2nd horn is located 10.5 m downstream of the
1st horn, and play a role of a reflector which re-focuses over-bent low energy pions as well as
under-bent high energy pions. Except for the target part, central region of both horns is madeto be vacant in order to avoid a loss of pion yield due to its secondary interaction with horn
materials. The horn conductors are also made to be as thin as the requirement for strength is
Ph.D. Thesis by Issei Kato, July 2004

20

Chapter 3. Experimental Components and Their Performances
2nd Magnetic Horn
1st Magnetic Horn
12 GeV
Protonsπ+

B
I = 250 kA (2 msec)
Production Target

B
I = 250 kA (2 msec)

10.5 m02 (m)Figure 3.3: Schematic view of the two horn mangeds. Electrical current of 250 kA is supplied
to the both horns, making toroidal magnetic field inside the horns. The production target,
an aluminum rod of 66 cm in length and 3 cm in diameter, is embedded inside the 1st horn
magnet, which also plays a role of inner conductor of horn. The 2nd horn is located 10.5 m
downstream of the 1st horn.

permitted.
Pulsed coaxial electrical current of a duration of 2 msec and an amplitude of 250 kA is
supplied to the inner and outer conductors of the horns. This current makes toroidal magnetic
field between the inner and outer conductors of the horn. The operation in pulsed mode is needed
to avoid the conductors melted down. The repetition cycle is 2.2 sec which is synchronized withthe beam cycle. The peaking time of the current is adjusted to match with the beam timing.
When the current of Ihorn [kA] is supplied, the magnetic field B [kG] at the point of radiusof r [cm] is

Ihorn


r (r 5 R, inside the target)


5R2
,
(3.1)
B=


I
horn


(r > R, outside the target)
5r
where R is the radius of the target rod, i.e. 1.5 cm. The maximum magnetic field of 33 kG
is achieved at the surface of rod when Ihorn = 250 kA. The direction of the magnetic field isclockwise seen from the upstream of the beam. Therefore, the positively charged particles arefocused to the forward direction, while the negatively charged ones are swept out. In this way,
π + ’s are selectively collected toward the decay volume. Typical transverse momentum focusedby the horn magnets is about 100 MeV/c per m, and pions after the horn magnets distribute
mainly around the momentum of 2−3 GeV/c, which corresponds to about 1.0−1.5 GeV in
the energy of neutrino decayed in the focused direction. In addition to the focusing effect ofhorns, since protons twine around the magnetic field inside the target, the targetting efficiency
improves. Monte Carlo simulation shows that almost all protons interact inside the target bysome interactions including elastic one. The horn magnets with 250 kA current gain 22 times
more flux of neutrinos above 0.5 GeV than that without horn current, as shown in Fig. 3.4.
Various measurements had been performed to understand the characteristics of the horn
magnets, such as measurements on magnetic field, tests for the performance of the coolingsystem, and so on. For example, the magnetic field inside the prototype of the 1st horn wasmeasured using pickup coils, resulting that the radial distribution of the field is in agreementwith the designed one and the azimuthal symmetry had been confirmed within a measurement
error of 15%. Including the descriptions on these measurements, more detailed descriptions onhorn magnets can be found in [29, 30, 32, 33].
Ph.D. Thesis by Issei Kato, July 2004

Arbitrary unit of neutrino flux

3.2. Primary beam monitors

21

with
HORN current

without
HORN current
0

1

2

3

4

5

Figure 3.4: Comparison of the neutrino energy spectrum at
SK between with and without horn current. The blank histogram is in the case of with horn current of 250 kA, andhatched one is in the case of without horn current, which showthat the horn magnet system gains 22 times more neutrino flux
than that without horn current. These histograms are estimated by Monte Carlo simulation.

Neutrino energy (GeV)

The values of the electrical current supplied to the horn magnets are read out by current
transformers put in power feeders and recorded by Flash-ADC on spill by spill basis. These data
are used to select the beam spills with good condition, which is described in Chapter 5.
Only at the beginning of the experiment, the experiment had been done with a different
configuration in the horn system. During the term of K2K-Ia, the diameter of the target was
2 cm and the peak current of horns was 200 kA. Due to mechanical problems, the target of 3 cm
in diameter has been used since Oct. 1999 (during the K2K-Ib period), and the horns have been
operated with the peak current of 250 kA, as mentioned above.

3.1.3

Decay volume and beam dump

The positive pions focused by the horn magnets are sent to a 200 m long decay volume, whichstarts from 19 m downstream of the production target. The decay volume is cylindrical pipein shape, and is separated into three sections with respect to their different dimensions. The
diameters of the pipe are 1.5 m, 2 m, and 3 m in the first 10 m, the following 90m, and theremaining 100 m sections, respectively. The decay volume is filled with helium gas of 1 atm toavoid a possible loss of pions by absorption and to avoid incontrollable pion production in thegas.
Inside the decay volume, π + decays into µ+ and νµ :
π + → µ+ νµ

.

(3.2)

Since pions are strongly boosted in the laboratory frame, neutrinos are emitted toward SK
within the decay angle of several 10 mrad.
After the decay volume, the beam dump is located to stop all the particles except for neutrinos. Schematic views of the beam dump are given in Fig. 3.5. It is consist of 3.5 m thickiron shield, 2 m thick concrete, and about 60 m long soil. There is a pit just downstream of theconcrete shield, and two detectors (MUMON) are installed there to measure the profile and intensity of muons penetrating through the shields (see Chapter 3.3.2). All the particle other thanneutrino are absorbed by iron, concrete, and soil shields, and only neutrinos can pass throughinto ND and SK.
Ph.D. Thesis by Issei Kato, July 2004

22

Chapter 3. Experimental Components and Their Performancesµ monitor (SSD)µ monitor (ICH)

11m

Fe

6m

8m

decay pipe
(He filled)

hole
earth

top view
3.5m
stairway
6.5m

5m
concrete7mside view

12m
stairway
5m
2m
concrete

5.5m

4m

Ph.D. Thesis by Issei Kato, July 2004Fe

decay pipe
(He filled)

Figure 3.5: Schematic viewsof the beam dump and themuon-pit. The upper and thelower figures shows the top
and the side views, respectively. The beam dump consists of 3 thick iron shield,
2 m thick concrete shield,
and about 60 m long soil.
Just after the iron and concrete shield, two types ofmuon profile monitor (MUMON) installed at 12 m deep
underground, called “muonpit”. In this figure, the beam
is passing from right to left.

3.2. Primary beam monitors

3.2

23

Primary beam monitors

In order to control and monitor the primary proton beam, two types of monitoring system,
current transformers (CTs) and segmented plate ionization chambers (SPICs), are installed ata number of points along the neutrino beam line, as shown in Fig. 3.2. CTs monitor the beam
intensity, while the SPICs monitor the profile and the position of the beam. The monitoringof both devices is done on spill-by-spill basis. In this section, brief descriptions on them areseparately given.

3.2.1

Intensity monitors

In order to monitor the intensity of the proton beam, integrated current transformers (CTs) areused, which pick up the induced current made by protons passing through the coil. The innerdiameter of CT is about 12 cm, as same size as that of the beam pipe, hence it is large enoughto contain the whole beam inside the CT.
Thirteen CTs are installed along the beam line. The locations of CTs are indicated by thecharacters “C” in Fig. 3.2. Most of the CTs are mainly used to measure the intensity at each CT
point and monitor the beam transportation efficiency. One of the CTs, called as “TGT-CT”,
placed in front of the production target is used to estimate the total number of protons delivered
onto the target.
Fig. 3.6 shows an oscilloscope image of a typical signal from CT, in which clear 9 bunches ofthe beam can be seen. The signals of CTs are led to the control room outside the radiation areaby several 10 m to 100 m long co-axial cables. Then, they are read out by charge integrating
ADCs with a gate width of 1.3 µsec which contains the whole beam spill.
The CTs had been calibrated by pulsed current source. Due to the noise induced in 100 mlong co-axial cables, the calibration has a systematic uncertainty of ±10%.

3.2.2

Profile and position monitors

Profiles and position of the proton beam are measured by segmented plate ionization chambers(SPICs). Twenty-eight SPICs are installed along the beam line, indicated as “S” in Fig. 3.2. A
schematic view of the SPIC is shown in Fig. 3.7 (left). SPIC is an ionization chamber consistof three copper sheet. The sheets with the thickness of 28 µm are used since the proton beam
directly hits them. These sheets are arranged with the gaps of 1 cm between each other. The
gap is filled with helium gas. The central plane is an anode one to which the negative highvoltage of typically −1000 V is supplied. The others are cathode planes for the horizontal andvertical readout.
Twenty-six SPICs out of 28 have the same structure, while two SPICs, one located just in
front of the target (TGT-SPIC) and another one located in front of the decay volume (P/PISPIC), have different structures from others. The 26 SPICs have a sensitive area of 16 cm ×
16 cm square, and have 32 channels with 5 mm pitch in both horizontal and vertical readout.
The TGT-SPIC is more fine-segmented to measure the profile of well-focused beam. Its pitchand sensitive area is 1.27 mm and 4.1 cm × 4.1 cm, respectively. The remaining SPIC, P/PISPIC, is to monitor the targeting and focusing by measuring the profile of scattered pions andprotons after the target and the horn magnets. It covers a large area of 2 m × 1.5 m, and has
192 and 160 channels in the horizontal and vertical projections, respectively, with a pitch of
20 mm.
The electrons ionized by protons (and pions in P/PI-SPIC) are collected to cathode strips
by the supplied high voltage, and the signal from each strip is read out by charge sensitive ADC,
Ph.D. Thesis by Issei Kato, July 2004

24

Chapter 3. Experimental Components and Their Performances

To ADCTo ADC

ProtonBeamProtonBeam−HV

ADC count

1400 TGT X
1200
1000
800
600
400
200
0

10

Constant
Mean
Sigma

20
Constant
Mean
Sigma

20

2120.
16.74
3.257

30
ch
1416.
19.78
5.495

30
ch

ADC count

2250
2000 V39out X
1750
1500
1250
1000
750
500
250
0
10

1400 V39out Y
1200
1000
800
600
400
200
0
10

ADC count

ADC count

Figure 3.6: An oscilloscope image of a typicalCT signal. The structure of 9 bunches can beclearly seen. The CT signals are read out by
charge integrating ADCs with 1.3µsec wide gate
covering the whole beam spill.

1600 TGT Y
1400
1200
1000
800
600
400
200
0
10

Constant
Mean
Sigma

20
Constant
Mean
Sigma

20

1390.
18.54
1.636

30
ch
1495.
11.86
4.880

30
ch

Figure 3.7: A schematic view of the segmented plate ionization chamber, SPIC, (left) and typical profilesof the proton beam measured by the V39out- and TGT-SPICs (right). The structure of SPIC is as
explained in the text. In the right figures, upper two plots show the profiles in the X (left) and Y (right)
directions measured at just after the V39 steering magnet (V39-SPIC), and lower two are corresponding
to those at just in front of the production target (TGT-SPIC).

Ph.D. Thesis by Issei Kato, July 2004

3.3. Secondary beam monitors

25

where amount of charge corresponds to the number of particles passing through the each strip
region. Fig. 3.7 (right) shows typical profiles of the proton beam at the SPIC just after thesteering magnet, “V39out-SPIC”, and at the TGT-SPIC.
The SPICs are used for steering of the beam. The proton targeting is continuously monitored
by TGT-SPIC. In addition, V39out- and TGT-SPICs are used to measure the beam emittance(or profile and divergence) just before protons hit on the target.
Further description on the SPIC can be found in [34].

3.3

Secondary beam monitors

In the K2K experiment, there are two secondary beam monitors, pion monitor (PIMON) andmuon monitor (MUMON). PIMON is a gas Cherenkov imaging detector, and is occasionallyinstalled just after the 2nd horn magnet to measure the momentum and angular distributions ofpions entering the decay volume. MUMON is consist of two detectors, an ionization chamber,and an array of silicon pad detectors, and is installed in a pit just downstream of the beam dump,
as shown in Fig. 3.5. MUMON is measuring the profile of muons after the beam dump in orderto monitor the direction of the beam on spill-by-spill basis. In this section, brief descriptions ofthese monitors are given.

3.3.1

Pion monitor

Most of neutrinos are produced by the well-known two-body decay of pions, i.e. Eq. (3.2). Theenergy of neutrino from the decay of pion with the momentum of pπ can be calculated byEν =m2π − m2µ1·2 Eπ − pπ cos θ

,

(3.3)

where mπ , mµ , and Eπ are the mass of pion, the mass of muon, and the energy of pion,
respectively, and θ is the polar angle of neutrino direction with respect to the pion direction in
the laboratory frame. Since pion is pseudo-scalar particle, its decay is isotropic in the rest frameof pion. Therefore, if the momentum of pions and the geometry of decay volume are provided,
the neutrino fluxes in any position can be predicted.
However, since there have been large uncertainty in the hadron production processes aroundthe energy region of protons in K2K experiment, the momentum distribution of pion is notaccurate enough to predict the neutrino fluxes at ND and SK. Pion monitor (PIMON) intends
to measure the 2-dimensional distribution of pion momentum (pπ ) versus divergence (θπ ) justafter the horn magnets. From this (pπ , θπ ) distribution, the neutrino fluxes at both ND and SK
are obtained, and we can confirm the validity of our Monte Carlo simulation by comparing theresults of PIMON with the estimation of the Monte Carlo simulation.
Fig. 3.8 shows a schematic view of PIMON. PIMON is a gas Cherenkov imaging detector
which consists of a gas vessel, a spherical mirror, and an array of 20 photo-multiplier tubes.
Gas vessel
The gas vessel of PIMON is a cylinder of 91 cm in diameter and 90 cm in length, with arm of
about 3 m attached (see Fig. 3.8). The vessel is made of 5 mm thick stainless steel. There are
two aluminum beam windows located at the entrance and exit of the beam. These windows areof 1 mm in thickness in order to reduce interactions in the windows. The radiation length andthe interaction length of window are corresponding to 0.01X0 and 0.0025λint , respectively.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 3. Experimental Components and Their Performances~ Design on May 11,’98 ~
th
ng

l
ca

le

Fo

Spherical
mirror15
0

230

Top view
mm
64
34
48
24

Al foil
470

Pion monitor
Gas volume

200

To decay
volume

2750

900

26

190

2100

Beam window

910

From
2nd Horn
527

Beam view
200

2
33

110

600

910

Photo detector
20 PMTs

Figure 3.8: A schematic view of the pion monitor (PIMON). PIMON is consist of a gas vessel, a sphericalmirror, and an array of 20 photo-multiplier tubes. The gas vessel is filled with freon gas R-318 (C4 F8 ).
A pie-shaped spherical mirror is set inside the gas vessel and Cherenkov right reflected by the mirror is
directed to the array of photo-multiplier tubes which is set on the focal plane of the spherical mirror.

Inside the cylinder, pie-shaped spherical mirror is set to reflect the Cherenkov light toward
the photo-detectors located in the arm. An aluminum foil of 50 µm in thickness is set 23 cm
in front the mirror to define the fiducial area of Cherenkov light emission. This area does notchange even if the beam windows is deformed by gas pressure.
The gas vessel is filled with freon gas R-318 (C4 F8 ) to achieve high refractive indices in orderto make the momentum threshold of pion as low as possible. However, the refractive index,n, is controlled not to become above 1.00242 in order to avoid the severe background from theprimary protons (see Fig. 3.9). This refractive index corresponds to the Cherenkov threshold of
2 GeV/c pion.
Gas pressure is controlled by an external gas system. By changing the gas pressure, the
PIMON data are taken with the different refractive index between n = 1.00024−1.00242, whichis corresponding to the momentum threshold of pion between 6.4−2.0 GeV/c. The absoluterefractive index is calibrated by Cherenkov photon distribution from 12 GeV primary protons
with n = 1.00294, where 12 GeV protons can emit Cherenkov light [35].
Ph.D. Thesis by Issei Kato, July 2004

arbitrary unit

3.3. Secondary beam monitors

10

6

10

5

10

4

27

e+, e-

ProtonThreshold for
n=1.00242

Threshold for
n=1.00024

Pion +
Pion Muon

0.996 0.9965 0.997 0.9975 0.998 0.9985 0.999 0.9995

Particle β

Figure 3.9: Distributions of β for
protons, pions, muons, and electrons/positrons after the 2nd horn
magnet. The refractive index, n, should
be lower than 1.00242 to avoid theprimary protons with the kinetic energyof 12 GeV to be above Cherenkov
threshold.

Spherical mirror
A schematic view of the spherical mirror used in PIMON is shown in Fig. 3.8. It focuses the
Cherenkov photons onto the same ring when they are emitted by particles with the same β
and the same direction, being independent of their emission points, as drawn in Fig. 3.10. β ofparticle appears as a size of ring image, and the direction of the particle appears as a positionof ring image.
The spherical mirror is made of Pyrex glass which is coated with aluminum and frosted bysand to make a pie-shape. The dimensions of the glass are 60 cm × 15 cm in area and 8 mm
in thickness. The radius of curvature of spherical mirror is 6 m. The mirror covers 12◦ ofazimuthal part of the beam. The kick angle, defined as the angle between the beam direction
and the normal of mirror, is 30◦ to reflect the Cherenkov photons to the photo-detectors.
The mechanical hardness for the radiation and heat-up of the mirror is tested using intense
proton beam at KEK-Booster. The optics of the mirror was confirmed by LED measurements.
The time variation of reflectivity caused by the partial radiation damage is monitored by alaser system. The results of the monitoring shows that the reduction of reflectivity during the
one-year run is less than 6%. These tests, measurements, and monitoring are described in detailin [35].
Photo-detectors
Twenty photo-multiplier tubes (PMTs) are used to detect the photons on the focal plane of
the spherical mirror. PMTs are located far away from the beam line, as shown in Fig. 3.8, inorder to avoid the radiation damage. They are aligned along the vertical direction with 35 mm
interval. Signal of each PMT is led by a 100 m long cable to a charge sensitive ADC placed in
the data acquisition room outside the radiation area.
The type of PMT in use is modified-R5600-01Q made by Hamamatsu Photonics Corporation.
The size is 15.5 mm in diameter of the outer socket and 8 mm in diameter of the photo-cathode.
There are three issues to be noted on this PMT: Quartz window is used against radiation
hardness. The tests for the radiation hardness had been done at KEK-PS-K3 beamline [35, 36].
Multi-Alkali (Sb-Na-K-Cs) photo-cathode material is used to enlarge the dynamic range against
intense light. This cathode does not saturate up to the photo-cathode current of 10 µA, whereasa Bi-alkali photo-cathode saturates around 0.1µA. They are operated with low gain to measure
the very intense light of ∼ 109 photoelectrons in each PMT. Typical gain in our operation is 300
in June 1999 run and 20 ∼ 50 in Nov. 1999 run.
Ph.D. Thesis by Issei Kato, July 2004

28

Chapter 3. Experimental Components and Their Performances

Side 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 3.10: The principle of spherical mirror. The mirror focuses the Cherenkov photons onto
the same ring when they are emitted by particles with the same β and the same direction, being
independent of their emission points. The size and the position of ring are corresponding to the βand the direction of particle, respectively.

The relative gain among 20 PMTs was adjusted and calibrated by Xe lamp before theexperiment. The gain ratio of neighboring PMTs was also checked using Cherenkov photons
during the run. From these measurements, the error on the relative gain calibration is estimatedto be 10% for June 1999 run and 5% for Nov. 1999 run [35]. The saturation of PMTs wasobserved in June 1999 run, while no saturation was observed in Nov. 1999 run. The nonlinearity was corrected by a 2nd polynomial function, which was applied only to the data in theJune 1999 run. Uncertainty of the correction was estimated to be 4% [35].

Up to now, the data taking of PIMON had been performed twice, one in June 1999 andthe other in November 1999, for different experimental configurations. As mentioned before, we
operated with a target of 2 cm in diameter and a horn current of 200 kA in June 1999, whilewith a target of 3 cm in diameter and a horn current of 250 kA in November 1999. PIMON
is set on the beam line only during the periods of data taking, and is not on the beam line
during the normal neutrino beam runs. The results of the PIMON measurements are describedin Chapter 6. Further explanations, the analysis method, and the results of PIMON can befound in [35].
Ph.D. Thesis by Issei Kato, July 2004

Pions / 50M p.o.t.

29

22500
20000
17500
15000

105
104
103

0

MUMON canobserve

10000
7500
5000
2500
0

Corresponding pions

10

12500
neutrinos

Muons / 10M p.o.t.

3.3. Secondary beam monitors

2

4

6
8
10
12
Pion momentum (GeV/c)

10

10Corresponding neutrinos

8

10

106

0

2

4

6

8

10

(GeV/c)

0

1

2

3

4
5
E ν (GeV)

Figure 3.11: The momentum distributions of muons, pions, and neutrinos at muon-pit. Left
figure shows the muon momentum distribution just before the beam dump. Only the muons
above 5.5 GeV/c can reach the MUMON. Right figures show the momentum distributions ofgenerated pions (top) and neutrinos (bottom) in the beam line. The hatched histograms inthese figures are corresponding pions and neutrinos to the muons above 5.5 GeV/c. These
histograms are estimated by a Monte Carlo simulation.

3.3.2

Muon monitors

Muon monitors (MUMONs) measure the profile of secondary muons after the beam dump, whichmuons come from the decay of pions, π + → µ+ νµ . Since pion is a pseudo-scalar meson, theprofile center of muons is same as that of neutrinos. Using this fact, we can monitor the directionof neutrino beam on spill-by-spill basis.
MUMON is set in a pit, so-called “muon-pit”, located at 220 m downstream of the production
target, just downstream of the beam dump. The beam dump consists of 3.5 m thick iron and 2 mthick concrete shields, as shown in Fig. 3.5. Due to the energy loss and the hadron interactionsin the beam dump, only muons with the momentum of greater than 5.5 GeV/c can reach themuon-pit. Fig. 3.11 shows the momentum distribution of muons before the beam dump. A
fraction of 2.1% of muons are expected to be above 5.5 GeV/c. Their flux is roughly 104 muons
per 1 cm2 . Fig. 3.11 also shows the momentum distributions of pions and neutrinos whichcorrespond to the muon above 5.5 GeV/c, indicating that only pions above 5.5 GeV/c can bemonitored by measuring the muons above 5.5 GeV/c. However, the direction of high energy
pions are more sensitive to the overall beam direction than the low energy ones. For example,
when mis-steering of the beam, such as incident proton profile or angle changes, or the horn
trouble occurred, then the muon profile always indicates the movement in its center position.
Therefore, MUMON works well as a good monitor for the overall beam steering toward the SK.
In addition, by monitoring the beam intensity at MUMON, the proton targeting can also bemonitored.
MUMON is consist of two types of detectors; one is an ionization chamber (ICH) and theother is an array of silicon pad detectors (SPD). Fig. 3.12 shows a schematic view inside themuon-pit.
Ph.D. Thesis by Issei Kato, July 2004

30

Chapter 3. Experimental Components and Their Performances

52.5cm
5cm
2m
X-readout(36 ch)52.5cm

HV

35cm

beam

2m

Y-readout(32 ch)5cm

35cm
3.45cm

ICH

2cm
3.4cm
1cm

SSD-Array

pit floor

Figure 3.12: A schematic view inside the muon-pit. An ionization chamber (ICH) andan array of silicon pad detectors (SPD) are located inside the muon-pit.

Ionization chamber
An ionization chamber (ICH) in the muon-pit is a segmented plate chamber just like SPIC in
the primary beam line. In order to measure the broad muon profile, it is made to be as large as
190 cm (horizontal) × 175 cm (vertical).
There are three G10 planes, two cathode planes for horizontal and vertical projections, andone anode plane. They are arranged with gaps of 1 cm between these planes. The each cathodeis segmented into strip lines of width of 5 cm in each direction. The numbers of readout channels
are 36 in horizontal and 32 in vertical direction. Due to the difficulty to make a large G10 plate,the ICH consists of six modules of the size of 60 cm × 90 cm, 3 modules in horizontal and 2
modules in vertical direction. The corresponding strip lines of adjoining modules are electricallyconnected to make long strip lines of a length of ∼180 cm. There are gaps between modules;
25 cm in horizontal and 15 cm in vertical, and hence they are insensitive regions. Since theelectric field is deformed around the edge strips in each module, the numbers of strips available
for the measurement are 30 in horizontal and 28 in vertical directions.
Whole modules are installed inside the gas vessel filled with Ar gas. The high voltage of−500 V is supplied to the anode plane. Electrons ionized by the passing muons are collected by
the strips and their signals are recorded by charge sensitive ADCs. The quantity of charge readout from each strip corresponds to the number of muons passing through each strip, hence themuon profile is obtained.
The channel-to-channel uniformity is calibrated by moving ICH horizontally and vertiPh.D. Thesis by Issei Kato, July 2004

3.3. Secondary beam monitors

1000

North

ICH-X

South

1200

Bottom

ICH-Y

Top

1000

800

800

600

600

400

400

200

200

0

31

-50

0

0

50

-50

0

50

cm
900
800
700
600
500
400
300
200
100
0

North SPD-X

South

-50

50

0

cm
900
800
700
600
500
400
300
200
100
0

cm

BottomSPD-Y

-50

0

Top

50

Figure 3.13: Typical muon profiles measured by ionization chamber (ICH) and silicon pad detector arrays (SPD). Upper two
figures are of ICH in the horizontal (left) andthe vertical (right) directions. Gaps shownin these figures are corresponding to the insensitive regions of ICH as described in the
text. Lower two are of SPD also in the horizontal (left) and the vertical (right) directions.

cm

cally [35] assuming the stability of muon beam. This measurement had been performed several
times during long run periods. The relative gain of channels has been stable within an accuracyof several %. With the use of these correction factors, muon profile is measured on spill-by-spillbasis. We can also measure the intensity of the beam by summing the charge of all channels
up. The upper two figures in Fig. 3.13 shows a typical muon profile in horizontal and verticaldirections measured by ICH. It can measure the profile precisely enough to monitor the beam
direction.
Silicon pad detector array
As is shown in Fig. 3.12, arrays of semi-conducting detectors, silicon pad detectors (SPDs) arealso installed on the downstream wall in the muon-pit. There are 17 small-type SPDs arranged
along the horizontal and the vertical axis with 35 cm interval, and 9 large-type SPD in diagonalarrays with 74.2 cm interval. The small-SPD has a sensitive area of 1 cm × 2 cm with a depletion
layer thickness of 300 µm, while the large-SPD has a sensitive area of 3.4 cm × 3.05 cm with adepletion layer thickness of 375 µm.
A muon passing through the SPD, 2.3 × 104 and 2.9 × 104 electron-hole pairs are created in
the depletion layers of small and large SPD, respectively. They are collected by the bias voltageof 100 V for small SPDs and 70−80 V for large SPDs, and the signals are recorded by charge
sensitive ADCs.
Uniformity of the sensitivity of small SPDs was measured using LED light source at a test
bench. The results show that the sensitivity of each small SPD agrees within 6% [35]. For largeSPDs, the uniformity was measured using muon beam at the muon-pit. All the large SPDs wereonce aligned along the beam axis, and the readout charges from each SPDs were compared, thenthe relative gain factor for each SPD was obtained although they have an uncertainty of 10%
level due to the z-dependence of the muon beam intensity [35].
By measuring the charge from each SPD, the muon profile can be monitored on spill-by-spillbasis. The typical profiles measured by SPD are also shown in Fig. 3.13 (lower 2 figures).
Ph.D. Thesis by Issei Kato, July 2004

32

Chapter 3. Experimental Components and Their Performances
Further information about MUMON can be found in [35],

3.4

Data acquisition system of beam line monitors

All the data acquisition (DAQ) systems in the KEK site are triggered by the common signal
provided by the accelerator. There are two trigger signals synchronized with the timing of the
kicker magnet excitation.
One trigger signal is provided 1.1 msec before the beam extraction. This signal is used only
to make the horn magnets fire since it takes about 1 msec to achieve the peak current of horns.
The other signal is provided 120 µsec before the beam extraction. This signal is used as thebeam spill trigger for the data acquisition in all beam line monitors and all detectors at nearsite. Simultaneously 16-bit spill number is distributed to and recorded at each DAQ site to
identify a spill from others.
Signals from beam line detectors, CTs, SPICs, MUMON, and PIMON during the PIMON
runs are all digitized and recorded by charge sensitive ADCs on spill-by-spill basis, as described
before. There are 4 rooms and 6 front-end computers for DAQ system along the beam line and1 host PC controls data acquisition processes on other front-end computers.
In addition to the detector information, the beam extraction timing is recorded by the GPStime recording system for the time synchronization with SK. Furthermore, the time interval
between previous and current spills is also recorded by VME Trigger Module (TRG). Descriptions
about GPS system will be provided in Sec. 3.7.

Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

33

Figure 3.14: A schematic view of near detector system. From upstream of the beam, 1 kt water
Cherenkov detector (1KT), scintillating fiber tracker (SciFi), lead glass calorimeter (LG), and muon
range detector (MRD) are located. Surrounding the upstream and the downstream of SciFi, planes ofplastic scintillators (trigger counter, TGC) are installed. In this figure, the neutrino beam is coming fromright and going to left side.

3.5

Near neutrino detectors

Near neutrino detector system (ND) is located at the distance of 300 m from the production
target, 80 m downstream of the beam dump. Since the beam is tilted downward by about 1◦ ,the experimental hall is at 16 m below ground.
ND consists of a 1 kt water Cherenkov detector (1KT), a scintillating fiber tracker (SciFi), a
lead glass calorimeter (LG), and a muon range detector (MRD), as shown in Fig. 3.14. Planes ofplastic scintillators (trigger/veto counters, TGC) is surrounding the upstream and downstreamof SciFi. The detector system of SciFi, LG, MRD, and TGC is called “fine-grained detector
system (FGD)”. In this section, a description of each detector, mainly 1KT, and its performanceis provided.

3.5.1

1 kt water Cherenkov detector

1KT is a water Cherenkov type detector located most upstream of the experimental hall. The
center of the water tank is at 294 m downstream of the production target. It measures theneutrino beam properties such as the flux and the energy spectrum. The advantage to use 1KT
is to cancel out most of the systematic uncertainties in comparing the measurements in 1KT and
SK because of the same detection principle and the same material for neutrino target (H2 O).
Ph.D. Thesis by Issei Kato, July 2004

34

Chapter 3. Experimental Components and Their Performances

ID PMT (20-inch)
OD PMT (8-inch)
ν bea

m

Figure 3.15: A schematic view of 1KT detector. The diameter and height of the tank are both10.8 m, and the tank is fill with about 1,000 tons
water. Inside the tank, the volume is opticallyseparated into two parts; the inner volume andthe outer volume. The dimensions of inner volume are 8.6 m in diameter and 8.6 m in height.
There are 680 20-inch PMTs mounted on the wallof inner volume facing inward with the spacing of
70 cm grid. On the 1/3 part of upstream wall andthe bottom wall of outer volume, 68 8-inch PMTs
are mounted facing outward with the spacing of
140 cm.

The structure of 1KT
As shown in Fig. 3.15, 1KT consists of cylindrical tank of 10.8 m in diameter and 10.8 m inheight, filled with approximately 1,000 tons pure water. Inside the tank, it is optically separated
into two parts; the inner detector (ID) of the cylindrical volume of 8.6 m in diameter and 8.6 m
in height, and the outer detector (OD) surrounding ID. Between ID and OD, there is stainlesssteel frame (support frame) which PMTs are mounted on.
There are 680 20-inch PMTs mounted on the support frame facing inward, 456 PMTs areon the barrel wall, 112 PMTs are on the top wall, and the remaining 112 PMTs are on thebottom wall. These PMTs are aligned in 70 cm grid, which is the same spacing of PMTs in SK.
The fraction of photocathode coverage is about 40% of the surface of ID, and the rest of thewall surface is covered by black polyethylene telephthalate sheets which suppress the reflectionof Cherenkov light on the wall.
The OD is originally used to veto the incoming particles from outside, whereas it is also
used to trigger the through-going/stopping cosmic-ray events for the detector calibration. The
thickness of water in OD is 1 m for the barrel part and 0.6 m for the bottom part. There are
68 8-inch PMTs mounted on the support frame facing outward, 42 of them are mounted on 1/3
part of the upstream barrel wall, and the remaining 24 PMTs are on the bottom wall. The
spacing of PMTs is 140 cm. A 60 cm × 60 cm square plate of wavelength shifter is attached on
the surface of each PMT in order to increase the light collection efficiency. Tyvec sheets, which
is known as reflective material, cover the OD wall to enlarge the detection efficiency.
PMT is normally influenced by magnetic field around it, and its gain and time response mayvary even if the magnetic field is as small as the magnitude of geomagnetic one. The PMTsof 50 cm in diameter are used in 1KT, and hence the effect becomes larger than small PMTs.
In order to prevent PMT to be affected by the magnetic field, a diameter of the first dynodeis made to be as large as possible by adopting a Venetian blind type dynode. Furthermore,
Helmholtz type coils are set around the tank in both vertical and horizontal directions in order
to compensate the geomagnetic field inside the tank. Thanks to the compensation coils, themagnitude of magnetic field inside the tank is suppressed to be around 50 mG.
Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

35~ 70000

cable length
φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure

Figure 3.16: A schematic view of 20inch photo-multiplier tube used in 1KT
and SK.

( 610 20 )

~ 720

(mm)

Cherenkov light
Cherenkov photons are emitted by a charged particle traveling in water with the velocity fasterthan the light velocity in water. These photons are emitted onto a cone around the particle
path. The opening angle of the Cherenkov cone, θ, is determined by the refractive index ofwater, n, and the velocity of particle, β, ascos θ =

1
nβ

,

(3.4)

where, for water, n = 1.33−1.36 depending on the wavelength of light. The momentum thresholdof Cherenkov radiation for electron, muon, pion, and proton are 0.57, 118, 156, and 1048 MeV/c,
respectively.
The number of Cherenkov photons, N , emitted by a particle with single charge per unit path
length, x, per unit wavelength, λ, is given by
d2 N
2πα
= 2
dxdλ
λ

µ
1−

1
n2 β 2¶,(3.5)

where α is the fine structure constant (∼ 1/137). A particle with β = 1 emits about 340 photons
per 1 cm in the wavelength of 300 to 600 nm, to which wavelengh our PMT has sensitivity.
20-inch photo-multiplier tube
Twenty-inch PMTs, R3600 made by Hamamatsu Photonics Corporation, are used in ID of 1KT,
as well as SK, to detect Cherenkov photons. The specifications of the PMT are summarized inTable 3.2. The photo-cathode is made by bi-alkali (Sb-K-Cs) which sensitive region matches the
wavelength range of Cherenkov light. The quantum efficiency is about 22% at the wavelenghtof 390 nm. A Venetian blind type dynode is used in it. The average collection efficiency isabout 70%. The gain is as high as 107 at a supplied high voltage of 2 kV. Thanks to this highgain, single photoelectron can be distinguished. The typical timing resolution is 2 nsec. Further
description for the PMT is given in [37, 38].
Ph.D. Thesis by Issei Kato, July 2004

36

Chapter 3. Experimental Components and Their Performances

Table 3.2: Specifications of 20 inch photo-multiplier tube, R3600 madeby Hamamatsu Photonics Corporation, used in 1KT and SK.
Parameters
Photo-cathode area
Shape
Window material
Photo-cathode material
DynodesQuantum efficiency
Sensitive wavelength
Typical gain
Dark current
Dark pulse rate
Cathode non-uniformity
Anode non-uniformity
manufactured

Values50cm in diameter
Hemispherical
Pyrex glass, 4 ∼ 5 mm
Bialkali (Sb-K-Cs)
11 stages, Venetian blind type
22% at λ = 390 nm
300 nm to 600 nm, peak at 390 nm
107 at ∼ 2000 V
200 nA at gain 107
3 kHz at gain 107
less than 10%
less than 40%
Hamamatsu Photonics K.K.

fast recirculation
1−um filterby−pass
pre−UVwater
sterilizer

deionizer

filterUV
watersterilizer

ultra−filter

chillerhigh purity recirculation

1KT tank

overflowpipe

Water System Tent
pump

Figure 3.17: A schematic diagram of the water purification system in 1KT. Solid lines show main
circulation flow, and dotted lines show supplementary one. The equipments inside the green box
are located in water system tent on the ground.

Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

37

Water purification system and water transparency
Impurities in water, such as small dusts, bacteria, metallic ions, and resolved gases, cause attenuation or scattering of the Cherenkov light, making the event reconstruction performance worse.
For this reason, a water purification system is employed in 1KT to remove these impurities.
Fig. 3.17 shows the flow diagram of the water purification system in 1KT. The system islocated in the water system tent on the ground, next to the experimental hall. Water whichcomes from 1KT tank is send to the system using pump at the underground level in the hall.
Pre-UV water sterilizer and UV water sterilizer kill bacteria in the water. Filter removes small
dust of the order of 1 µm. Metallic ions resolved in water is removed by the deionizer. Ultrafilter removes much smaller dust of order of 10 nm. The water to be sent to 1KT tank is cooledby chiller down to around 10◦ C in order to prevent bacteria to breed in water. This system
circulates the water with 20 tons per hour. Purity of the water is monitored by measuring its
electrical resistance, which is usually 10 MΩ/cm. The temperature and the purity of the water
have been controlled to be around these values during the whole run periods.
Water transparency is measured by using cosmic-ray muons. By taking the ratio of Cherenkov
light inside and outside the Cherenkov cone of cosmic-ray muon’s, amount of scattering light
can be measured. The attenuation length is over 50 m and is stable through the whole runs.
Data acquisition system of 1KT
Signals from 748 PMTs (680 PMTs in ID, 68 PMTs in OD) are sent through co-axial cables into
the electronics hut on the ground level, and then they are processed by data acquisition system
to digitize signals and store the data. Fig. 3.18 shows a schematic view of the data acquisition
system in 1KT. Detailed descriptions on the system can be found in [39], and they are briefly
described here.
Front-end electronics: Front-end electronics digitize and record the charge and the timing information from PMTs, and at the same time, they generate the discriminated pulses for thetrigger logics. For these purpose, TKO modules which perform analog-to-digital conversion,
named “ATM (Analog Timing Module)” [40, 41], are employed. They had been developed forthe use in SK. In one ATM module, 12 PMT signals are precessed, and 66 ATMs are used in
total in 1KT. Two sets of TDC and ADC are prepared for each channel inside an ATM to reducethe dead time of the module.
Signal from each channel is, first, divided into four streams; one is led to a discriminator,
two are led to two independent ADCs, and the other is used to make an analog sum of 12 PMT
signals, called “PMTSUM”. The discriminator threshold is set to be equivalent to typically
0.3 photoelectron signal of PMT. The discriminated signal is sent to two independent TDCs,
and also used for the timeout signal against the AD conversion of TDCs and ADCs. If GONG
(Go/NotGo) module receive a trigger signal before the timeout of ATM, which is about 1.1 µsec,
TDC and ADC start digitizing the signals, 12-bit data is stored in the FIFO memories of ATM,and the data is sent to SCH (Super-Control-Head) module. The conversion factors of TDC and
ADC are 0.4 nsec/count and 0.15 pC/count, respectively. Furthermore, a rectangle pulse witha width of 200 nsec, “HITSUM”, is generated using the discriminated signal. The pulse heightof HITSUM corresponds to the number of hit channels in the ATM, which is about 10 mV per
one hit channel.
One different usage of ATM from that in SK is to use the accelerator beam timing as enable
signal for the module. ATMs are allowed to proceed the above processes only during 1.3 µsec
Ph.D. Thesis by Issei Kato, July 2004

38

Chapter 3. Experimental Components and Their Performances

20−inch PMT

TKO
SCH
x12

........

........

x228

ATM
CAMAC
x19

PMTSUM

FADC

ATM
GONG
20−inch PMTinterface........

x228

SCH

SMP

ATM

SMP

........

x12

SMP

x19

SUN
Online CPU

SMP
TMC

ATM
GONG

TRG
20−inch PMT

VME
SCH
x12

........

........

x224

ATM
x20
HITSUMATM

Trigger
Processor
NIM

GONG

8−inch PMT
SCHx12........

........

x68

Trigger Signal

ATM
x8
Enable signal by accelerator beam timing

ATM
GONG
PMT x 748

ATM x 66

SMP x 4

Online CPU x 1

Figure 3.18: A schematic diagram of the data acquisition system in 1KT.

Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

39

synchronized with the beam timing. This enable signal is generated by the accelerator trigger
signal which come 120 µsec before the beam spill, mentioned in Sec. 3.4.
All PMTSUM signals from ID-PMTs are summed up and sent to CAMAC Flash-ADC(FADC) to record the signal shape. The sampling rate and dynamic range of the FADC is
500 MHz and 8-bit, respectively. This data is used to count the number of events in each beam
spill by counting the number of peaks in the PMTSUM signal.
The pulse reflection at the input of ATM had been observed during the run in 1999 dueto the impedance mis-matching. In order to avoid the reflection, buffer-amplifiers have been
installed on the ATM input since January 2000.
ATM module has its responses dependent on temperature [42], the data acquisition system
mentioned above are all in the electronics hut where temperature is controlled to be stable ataround 25◦ C.
Rear-end and other electronics: Four VME-SMPs (Super Memory Partner) are used to collectand temporarily store the data from ATMs. VME-TRG module records the trigger bit of each
event and time interval between the previous and the current events. VME input register is used
to record the spill number distributed by the beam line DAQ mentioned in Sec. 3.4. VME-TMC(multi-hit TDC) records the event timing in 1KT with respect to the trigger signal sent fromaccelerator. TMC is also used to record the muon timing which signal comes from MUMON at
muon-pit in order to monitor the stability of the time interval between the accelerator trigger
signal and the real beam timing. This monitor is very important because all the detectors in
KEK is triggered by the accelerator signal.
Trigger electronics: The readout processes are triggered if the 1KT has an event with more thanabout coincidence of 40 hit PMTs. The coincidence is identified using HITSUM signals from
ATMs as following: All HITSUM signals from ID-PMTs are summed up, and then discriminatedwith the threshold of 450 mV, which corresponds to 40 hit PMTs in 200 nsec time window.
The trigger signal is sent to TRG module, and then distributed to GONGs, VME-SMPs,
FADC, and TMC. The signals to GONGs make ATMs start the readout processes. Then, thesignals to SMPs force SMPs to collect the data stored in ATMs into SMPs. After all the ATM
data are stored in SMPs, it is ready to be read out by online computer. The trigger signal isalso sent to TMC to record the trigger timing of the event with respect to the accelerator trigger
timing. Delayed trigger signal is sent to FADC to stop its sampling.
Online computer: When all the modules become ready to be read out, an online computer
starts collecting the data from SMPs, FADC, TMC, input register, and TRG module. After
collected data are sorted on the computer, they are sent to a host computer, or “event builder”,
of ND. The event builder makes data from each detector to be of the form of 1-spill data basedon the spill number recorded in each detector system.
The event trigger mentioned above is permitted only during four timing gates per one beam
spill cycle; “on-spill gate” which is the main gate opened during neutrino beam timing, “delayed gate” which is sequential gate following the on-spill gate to take the succeeding neutrino
event such as decay electron from the neutrino-induced muon, “off-spill gate” which is opened
1 msec after neutrino beam spill with the same duration as on-spill gate to estimate the rate of
background events such as accidentally incoming cosmic rays, and “cosmic ray gate” which is
to collect cosmic ray muons between spills to check the stability of the energy scale of 1KT.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 3. Experimental Components and Their Performances

4000
3500
3000
2500
2000
1500
1000
500
0

TDC counts

ADC counts

40

3500
3000
2500
2000
1500
1000

200

400

250 500 750 1000

600

50
25
0
−25
−50
−75
−100
−125
−150
0

T (nsec)
Deviation (counts)

Deviation (counts)

Q (pC)

20
0
−20
−40

200

400

600

−60

250 500 750 1000

Q (pC)

Figure 3.19: Charge-to-counts and Timeto-count responses of ADC and TDC in
ATM module. Left two figures are for ADC,
and right two are for TDC. The upper figures show the charge-to-count and the timeto-count responses of ADC and TDC, andthe lower figures show their deviations fromlinear fitting.

T (nsec)

ATM calibration
The ADC and TDC in ATM module almost linearly response to the input charge and timing,
respectively, but they are not perfectly linear responses. In order to correct these non-linear
responses, ATM calibration had been performed before the experiment started, and also whenthe experimental configurations had been changed, such as installation of the buffer-amplifiers.
CAMAC CTG (charge time generator) is used for the ATM calibration. In order to measure
the response to the input charge and input timing, pulses with charge of the magnitude of from0 to 600 pC by 10 pC step and with the timing of from 0 to 1.2 µsec by step of 10 nsec are
generated by CTG, and put to each ATM channel. Fig. 3.19 shows the responses of ADC and
TDC to the input charge and timing and the deviations of their responses from linear fittings. As
is shown in the figure, the responses have some non-linearity. In order to obtain the conversion
factors of ADC and TDC counts to charge and timing at any point, intervals between measured
points are complemented by linear lines. The deviation of the ADC/TDC count estimated by thecomplemented lines from actually measured one is known to be within 1 count at any point [42],which is sufficient accuracy.
Timing calibration
The timing when each PMT receives Cherenkov light is very important for the water Cherenkov
detector to reconstruct the vertex of event. However there are several causes which make variation of the timing; PMT-by-PMT different transit time, the cable length, charge-to-timing
correlation, and so on. Especially, there is clear correlation between the pulse height of signal
and the timing when signal gets over threshold level of the discriminator in the ATM. In order
to correct these effects in situ, a timing calibration had been performed using laser calibration
system.
Fig. 3.20 shows a schematic view of the laser calibration system. A dye/Nitrogen laser isused as a light source since its pulse width is as short as the order of 1 nsec and hence a lightemission with a definite timing is available. The wavelength of laser light is 390 nm, which issimilar to that of Cherenkov light. The laser light is divided into two paths by a half mirror.
Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

41

Aluminium Box
Half
MirrorDye/Nitrogen
Laser

P. D.

Variable
ND Filter
Fiber
20inch PMTs

Diffuser Ball

Trigger

Figure 3.20: A schematic view of the laser calibration
system in 1KT. Dye/Nitrogen laser light divided into 2
paths by a half mirror, one goes to photo-diode, marked
P.D. in the figure, to make a trigger signal, and theother is injected to a optical fiber which another edge
light diffusing ball is put on. The light diffuser ball is
set at the center inside the 1KT tank, and laser lightis almost isotropically emitted from the ball.

Detector

One light path goes to photo-diode detector (PD), which has a fast response to the input light.
The PD signal is used for the trigger timing. The other light path is attenuated by a variable
neutral density filter (ND filter) and injected to a optical fiber which goes into the 1KT tank.
Light diffusing ball is put on the other side of the fiber which diffuses the laser light to isotropic
direction [43]. The ball is set at the center of the 1KT tank. By changing the magnitude ofattenuation at ND filter, light with various intensity is sent to PMTs in 1KT.
The time of flight of light from the diffuser ball to each PMT considered, the light detection
timing in each PMT with respect to the trigger timing is obtained at various light intensity,
which is in a form of correlation plot of amount of detected charge versus detection timing ineach PMT, so-called “T-Q map”. Fig. 3.21 shows a typical T-Q map. The detection timing iscorrected according to T-Q map for each PMT,
T-Q maps had been taken before the experiment, and also when the experimental configuration had been changed.
Equalization of PMT gain
In order to measure the energy of particle presicely, the gain of each PMT should be adjusted
so that all the PMTs have almost the same gain. Here, the method to equalize the gain of each
PMT is described.
There are 103 PMTs out of 680 ID-PMTs, called “pre-calibrated PMTs”. Before the installation of PMTs into 1KT, the values of high voltage supplied to each of these PMTs had
been determined to adjust its gain to be 6 × 106 within 1% precision [43]. The location of precalibrated PMTs is shown in Fig. 3.22. The pre-calibrated PMTs provide the standard gains
to which the gains of all the other PMTs are adjusted. Hamamatsu Photonics Corporation had
measure the gain of all PMTs before shipping, and provided the high voltage values which give
6 × 106 gain. The high voltage values provided by Hamamatsu Photonics are supplied to PMTs
Ph.D. Thesis by Issei Kato, July 2004

T (nsec)

42

Chapter 3. Experimental Components and Their Performances

870
865
860
855
850
845
840

0

100

200

300

400

500

600
Q (pC)

Figure 3.21: A typical plot of the detected charge versus
timing in a PMT, “T-Q map”. The horizontal axis isamount of charge detected by PMT, and the vertical one
is the detection timing with respect to the trigger timing
provided by the photo-diode.

Top

BarrelBottomFigure 3.22: Position of the pre-calibrated
PMTs in 1KT. Circles indicate the position of
PMTs, and black closed circles show the “precalibrated PMTs” which are used as standard
PMTs to equalize the gain of all the other PMTs.

other than pre-calibrated PMTs. By the adjustment of the high voltage for each PMT, thePMT gains are equalized with variation of about 10−20% level.
In order to equalize the PMT gains more precisely, the relative gain to the pre-calibrated onesis measured for each PMT after their installation into the 1KT tank by illuminating uniform lightfrom the center of the tank to all PMTs. This measurement is done using a Xenon calibration
system shown in Fig. 3.23. A Xenon lamp is used as a light source of the calibration. The UV
filter makes the light with the wavelength of 300−400 nm, the ND filter attenuate the light tobe appropriate intensity, and diffuser makes the light uniform. Then the light is injected to four
optical fibers; two fibers go to two photo-diodes to monitor the intensity of the light, one fiber
goes to 2-inch PMT which makes a trigger signal, and one fiber goes into the 1KT tank. A
scintillator ball is put on the other end of the last fiber. Absorbing and re-emitting the Xenon
light, the ball almost uniformly illuminates all PMTs inside the tank. The scintillator ball was
rotated in the azimuthal direction ( φ-direction ) in order to cancel out the non-uniformity of
the light emission in φ-direction.
Other sources of non-uniformity to detect the light in each PMT, such as the non-uniformityof the light emission in θ-direction, the solid angle of each PMT seen from the scintillator ball,Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

43

Aluminium Box
Defuser
Fiber

Xe
Lamp

P. D.
P. D.

UV
ND
Filter Filter

2inch PMT

20inch PMTs
Trigger

Scintillator Ball

Detector

ADC

Figure 3.23: A schematic view of the Xenon calibration system in 1KT. A Xenon lamp is used asa light source. UV filter makes only the light withthe wavelength of 300−400 nm permeate through.
ND filter attenuates the intensity of light in order for PMTs to receive ∼ 100 photons. Diffuser
diffuses the light to be uniform. Then light is injected to 4 optical fibers. Two fibers go to photodiode detectors and is read out by CAMAC ADC
to monitor the intensity of light. One of four
fibers goes to 2-inch PMT which signal is used
for the trigger. The remaining fiber goes into the
1KT tank, on another edge of which fiber, a scintillator ball is put. The ball absorbs the Xenon
light and re-emits scintillating photons isotropically. The ball is usually set at the center of the
1KT tank.

and the attenuation of the light in the water, are corrected using correction functions, whichwere measured in advance [43, 44].
By taking a ratio of detected charge in each PMT to those in pre-calibrated ones located atgeometrically same position, most of systematic uncertainties are canceled out, such as water
attenuation, solid angle of PMT, non-uniformity of light source in θ-direction, the light reflection
on the surface of PMTs, and any geometrical effects. Using the relative gain factors to precalibrated one, the PMT gains are corrected with the precision of several % level.
However, it is known that the geomagnetic field in 1KT is not uniform, and there exists small
difference in PMT gains at lower and upper parts of 1KT. The correction against this effecthad been done by using vertically and horizontally through-going cosmic-ray muons, which is
described in the next section.
Energy scale calibration
In order to calibrate the energy scale in 1KT, cosmic-ray muons are in use. As mentioned in
the previous section, since the gains of PMTs at lower and upper part of 1KT are different due
to the different magnetic field, the gain correction between the bottom part and barrel part of
PMTs is also done using cosmic-ray muons. Two different triggers for cosmic-ray muons weremade; one is to trigger the vertically through-going muons (vertical-µ) and the other is to trigger
the horizontally through-going muons (horizontal-µ).
The vertical-µ events are triggered by the coincidence of the scintillation counter set atthe top of the tank and the bottom OD-PMTs, while horizontal-µ events are triggered by thecoincidence of the OD-PMT of upstream barrel part and Trigger/vete counter plane (TGC)
which located at the downstream of 1KT tank. Typical event displays for the vertical-µ andthe horizontal-µ event are shown in Fig. 3.24. Major part of Cherenkov light is deposited onto
the bottom part of 1KT in vertical-µ events, while that is deposited onto the barrel part inhorizontal-µ events. Difference of gain in bottom and barrel PMTs, and overall gain factor are
Ph.D. Thesis by Issei Kato, July 2004

44

Chapter 3. Experimental Components and Their Performances

tuned by adjusting the data to agree with a Monte Carlo simulation.
The distribution of the number of total photo-electrons per unit track length of muon, socalled “charge ratio”, is used to compare data with MC. Upper two figures in Fig. 3.25 show the
distributions of charge ratio in vertical-µ and horizontal-µ events after tuning the gain factors.
Data and MC show the reasonable agreement in both distribution. The difference in the meanvalue of the distribution between data and MC ( (MC − data)/data ) is +2.0 ± 0.1% in vertical-µand −2.3 ± 0.5% in horizontal-µ.
The energy scale has also been checked using the charge ratio of cosmic-ray muons stopping
inside 1KT (stop-µ), resulting in the difference of mean value between data and MC of +1.2 ±0.1%.
The PC events, in which the muon produced by a neutrino interaction in 1KT goes outside the
1KT, are also used to check the energy scale. In PC events, the number of total photoelectrons
is directly compared between data and MC. The discrepancy between them is estimated to be−2.6 ± 0.3%.
One more check for the energy scale is done using π 0 induced neutrino events. Eventswith two electron-like Cherenkov rings (2-ring both e-like events) are selected to enhance π 0candidates. Using the energy and the direction of each ring and assuming both 2 rings are
generated from a common vertex, the invariant mass is reconstructed in each event. The lower
figure in Fig. 3.25 shows the distribution of the reconstructed invariant mass for 2 rings elike events, showing the clear peak around π 0 mass. Fitting the peaks in data and MC, thediscrepancy between data and MC is found to be −2.1 ± 0.2%.
Fig. 3.26 summarizes the all measurements on the calibration of the energy scale in 1KT.
All the measurements settled to be within +2−3 % differences. Therefore, we quoted this value
as the systematic error on the measurement of particle momenta in 1KT. Fig. 3.27 shows the
distribution of total number of photoelectrons for the neutrino events which have one muon-like
Cherenkov ring with the charged particle track fully contained inside the inner detector of 1KT(FC 1-ring µ-like events: 1Rµ). The distributions in Data and a Monte Carlo simulation isreasonably agrees, showing the energy scale of 1KT is well calibrated.
Stability of the energy scale
The stability of the energy scale has been monitored using the charge ratio of vertical-µ. The
vertical-µ events were sometimes taken during the neutrino beam was off. In addition, cosmic-ray
events have been also taken between beam spills since Jan. 2001.
Fig. 3.28 shows the stability of the energy scale since Jun. 1999. The energy scale at thevery beginning of the experiment was about 3% lower than that of the rest of the periods. It
has been stable within 1% since the run in 2000. In the estimation of the expected number ofneutrino events in SK, data in 1999 is also used as well as the rest of the data. However thedifference of 3% in the energy scale makes only negligible error of less than 1% on the expected
number of neutrino events. In the spectral analysis, the data in 1999 is discarded due to thedifferent configuration of horn magnets in June 1999 and a hardware problem in November 1999
(1/4 part of PMTSUM was disconnected from FADC by mistake, mentioned in Sec. 7.1.1).

3.5.2

Trigger/veto counters

Two planes of plastic scintillators are located upstream and downstream of the SciFi detector,
called trigger/veto counters (TGC). The upstream TGC is used to veto the charged particle
coming from upstream of the beam or cosmic-rays. It consists of 20 scintillators of 466 cm inlength, 20 cm in width, and 4 cm in thickness, covering an area of 466 cm × 400 cm in front of
Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

45

NUM
14
RUN
602040SPIL
98
SUBRUN
1
EVENT
257
DATE **-Dec-24
TIME
14:22:43
TOT PE:
26620.8
MAX PE:
299.4
NMHIT :
675
ANT-PE:
0.0
ANT-MX:
0.0
NMHITA:
0

NUM
10
RUN
602051SPIL
64
SUBRUN
1
EVENT
63
DATE **-Jan-14
TIME
20: 4:36
TOT PE:
26355.7
MAX PE:
272.9
NMHIT :
680
ANT-PE:
0.0
ANT-MX:
0.0
NMHITA:0

90/00/00:NoYet:NoYet
TRG ID :00000001
0:NoYetTMC Ch1:TMC Ch2:TMC Ch3 90/00/00:;R=R :Z : PHI : GOOD
T diff.:0.
us
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MSQ thr. :0.0
SUB EV : 0/ 0

TRG ID :00100000
TMC Ch1:TMC Ch2:TMC Ch3
T diff.:0.
us
Q thr. :0.0
SUB EV : 0/ 0

Comnt;

Comnt;

Entries

EntriesFigure 3.24: Typical event displays of vertical (left) and horizontal (right) cosmic-ray muons. The majorpart of Cherenkov light is deposited onto the bottom part of 1KT in vertical-µ events, while onto thebarrel part in horizontal-µ events. Asterisk marks “*” represent dead PMTs.

4000

300

3500
250

3000

DATA

2500

MC

2000

DATA
200

MC

150

1500

100

1000
50

500

Entries

0
15

20

25

30
35
40
Total p.e./track length (p.e./cm)

1200
DATA

1000

MC
800
600
400
200
0

0

50

100

150

200
250
300
0
2
π mass (MeV/c )

0
15

20

25

30
35
40
Total p.e./track length (p.e./cm)

Figure 3.25: The comparison between data
and Monte Carlo simulation in the charge ratio distribution of vertical-µ and horizontal-µ
events, and the distribution of reconstructed π 0invariant mass. Upper left and right figures are
the distribution of charge ratio in vertical-µ andhorizontal-µ, respectively, and the lower figureis the distribution of reconstructed π 0 invariant mass. In all figures, red crosses and blackboxes show data and Monte Carlo simulation,
respectively. The difference between Monte
Carlo simulation and data in the mean valueof charge ratio is +2.0 ± 0.1% in vertical-µ and−2.3 ± 0.5% in horizontal-µ, and the differencein the peak values of π 0 mass is −2.1 ± 0.2%.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 3. Experimental Components and Their Performances(MC-Data)/Data (%)

46

5
4
3

Verticalthru-µ2

VerticalStop-µ

2.0±0.1%1

1.2±0.1%0-1-2.3±0.5%-2.1±0.2%-2.8±0.3%

Horizontal
thru-µπ0-mass-2-3-4

Figure 3.26: The summary of various measurementson the energy scale in 1KT. All the results settled to bewithin +2−3 % difference. This is quoted as the systematic
error on the measurements of particle momentum in
1KT.

PC

Entries

-5

2250

Data

2000

MC

1750
1500
1250
1000
750
500
250

peak of total p.e. / track length (pe/cm)

0

0

5000

10000
15000
Total number of p.e.

Figure 3.27: The distribution of the total number ofphotoelectrons for single ring µ-like events with theparticle fully contained in the inner detector of 1KT.
Red circles are for data and black boxes are for a Monte
Carlo simulation. They reasonably agree, showing theenergy scale of 1KT is well calibrated.

30
28
26

1999

2000

2001

24
22
20
18
16
14
12
10
8
6
4
2

Ph.D. Thesis by Issei Kato, July 2004

AUG

JUN

APR

FEB

DEC

OCT

AUG

JUN

APR

FEB

DEC

OCT

AUG

JUN

0

Figure 3.28: Stability of the energy scale in 1KT
during K2K-I period. The charge ratio for vertical-µ
events is plotted. Closed (open) circles show the datataken with (without) the buffer-amplifiers on the input
of ATM. Since Jan. 2001, cosmic ray data have beentaken between beam spills during neutrino beam is on,which are drawn by crosses.

3.5. Near neutrino detectors

47

Figure 3.29: A schematic view of
SciFi detector. It is consist of 20 setsof X- and Y- scintillating fiber sheets,
19 water-filled aluminum layers, and 24
image intensifier tubes (IITs).

SciFi. A PMT is attached to each end of a scintillator to read out the scintillation light. The
downstream TGC is used as trigger for SciFi and MRD. It is consist of 40 scintillators. The
dimensions of each scintillator are 466 cm in length, 10 cm in width, and 4 cm in thickness,covering the same area as upstream TGC. PMTs are attached to both ends of a scintillator.
The signals from PMTs are fed to TMCs (Time Mean Cell) and ADCs, where the information
on event timing and deposit energy are recorded. Using the relative timing of two PMTs on
both ends of a scintillator, the horizontal hit position can be measured with the resolution of
better than 5 cm. The energy resolution for minimum ionizing particles (MIP) is measured
using cosmic-ray data to be 7.4%.

3.5.3

Scintilating fiber tracker

Scintillating fiber tracker [45] with water target tanks (SciFi) is located downstream of the 1KT
tank, between the upstream and downstream TGC. The upstream surface of SciFi is at 300 m
downstream of the production target.
Fig. 3.29 shows a schematic view of SciFi detector. It consists of 20 tracking layers of 240 cm
wide, 19 aluminum tube layers filled with water, and 24 image intensifier tubes (IITs) with
CCD cameras (IIT-CCD). Each tracking layer is made of two scintillating fiber sheets, one is invertical direction (X-layer) and the other is in horizontal direction (Y-layer). The gaps between
tracking layers are 9 cm, where water-filled tanks are put. The thickness of the water-fill tanks
is 6 cm with aluminum wall of 0.18 cm thick. The water inside the tanks is designed to be thetarget of neutrino interactions, which is the same as SK and hence the systematic uncertainty
on the neutrino cross-section can be reduced. The total target mass is 6.0 tons of water and1.4 tons of aluminum structures.
When the charged particle passes through the tracking layer, the scintillation light is emitted
inside the scintillating fibers, and it is transmitted along the fibers to their edge. Then the lightis read out by IIT-CCDs. By analyzing the images detected by CCDs, the hit fibers are identified
as pixel clusters, and the tracks of particles are reconstructed by connecting these hits. The
resolution of hit position is estimated to be 0.73 mm for muons with the energy of less than
Ph.D. Thesis by Issei Kato, July 2004

Efficiency

48

Chapter 3. Experimental Components and Their Performances

1.2
1
0.8
1999 cosmic data
2000 cosmic data

0.6

2001 cosmic data

0.4
0.2
0

0

2.5

5

7.5

10

12.5 15 17.5 20
Track Length (Layers)

Figure 3.30: The track finding efficiency
in SciFi as a function of the length of
track. The horizontal axis is the numberof SciFi layer tracks penetrate. Efficiency
is ∼ 70% (∼ 87%) in the track length of
3 (4) SciFi layers, and approaches 100% in
longer tracks. These values are estimatedusing cosmic-ray data.

1 GeV and 0.61 mm for muons with the energy of greater than 1 GeV [46]. Since SciFi does
not have good timing information due to slow light emission of fluorescence sheet in IIT, eventsin which charged particle penetrates into TGC downstream of SciFi are used in the analysis.
Using the timing information of TGC, events in beam spill are selected.
The noise hits in SciFi had been measured using cosmic-ray and random trigger data. Thesehits are reproduced by Monte Carlo simulation. The average number of noise hits per event due
to noise of IIT-CCD is estimated to be 52, and 17 hits per event due to the beam associatedbackgrounds, which is quite low considering the total number of fibers (274,080) [46].
The hit finding efficiency is estimated to be about 95% for all IIT-CCDs, and it has beenstable through the whole run periods within 2% fluctuation [46]. Tracks with more than 3
hit layers are reconstructed in out algorithm. The efficiency to find a track is estimated using
cosmic-ray data to be ∼ 70% in tracks with the length of 3 layers, ∼ 87% in tracks with thelength of 4 layers, and it approaches 100% in longer tracks [46], as shown in Fig. 3.30.
More detailed descriptions on SciFi can be found in [45, 46, 47].

3.5.4

Lead glass Cherenkov calorimeter

Lead glass Cherenkov calorimeter (LG) is located downstream of the SciFi detector in order todistinguish electrons from muons for the measurement of the contamination of electron neutrinosin the beam. Fig. 3.31 shows schematic views of a cell and a module of LG. LG consists of 10
modules, and each module consists of 60 LG cells arranged in 12 × 6. The dimensions of a LG
cell are about 10 cm × 10 cm × 34 cm. A 5-inch PMT, R1652 made by Hamamatsu Photonics
Corporation, is attached to each LG cell to read out the Cherenkov light which is emitted bycharged particles passing through the LG cell. LG was once used in the TOPAZ experiment [48],and we re-use it in the K2K experiment.
Information of each cell on hit timing and light yield is recorded by TMC and ADC. ADC
information is used to cluster hits and to match the SciFi track with LG cluster.
The energy deposit of MIP in LG is estimated to be 280 MeV when a particle penetrates
perpendicular to LG module, i.e. the path length of 34 cm in LG.
Further information on the performance of LG can be found in [49].
Ph.D. Thesis by Issei Kato, July 2004

3.5. Near neutrino detectors

49

113 mmLead Glass

PMT

light guide

122 mm

135 mm

φ76

3.70

122 mm

140 mm

340 mmlead glass 12 x 5

Al support
1 module
Figure 3.31: Schematic views of a cell (upper) and a module (lower) of lead glass Cherenkov
calorimeter. One module consists of 60 cell arranged in 12 × 5.

3.5.5

Muon range detector

The muon range detector (MRD) [50] is a range type calorimeter located at the most downstream
of ND. The purpose of MRD is to measure periodically the intensity, profile, and energy spectrumof the neutrino beam. It is also used to measure the energy of neutrino induced muons whichinteractions take place inside SciFi.
Fig. 3.32 shows a schematic view of MRD. It consists of 12 iron absorbers sandwiched with
13 sets of vertically and horizontally aligned drift chambers. The size of each layer is about
7.6 m × 7.6 m in area. The most upstream 4 iron plates are of thickness of 10 cm in order toobtained a good energy resolution. The remaining plates are of thickness of 20 cm. The total
thickness of iron absorbers is 200 cm which covers the energy of muons up to 2.8 GeV/c. Total
mass of iron plates is 864 tons which can induce statistically enough neutrino interactions tomonitor the stabilities of the intensity and profile of the neutrino beam by each week and theenergy spectrum of neutrino beam by each month.
The drift chambers in use are once used in the VENUS detector [51, 52] at TRISTAN. There
are 829 modules. Each module has 8 drift tubes of 5 cm × 7 cm in cross section and 7.6 m inlength. Each drift tube has a tungsten wire of 70 µm in diameter. Twenty-five modules arearranged to make up one layer of drift tubes. The layer covers an area of 7.6 m × 7.6 m to besensitive. There are 6,632 drift tubes in total. Each drift tube is filled with P10 gas which is the
mixture of 90% argon and 10% methane. Negative high voltage of 2.7 kV is supplied to eachwire in MRD operation.
The timing of each hit wire with respect to the beam spill timing is recorded by 6-bit singlehit TDC with 20 MHz clock. The hit efficiency and the tracking efficiency are estimated using
cosmic-ray data. The hit efficiency becomes plateau to be about 97% around 2.5 kV suppliedhigh voltage [50]. The tracking efficiency is about 65% for the tracks with one traversed ironplate and about 95% for the tracks with two traversed plates, and it goes up to 97.5% for much
Ph.D. Thesis by Issei Kato, July 2004

50

Chapter 3. Experimental Components and Their Performances

Top View

νSide Viewνchamber

Figure 3.32: A schematic view of the muon
range detector (MRD). MRD consists of 12
iron absorbers sandwiched with 13 sets of vertical and horizontal drift chambers. The sizeof each layer is 7.6 m × 7.6 m in area. First 4iron plates are of thickness of 10 cm, and therests are 20 cm.

iron plate

=E
@
=? C

DD?
BC

>?A@=






 


9;:<  !#"%$'&(*)+$-,/."%$102"3 45$1&6!7,8"%$-0

Ph.D. Thesis by Issei Kato, July 2004

Figure 3.33: The tracking efficiency as a function of
the track length in MRD. For the tracks with one(two) traversed iron plate, the tracking efficiency isabout 65% (95%). It goes up to 97.5% for much longer
tracks.

3.5. Near neutrino detectors

51

Front detector DAQ
online WS

Analog signal

monitor PC

Digital signal

DATA server
Ethernet

ADC

Fastbus

MemoryModuleFrontend
Board

ADC

Sun Bit3

FADC
(NIM)

ATM

ADC TDC

DORAE
module

TDC

MP

F-I/F

TMC

MP

Input
Register

TKO

HPRT
FIFO

MP

HPRT

Discri.

Muon Range
Detector

TGC
PMTs

LG
PMTs

IIT,CCDSCIFI

1kt detector
PMTs

Figure 3.34: A schematic diagram of thedata acquisition system in ND. Three onboard computers are devoted to collect data
in ND. One is SUN Bit3 which is dedicatedto 1KT, and the others are to FGD. Another
online computer, “event builder”, collect datafrom each detector, sort it using the beam
spill number, and build up a spill data.

longer tracks [50], as shown in Fig. 3.33.
The number of noisy channels in MRD are monitered during the data taking. It is typically
about 40−50 channels out of 6,632 channels, which is small enough not to affect the tracking
performance.
The more detailed descriptions on MRD can be found in [50, 53].

3.5.6

Data acquisition system in ND

The data of each detector in ND is taken spill by spill, which is triggered by the beam timing
signal distributed by the accelerator 120 µsec before each beam spill.
Fig. 3.34 shows a schematic diagram of the data acquisition system in ND. The DAQ system
in ND has 3 front end computers. A SUN Bit3 computer collects 1KT data from ATM, TRG,
FADC, and TMC modules. Two on-board computers, HP-RT, collect FGD data, one is dedicatedto the data acquisition in SciFi, and the other is for MRD, LG, and TGC. These computerssend the data to another online computer called as “event builder”. The event builder sorts thedata from each detector using the beam spill number, and build up “one spill data”. The data
size of ND is about 1 MB per spill.

Ph.D. Thesis by Issei Kato, July 2004

52

Chapter 3. Experimental Components and Their Performances

Figure 3.35: A schematic view of Super-Kamiokande detector. SK is located 1,000m underground in
the Kamioka mine, just below Mt. Ikenoyama. The tank of SK is cylindrical in shape, and its size is41.4 m in height and 39.3 m in diameter. The tank is optically separated into inner and outer region.
The size of inner region is 36.2 m in height and 33.8 m in diameter, and the thickness of outer region isabout 2 m. On the wall of inner tank, 11,146 20-inch PMTs are installed, while 1,885 8-inch PMTs are
installed on the wall of outer tank.

3.6

Far neutrino detector

Super-Kamiokande detector (SK), a cylindrical 50 kt ring image water Cherenkov detector, isemployed as the far detector of the K2K experiment. Fig. 3.35 shows a schematic view of
SK site. It is located in the Kamioka Observatory of Institute for Cosmic Ray Research, theUniversity of Tokyo, in the Kamioka mine in Gifu. It is 250 km far from KEK, and at 1,000 m
underground (2,700 m water-equivalent) just below the peak of Mt. Ikenoyama, which shields
cosmic-rays and the intensity of cosmic-ray muons is about 1/100,000 of that on the ground.
The Super-Kamiokande experiment started its data taking on April 1, 1996 for various physics
motivations, such as nucleon decay search, observation of atmospheric neutrinos, solar neutrinos,
and Supernova neutrinos.
Since there exist a number of documents on the Super-Kamiokande detector [54, 55, 56,57], only brief descriptions about the detector, the data acquisition system, and the detector
calibrations are provided here.
Ph.D. Thesis by Issei Kato, July 2004

3.6. Far neutrino detector

3.6.1

53

Detector structure

The detector is quite similar to 1KT, except for its size; a cylindrical tank with the dimensionsof 41.4 m in height and 39.3 m in diameter. It is filled with 50 kt water. The tank is opticallyseparated into two concentric cylindrical regions by PMT support structure and opaque sheets.
The size of inner region is 36.2 m in height and 33.8 m in diameter containing 32 kt water.
This part of detector is referred as the inner detector (ID). On the wall of ID, 11,146 20-inch
PMTs, R3600 made by Hamamatsu Photonics Corporation, are attached to the support framewith inward-facing. PMTs are uniformly distributed with 70 cm intervals between PMTs. The
photocathode coverage of ID is about 40%. The rest of the surface of the ID wall is covered
with black polyethylene telephthalate sheets.
The outer region completely surrounds the ID with the thicknesse of 2.05 m on the top andbottom and 2.2 m along the barrel wall. This part is referred as outer detector (OD). To theouter side of the support structure, 1,885 8-inch PMTs, R1408, are attached in order to veto
the incoming particles. The wall of OD is covered with reflective Tyvec sheets to maximize thedetection efficiency.

3.6.2

Water purification system and water transparency

The water for SK is provided from the abundant spring water in the Kamioka mine. Dustand radioactive materials in the water make water transparency worse and become sources ofbackground events. In order to reduce them, ultra-pure water is filled in the tank by employing
a water purification system. The water system in SK is almost the same as that in 1KT: Thebacteria is killed by UV sterilizer, dusts of the size of down to 10 nm are filtered out, and thetemperature of the water is kept to be around 13◦ C to suppress the growth of bacteria. One
difference from the system in 1KT is that the vacuum degasifier is employed to remove thedissolved gases in the water, such as oxygen and radon; oxygen makes the water transparency
worse, which becomes a problem in a large detector, and radon can become a source of background events in the observation of low energy neutrinos such as solar neutrinos. Furthermore,radon-free air is supplied to the SK site in order to prevent radon dissolving into the water.
The water quality is measured and monitored by two methods; one is a direct measurementof an attenuation length using a light source and photo-detector, and the other is a measurement
using cosmic-ray muons.
The dye laser light with several wavelength is led into the tank via a optical fiber and diffusedby a diffuser ball which is put on an end of the fiber. The light from the diffuser ball is detectedby a CCD camera which is set at the top of the tank. The light intensity is measured with the
diffuser ball set at several water depth, and then the attenuation length of the water is directly
obtained, which gives an attenuation length of about 98 m [54].
The water transparency is also measured using the Cherenkov light of cosmic-ray muons. The
track of muon is reconstructed by connecting the entrance and the exit point, and then the path
length of the Cherenkov light from the muon track to each PMT can be calculated. By looking
at the dependence of the Cherenkov light intensity on the path length of light, an attenuation
length is obtained. This measurement gives the attenuation length of about 95 m [54], which isconsistent with the results mentioned above.
The light scattering parameters, such as coefficients of Rayleigh scattering, Mie scatteringand absorption, are also measured in SK by injecting well-directional light into the water [54].
All the water parameters are put into our detector simulation.
Ph.D. Thesis by Issei Kato, July 2004

54

Chapter 3. Experimental Components and Their Performances

Inner DAQ
×6

20-inch PMT´ 8· PMT ´ 11146

SCH
ATM

· ATM ´ 946

´ 20

´ 240

ATM
GONG

TKO

· SMP ´ 48

SUN classic· online computer
server ´ 9host ´ 1

onlinecomputer(server)interfaceSMP´ 6

SUN sparc10

trigger signal(to ATMs)HITSUM(from ATMs)

VME

trigger logic

onlinecomputer(host)

SUN classic

VME

FDDI

onlinecomputer(server)interface
TRG

NIM

Local Hitsum

QTC
Modulex40/quadx10/quad

TDC
x5
4 LSBsHigh Voltage

16 bit event #TDC

FASTBUSPMT

Paddle Card

StruckSupply~470/quadrant

FSCC

AUX

84 pin data ribbon cables

Ethernet FSCC Control

Figure 3.36: Schematic diagrams of the data acquisition system for the inner (upper) andouter (lower) detectors in SK.

3.6.3

Data acquisition system in SK

Electronics for inner detector
The data acquisition system for ID in SK is almost the same as that in 1KT described inSec. 3.5.1. The upper figure in Fig. 3.36 shows a schematic diagram of the data acquisition
system for ID in SK. Four electronics huts are located on the top of the SK tank, each of whichcollect data of 1/4 part of ID with 2 online computers. In order to receive, digitize, and record
charge and timing information from ID-PMTs, 946 ATMs are used in total. The HITSUM
signals from ATMs are summed up in each electronics hut and sent to the central hut which isalso located on the top of the tank. In the central hut, HITSUM signals from 4 electronics huts
are further summed up, and the global trigger decision is made using summed-up HITSUM. If
the global trigger is generated, the data in ATMs are read out separately by 8 online computers
through 48 SMP modules. Data collected by computers in each huts are transfered to the on-line
Ph.D. Thesis by Issei Kato, July 2004

3.6. Far neutrino detector

55

host computer via FDDI network and merged to make up a complete event.
Electronics for outer detector
The lower figure in Fig. 3.36 shows a quadrant of OD electronics. Signals from OD-PMTs aresent via paddle cards to QTCs (charge-to-timing converter). The QTC makes rectangular pulse
whose leading edge corresponds to the signal arrival timing and whose width is proportional tothe input charge. QTC also makes HITSUM signal which is sent to the central hut to make a
trigger decision. The pulses from QTCs are digitized by LeCroy 1877 multi-hit TDC modules
in a FASTBUS crate. The dynamic range of TDC is set to be 16 µsec with the minimum time
unit of 0.5 nsec. The control and read-out of TDC modules are performed by FASTBUS smart
crate controller (FSCC) and stored data are sent to the online computers through a VME bus.
In addition to the OD-PMT information, GPS timestamps are also taken by a VME module of
the OD electronics. The OD data collected by each online computer are also sent to the online
host computer to be merged with each other.
Trigger decision
The global trigger decision is made in the central hut using the pulse height of ID and OD
HITSUM signals which are sent from 4 electronics huts. SK has 4 types of trigger; high energy(HE), low energy (LE), super low energy (SLE), and OD trigger, among which first three triggers
are of ID.
The HE trigger is used mainly to record atmospheric neutrino events, proton decay candidates, cosmic-ray muons, and K2K-beam neutrino events, The threshold for ID HITSUM is set
to be 340 mV which is corresponding to 31 hits in 200 nsec time window. Its trigger rate isabout 5 Hz.
The LE trigger is used for solar neutrino events with the energy of greater than 5−6 MeV.
The threshold of HITSUM is 320 mV corresponding to 29 hits in 200 nsec time window. The
trigger rate for LE events is typically about 11 Hz.
The SLE trigger have been used since May 1997, in order to lower the analysis threshold ofsolar neutrino to be about 4.6 MeV.
The LE and SLE triggers are not used at all for K2K analysis.
The OD trigger is used to reject cosmic-ray muon events. The threshold is set to be about
19 OD-PMT hits in 200 nsec time window.
If the global trigger is generated, the trigger signal is distributed to all electronics hut torecord the data into online computers. The VME-TRG module records the trigger type of each
event. The GPS time stamp is also acquired when the trigger type of the event is HE or OD.

3.6.4

ATM, PMT gain, and timing calibrations

Several calibrations had been done to obtain better PMT information. The way of each calibration is very similar to that done in 1KT described in Sec. 3.5.1.
The linearity of responses of all ATM channels had been measured in the same method as
1KT described in Sec. 3.5.1. PMT hit timing versus signal pulse height correlation, so-called“T-Q map”, is also measured using laser system. It is also quite the same as 1KT case describedin Sec. 3.5.1. These results are used to correct the charge and timing information.
The relative PMT gain is measured by Xenon system. Using its results, the high voltage
values supplied to PMTs are determined so that all the PMTs give a common gain. After the
Ph.D. Thesis by Issei Kato, July 2004∆(M.C./DATA) (%)

56

Chapter 3. Experimental Components and Their Performances

10
8
6
4
2
±2.5%

0
-2
-4
LINAC
decay-e0π-6-8low E stop-µ
high E stop-µ

-10
10

2

10

3

10

4

10

5

Figure 3.37: The results of the measurements of absolute energy scale with several
calibration sources in SK. The correspondence of each point to the calibration source
is as shown in the figure. Through the entire range of momentum from 16 MeV/c to
10 GeV/c, the data and our Monte Carlo simulation are in agreement at 2.5% accuracy.

Momentum(MeV/c)

adjustment of supplied high voltage, the spread of relative gain among PMTs is about 7% [54].
The remaining gain differences are corrected by software.
The absolute gain scale of PMTs had been determined by using the charge distributionof the single photoelectron signal, which is obtained by the low energy gamma emission fromthe thermal neutron capture on nickel, where 252 Cf is used as a neutron source. A cylindricalpolyethylene vessel, which contains Ni wires together with 252 Cf and water, was set at the centerof the tank. The neutrons emitted by 252 Cf are thermalized in the water and captured by Ni
wires. Then the gamma-rays of the energy of 6−9 MeV are emitted by the nuclear reaction of thecapture. The gamma-rays are converted to electron via Compton or photo-electron scattering,and the Cherenkov light is emitted. In these low energy events, the number of photoelectrons
detected in a PMT is at most one, and hence a single photoelectron distribution can be obtainedby collecting these events. From this calibration, single photoelectron signal is determined tocorrespond to 2.055 pC [55, 56, 57].

3.6.5

Calibration of the absolute energy scale

The determination of absolute energy scale had been done by using four calibration sources;
an electron linear accelerator (LINAC), decay electrons from stopping cosmic-ray muons, theinvariant mass of π 0 induced by neutrino interactions, and cosmic-ray muons stopping inside
the tank.
LINAC is used to understand the performance of the detector in the low energy region.
Electrons of the energy of 16 MeV accelerated by LINAC are injected into the water, and thereconstructed momentum was compared with a Monte Carlo simulation.
For the energy region of a few tens MeV, electrons emitted by muon decay are in use. The
mean value of the energy spectrum of the decay electrons is compared with that of MC.
Neutrino induced π 0 invariant mass is also used to understand the absolute energy scalearound 100 MeV. It is the same as 1KT case described in Sec. 3.5.1.
The relation between the Cherenkov angle and the momentum of stopping muons with themomentum of . 350 MeV/c is used to check the energy scale. For high energy stopping muons,
the relation between the track length and the momentum is used. In this sample, muons withthe track length of greater than 7 m are selected, corresponding to the energy of greater thanabout 1.7 GeV. These data are also compared with MC.
Fig. 3.37 shows the summary of the absolute energy scale calibrations. As shown in the
Ph.D. Thesis by Issei Kato, July 2004

3.7. Global positioning system for the time synchronization57

figure, the momentum range from 16 MeV/c to 10 GeV/c is examined, and data agree with ourMonte Carlo simulation within 2.5% precision throughout the entire momentum range. Fromthese results, we have quoted the uncertainty of the absolute energy scale in SK to be 3%.

3.7

Global positioning system for the time synchronization

As previously mentioned, the time synchronization between KEK and SK sites is essential todistinguish the beam neutrino events from atmospheric neutrino background. The global positioning system (GPS) is employed for the time synchronization.

3.7.1

Overview of GPS

GPS is a satellite navigation system founded and controlled by the U.S. Department of Defense(DOD). There are 27 satellites in six orbital planes. Each satellite has an atomic clock, whichrefers to the master clock at the U.S. Naval Observatory (USNO) and steered to Universal Time
Coordinate (UTC). These satellites send their time and position by radio wave. Receiving theinformation from 4 satellites at the same time, a GPS receiver can calculate its precise position
and time.

3.7.2

Time synchronization between KEK and SK

Fig. 3.38 shows a schematic view of GPS system used in the K2K experiment. It consists of GPS
receivers, a VME receiver, and a 50 MHz 32-bit local time clock (LTC). Two independent GPS
receivers (GPS1 and GPS2) are used in parallel in both KEK and SK sites for the hardware
backup as well as their quality check with each other. Identical sets of GPS system are set bothat KEK and at SK sites. The GPS/VME receivers and LTC are located in the beam line control
room and the GPS antennae are mounted on the roof of the room in the KEK site. On theother hand, in SK site, the GPS receivers and their antennae are located at a house outside the
Kamioka mine near its entrance, and the VME receiver and LTC are set in the central hut on
the top of the SK tank in the mine. The GPS signal is sent to the central hut via a optical fiber
through the distance of 1.7 km.
The GPS receiver provides UTC time stamps every 1 sec and 1 Hz square pulses whichleading edges are synchronized to UTC. Its accuracy is better than 40 nsec in average and
150 nsec at the worst. UTC time stamp of GPS receiver is sent to and decoded by the VME
receiver. LTC is a free-running 50 MHz 32-bit clock counter. It has two input channels. The
1 Hz pulse from the GPS receiver is fed to one of LTC inputs. To another input channel of LTC,
beam spill trigger is fed in the KEK site and logical OR of the HE trigger and OD trigger is
fed in the SK site. The UTC time stamp and the current count of LTC are recorded when LTC
receives the GPS 1 Hz pulse (“GPS-data”), while only the current count of LTC is recorded
when it receives an event trigger signal (“event-data”). UTC time stamp and LTC counts areread by online computer.
The principle to determine the event triggered time is also shown in Fig. 3.38. The event
triggered time is calculated as followings: When event is triggered, the LTC count at the event
trigger Nev is recorded as an event-data. By looking at the latest two GPS-data, two sets of
UTC time stamp and LTC count can be known, i.e. (Tn−1 , Nn−1 ) and (Tn , Nn ). The time ofthe event trigger Tev is obtained by the linear interpolation;
Tev = Tn +Nev − Nn
Nn − Nn−1

.

(3.6)

Ph.D. Thesis by Issei Kato, July 2004

58

Chapter 3. Experimental Components and Their Performances

Time stamp(every 1sec)

UTC

VME receiver(decode to UTC)GPS receiver

OnlineComputer

1pps

LTC (50MHz
32bit clock)

LTC count

Event trigger

1 sec
GPS receiver/VME receiver

UTC=T n-1

UTC=T nLTC=Nn-1

LTC=NnEvent Trigger

LTC

Record DATA

UTC&LTC

UTC&LTC

Event time = Tn +LTC=Nev
LTC

Nev- N n
Nn - N n-1µsec

Figure 3.38: A schematic view of GPS system in the K2K experiment. It consists of GPS receiver,VME receiver, and 50 MHz 32-bit LTC clock. The identical systems are set at KEK and SK.

1

0

-1

-2

-3

7500

8000

8500

9000

9500 10000
SK run number

Ph.D. Thesis by Issei Kato, July 2004

Figure 3.39: The stability of LTC in SK site. The
vertical axis is the difference of the LTC count for
1 sec interval from the nominal one (50 MHz) expressed in the unit of µsec. Horizontal axis is the run
number of Super-Kamiokande, which range is corresponding to the whole run period, i.e. from June
1999 to July 2001.

3.7. Global positioning system for the time synchronization

59

The synchronization of GPS receivers at KEK and SK had been taken using an atomic clock
before the experiments started. The difference of these two GPS times with respect to theatomic clock was measured to be 115 ± 142(syst.) nsec [58]. The absolute time synchronization
had been done with this accuracy.

3.7.3

Stability of GPS system

Two independent GPS were compared as a check of the system, resulting in the agreement witheach other within 100 nsec (HWHM) [59]. The stability of the system is continuously monitored
in SK site by looking at LTC count in 1 sec, Nn − Nn−1 . Fig. 3.39 shows the stability of the
LTC frequency during the whole run period, i.e. from June 1999 to July 2001. The verticalaxis shows the difference of Nn − Nn−1 from the nominal one (50 MHz). In our calculationof the event time, as long as the LTC frequency does not vary abruptly, slow drift of the LTC
frequency is not problem since we use LTC count of just 1 sec before. It is stable within 200 nsec
throughout the whole run period although there happened jumps several times.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 4Monte Carlo Simulations
In order to study our detection schemes and various systematics, Monte Carlo simulations areused. Our Monte Carlo simulations consist of three modules; a simulation for the neutrino beam
“Beam-MC”, a simulation for neutrino interactions “Neut-MC”, and a simulation for detectors“DetSim”. In this chapter, information on these simulation tools is provided in this order ineach section.

4.1

Neutrino beam simulation: Beam-MC

A neutrino beam simulation, Beam-MC, simulates properties of our neutrino beam. It starts
from the proton injection onto the production target, produces secondaries, then focuses themin the horn magnets, and track them until they decay into neutrinos. The tracks of neutrinos
extraporated to ND and SK, the fluxes and the energy spectrum at ND and SK are provided.

4.1.1

Proton injection onto the production target

Protons with a kinetic energy of 12 GeV are injected onto the aluminum production target. The
profile and divergence of the primary proton beam are the input parameters to the Beam-MC,
which are measured using V39out- and TGT-SPICs.
Fig. 4.1 shows a schematic view of the measurements for the profile and the divergence of the
proton beam. The distance between V39out- and TGT-SPICs (L) is 128 cm and that between
TGT-SPIC and the surface of the target (l) is 37 cm. The x and y profiles of the beam at
V39out-SPIC and TGT-SPIC are measured and fitted by Gaussian functions with the width of
σ1x,1y and σ2x,2y , respectively. Then, they are extrapolated to the surface of the target to obtain
the profile at the surface of the target;
σx,y = σ2x,2y + (σ2x,2y − σ1x,1y ) ·

l
L

.

(4.1)

V39 quadrupole
magnet
































1st HORN
V39-SPIC

TGT-SPIC







σ2

σ1













σx 
 Target
 
 
 
 
 rod
 







L=128cm









 
 
 
 
 
 
 









l =37cm

61

Figure 4.1: A schematic view of the measurements of the profile and the divergence of the
primary proton beam. The distance between
V39out-SPIC and TGT-SPIC is 128 cm andthat between TGT-SPIC and the surface of thetarget is 37 cm.

62

Chapter 4. Monte Carlo Simulations

Table 4.1: Summary of the beam parameters for the runs in K2K-Ia and K2K-Ib.
Parameters
Target material
Rod diameter
Horm current
Beam spread in x (σx )Beam spread in y (σy )Beam divergence coefficient in x (kx )Beam divergence coefficient in y (ky )K2K-Ia (in June 1999)
Al 6061-T
2 cm
200 kA
1 mm
6 mm−8 mrad/mm−0.4 mrad/mm

K2K-Ib (since Nov. 1999)
Al 6061-T
3 cm
250 kA
3.4 mm
7.2 mm−2.5 mrad/mm−0.14 mrad/mm

Assuming the linear correlation in (x, θx ) and (y, θy ) planes, the injection angle (or divergence)of proton (θx , θy ) at the position of (x, y) is obtained;
θx = kx · xandθy = ky · y

,

(4.2)

where kx,y is the correlation coefficient determined by
kx,y =

σ2x,2y − σ1x,1yσ2x,2y · L + (σ2x,2y − σ1x,1y ) · l

.

(4.3)

For our standard Beam-MC, the center of the proton beam is set to be at the center of thetarget rod. Table 4.1 summarizes the parameters of the beam properties for the runs in June
1999 (K2K-Ia) and in the rest of the periods (K2K-Ib).

4.1.2

Production of secondary particles in the target

There have been various pion production experiments in the energy region of the K2K experiment, whose results are inconsistent with each other. This causes one of the largest ambiguities
in the Monte Carlo simulation. There are some models for the pion production, among which
three kinds of models are used in our study.
1. GCALOR/FLUKA model;
GCALOR/FLUKA model [60, 61, 62] is a package of hadron simulation prepared for
GEANT [63] detector description and simulation tool. This model has larger p -Al crosssection than other models.
2. Fit to measurements (I), Sanford-Wang;
This model is the result of the compilation of the measurements done by Lundy et al. at
a proton momentum of 13.4 GeV/c [64], Dekkers et al. at 11.8, 18.8, and 23.1 GeV/c [65],and Baker et al. at 10.9, 20.9, and 30.9 GeV/c [66], fitted to an empirical formula of thedifferential cross-section for secondary particle production suggested by J. R. Sanford and
C. L. Wang [67, 68]: Yamamoto’s measurements [69] agrees well with the results of thiscompilation.
3. Fit to measurements (II), Cho-ANL and Cho-CERN;
These are other results of the compilations to fit several measurements to the Sanford-Wang
formula. The measurements done by Marmer et al. at 12.3 GeV/c [70, 71], Cho et al. at
12.4 GeV/c [72], Asbury et al. at 12.5 GeV/c [73], and Allaby et al. at 19.2 GeV/c [74] areused in the Cho-ANL compilation [72]. There exists another result of compilation called
Cho-CERN [75], which uses the data set of mainly from Cho et al. at 12.4GeV/c. These
two compilations give almost the same differential cross-sections.
Ph.D. Thesis by Issei Kato, July 2004

4.1. Neutrino beam simulation: Beam-MC

63

Table 4.2: The fitted parameters of the Sanford-Wang formula for the positive pion
production in Sanford-Wang [68], Cho-ANL [72], and Cho-CERN [75] compilations.
Compilations
Sanford-Wang
Cho-ANL
Cho-CERN

C1
1.09
0.96
1.05

C2
0.65
1.08
1.01

C3
4.05
2.15
2.26

C4
1.63
2.31
2.45

C5
1.66
1.98
2.12

C6
5.03
5.73
5.66

C7
0.17
0.13
0.14

C8
82.7
24.1
27.3

As mentioned above, the Sanford-Wang formula gives a quantitative description for thesecondary particle production. It is an empirical formula based on experimental data as follows;
Ã
!
¶
µ
d2 n
C 3 pC 4
p
C2
C8= C1 p1−
exp − C5 − C6 θ (p − C7 pB cos θ)
,
(4.4)
dΩdp
pB − 1pB
where d2 n/dΩdp is the differential particle yield per interacting proton, θ is the angle between
the secondary particle and the beam axis in the laboratory frame, p and pB are the momentumof the secondary particle and the incident proton, respectively, and Ci ’s are the constants tobe found by fitting. The fitted results about the positive pion production for Sanford-Wang,
Cho-ANL, and Cho-CERN compilations are summarized in Table 4.2. The resulting parametersof the negative pion production for the Sanford-Wang and the Cho-ANL compilations are listed
in [72] as well as those of the positive pion production. The comparison of the experimental
measurements with the fitting curve of Cho-CERN are shown in Fig. 4.2.
In the case of use of GCALOR/FLUKA model, the GEANT automatically simulates everything using the GCALOR/FLUKA package.
In use of other models, the hadron production is simulated according to the formula (4.4) only
when enegetic protons with the energy of more than 10 GeV interact with the target aluminum,and other cases of interaction are simulated according to GCALOR model. In our simulation,
the negative pion production is simulated using the parameters of Sanford-Wang model even in
the use of Cho-ANL or Cho-CERN models. For the kaon production parts, the formula (4.4) isused with the kaon parameters in reference [69] in all three models.
Since the momentum and anlular distribution of the pions measured by PIMON favors the
Cho-CERN model better than the others although the PIMON results are consistent with all
the models within its errors, we have adopted it as the standard hadron production modelin our simulation, while the others are used for comparison and the estimation of systematic
uncertainties.

4.1.3

Particle tracking through the horn magnets and decay volume

By using GEANT with GCALOR hadron simulator, scattered protons and generated secondary
particles are traced through 2 horn magnets and decay volume until they decay into neutrinos orabsorbed in materials. As described in Sec. 3.1.2, the toroidal magnetic field given by Eq. (3.1)
is made inside the horn magnets. The focusing effect of the magnetic field is also simulated by
GEANT.

4.1.4

Particle decays into neutrino

In the GEANT simulation, the flavor of neutrinos and their anti-particles are treated as identicalparticles. However, in our use, they have to be treated differently since we also want to know how
Ph.D. Thesis by Issei Kato, July 2004

Chapter 4. Monte Carlo Simulations

d σ/dΩdP (mb/sr/(GeV/c))

64

o

2

o

4

o

6

o

8

o

2

2

10

0

10

Cho et al. (1971) : 12.4GeV/c 0-12deg
Marmer et al. (1969,1971) : 12.3GeV/c 0,10deg
Asbury et al. (1970) : 12.5GeV/c 12deg

CERN compilation fit using mainly Cho et al. data

12

1
0

1

2

3

4

5

o

6

10

o

7

Pπ(GeV/c)

Figure 4.2: The differential cross-section of positive pion production in past experiments andfitted curves of Cho-CERN model. The correspondence of data points to measurements areshown in the figure. The solid lines are drawn according to the Sanford-Wang formula with
Cho-CERN parameters.

much fraction of the beam is contaminated by neutrinos other than muon neutrino although wewant to know the fluxes of muon neutrino at ND and SK. Therefore, the particle decays whichemit neutrino, i.e. the decays of charged pions, charged and neutral kaons, and muons in ourenergy region, and the type of neutrino are treated properly by our self-made simulator.
Decay of charged pions±) with branching
Pion decays into muon and neutrino (π + → µ+ νµ , π − → µ− ν µ , called πµ2
fraction of almost 100%, and hence only this mode is taken into account for the pion decay.
Therefore, neutrino from pion decay is always treated as muon neutrino. Since pion is a pseudoscalar particle, neutrino is emitted isotropically in the pion rest frame, and then it is boosted
toward the flight direction of the parent pion to obtain the 4-momentum of neutrino.

Decay of charged and neutral kaons
Since kaons are also pseudo-scalar particles, their decays are isotropic in the kaon rest frame.
The decay modes listed in Table 4.3 are taken into account for the calculation of the neutrino
fluxes in our Beam-MC. Other decays are ignored since their branching fractions are quite small.
Neutrinos from KS0 are also ignored for the same reason.
±
In Kµ2decays, which is just the two-body decay, the calculation method of neutrino energy
Ph.D. Thesis by Issei Kato, July 2004

4.1. Neutrino beam simulation: Beam-MC

65

Table 4.3: The kaon decay modes taken into account for the contribution to neutrino
beam in Beam-MC. In the KL0 decays, the charge asymmetry is correctly considered to
produce neutrinos or antineutrinos.
Kaon decay modes
K + → µ+ νµ , K − → µ− ν µ
K + → π 0 e+ νe , K − → π 0 e− ν e
K + → π 0 µ+ νµ , K − → π 0 µ− ν µ
KL0 → π − e+ νe , π + e− ν e
KL0 → π − µ+ νµ , π + µ− ν µBranching fraction
63.43%
4.87%
3.27%
38.79%
27.18%+(called Kµ2)+)(called Ke3+(called Kµ3)0(called Ke3 )0(called Kµ3)±
and direction in the laboratory frame is quite the same as that in πµ2
decay.
In K`3 decays, the Dalitz plot density ρ(Eπ , E` ) of V −A theory [20, 76] is employed in orderto obtain the neutrino energy in the kaon rest frame;ρ(Eπ , E` ) ∝ f+2 (t)[A + Bξ(t) + Cξ 2 (t)] ,

(4.5)

where
t = (PK − Pπ )2 ,f± (t) = f± (0)[1 + λ± (t/m2π )], ξ(t) = f− (t)/f+ (t),
¶
µ
1
1 0
0
2
A = mK [2E` (mK − Eπ − E` ) − mK Eπ ], B = m` Eν − Eπ , C = m2` Eπ0 ,
2
4
2
2
2
m + mπ − m`
Eπ0 = Eπmax − Eπ = K− Eπ .
2mK
Assuming time reversal invariance and also λ− = 0, the K`3 decay distribution is described by
the two parameters, λ+ and ξ(0). Referring to [20], the set of parameters (λ+ , ξ(0)) is taken tobe (0.028, −0.19) for the K ± decays and (0.030, −0.01) for the KL0 decay in our MC.
The charge asymmetry, δL (`) ≡ [Γ(π − `+ ν` ) − Γ(π + `− ν ` )]/[Γ(π − `+ ν` ) + Γ(π + `− ν ` )], is also
0 . We set δ (e) = 0.333 and δ (µ) = 0.304 forcorrectly taken into account in the decays of K`3L
L
0 and K 0 decays, respectively [20].
the Ke3µ3
The neutrino direction is randomly made in the kaon rest frame, and then the 4-momentumof neutrino is boosted by Lorentz boost according to the 4-momentum of the parent kaon.
Decay of muons
Muon decays via µ± → e± νe (ν e ) ν µ (νµ ), called µ±
e3 , with the branching fraction of almost 100%.
Polarization of muon is properly taken into account. The energy and angular distributions of
the muon antineutrino and the electron neutrino emitted from a positive muon in the muon rest
frame are, respectively, calculated by Michel spectra of V −A theory [76];d2 Nν µdxdΩcmd2 NνedxdΩcm∝∝2x2[(3 − 2x) + (1 − 2x)Pµ cos θcm ] ,4π
12x2(1 − x)(1 + Pµ cos θcm ) ,
4π

(4.6)
(4.7)

where x ≡ 2Eν /mµ , θcm is the angle between the neutrino momentum vector and the muon spin
direction, and Pµ is the average muon polarization along the beam direction. Corresponding
distributions for muon neutrino and electron antineutrino from negative muon decay are obtainedby the replacement of Pµ → −Pµ . Then, 4-momentum of each neutrino are boosted toward themuon direction by Lorentz transformation.
Ph.D. Thesis by Issei Kato, July 2004

66

4.1.5

Chapter 4. Monte Carlo Simulations

Monte Carlo prediction of neutrino properties at ND and SK

Since the horn magnets focus positively charged particles and the hadrons produced in thetarget are mainly pions, the composition of the neutrino beam is dominated by muon neutrino.
Fig. 4.3 shows the energy spectra of each type of neutrino at ND and SK estimated by BeamMC. About 97.3% (97.9%) of neutrinos at ND (SK) are muon neutrinos decayed from positive
pions, and small fraction of the beam is contaminated with neutrinos other than muon neutrino;νe /νµ ∼ 0.013 (0.009), ν µ /νµ ∼ 0.015 (0.012), and ν e /νµ ∼ 1.8 × 10−4 (2.2 × 10−4 ) at ND(SK). Contributions of each decay mode to each type of neutrinos are shown in Fig. 4.4. Main+−+0contribution to the fluxes of νµ , νe , ν µ , and ν e are πµ2, µ+e3 , πµ2 /µe3 , and Ke3 , respectively, while+
the higher energy part of νµ is dominated by Kµ2 decay.
The difference of the energy spectra estimated using different hadron production models,
GCALOR/FLUKA, Sanford-Wang, and Cho-CERN, are compared in Fig. 4.5. In this figure, thespectra of only muon neutrino are shown. In addition, the far-to-near spectrum ratio (F/N ratio)
predicted by Monte Carlo simulations with these hadron production models is also compared inFig. 4.5.
The behavior of F/N ratio as a function of the neutrino energy is qualitatively explained
as follows. First, the acceptance of neutrinos for SK does not change so much as a functionof neutrino energy because the decay volume seems to be point-like seen from SK. However,in ND, the acceptance of low energy neutrinos below about 1 GeV is smaller than that forhigh energy neutrinos and it strongly depends on the energy, since the low energy neutrinos,
which come from the decay of low energy pions, are emitted mainly at upstream region of decay
volume, and the flight length of pions before their decay becomes longer as pion energy becomes
higher. This causes a rise of the acceptance for ND as neutrino energy goes up, resulting in
the decrease of F/N ratio as neutrino energy increases in the low energy region. On the other
hand, neutrinos with the energy of above 1 GeV come from the pion with the momentum ofabove 2 GeV/c, which decay point is almost uniformly distributed along the decay volume, andhence the acceptance does not change so much as a function of neutrino energy. However ND
have larger solid angle than SK, and ND sees more off-axis neutrinos than SK. This makes theenergy spectrum in ND softer than that in SK, making the increase of F/N ratio above 1 GeV
as the neutrino energy goes up.
The difference of the energy spectra for the configurations in June 1999 (K2K-Ia) and afterNov. 1999 (K2K-Ib) are shown in Fig. 4.6. The mean energy of neutrino beam at SK is 1.24 GeV
in K2K-Ia, while it is 1.30 GeV in K2K-Ib.

Ph.D. Thesis by Issei Kato, July 2004

10
10

11

KEK
νµ

10

10

9

10

8

10

7

10

6

10

5

_

νe

_

νµ

νe

67
ΦνSK [cm-2 (0.1 GeV)-1 (1020 POT)-1]

ΦνFD [cm-2 (0.1 GeV)-1 (1020 POT)-1]

4.1. Neutrino beam simulation: Beam-MC

10Super-Kamiokande

5

νµ

10

4

10

3

νµ

10

2

νe

_

_

νe

10
1
-1

0

1

2

3

4

5

6

7
8
Eν [GeV]

10

0

1

2

3

4

5

6

7
8
Eν [GeV]

10

11
10

10

9

10

8

10

7

10

6

10

5

ΦνFD [cm-2 (0.1 GeV)-1 (1020 POT)-1]

0

νµ

π+µ2
νtotal
µ

K+µ2
K+µ3
Kµ03

µ–e3

1

2

3

4

5

6

_

10

9

10

8

10

νtotal
µ

10

6

10

5

_

νµ

Kµ–2
Kµ03

µ+e3

Kµ–3

0

1

2

3

4

5

6

10

10

7
8
Eν [GeV]

νe

9

µ+e3

8

K+e3
10

7

10

6

10

5

7
8
Eν [GeV]πµ–27ΦνFD [cm-2 (0.1 GeV)-1 (1020 POT)-1]

10ΦνFD [cm-2 (0.1 GeV)-1 (1020 POT)-1]

ΦνFD [cm-2 (0.1 GeV)-1 (1020 POT)-1]

Figure 4.3: The energy spectrum for each type of neutrinos at ND (left) and SK (right) estimatedby Beam-MC. The neutrino beam is 97.3% (97.9%) pure muon neutrino with the contaminations ofνe /νµ ∼ 0.013 (0.009), ν µ /νµ ∼ 0.015 (0.012), and ν e /νµ ∼ 1.8 × 10−4 (2.2 × 10−4 ) at ND (SK).

νetotal

K0e3

0

1

νetotal

10

7

10

6

10

5

10

4

2

3

4

5

6

_

_

νe

K0e3

0

7
8
Eν [GeV]

µ–e3
K–e3

1

2

3

4

5

6

7
8
Eν [GeV]Figure 4.4: Contributions of each decay mode to each type of neutrino. Top-left, top-right, bottomleft, and bottom-right figures are for νµ , νe , ν µ , and ν e , respectively. The fluxes shown here arethose estimated by Beam-MC at the position of ND (300 m downstream the production target).

Ph.D. Thesis by Issei Kato, July 2004

Chapter 4. Monte Carlo Simulations

Near Detector

1.2

GCALOR/FLUKA
Sanford-Wang
Cho-CERN

1

0.8
0.6
0.4
0.2
0

9

Far/Near Ratio [×10-6]

ΦνFD [×1011 cm-2 GeV-1 (1020 POT)-1]

1.4

ΦνSK [×104 cm-2 GeV-1 (1020 POT)-1]

68

Super-Kamiokande
8

GCALOR/FLUKA
Sanford-Wang
Cho-CERN

7
6
5

Far/Near Ratio
3.5
3

GCALOR/FLUKA
Sanford-Wang
Cho-CERN

2.5

integrated

2

4
1.5

3

1

2

0.5

1
0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Eν (GeV)4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Eν (GeV)0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Eν (GeV)Near Detector

1.2

Horn Current = 200 kA

1

0.8
0.6
0.4
0.2
0

0

0.5

1

1.5

2

2.5

3

3.5

ΦνFD [×1011 cm-2 (0.1 GeV)-1 (1020 POT)-1]

1.4
Near Detector

1.2

Horn Current = 250 kA

1

0.8
0.6
0.4
0.2
0

0

0.5

1

1.5

2

2.5

3

3.5

4 4.5 5Eν (GeV)

9Super-Kamiokande
8Horn Current = 200 kA

7
6
5
4
3
2
1
0

4 4.5 5Eν (GeV)ΦνSK [×105 cm-2 (0.1 GeV)-1 (1020 POT)-1]

ΦνFD [×1011 cm-2 (0.1 GeV)-1 (1020 POT)-1]

1.4

ΦνSK [×105 cm-2 (0.1 GeV)-1 (1020 POT)-1]

Figure 4.5: The energy spectra of muon neutrino at ND (most left) and SK (middle), and their ratio(most right) predicted by several hadron production models. The energy above 3 GeV is integrated in
F/N ratio. In each figure, black, blue, and red histograms are corresponding to GCALOR/FLUKA,
Sanford-Wang, and Cho-CERN models, respectively.

0

0.5

1

1.5

2

2.5

3

3.5

4 4.5 5Eν (GeV)

9Super-Kamiokande
8Horn Current = 250 kA

7
6
5
4
3
2
1
0

0

0.5

1

1.5

2

2.5

3

3.5

4 4.5 5Eν (GeV)Figure 4.6: The difference of the neutrino energy spectra at SK between the configurations in June
1999 (K2K-Ia) and since Nov. 1999 (K2K-Ib). Top two figures show the spectra in K2K-Ia, andbottom two show those in K2K-Ib. In both top and bottom figures, left and right ones are thespectra at ND and SK, respectively.

Ph.D. Thesis by Issei Kato, July 2004

σ per one nucleon (× 10-38cm2)

4.2. Neutrino interaction simulation: Neut-MC

69

6

Total cross section (H2O)
5

4

3

NC

2

CC multi-π10CC single-meson

0

4.2

1

2

CC quasi-elastic
3
4

5

Figure 4.7: Cross-section of each neutrino interaction
channel with water as a function of incident neutrinoenergy. The interaction of CC coherent pion production is assorted to that of CC single-meson production.
These cross-sections are provided by NEUT simulator.

Energy (GeV)

Neutrino interaction simulation: Neut-MC

The simulated neutrino fluxes described in Sec. 4.1 are passed to a neutrino interaction simulator,“Neut-MC (or NEUT)” [77], which is originally developed and used in the atmospheric neutrino
analysis in the Super-Kamiokande experiment [55, 56, 57, 78], although, in our analysis, we haveused the cross-section modified from NEUT according to some models in order to reproduce ourdata well. It simulates neutrino interactions with the target material through the charged
current (CC) and the neutral current (NC) weak interactions, providing the 4-momentum of theparticles produced in the interaction. The material of neutrino interaction target is H2 O in thewater Cherenkov detector. In this section, the calculation method of the cross-section for theseinteractions in NEUT and the modifications to it for our application are described.

4.2.1

Neutrino interactions in a few GeV region

The neutrino interactions in the energy region of our interest, i.e. Eν ∼ 1 GeV, are as follows:
•
•
•
•
•
•
•
•

CC quasi-elastic scattering (CC-qe)
NC elastic scattering (NC-elastic)
CC single-meson production (CC-1π)
NC single-meson production (NC-1π)
CC deep inelastic scattering (CC-DIS)
NC deep inelastic scattering (NC-DIS)
CC coherent-pion production (CC-coh.π)
NC coherent-pion production (NC-coh.π)

ν N → ` N0
ν N →ν N
ν N → ` N0 π
ν N → ν N0 π
ν N → ` N 0 mπ’s (m ≥ 2)
ν N → ν N 0 mπ’s (m ≥ 2)
ν 16 O → `∓ 16 O π ±ν 16 O → ν 16 O π 0(∼ 27%)(∼ 13%)(∼ 28%)(∼ 10%)(∼ 14%)(∼ 4%)(∼ 2%)(∼ 1%)

where N and N 0 denote nucleons and ` is charged lepton. The fraction of each interaction
mode is shown at the end of each line, where the cross-section is integrated over the neutrinoenergy of our beam. In the single-meson productions and deep inelastic scattering, the generated
meson and hadrons are pions in the most of the cases. Fig. 4.7 shows the cross-section of eachinteraction channel with water, calculated by NEUT simulator, as a function of incident neutrinoenergy.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 4. Monte Carlo Simulations

1.8

CC quasi-elastic
1.6

σ for free neutron (10

-38

2

cm )

70

ANL-12ft, 1977
BNL-7ft, 1981
CPS-GGM, 1977
Serpukhov, 1985

2

MA=1.01GeV/c
2
MA=1.11GeV/c2
MA=0.91GeV/c

1.4
1.2
1

0.8
0.6
0.4
0.2
0

0

4.2.2

1

2

3

4
5
Energy (GeV)

Figure 4.8: Cross-section of CC-qe interaction on afree neutron in our simulation, together with the results of the measurements by bubble chamber experiments. Horizontal axis is the incident neutrino energy. Solid, dashed, and dotted lines show the calculation of the cross-section in our simulation with
MA = 1.01, 1.11, and 0.91 GeV/c2 . Data points
are from ANL [79],BNL [80], GGM [81], and Serpukhov [82].

CC quasi-elastic and NC elastic scattering

The charged current quati-elastic (CC-qe) and neutral current elastic (NC-elastic) interactions
are the two-body scatterings of neutrino on a nucleon. The differential cross-section for themis described by the 4-momentum transfer squared of the interaction, Q2 ≡ −q 2 = −(pν − p` )2 ,where pν and p` are momenta of incident neutrino and out-going lepton, respectively. Since thetarget hadron has internal structure, vector and axial vector form factors have to be taken into
account. The hadron current is expressed by [83];¸·iσλν q ν ξFV2 (Q2 )
2
0
0
1
2
+ γλ γ5 FA (Q ) u(N ) ,(4.8)
hN |Jhad |N i = cos θc ū(N ) γλ FV (Q ) +2mN
where θc is the Cabbibo angle, mN is the nucleon mass. The vector form factors, FV1 , FV2 , arerepresented as followings;
µ
¶−1 ·
¸
Q2
Q2 V
2
V
2
1+
GE (Q ) +G (Q ) ,4m2N
4m2N M
µ
¶−1
£ V
¤
Q2
2
2
ξFV (Q ) = 1 +GM (Q2 ) − GVE (Q2 ) ,
2
4mN
1
1+ξ
V
2
GVE (Q2 ) = ¡¢2 , GM (Q ) = ¡¢2 ,2
1 + Q2 /MV
1 + Q2 /MV2
FV1 (Q2 ) =(4.9)(4.10)(4.11)

where ξ ≡ µp − µn = 3.71 (anomalous magnetic dipole moments), and the vector mass MV is
set to be 0.84 GeV/c2 . The axial vector form factor, FA , is given by−1.23
FA (Q2 ) = ¡¢2 ,1 + Q2 /MA2

(4.12)

where MA is the axial vector mass. MA for (quasi-)elastic scattering was set to be 1.01 GeV/c2
in NEUT, which is a typical value determined by e-p and ν-p scattering experiments [84] withlarge errors. However, as described later in the analysis chapters, since the experimental dataof K2K favors lager MA value than 1.01 GeV/c2 , i.e. K2K data have larger scattering angle
Ph.D. Thesis by Issei Kato, July 2004

4.2. Neutrino interaction simulation: Neut-MC

71

than that in NEUT with 1.01 GeV/c2 , we set MA to be 1.11 GeV/c2 for CC-qe and NC-elastic
scatterings as a default value for the oscillation analysis, and is varied by ±10% as its systematic
uncertainty in our analysis.
Finally the cross-section is expressed as following;·¸2
m2N G2F cos2 θcdσ ν22 (s − u)
2 (s − u)=A(Q ) ∓ B(Q )+ C(Q ),
(4.13)
dQ2
8πEν2
m2N
m4N
where GF is the Fermi coupling constant, (s − u) ≡ 4mN Eν − Q2 − m2` , m` is the lepton mass,
and³³(m2` + Q2 ) h³
Q2 ´
Q2 ´ 1 2
Q2
Q2 ´
2 2
2
|ξF
|
4
+
|F
|
−
4
−
|F
|
+
1
−
A
V
V
4m2N
m2N
m2N
m2N
4m2N
´i
m2` ³ 14Q2 FV1 ξFV2
2 2
2
+
−
|F
+
ξF
|
+
|F
|
,
(4.14)
A
V
V
m2N
m2N
³
´
Q2
B(Q2 ) = − 2 FA FV1 + ξFV2
(4.15)mN
1³
Q2 ξF 2 ´C(Q2 ) =(4.16)|FA |2 + |FV1 |2 + 2 | V |24mN 2
A(Q2 ) =Fig. 4.8 shows the cross-section for the CC-qe interaction used in Neut-MC as a function ofincident neutrino energy, giving a consistent result with various bubble chamber measurements
around a few GeV region [79, 80, 81, 82].
For the NC elastic scattering, following relations are used [85, 86];σ(ν p → ν p) = 0.153 × σ(ν n → e− p) and σ(ν n → ν n) = 1.5 × σ(ν p → ν p).

(4.17)

Fermi motion and Pauli blocking effect have to be considered when the target nucleons arebounded in the nuclei. In our simulation, Fermi gas model is adopted to simulate the effect ofPauli blocking by requireing the final nucleon momentum to be larger than the Fermi surface
momentum, which is estimated to be 217 MeV/c for 16 O nulei by using the results of e-12 C
scattering experiment [87].

4.2.3Single-meson production

Single meson production is simulated based on the Rein & Sehgal’s model [88, 89]. This model
assumes that the interaction occurs via an intermediate baryon resonance state:ν + N → ` + N∗
N ∗ → N 0 + meson,(4.18)

where N and N 0 are initial and final nucleons and N ∗ is an intermediate baryon resonance state.
The differential cross-section of single resonance production with its mass of M and its
negligible decay width is written by
d2 σ
1
1 X
=
|T (νN → `N ∗ )|2 · δ(W 2 − M 2 ) ,· ·2
2dQ dEν
32πmN Eν 2

(4.19)

spins

where W is the invariant mass of the final state hadronic system, and T (νN → `N ∗ ) is the amplitude of resonance production which is calculated using the FKR (Feynman-Kislinger-Ravndal)
Ph.D. Thesis by Issei Kato, July 2004

Chapter 4. Monte Carlo Simulations

2

cm )

72

Our simulation±30% scaled

0.8
0.6

ANL-12ft, 1982
BNL-7ft, 1986
CPS-GGM, 1979

0.4
0.2
0

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

νn → µpπ02+

νp → µpπ1σ (10mass cut M(pπ)<1.4GeV

1.2

-38

CC-singleπ

4Energy (GeV)

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

2

4
Energy (GeV)+

νn → µnπ024Energy (GeV)

Figure 4.9: Cross-section of CC-1π production
calculated by our simulator, together with theexperimental results. Solid line shows our calculation and dashed lines show the cross-section
scaled by ±30%, where MA = 1.01 GeV/c2 .
The experimental results come from ANL [92],
BNL [93], and GGM [94].

baryon model [90]. The value of the axial vector mass MA for CC-1π and NC-1π is set to be
1.01 GeV/c2 in NEUT, although we have modified it to be 1.21 GeV/c2 as our spectrum andoscillation analysis for the same reason as in the case of CC-qe and NC-elastic scatterings. MA isvaried by 20% as its systematic uncertainty [91]. The differential cross-section for the resonancewith a finite decay width Γ can be derived by replacing the δ-function in Eq. (4.19) with a
Breit-Wignar formula;δ(W 2 − M 2 ) →Γ
1·
2π (W − M )2 + Γ2 /4.

(4.20)

The cross-section for the single-meson productions can be calculated as a product of theamplitude of each resonance production and the probability of the resonance decay into a mesonand a neucleon. In our simulation, ∆(1232) and other 17 resonance states with W < 2.0 GeV/c2
are considered. Fig. 4.9 shows our calculation of the cross-section for single-meson production
with MA = 1.01, comparing with the experimental measurements [92, 93, 94].
The decay kinematics of ∆(1232) is determined by the Rein & Sehgal’s model in which theeffects of the polarization of the produced resonance are properly considered. For the otherresonances, angular distribution of generated meson is set to be isotropic in the rest frame of
the resonance state.

4.2.4

Deep inelastic scattering

The charged current deep inelastic scattering, CC-DIS, produces more than one meson with theinvariant mass of the hadronic system W greater than 1.3 GeV/c2 . The cross-section of CC-DIS
is calculated based on Bjorken scaling, expressed as following;·¸
G2F mN Eν
1 2
1d2 σ ν
=(1 − y + y + C1 )F2 (x) + y(1 − y + C2 )[xF3 (x)] ,
dxdy
π
2
2
m2` (y − 2) mN xy
m2`(4.21)C1 =−−,
4mN Eν x
2Eν
4Eν2
m2`
,
C2 = −
4mN Eν x
Ph.D. Thesis by Issei Kato, July 2004

4.2. Neutrino interaction simulation: Neut-MC

73

where x ≡ Q2 /(2mN (Eν − E` ) + m2N ) and y ≡ (Eν − E` )/Eν are the Bjorken scaling variables,and mN , m` , Eν , and E` are the nucleon mass, the lepton mass, the incident neutrino energy,
and the final lepton energy, respectively. The nucleon structure functions, F2 and xF3 , are takenfrom GRV94 [95] in NEUT. However, in our oscillation analysis, a modification to the original
GRV94 parton distribution functions (PDFs) has been performed, following a model by Bodek
and Yang [96] in order to fit the experimental data globally down to low energy region. This
modification effectively changes the cross-section by a Q2 -dependent factor;
d2 σ ν
dxdy=⇒

Q2d2 σ ν
×
Q2 + 0.188 dxdy.

(4.22)

Other modifications and corrections done in [96], such as increacing d/u ratio at high x and themodification of the scaling variable x to be xw = x(Q2 + 0.624)/(Q2 + 1.735x), are ignored in our
simulation since they make only negligible effects in our energy region. With this modification,
the cross-section in low Q2 is suppressed, which behavior is favored by the experimental data ofK2K.
The cross-section for NC-DIS is assumed to have following relations;
0.26(Eν <3 GeV)
σ(NC-DIS) = 0.26 + 0.04(Eν /3 − 1) (3 GeV< Eν <6 GeV)
(4.23),σ(CC-DIS) 
0.30(6 GeV< Eν )which are extimated from experimental results [97, 98].
The kinematics of hadronic system is simulated by two different methods depending on
the range of its invariant mass W ; one for 1.3 < W < 2.0 GeV/c2 region and the other for
W > 2.0 GeV/c2 region.
In the region of 1.3 < W < 2.0 GeV/c2 , only pions are considered as outgoing mesons.
The mean multiplicity of pions, hnπ i, is estimated from the results of 15-foot hydrogen bubble
chamber experiment at Fermilab [99] assuming hnπ+ i = hnπ− i = hnπ0 i ashnπ i = 0.09 + 1.83 ln W 2.

(4.24)The number of pions in each event is determined by using KNO (Koba-Nielsen-Olesen) scaling [100], which describes the pion multiplicity with the mean multiplicity of hnπ i. Since therange of W overlaps with that in single-meson production, nπ ≥ 2 is required in this W region inorder to keep the consistency between the single-meson production and the deep inelastic scattering channels. The forward-backward asymmetry of pion multiplicity in the hadron center-of-masssystem is included according to the results from the BEBC experiment at CERN-SPS [101];
0.35 + 0.41 ln W 2
hnFπ i=hnB
0.5 + 0.09 ln W 2
πi.

(4.25)In the region of W > 2.0 GeV/c2 , the kinematics of the hadronic system are calculated byusing JETSET/PYTHIA package [102].

4.2.5

Coherent pion production

Coherent pion production, CC-coh.π/NC-coh.π, is a neutrino interaction with a whole nucleus,
oxygen for water target, in which the nucleus remains intact without any change in its charge
and isospin. One pion with the same charge as the intermediating weak boson is produced in
the reaction. Since the momentum transfer is small in this interaction, the angular distributionof the outgoing leptons and pions are forward peaking.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 4. Monte Carlo Simulations

Cross Section σcoh. (10-38 cm2)

74

10
CC coherent π
NC coherent π
Rein-Sehgal (1983)

1

-1

10
J.Marteau et al. (2000)
-2

10

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 5
Eν (GeV)Figure 4.10: Cross-section of the coherent pion
production calculated in our simulation, as afunction of incident neutrino energy. Solid lines
show the cross-section of CC-coh.π and dashedlines show that of NC-coh.π. The cross-section
modeled by Rein & Sehgal [103] and Marteau etal. [106] are both drawn here with blue and redlines, respectively.

The cross-section and kinematics of coherent pion production in NEUT is calculated basedon the Rein & Sehgal’s model [103, 104], which is expressed by following formula;d3 σ
dQ2 dydt=r =G2F mN Eν 2 2
1(σ πN )2 (1 + r2 )fπ A (1 − y)22π
16π tot
Re[fπN (0)],Im[fπN (0)]µMA2MA2 + Q2¶2e−bt Fabs , (4.26)(4.27)

where fπ is the pion decay constant taken to be 0.93 mπ , A is the atomic number which is 16
for oxygen, b = (R0 A1/3 )2 /3 is of the order of traverse dimension of the nucleus taken to be
80 GeV−2 , and t is the square of the 4-momentum transfer to the nucleus. Fabs is a factor whichtakes the pion absorption in the nucleus into account.
Here again, we have made a correction to NEUT in our oscillation analysis according toa neutrino-nucleus interaction model by J. Marteau et al. [105, 106], in which the interaction
ν 16 O → `− X is considered. In Fig. 4.10, the cross-sections of the CC and NC coherent pion
production as a function of incident neutrino energy are shown. The models by Rein & Sehgal
and Marteau et al. are both included in this figure. In the Model by Marteau et al., thecross-section is slightly reduced in the low energy region compared with that by Rein & Sehgal.

4.2.6

Nuclear effects

Mesons and nucleons generated in the neutrino interactions often cause secondary interactions
with nucleons before leaving 16 O nucleus, which is called “nuclear effect”. The inelastic scattering, charge exchange, and absorption of the pions in 16 O nucleus are considered in our simulation.
The neutrino interaction point in a nucleus is determined based on the Wood-Saxon type nucleon
density distribution, ρ(r),Z
1(4.28)
ρ(r) = ρ0³´ ,A 1 + exp r − cawhere we choose ρ0 = 0.48 m3π , a = 0.41 fm, and c = 2.69 fm for 16 O nucleus. The cross-sectionof each interaction is calculated using the model by L. Salced et al. [107]. Fermi motion of
nucleons in the nucleus and the Pauli blocking effect are taken into account in the simulation.
Ph.D. Thesis by Issei Kato, July 2004

cross section for π + + 16 O (mb)

4.2. Neutrino interaction simulation: Neut-MC

75

600

500

400

(i)+(ii)+(iii)

300

200

(i) inelastic(ii) absorption

1000(iii) charge exchange
0

100

200

300

400

500

600

momentum of π + (MeV/c)

Figure 4.11: The cross-section of π + -16 O interactions. Lines show the results of our calculation
based on [107], and the points show the experimental data from [108].

The Fermi surface momentum is defined aspF (r) =

³3
2

´1
3
π 2 ρ(r).

(4.29)The kinematics in the scattering is determined by using the results of π-N phase shift
analysis [109]. Fig. 4.11 shows the calculated π + -16 O interaction cross-section together withexperimental data from C. H. Ingram et al. [108], which agrees well with each other.

4.2.7

Summary of modifications in Neut-MC

As mentioned up to now, we have modified the neutrino interaction models for the spectrum
analysis in ND and the oscillation analysis which are, respectively, described in Chapter 7 andChapter 9. Here, the modifications are summarized.
Quasi-elastic and elastic scattering
In our oscillation analysis, we set the axial vector mass MA in the dipole formula to be 1.11 GeV/c2 ,while it is 1.01 GeV/c2 in NEUT. The uncertainty of MA to be ±10%. Therefore the analysis
results with these two valus are compared.
Single meson production
We set MA to be 1.21 GeV/c2 in our oscillation analysis, while it is 1.01 GeV/c2 in NEUT. We
quote the uncertainty of MA to be ±20%. The results with MA = 1.01, 1.11, 1.21, 1.31, and1.41 are compared in our analysis.
Deep inelastic scattering
We use the model by Bodek et al. as a default one in our oscillation analysis, while GRV94 isused in NEUT. Difference of these two models are compared.
Coherent pion production
We uses the model by Marteau et al. as a default one in our oscillation analysis, while the modelby Rein & Sehgal is used in NEUT. Difference of these two models are compared.
Ph.D. Thesis by Issei Kato, July 2004

76

Chapter 4. Monte Carlo Simulations

Abbrebiation for the models
Here, we define the four-digit numbers, “NEUT-abcd”, to express the models we have comparedin our analysis. Among the numbers of four-digit, the first one, a, is for the model of the quasielastic and elastic scattering, the second one, b, is for the single meson production, the third one,c, is for the coherent pion production, and the last one, d, is for the deep inelastic scattering.
For the quasi-elastic and elastic scattering, a = 0 and 1 stand for MA = 1.01 and 1.11 GeV/c2 ,respectively. For the single meson production, b = 0, 1, 2, 3, and 4 means MA = 1.01, 1.11,
1.21, 1.31, and 1.41 GeV/c2 , respectively. For the coherent pion production, c = 0 expresses themodel by Rein & Sehgal, whereas c = 1 expresses the model by Marteau et al.. Finally, for the
deep inelastic scattering, d = 0 is GRV94, and d = 1 is the model by Bodek et al..
According to this notation, the original NEUT is expressed by “NEUT-0000”, or we call it
simply “NEUT-std (standard NEUT)”, while the model we employed in our analysis is expressedby “NEUT-1211”. In Table 4.4, the correspondance of abbrebiations to models is shown.

4.3

Detector simulation: DetSim

The particles generated by Neut-MC are fed to the detector simulators, “DetSim’s”. It simulates
the propagation and interaction of particles in the detectors and the responses of the detectors
and the readout electronics.

4.3.1

Simulation of water Cherenkov detector, 1KT and SK

The DetSim program for the water Cherenkov detectors, 1KT and SK, has been developed basedon GEANT package [63]. The materials of the detector are all implemented in the simulation
code. The processes listed in Table 4.5 are considered in the DetSim. The CALOR package [60,61] is employed in order to simulate the hadronic interaction in water. This package is known toreproduce well the pion interactions including low energy region of down to ∼ 1 GeV. For still
lower energy region (pπ ≤ 0.5 GeV/c), a custom made program [110] is used in DetSim, which
program is based on the experimental data from π-16 O scattering [111] and π-p scattering [112].
In this custom made simulator, the elastic scattering, the inelastic scattering, the absorption,and the charge exchange of pions are taken into account.
The Cherenkov photons are generated along the passage of charged particles according to
Eq. (3.4) and Eq. (3.5). In the propagation of the Cherenkov photons in the water, Rayleighscattering, Mie scattering, and absorption are considered: Rayleigh scattering is the interactionof light with small objects like molecule of water, and the Rayleigh scattering coefficient is known
to have λ−4 dependence, where λ is the wavelength of the light. Mie scattering takes place when
the light is scattered by the objects of the same size as or larger than the wavelength. The
attenuation coefficients used in our simulation are tuned to reproduce the measurements using
the laser system and the cosmic-ray muons described in Sec. 3.5.1 and Sec. 3.6.2. The lightreflection and absorption on the surface of detector materials, such as the surface of PMTs andblack sheets, are also simulated using probability functions depending on the photon incident
angle, which functions are estimated from a direct measurement.
For the simulation of the PMT response, measured quantum efficiency is used. The total
amount of photoelectrons detected in each PMT is derived by summing up individual photoelectron signal which is made according to the measured single photoelectron distribution. The
hit time of each PMT is smeared according to the time resolution of PMT. The properties ofthe electronics system, such as the time width of ADC gate and the signal threshold, are taken
into account in our simulator.
Ph.D. Thesis by Issei Kato, July 2004

4.3. Detector simulation: DetSim

77

Table 4.4: The list of the correspondence of abbrebiations to models. NEUT-0000 is used in the original
Neut-MC, while NEUT-1211 is employed in the spectrum analysis in ND and the oscillation analysis.
Abbrebiations
NEUT-0000 (std-NEUT)
NEUT-0001
NEUT-0010
NEUT-0011
NEUT-0100
NEUT-0101
NEUT-0110
NEUT-0111
NEUT-0200
NEUT-0201
NEUT-0210
NEUT-0211
NEUT-0300
NEUT-0301
NEUT-0310
NEUT-0311
NEUT-0400
NEUT-0401
NEUT-0410
NEUT-0411
NEUT-1000
NEUT-1001
NEUT-1010
NEUT-1011
NEUT-1100
NEUT-1101
NEUT-1110
NEUT-1111
NEUT-1200
NEUT-1201
NEUT-1210
NEUT-1211 (our case)
NEUT-1300
NEUT-1301
NEUT-1310
NEUT-1311
NEUT-1400
NEUT-1401
NEUT-1410
NEUT-1411

CC-qe/NC-elastic(MA [GeV/c2 ])
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11
1.11

CC/NC-1π(MA [GeV/c2 ])
1.01
1.01
1.01
1.01
1.11
1.11
1.11
1.11
1.21
1.21
1.21
1.21
1.31
1.31
1.31
1.31
1.41
1.41
1.41
1.41
1.01
1.01
1.01
1.01
1.11
1.11
1.11
1.11
1.21
1.21
1.21
1.21
1.31
1.31
1.31
1.31
1.41
1.41
1.41
1.41

CC/NCcoh(model in use)
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek
Rein&Sehgal
Rein&Sehgal
Bodek
Bodek

CC/NCDIS(model in use)
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau
GRV94
Marteau

Ph.D. Thesis by Issei Kato, July 2004

78

Chapter 4. Monte Carlo Simulations

Table 4.5: The list of the processes considered in our detector simulation.
Particlesγe±µ±hadrons

4.3.2

Simulated processes(e+ , e− ) pair production, Compton scattering, photoelectoric effectmultiple scattering, ionization, δ-rays production, bremsstrahlung,annihilation of e+ , Cherenkov radiation
multiple scattering, ionization, δ-rays production, bremsstrahlung,nuclear interaction, decay, Cherenkov radiation, µ− capture in 16 O
multiple scattering, nuclear interaction, ionization, δ-ray production,
decay, Cherenkov radiation

Simulation of fine-grained detector

In the simulation of the fine-grained detector, GEANT package is also employed. All the materials making up SciFi, TGC, LG, MRD, and their supporting structures are implemented in
the code. CALOR hadronic package is also used to propagete hadrons in the detectors.
In the simulation of SciFi, the light yield of the scintilating fibers and the responce of IITCCD pixels are simulated according to the calibration data using cosmic-ray muons, radioactive
source, and LED light [47]. The noise hits are also simulated, which are estimated using cosmicray and randomly triggered data.
The responses of the light yield in the TGC and LG simulator are tuned to reproduce thecosmic-ray muon data and results of the beam test [49].
The hit timing information is saved in the MRD simulator. The hit efficiency of about 97.5%
and the noise hits are also simulated [53].

Ph.D. Thesis by Issei Kato, July 2004

Chapter 5
Analysis Strategy and Data Set for Analysis
Up to here, the general descriptions on the K2K experiment and the simulations employed in
our analysis have been given. From here, we will describe the analysis method and its results indetail. In this chapter, first the overview of our analysis is provided. Then, the data set usedin the analysis is summarized. The stabilities of the primary, the secondary, and the neutrino
beams are also shown in this chapter.

5.1

Overview of the analysis

In order to probe the neutrino oscillation by the reduction in the number of neutrino eventsand the distortion in energy spectrum, the flux and energy spectrum of the original neutrino
KT , is measured in 1KT tobeam must be understood. The number of neutrino interactions, Nintestimate the absolute flux, while the energy spectrum of neutrino beam at the location of ND,
ΦND (Eν ), is measured by whole ND system. These results are extrapolated to those in SK by
SK/ND
SK/ND
far-to-near ratio, Rint
and Rflux (Eν ), which are estimated by Beam-MC. Reliability of
the Beam-MC is cross-checked by the PIMON measurements. The expected number of neutrino
SK , is derived byevents in SK, Nexp
SK/1KTSK
1KT
Nexp= Nint· Rint

·

POTSK
· ²SK
POT1KT,(5.1)

where POTSK(1KT) is the number of protons on target used in the SK (1KT) analysis, and ²SK isthe average detection efficiency for neutrino events in SK. In this formula, the far-to-near ratio,
SK/1KT
Rint, is the ratio of the number of neutrino interactions in SK and 1KT, which is given byZΦSK (Eν ) · σH2 O (Eν ) · MSK dEν
SK/1KT
Rint
=Z
,
(5.2)
Φ1KT (Eν ) · σH2 O (Eν ) · M1KT dEν
where ΦSK(1KT) (Eν ) is the neutrino spectrum at SK (1KT), σH2 O (Eν ) is the cross-section ofneutrino interaction with water, and MSK(1KT) is the fiducial mass of SK (1KT).
The neutrino spectrum measured in ND is extrapolated to SK by the far-to-near flux ratio,
SK/ND
Rflux (Eν ),SK/ND
ΦSK (Eν ) = Rflux (Eν ) · ΦND (Eν )
(5.3)
SK/ND

in the case of no oscillation, where Rflux

SK/ND

Rflux

(Eν ) is easily written by(Eν ) =
79

ΦSK (Eν )ΦND (Eν )

.

(5.4)

80

Chapter 5. Analysis Strategy and Data Set for Analysis

Accumulated POT (1018)

70
60

1999

2001

2000

50
40
30
20

5.6x1019POT(July 12,2001)

Protons/Pulse (1012)

10
0
6
4
2
0 Jan

Apr

Jul

Oct

Jan

Apr

Jul

Date

Oct

Jan

Apr

Jul

Figure 5.1: The number of protons delivered onto the production target in the period of from June 1999 to July 2001. Horizontal axis correspond to the date. Upper
figure shows the number of protons on target (POT) accumulated from June 1999, andlower figure shows the POT per spill. Up to
July 2001, 5.6 × 1019 POTs are delivered by
the KEK-PS accelerator, among which thedata corresponding to 4.7 × 1019 POTs areused in the analysis.

In the oscillation analysis described in Chapter 9, these expressions become more complicatedand written in more exact forms in order to take the advantage of the systematic uncertainties
of measurements canceled out, which is described in detail in Chapter 9.

5.2

Data set for analysis

The data taken in the period of from June 1999 to July 2001 (K2K-Ia and K2K-Ib) are usedin this analysis. The corresponding runs are RUN-I, IIa, IIb, and III in Table 2.2. During thisperiod, 5.601 × 1019 protons are delivered onto the production targer by KEK-PS accelerator
to make the neutrino beam, as shown in Fig. 5.1. The corresponding number of beam spills
recorded by our data aquisition system is 1.07 × 107 . Among these beam spills, those with good
beam condition, SK being alive, valid GPS status in both KEK and SK are selected as “goodbeam spills” and used in the analysis.

5.2.1

Good beam condition

Beam spills with good beam condition is defined by the following criteria.
1. Beam spills from June 1999 to July 2001.
2. Beam spills with normal machine status. The beam spills during the periods of the machine
study, beam tuning, and the PIMON measurements are discarded.
3. Beam spills with no trouble in the beam line components and data acquisition system.
4. Beam spills with the proton intensity greater than 1×1012 protons per spill (or protons per
pulse, ppp). Since typical number of protons per spill is 4−6 × 1012 , as shown in Fig. 5.1,
beam spills with too low intensity is discarded.
5. Beam spills with the current of the horn magnets greater than 240 kA (190 kA) in K2K-Ib(K2K-Ia). Instability in the horn current makes different pion focusing effect, and hence
makes different neutrino flux and energy spectrum. Beam spills with too low horn current
are discarded.
Ph.D. Thesis by Issei Kato, July 2004

5.2. Data set for analysis

5.2.2

81

Good GPS status

The validity of GPS is very important in our analysis in order to make time synchronization
between KEK and SK. GPS system has status bits to record if the current GPS status is goodor not. The GPS status bits include the information whether signals from more than four
GPS satellites are received or not, there happens an increment by one pulse per second or not,and LTC time stamp is accurate or not. As mentioned in Sec. 3.7, there are 2 GPS receivers
equipped in both KEK and SK site. Using their information, beam spills with good GPS status
are selected as followings.
In KEK site,
1. If the time difference of GPS1 and GPS2 of a spill, |TGPS1 − TGPS2 |, is less than 200 nsec,
the spill is used for analysis.
2. If criterion 1 is not satisfied, require the status bit of GPS1 to be good. Then, take thetime differences of consecutive two spills of GPS1 and TRG,
n−1
n
∆TGPS1 = TGPS1− TGPS1∆TTRG =n−1
n
TTRG
− TTRG

,
,

(5.5)
(5.6)

where ∆TTRG for each spill is recorded by VME-TRG module, as mentioned in Sec. 3.4.
If |∆TGPS1 − ∆TTRG | < 200 nsec, the spill is used for analysis with GPS1 giving the beam
spill time.
3. If criterion 2 is not satisfied, the same check as criterion 2 is done for GPS2, and if GPS2
status bit is good and |∆TGPS2 − ∆TTRG | < 200 nsec, the spill is used for analysis with
GPS2 giving the beam spill time.
4. If all the criteria above are not satisfied, the spill is discarded.
Beam spills of about 0.1% are discarded by invalid GPS status in KEK site.
The selection criteria in SK site are,
1. Check GPS status bit for each events. If good, use the spill.
2. If one subrun of SK contains more than 10% of events with bad GPS status bit, the wholesubrun is discarded.
3. If GPS status bit of a events is bad, the time difference between GPS1 and GPS2, |TGPS1 −TGPS2 |, and the time difference between GPS1 and LTC, |TGPS1 − TLTC | are taken. If bothtime differences are greater than 200 nsec, then the event is discarded.
So far, there was no event which satisfies the criterion 3, and the number of subruns which werediscarded by invalid GPS status is 6 subruns during K2K-I period, where one subrun in SK iscorresponding to the data taken in about 90 seconds.

5.2.3

Status of data taking in ND and SK

Beam spills during SK being alive are selected. In order to use as much neutrino beam as
possible, all the beam spills are used for the analysis as far as SK is alive, even if ND system,
especially 1KT, is dead. A chart of the definition of beam spills in use is shown in Table 5.1. In
extrapolation of the number of neutrino interactions in 1KT to that expected in SK, the deadPh.D. Thesis by Issei Kato, July 2004

82

Chapter 5. Analysis Strategy and Data Set for Analysis

Table 5.1: Chart of the definition of beam spills in use. The values in parentheses is corresponding POT accumurated from June 1999 to July 2001. WhenSK is alive, all the beam spills are used whenever 1KT is alive or dead.
1KT aliveused(4.29 × 1019 POT)
not used

SK alive
SK dead

1KT dead
used, need correction(0.50 × 1019 POT)
not used

Table 5.2: Summary of the number of protons on target used in the analysis for each month.
periodTarget diameter
Horn current
From
To
POTSK (×1018 )POT1KT (×1018 )Jun.’992 cmφ
200 kA
04-Jun.
26-Jun.
3.10
2.60

Nov.’99

Jan.’00

29-Oct.
24-Nov.
3.57
2.62

14-Jan.
29-Jan.
2.22
1.81

periodTarget diameter
Horn current
From
To
POTSK (×1018 )POT1KT (×1018 )Jan.’01

Feb.’01

Mar.’01

14-Jan.
05-Feb.
3.20
2.92

05-Feb.
08-Mar.
5.04
4.75

08-Mar.
03-Apr.
4.60
4.27

In total :POTSK
POT1KT

Feb.’00 Mar.’00
3 cmφ
250 kA
02-Feb. 01-Mar.
26-Feb. 23-Mar.
4.04
3.70
3.74
3.35

May.’00

Jun.’00

11-May28-May2.56
2.42

31-May21-Jun.
3.76
3.17

Apr.’01
3 cmφ
250 kA
11-Apr.
26-Apr.
2.76
2.47

May.’01

Jun.’01

Jul.’01

17-May27-May1.75
1.60

27-May.
01-Jul.
6.12
5.79

01-Jul.
11-Jul.
1.54
1.43= 4.79 × 1019 POT= 4.29 × 1019 POTtime of 1KT is corrected by a factor of POTSK /POT1KT . The error on this correction, δPOT , isestimated as following;
POTSK
POT1KTPOTSK − POT1KT,
POT1KTPOTSK − POT1KT
× δS1KT
POT1KT= 1+

δPOT =

(5.7)
,

(5.8)

where δS1KT is a fluctuation of the neutrino event rate measured in 1KT, which is estimated to
be 6%.

5.2.4

Total number of POT used in the analysis

After all the criteria for good beam spill selection are imposed, the total number of protons on
target for the analysis is 4.79 × 1019 POT (4.29 × 1019 POT) in SK (1KT). The number of POT
accumulated in each month is summarized in Table 5.2
Ph.D. Thesis by Issei Kato, July 2004

5.3. Beam stability during the data taking

5.3

83

Beam stability during the data taking

The stabilities of the neutrino beam intensity and direction have been monitored by MUMON
on spill-by-spill basis by measureing the yield and profile of muon from pion decay . In addition,
stabilities of the profile and intensity of neutrino beam itself have been measured by MRD every
a few days.
Fig. 5.2 shows the stability of the muon yield normalized to 5 × 1012 POT measured by thesilicon pad detector array (SPD) in MUMON, which indicates that the targetting efficiency ofthe proton beam have been stable within a few %. Fig. 5.3 shows the stability of the center ofthe muon profile measured by the ionization chamber (ICH) in MUMON. The beam have been
pointed to the direction of SK within ±1 mrad during whole run period.
By looking at the distribution of the neutrino interaction vertex in ND, the profile of neutrino
beam itself is also monitored, although 3 or 4 days data for each point is needed to accumulate
enough statistics. Fig. 5.4 shows the x- (horozontal) and y- (vertical) vertex profile measuredin MRD, and the stabilities of their center are shown in Fig. 5.5. It provides that the directionof the neutrino beam itself is also stable within ±1 mrad except for the statistical fluctuation.
The stability of the neutrino event rate measured in MRD is shown in Fig. 5.6, in which
the event rate is normalized to 5 × 1012 POT. The event rate is also stable within statisticalfluctuation.
Finally, Fig. 5.7 shows the stabiliteis of the energy and the angular distributions of muons
produced in the neutrino interactions in MRD. Each point is corresponding to one-month accumulated data. Both distributions are stable during whole run period, showing that the energy
spectrum of the neutrino beam itself is also stable.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 5. Analysis Strategy and Data Set for Analysis

0.25

12

Silicon-peak (ADCcount) / 5 ×10 pot

84

0.225
0.2
0.175
0.15
0.125
0.1
0.075
0.05
0.025
0
integrated day (1 data point / 12 hours)

distribution center x (ch)Figure 5.2: Stability of muon yield measured by the silicon pad detector array (SPD) in MUMON.
The vertical axis is in arbitrary unit, but each data point is normalized to 5 × 1012 POT.

35
30
25
20
15
10
5

South

North

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

35
30

Upward

25
20
15
10
5

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

Figure 5.3: Stability of the center of muon profile measured by the ionization chamber (ICH) in
MUMON. Upper figure shows the profile center of horizontal direction and lower figure shows thatof vertical direction. Horizontal solid lines show the nominal beam direction to SK measured byGPS, while dotted lines show the direction of ±1 mrad off the center.

Ph.D. Thesis by Issei Kato, July 2004

5.3. Beam stability during the data taking

85

90000

90000
DATA

80000

80000

MC

70000

70000

60000

60000

50000

50000

40000

40000

30000

30000

20000

20000

10000

10000

0

-200

0

0

200

x (cm)

-200

0

200

y (cm)

Vertex contained

Vertex contained

distribution center x (cm)Figure 5.4: Profile of the vertex of neutrino events measured in MRD. Left figure shows the xvertex (horizontal) distribution, and right figure shows the y-vertex (vertical) distribution. This iscorresponding to the profile of the neutrino beam.

100 South
80
60
40
20
0
-20
-40
-60 North-80 1999
-100
Jun

2000

2001

Nov Jan Feb Mar May Jun Jan

Feb Mar Apr

May Jun Jul

distribution center y (cm)integrated day (1 data point / 5 days)
80 Up
60
40
20
0
-20
-40
-60
-80 Down-100 1999
Jun

2000

2001

Nov Jan Feb Mar May Jun Jan

Feb Mar Apr

May Jun Jul

integrated day (1 data point / 5 days)

Figure 5.5: Stability of the center of neutrino beam profile measured in MRD. Upper and lower
figures show the profile center of horizontal and vertical directions.

Ph.D. Thesis by Issei Kato, July 2004

86

Chapter 5. Analysis Strategy and Data Set for Analysis

12

Fe event / 5×10 pot

0.07

0.06

0.05

0.04

0.03

0.02

0.01
99Jun 99Nov 00Jan 00Feb00Mar00May00Jun 01Jan 01Feb01Mar 01Apr 01May01Jun 01Jul

0
integrated day (1 data point / 2 days)
Figure 5.6: Stability of the neutrino event rate measured in MRD. Each point corredponds toabout two days data, which is normalized to 5 × 1012 POT.

Muon angle distribution stability

0.9

99Nov
00Jan

0.8

00Feb

arbitrary unit

arbitrary unit

Muon energy spectrum stability
1

1
0.9

99Nov
00Jan

0.8

00Feb

00Mar

0.7

00May

00Mar

0.7

00May

00Jun

0.6

01Jan

00Jun

0.6

01Jan

01Feb

0.5

01Mar

01Feb

0.5

01Mar

01Apr

0.4

01May

01Apr

0.4

01May

01Jun

0.3

01Jul

01Jun

0.3

0.2

0.2

0.1

0.1

0

0

0.5

1

1.5

2

2.5
3
Eµ (GeV)

0

01Jul

0

10

20

30

40

50

60

70

80
90
θµ (deg.)

Figure 5.7: Stability of the energy (left) and angular (right) distribution of muons scattered by theneutrino interaction in MRD.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 6
Far-to-near Neutrino Spectrum Ratio
As mentioned in Sec. 2.2.3, since the fluxes does not simply obey the L−2 law, a factor, so called“far-to-near ratio (F/N )”, is needed. F/N ratio extrapolates the flux and energy spectrumof the neutrino beam measured in ND to those expected in SK. If we know the momentum
and angular distribution of parent pions, we can predict the spectrum at any distance because
it is determined only by the decay kinematics of pion and the geometry of the beam line.
For this purpose, PIMON measurements had been done in the K2K experiment. Since there
are some documents in which the PIMON measurements are described in detail [35], only thebrief description and the results from the measurements are provided in this chapter. Here,the estimated error matrix for F/N is also given, which is used in the oscillation analysis in
Chapter 9.

6.1

Measurements of pion monitor

The PIMON measurements had been done in June 1999 with the horn current of 200 kA and in
November 1999 with the horn current of 250 kA using special beam time for the measurements.
The PIMON data were taken with the beam intensity of 7 × 1010 ppp of 1 bunch operationin June 1999 run, and with 7 × 1011 ppp of 9 bunch operation in Nov. 1999 run. This low
intensity operation was needed to avoid PMT saturation. Large saturation was observed inJune 1999 run, and it had been improved in the Nov. 1999 run thanks to the studies on PMT
gain adjustment. The operation parameters are summarized in Table 6.1.
In each runs, the refractive index of the freon gas (n) was set to be 9 points which makes
pions with different momentum above 2 GeV/c to be sensitive. For each point, the spacial
distribution of Cherenkov light was taken by the PMT array placed on the focal plane. A

Table 6.1: Summary of the operation of the PIMON measurements inJune 1999 and Nov. 1999 runs.
Parameters
Target diameter
Horn current
Beam intensity
Number of bunches
Refractive index
PMT gain
PMT saturation

June 1999
2 cmφ
200 kA
7 × 1010 ppp
1
9 points
300
exist

87

Nov. 1999
3 cmφ
250 kA
7 × 1011 ppp
9
9 points
20 or 50no

CT corrected ADC count mean

88

Chapter 6. Far-to-near Neutrino Spectrum Ratio

600
500
400
300
200
100
0

2

4

6

8

10

12

14

16

18

20

CT corrected ADC count mean

PMT number
300
250
200
150
100
50
0

2

4

6

8

10

12

14

16

18

20

Figure 6.1: A typical Cherenkov light distribution observed by the PMT array in PIMON measurements. Horizontal axis stands
for the PMT numbers corresponding to thevertical position on the focal plane. PMT1 is at the top and PMT-20 is at the bottom. One step of PMT number corresponds
to 3.5 cm. Upper figure shows the light distribution with mirror-on and -off, and lower
figure shows that with the mirror-off distribution subtructed.

PMT number

typical Cherenkov light distribution observed by the PMT array is shown in the upper figure of
Fig. 6.1. In order to subtract the background contained in the raw distribution, a measurementwith the mirror directed off from the direction of PMT array (“mirror-off data”) are taken, andthen it is subtracted from “mirror-on” data. The lower figure of Fig. 6.1 shows the backgroundsubtracted light distribution. The PMT array was shifted by a half PMT interval to obtainfiner distributions, and hence 40 data points (one point for every 1.75 cm) are taken for a light
distribution with each refractive index.
There is still non-negligible background from electro-magnetic showers which mainly comefrom the decay of neutral pions, π 0 → 2γ. The light distribution of this background is estimatedusing Beam-MC. The normalization of the subtraction is done by the distribution measured
with the lowest refractive index, where the contribution from the electro-magnetic components
is dominant.
After all the backgrounds are subtracted, the distribution of the Cherenkov light emitted
from pions is obtained for each refractive index, as shown in Fig. 6.2, where the prediction of
Beam-MC is also superimposed.

6.2

Extraction of pion momentum and angular distribution

In order to extract (pπ , θπ ) 2-dimensional distribution from the Cherenkov light distributions
with various reflactive indices, χ2 -fitting is employed. The method is as following:
1. (pπ , θπ )-plane is binned into 5 × 10 bins; 5 bins in pπ above 2 GeV/c with 1 GeV/c step(pπ > 6 GeV/c is integrated) and 10 bins in θπ from −50 mrad to 50 mrad with 10 mrad
step.
2. Using a Monte Carlo simulation, a template of the Cherenkov light distribution emitted
by pions in each (piπ , θπj )-bin (i = 1−5, j = 1−10) is produced for each refractive index,
separately. Here, the template distribution for the (piπ , θπj )-bin with the k-th refractive
Ph.D. Thesis by Issei Kato, July 2004

6.3. Neutrino energy spectra at ND and SK and their ratio

89

ADC counts

ADC counts

data vs. MC
20
15
10
5
0

10

20

20
10
0

30

40
30
20
10
0

10

20

20

20

ADC counts

10

20

100
50
10

20

30

300
200
100
0

30

PMT number (n=1.00176 meas.)30

PMT number (n=1.00129 meas.)
ADC counts

ADC counts

0

20

150

0

30

100

10

PMT number (n=1.00074 meas.)

PMT number (n=1.00095 meas.)

200

30

40
0

30

ADC counts
10

20

60

PMT number (n=1.00058 meas.)
100
75
50
25
0

10

PMT number (n=1.00048 meas.)
ADC counts

ADC counts

PMT number (n=1.00041 meas.)

10

20

30

Figure 6.2: Cherenkov light distributions
for various refractive indices measured in
Nov. 1999. Dots show data and the histgrams show the Beam-MC. The refractive
index for each plot are as written in the figure.

PMT number (n=1.00242 meas.)index is expressed by distMC(i,j),k (l), where l is the light intensity on the l-th PMT position(l = 1−40).
3. We measured Cherenkov light distribution with the k-th refractive index, distdata(l). Thiskdistribution should be expressed by a superposition of distMC
(l)
using
the
weighting(i,j),kfactors W(i,j) . Therefore, χ2 function is defined asχ

2¶
ref.index
X µ PMTmax
X distdata(l) − W(i,j) · distMCk(i,j),k (l)=[σk (l)]2
k
l=1

,

(6.1)

where σk (l) is the error on the measurement of l-th PMT with the k-th refractive index.
Fifty W(i,j) ’s being weighted as fitting parameters, this χ2 -function is minimized to obtainthe fitted W(i,j) values, which give the relative population of pion in (piπ , θπj )-bin.
In this way, the relative pion population in each (piπ , θπj )-bin, W(i,j) , is obtained.
This fitting had been done for the data in June 1999 and in Nov. 1999, separately. The
resulting values of fitting parameters and errors on them in Nov. 1999 run are shown in Fig. 6.3.

6.3

Neutrino energy spectra at ND and SK and their ratio

In order to extract the neutrino spectrum at ND and SK, the contribution of (piπ , θπj )-bin to
ND(SK)
the n-th bin of neutrino spectrum at ND (SK), φn,(i,j) , is calculated using MC simulation,
which calculation depends almost only on the decay kinematics of pion and the geometry of thebeam line. The neutrino energy is binned into 0.5 GeV bins upto 2.5 GeV, and integrated above
2.5 GeV. Therefore, we have 6 bins in neutrino energy. Then the flux of the n-th bin of the
Ph.D. Thesis by Issei Kato, July 2004

Chapter 6. Far-to-near Neutrino Spectrum Ratio
5

Pion angle (*10mrad)

Pion angle (*10mrad)

90

4

3

5

4

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

-4

-4

-5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

-5

7

2

2.5

3

3.5

4

4.5

5

Pion momentum (GeV/c)

5.5

6

6.5

7

Pion momentum (GeV/c)

Figure 6.3: The fitting results of pion (pπ , θπ ) distribution in Nov. 1999 run. The left figure shows theresulting central value of the weighting parameters W(i,j) , and the right figure shows the estimated fitting
errors on them.

ND(SK)

neutrino energy at ND (SK), Φn

ND(SK)(W ), is derived by a superposition of φn,(i,j) ;ΦND(SK)(W ) =n50
X

ND(SK)

W(i,j) · φn,(i,j)

.

(6.2)

(i,j)=1

The n-th bin of F/N ratio, Rn (W ), is obtained by
Rn (W ) =ΦSKn (W )ND
Φn (W ).

(6.3)

Since the PIMON data are available only above 2 GeV/c , the neutrino fluxes and the F/Nratio above the neutrino energy of 1 GeV can be obtained from the PIMON data.
Fig. 6.4 shows the results of the extraction of the neutrino spectra and the F/N ratio from the
PIMON data for June 1999 and Nov. 1999 runs. The predictions of the Beam-MC are also shownin this figure. The errors on the measurements quoted in the plots include all the estimatedsystematic uncertainties in the PIMON measurements, which are described in Appendix C. The
Beam-MC predictions are consistent with the results of the PIMON measurements. Therefore,
the Beam-MC is used to calculate the central values of the neutrino spectrum and F/N ratio
for whole energy region, while their errors estimated by PIMON is used for the region above
1 GeV. The errors on the region below 1 GeV are estimated using the Beam-MC by varying thevalue of parameters in Eq. (4.4) within 90% C.L.

6.4

Systematic errors on the PIMON measurements

Systematic errors on the neutrino spectra at ND and SK and F/N ratio due to various sources
are estimated in the PIMON analysis. The methods to estimate them are described in detailin [35], and also briefly explained in Appendix C. The errors on the spectra at ND and SK in
Ph.D. Thesis by Issei Kato, July 2004

6.4. Systematic errors on the PIMON measurements

x 10 8KEK flux

6000

-5

x 10

far/near

7000

91

MC
Pion monitor Integrated

5000

0.5

above 2.5GeV

4000

0.4

3000
2000
1000

0.3
0

x 10

0.5

1

1.5

2

2.5

3

Pion monitor
MC

2

SK flux

5000

0.2

MC
Pion monitor

4000

Integrated
above 2.5GeV

3000

0.1

Integrated
above 2.5
GeV

2000
1000
0

0.5

1

1.5

2

2.5

0

3

0

0.5

1

1.5

2

2.5

x 10

KEK flux

MC

5000

Integrated

Pion monitor above 2.5GeV

4000

far/nearx 10 86000

3Eν(GeV)Eν(GeV)-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 6.4: The neutrino energy spectrum at ND and SK and F/N ratio for June 1999 and Nov. 1999
runs. Upper two figures are for June 1999 run and lower two figures are for Nov. 1999 run. In bothruns, the left upper figure is the neutrino energy spectrum at KEK (300 m downstream the target), theleft lower one is that at SK (250 km downstream the target), and the right figure is the F/N ratio as afunction of the neutrino energy. In all figures, cross points with error bars show the results of PIMON
measurements and hatched boxes show the prediction of the Beam-MC. The normalization of the neutrinoenergy spectra between data and MC is done by their entries above 1GeV at KEK.

Ph.D. Thesis by Issei Kato, July 2004

92

Chapter 6. Far-to-near Neutrino Spectrum Ratio

June 1999 and in Nov. 1999 are separately summarized in Table C.1, and Table C.2, and theerrors on F/N ratio are summarized in Table C.3. These errors are used in the ND analysis
to estimate the errors on the expected number of neutrino events in SK, which is described in
Chapter 7, and also used in the oscillation analysis described in Chapter 9. Furthermore, for the
spectral studies in the oscillation analysis, the errors on F/N ratio in Nov. 1999 are re-estimatedand expressed in the form of error matrix, which is descrived in the next section.

6.5

Error matrix for the far-to-near ratio

In order to implement the F/N ratio into the oscillation analysis and take the correlation between
energy bins into account, the errors on F/N ratio must be expressed in the form of an error
matrix. Since only the data taken during K2K-Ib period are used in the spectrum shape analysis,
we evaluated the error matrix for K2K-Ib configuration. The description on the derivation of
the error matrix of F/N ratio is given in this section.

6.5.1

The form of error matrix

As mentioned before, neutrino energy is divided into two regions in F/N ratio: One is below
1 GeV where PIMON is insensitive and the errors on F/N are quoted from hadron production
model. The other is above 1 GeV where PIMON is sensitive and the errors are quoted fromthe uncertainties of PIMON measurements. Since the methods of derivation of errors on F/Nbelow and above 1 GeV are quite different, uncorrelated errors on these two parts are assumed.
Therefore, the error matrix of F/N , MF/N , is assumed to have following form:Ã
MF/N =

hadron
MF/N
0
PIMON
0
MF/N

!
,

(6.4)

hadron is a 2 × 2 matrix corresponding to 2 bins below 1 GeV (0.0−0.5 and 0.5−1.0 GeV
where MF/N
PIMON is a 4 × 4 matrix corresponding to 4 bins above 1 GeV (1.0−1.5, 1.5−2.0,bins), and MF/N
2.0−2.5, and >2.5 GeV bins).

6.5.2

Error matrix below 1 GeV

hadron , several sets of Beam-MC withIn order to evaluate the error matrix below 1 GeV, MF/N
several sets of Sanford-Wang parameter values are employed [113, 114]. It is derived by adding
4 error matrices; uncertainty in Sanford-Wang fitting, uncertainty in extrapolation of nuclear
difference, uncertainty in kaon contribution, and uncertainty in beam properties.
Dominant contribution to neutrinos below 1 GeV come from pions below 2 GeV/c, andhence pion production data of below 2 GeV/c is re-fitted to Sanford-Wang formula given by
Eq. (4.4). Then Beam-MCs with several sets of Sanford-Wang parameters were generated, where
the parameters were randomly generated so that each parameter has a value within its fitting
error with the correlations with other parameters. Using the set of Beam-MC, the covariancematrix for F/N ratio is calculated.
The data of Cho et al. [72] was acquired using Beryllium target, while our production target
is made of aluminum. Therefore, we need to extrapolate their data to aluminum one. It makes
only small effects.
Contribution of kaons to neutrinos is small, but exists. The errors from this part is estimatedby considering the results of [69].

Ph.D. Thesis by Issei Kato, July 2004

6.5. Error matrix for the far-to-near ratio

93

Finally, the effect of the injection point and profile of the proton beam is studied by changing
these parameters based on the measurements of the beam monitors.
The error matrices due to these uncertainties are summarized in Table 6.2. By adding thesehadron , is obtained to be
4 matrices, the total error matrix for the energy below 1 GeV, MF/N
0.0−0.5 0.5−1.0
hadronMF/N=  0.0−0.5
6.603−2.7  × 10−4
0.5−1.0
−2.7
18.14

6.5.3

.

(6.5)

Error matrix above 1 GeVPIMON , is derived from the uncertainties
The error matrix for the neutrino energy above 1 GeV, MF/Nof the PIMON measurements. The errors listed in Table C.3 are included in the matrix. Amongthe errors, fitting error, mirror refrectivity, proton injection point, pion decay before PIMON,
radial distribution of pions, and binning of pion kinematics are relatively small compared to theothers, and hence these are treated as non-correlated errors, i.e. non-diagonal elements are set
to be zero, and the squared values are added to the diagonal elements. The other errors are
re-evaluated by randomly changing the systematic parameters within their errors and generating
several sets of Beam-MC with these systematic parameters, and then covariance of F/N ratio
is calculated. The resulting error matrices for the uncertainties treated as correlated ones are
summarized in Table 6.3.
In total, the error matrix for the energy above 1 GeV is obtained by summing up all thematrices in Table 6.3 and adding uncorrelated errors to the diagonal elements:
1.0−1.5 1.5−2.0 2.0−2.5> 2.5
 1.0−1.5
42.67
5.747
−3.19 −16.15 


−4
PIMON

(6.6)
.
MF/N
=  1.5−2.0
5.747
108.8
90.85
24.53  × 10 2.0−2.5−3.19
90.85 122.84
52.17> 2.5 −16.15
24.53
52.17 147.75

6.5.4

Resulting error matrix of far-to-near ratio

In summary, by referring to Eq. (6.4), (6.5), and (6.6), the error matrix of F/N ratio becomes
following:
2.6 −1.6
0000 −1.6
4.3
0
0
0
0 


q

0
0
6.5 2.4 −1.8 −4.0  ,sign(MF/N ) |MF/N | = 
(6.7)

0
0
2.4
10.4
9.5
5.0



7.2 
0
0 −1.8 9.5 11.1
00 −4.0 5.0
7.2 12.2
where 6 columns/raws correspond to 6 bins in the neutrino energy, and the values are expressedin the unit of %. This martix is used in the oscillation analysis described in Chapter 9.

Ph.D. Thesis by Issei Kato, July 2004

94

Chapter 6. Far-to-near Neutrino Spectrum Ratio

Table 6.2: Components of error matrices contributing to the error matrix ofhadronF/N ratio below 1 GeV, MF/N
. All values are written in the unit of 10−4 .

0.0−0.5 GeV
0.5−1.0 GeV

0.0−0.5 GeV
0.5−1.0 GeV

Sanford-Wang fitting error
0.0−0.5 GeV 0.5−1.0 GeV
4.65
−0.92
−0.92
4.07
Kaon contribution
0.0−0.5 GeV 0.5−1.0 GeV
0.07
−0.17
−0.17
0.62

Extrapolation Be → Al
0.0−0.5 GeV 0.5−1.0 GeV
0.63
−2.58
−2.58
10.60
Beam steering0.0−0.5 GeV 0.5−1.0 GeV
1.25
0.97
0.97
2.85

Table 6.3: Error matrices of each uncertainty in the PIMON measurements.
Only errors which correlation between bins are taken into account are listed,
here. All values are written in the unit of 10−4 .
Low and high beam intensity
1.0−1.5 GeV 1.5−2.0 GeV 2.0−2.5 GeV
1.0−1.5 GeV
3.70
4.38
3.35
1.5−2.0 GeV
4.38
16.3
7.48
2.0−2.5 GeV
3.35
7.48
7.25
> 2.5 GeV
−4.35
−11.4
−6.60
Wavelength dependence of the refractive index
1.0−1.5 GeV 1.5−2.0 GeV 2.0−2.5 GeV
1.0−1.5 GeV
8.13
0.21
1.15
1.5−2.0 GeV
0.21
9.93
15.1
2.0−2.5 GeV
1.15
15.1
24.7
> 2.5 GeV
2.65
7.60
12.7
Beam stability
1.0−1.5 GeV 1.5−2.0 GeV 2.0−2.5 GeV
1.0−1.5 GeV
5.03
−3.06
−3.41
1.5−2.0 GeV
−3.06
14.3
16.4
2.0−2.5 GeV
−3.41
16.4
20.1
> 2.5 GeV
−5.53
9.02
10.7
φ asymmetry of the horn magnetic field
1.0−1.5 GeV 1.5−2.0 GeV 2.0−2.5 GeV
1.0−1.5 GeV
7.19
10.6
2.26
10.6
43.5
33.4
1.5−2.0 GeV
2.0−2.5 GeV
2.26
33.4
35.1
1.13
19.3
20.2
> 2.5 GeV
Fitting method
1.0−1.5 GeV 1.5−2.0 GeV 2.0−2.5 GeV
1.0−1.5 GeV
7.65
−6.37
−6.53
−6.37
17.2
18.5
1.5−2.0 GeV
2.0−2.5 GeV
−6.53
18.5
20.7
−10.0
14.6
15.3
> 2.5 GeV

Ph.D. Thesis by Issei Kato, July 2004

> 2.5 GeV
−4.35
−11.4
−6.60
12.2
> 2.5 GeV
2.65
7.60
12.7
7.02
> 2.5 GeV
−5.53
9.02
15.3
17.2
> 2.5 GeV
1.13
19.3
20.2
11.6
> 2.5 GeV
−10.0
14.6
15.3
25.9

Chapter 7
Analysis in Near Detector
In the near detector system (ND), the properties of the neutrino beam such as its flux and energy
spectrum are measured, which are extrapolated to their expectation in SK by F/N ratio. The
number of neutrino events is measured in 1KT, while the energy spectrum of neutrino beamis measured in whole ND system by combining 1KT and FGD data. In this chapter, first, themethod to reconstruct neutrino events in 1KT is given in Sec. 7.1. Then the analysis to obtainthe number of neutrino events in 1KT and its extrapolation to the expected number of neutrino
events in SK is described in Sec. 7.2 and Sec. 7.3. At last, spectral analysis using both 1KT and
FGD is given in Sec. 7.4. to obtain the neutrino energy spectrum at the near site.

7.1

Analysis flow in 1KT

First, we describe the analysis flow in 1KT. Fig. 7.1 shows a typical neutrino event observed in
1KT. In order to estimated the number of neutrino interactions occurred in the fiducial volumeof 1KT, the data reduction, the event reconstruction process, and event selections are applied
to the data taken in 1KT. Furthermore, for the study of neutrino energy spectrum, the neutrino
events with only one muon-like Cherenkov ring and with the particle fully contained in the 1KT
inner detector is used in order to enhance the charged-current quasi-elastic scattering and to
make the energy of the produced muon measurable. In this section, the procedures of the data
reduction, the event reconstruction, and event selections for the analysis are provided step bystep in the order. The flow chart for the data reduction and event selection in 1KT is shown in
Fig. 7.2, while the that for the event reconstruction is shown in Fig. 7.6.

7.1.1

Data reduction(1) On-spill data selection
Among four trigger types taken in 1KT, only on-spill data is used for the analysis, which corresponds to the data synchronized to the neutrino beam timing as described in Sec. 3.5.1.
(2) Spills with no pre-activity
If any event, such as cosmic ray, accidentally happens before a beam spill, it occupies theelectronics buffer and the real beam event may not be recorded in the electronics. In order toavoid such events, spills which have any activity within 1.2 µsec (duration before the electronics
timeout) before the spill are rejected. The fraction of the spills with pre-activity event is about
1.9%. These spills are not counted in the accumulated number of spills and POT.
95

96

Chapter 7. Analysis in Near Detector

Figure 7.1: A typical neutrino event observed in 1KT. This is the expanded view of the cylindricalvolume of 1KT. The neutrino beam is directed to the center of this display. Colored circles show
the hit PMTs, and the color of each circle correspond to the charge measured in each PMT; violet(red) indicates small (large) charge. The Cherenkov ring pattern is clearly seen around the centerof the display.

(3) Low energy event rejection
Events with low visible energy are not reconstructed in our reconstruction method. The eventswith the total number of photoelectrons less than 200 photoelectrons are rejected.
The events which satisfy the criteria up to here will be reconstructed using our reconstruction method described later. However, after the event reconstruction, further selection criteria
independent from the reconstruction results are imposed to select the events for the analysis, as
following.
(4) Good spill selection
Spills with good beam condition is selected. The criteria for good beam are described in Sec. 5.2.
(5) Total photoelectrons threshold
Using the pulse shape of PMTSUM signal recorded by FADC (ref. right lower figure in Fig. 7.3),
peaks in FADC are searched. The threshold of pulse height to search for a peak is set to be
at 1,000 photoelectrons, which is equivalent to a visible energy of about 100 MeV. With thiscriteria, the background events with lower energy such as an electron from muon decay (which
Ph.D. Thesis by Issei Kato, July 2004

7.1. Analysis flow in 1KT

97(1) On−spill data selection(2) Spills with no pre−activity(3) Low energy event rejection

Event reconstruction procedure(4) Good beam spill selection(5) Total photoelectrons threshold(6) Single event selection(7) Fiducial volume cut
Used for the estimation of number of neutrino interaction(8) Visible energy > 30 MeV(9) Fully contained event selection(10) One Cherenkov ring event selection(11) Muon−like event selection(12) Total detected photoelectrons > 1000 p.e.
Used for the neutrino spectrum measurement

Figure 7.2: A flow chart of data reduction and event selection in the 1KT analysis. The event
sample remaining after the selection (7) is used to estimate the number of neutrino interactions in
1KT fiducial volume, while that remaining after all the selection is used to estimate the neutrinoenergy spectrum at the near site.

Ph.D. Thesis by Issei Kato, July 2004

98

Chapter 7. Analysis in Near Detector

35

 



e r of inne r P

NUM
6
RUN
2341
SPIL
54479
SUBRUN
9
EVENT
30490
DATE **-Feb- 4
TIME
18:33:51
TOT PE:
17108.8
MAX PE:
173.3
NMHIT :
669
ANT-PE:
2.2
ANT-MX:
1.6
NMHITA:
2

30
25
20
15



10



5
0
700

800

900 1000 1100 1200 1300 1400 1500 1600

TRG ID :00000001
TMC Ch1:TMC Ch2:TMC Ch3
0.23: 0.28: 0.90
0.70: 0.76: 1.37
T diff.:0.
us
Q thr. :0.0
SUB EV : 0/ 0

Inn e r P MTSU M pul

he i

ATM T (nsec)

8600

860
0

1000

2000

FADC T (nsec)

Figure 7.3: A typical event display (left), the distributions of PMT hit timing recorded by ATM (rightupper) and its PMTSUM signal recorded by FADC (right lower) for multiple event in a beam spill. In
the event display, there are two rings which originated from two neutrino interactions in a spill. Theircorresponding peaks in PMTSUM can be seen in the FADC data, whereas separation between these
events are not clear in the ATM timing distribution.

Nov.99Black − DATA
Red − MCPh.D. Thesis by Issei Kato, July 2004

Jan.00Figure 7.4: The efficiency curve for the
FADC peak search as a function of the total number of photoelectrons. Horizontal
axis shows the total number of photoelectrons observed by ID-PMTs. Left figure is
the efficiency curve for data in Nov. 1999
in which 1/4 of PMTSUM signal was notconnected to FADC by mistake. Right figure is a typical efficiency curve for datataken by normal situation.

Entries7.1. Analysis flow in 1KT

99

10

6

25000

10

5

20000

10

4

10

3

10

2

15000

10000

5000
10
1

2

3

4
5
(# of FADC peaks)/spill

0
-200

0

200

400

600

800

1000 1200
Time (nsec)

Figure 7.5: The number of PMTSUM peaks per spill counted using FADC data (left) and the peaktiming distribution (right). The 9-bunch micro structure of spill can be clearly seen in the right figure.

have energy typically less than 52 MeV) are eliminated. Fig. 7.4 shows the efficiency curve for
the FADC peak search. The efficiency is rising up around 1,000 photoelectrons and become flat
to be unity in larger photoelectron region. In Nov. 1999, the 1/4 of PMTSUM signal was notconnected to FADC by a mistake, and hence the behavior of the efficiency curve is different fromthat in the rest of the periods, as shown in the figure. For this reason, the selection efficiency
was decreased by 3.5% for the data in Nov. 1999.

(6) Single event selection
The spills which contain only one event are selected since it is hard to reconstruct the verticesof multiple events separately. Fig. 7.3 shows a typical event display for multiple events in aspill, where clear two peaks can be seen in the FADC data. The number of events in a spill ismeasured by counting the peak of PMTSUM signal in FADC. Fig. 7.5 shows the distribution of
the number of PMTSUM peaks per spill counted by the FADC peak search and the peak timing
distribution, where the 9-bunch micro structure of spill can be clearly seen. The spills whichhave only single peak in PMTSUM are selected as spills with single neutrino event. The fractionof spills with multiple events is about 10%, and it is taken into account for the estimation of
total number of neutrino interactions in 1KT.

7.1.2

Event reconstruction in 1KT

The vertex point of interaction, the number of Cherenkov rings, and the direction and momentumof each Cherenkov ring are reconstructed for the spill data which satisfy the selection criteria up
to (3) mentioned above. Following procedures are applied to reconstruct an event. The detailed
description for each reconstruction procedure is provided in Appendix B, and hence the brief
explanation of the reconstruction method is given here. A flow chart of the event reconstruction
is shown in Fig. 7.6.
Ph.D. Thesis by Issei Kato, July 2004

100

Chapter 7. Analysis in Near Detector(1) Vertex finding (auto−fit)(2) Ring counting(3) Particle identification (PID)(4) Precise vertex finding for 1−ring events (MS−fit)(5) Momentum determination(6) Ring correction(7) Ring correction II

Figure 7.6: A flow chart of the event reconstruction in 1KT.

(1) Vertex finding (auto-fit)
First, the interaction vertex point in each event is determined as a point at which the timing
residual (detected time minus time of flight of Cherenkov light) distribution of hit PMTs has
the sharpest peak by assuming a point-like source of Cherenkov light (point-fit). Next, thedirection and the outer edge of the dominant ring is estimated using the detected photoelectron
distribution as a function of polar angle with respect to the vertex point (ring edge search).
Then the vertex point and the direction of the dominant ring is more precisely fitted by taking
into account the track length of the charged particle (TDC-fit). These three steps are together
called “auto-fit”.
(2) Ring counting
With the knowledge of the vertex point and the direction of the dominant ring, the other possible
rings are searched using the Hough transformation. Each ring candidate is tested whether the
ring is really ring-like or not by a likelihood method, and the number of rings in each event isdetermined. Events which have only one reconstructed Cherenkov ring are called “single-ring”
events, and those which have reconstructed rings greater than one are called “multi-ring” events.
(3) Particle identification (PID)
Each ring in a event is classified into two types, showering type (e-like) or non-showering type(µ-like) using the pattern and the opening angle of the ring image. The showering type ring isa candidate for e± or γ, and the non-showering type ring is a candidate for µ± or π ± . Fig. 7.7
shows the distribution of PID estimator P1 in Eq. (B.20) for the CC-qe single-ring events ofmuon and electron neutrinos estimated by a Monte Carlo simulation. The muon events andthe electron events are clearly separated by the PID algorithm. According to our Monte Carlosimulation, 0.7% of muon neutrino events with single-ring is mis-identified as e-like events, andPh.D. Thesis by Issei Kato, July 2004

7.1. Analysis flow in 1KT

1400

101

µ-likee-like1200

νµ CCqeνe CCqe

1000
800
600
400
200
0

-20

-15

-10

-5

0

5

10
15
20
PID estimator

Figure 7.7: The distribution of PID estimator
for the CC-qe single-ring events of muon and electron neutrino in 1KT. Red (blue) histogram is formuon (electron) neutrino events. Events with the
PID estimator P1 greater (less) than zero are defined as µ-like (e-like) events. As shown in the
figure, the type of particles is almost correctly
identified by our algorithm. These distributions
are estimated by our Monte Carlo simulation.

3.7% of electron neutrino events with single-ring are mis-identified as µ-like ones.
(4) Precise vertex finding for single-ring events (MS-fit)
For single-ring events, the precision of vertex point determination in auto-fit is worse in thelongitudinal direction, since the sharpness of the time residual distribution is not sensitive tothe vertex point shift in the longitudinal direction. Assuming the PID of the Cherenkov ring
determined in the previous step, the vertex point is more precisely fitted using the pattern
information of the ring image. This algorithm is called “MS-fit”.
The resolution of the vertex reconstruction of MS-fit estimated by a Monte Carlo simulationis shown in Fig. 7.8. The resolutions for the single-ring FC events (in which all the secondary
particles generated in neutrino interaction are fully contained in the inner detector of 1KT. See
Sec. 7.4.1.), the single-ring PC events (in which some of the secondary particles generated inneutrino interaction are going outside the inner detector of 1KT), the multi-ring FC events, andthe multi-ring PC events are separately shown. For single-ring FC/PC events, to which MSfit is applied, the vertex resolution is 17.3 cm, while it is 33.1 cm and 35.3 cm for FC and PC
multi-ring events, respectively, for which events auto-fit result is used as the reconstructed vertex
point. Fig. 7.9 shows the resolution of the ring direction also estimated by our Monte Carlosimulation. The distributions of angle between the true muon direction and the reconstructedring direction for CC-qe single-ring FC and PC events are separately plotted. The directional
resolution is 1.80◦ for FC events and 1.47◦ for PC events.
Hereafter, we use MS-fit vertex point for single-ring events and auto-fit vertex point for
multi-ring events as the reconstructed vertex point of each event.
(5) Momentum determination
The momentum of each ring is determined by the number of photoelectrons inside the Cherenkov
ring. The conversion factor from the number of photoelectrons to the momentum is estimatedbased on a Monte Carlo simulation, which is validated by cosmic ray calibration (as described inSec. 3.5.1). Fig. 7.10 shows the momentum resolution of single-ring µ-like events as a functionof muon momentum. The resolution is about 2.0−2.5% in the whole momentum range of 1KT.
(6) First correction to the number of rings (ring correction)
A mis-fitted ring tends to have low momentum. Rings which have low momentum and overlappedwith the other energetic rings are discarded since they are possibly caused by mis-fit and are
Ph.D. Thesis by Issei Kato, July 2004

102

Chapter 7. Analysis in Near Detector

3500

8000
7000

FC single-ring

3000

FC multi-ring6000

σ = 17.3 cm

2500

σ = 33.1 cm

5000

2000

4000
1500

3000

1000

2000

500

1000
0

0

50

100

150
200
∆vertex (cm)

7000

0

50

100

150
200
∆vertex (cm)

1400

6000

PC single-ring5000

σ = 17.3 cm

800
600

2000

400

1000

200
50

100

150
200
∆vertex (cm)σ = 35.3 cm

1000

3000

0

PC multi-ring

1200

4000

0

0

0

0

50

100

150
200
∆vertex (cm)Figure 7.8: The resolution of the vertex reconstruction for fully contained (FC) and partiallycontained (PC) single-ring and multi-ring events in 1KT. Horizontal axis is the distance between
the true vertex point and the reconstructed vertex point. The hatched area shows the regionin which the 68% of events are contained, defining the 1σ of the resolution. These figures are
estimated by our Monte Carlo simulation.

800

FC single-ring700

PC single-ring700

σ = 1.80 degree600

σ = 1.47 degree

600

500

500

400

400
300

300
200

200

100

100

0

0

2

4
6
8
10
∆direction (degree)

0

0

2

4
6
8
10
∆direction (degree)

Figure 7.9: The resolution of the ring direction reconstruction for fully (FC) and partially(PC) contained single-ring events in 1KT. Horizontal Axis is the angle between the true muon
direction and the reconstructed ring direction for CC-qe events. The hatched area shows theregion in which the 68% of events are contained, defining the 1σ of the resolution. These figures
are estimated by our Monte Carlo simulation.

Ph.D. Thesis by Issei Kato, July 2004

Momentum resolution (%)

7.1. Analysis flow in 1KT

103

10
FC single-ring µ-like

9
8
7
6
5
4
3
2
1
0

0

0.5

1
1.5
momentum (GeV/c)

Figure 7.10: Momentum resolution for single-ring µlike FC events in 1KT as a function of muon momentum. Single-ring µ-like FC events of CC-qe interactionin our Monte Carlo simulation are used to estimate theresolution.

yFiducial−A(for profile, 170 t)

6m

ν−beam4m

Fiducial−B(for stability, 50 t)z
Fiducial−C(for analysis, 25 t)
2m
4m
6m

Figure 7.11: Definition of the fiducial volumes used in 1KT analysis. Fiducial-A and
B are used to measure the neutrino beamprofile and event rate stability, respectively.
Fiducial-C is used in main analyses to measure the number of neutrino interactions
and the energy spectrum of the neutrino
beam.

not real rings.
(7) Second correction to the number of rings (ring correction II)
In 1KT, we have sometimes very large hits which seem to be caused by electric noise and seemnot to be associated to any Cherenkov rings. These hits makes a fake (mis-fitted) ring. In thetwo ring events, a ring candidate which contains hits with large charge and isolated from theother Cherenkov ring is removed as a fake ring.

7.1.3

Fiducial volume in 1KT analysis

After all the data reduction and the event reconstruction procedures are applied, events whichvertex point is reconstructed to be inside the fiducial volume are selected for analysis in order
to select neutrino interactions inside 1KT.
Three different fiducial volumes are defined and used for different purposes. The definitionof each fiducial volume is as follows, as well as shown in Fig. 7.11.
(a) Fiducial-A, for the measurements of the neutrino beam profile. Cylindrical volume withthe radius of 3 m and the height of 6 m, oriented perpendicular to the beam direction andcentered at the center of 1KT ID tank. The fiducial mass is 170 t.
Ph.D. Thesis by Issei Kato, July 2004

104

Chapter 7. Analysis in Near Detector(b) Fiducial-B, for the measurements of the stability of neutrino event rate. Cylindrical volume
with the radius of 2 m and the length of 4 m, oriented along the beam direction and centeredat the center of ID tank. The fiducial mass is 50 t.
(c) Fiducial-C, for the measurements of the number of neutrino interactions and the energy
spectrum of the neutrino beam. Cylindrical volume with the radius of 2 m and the lengthof 2 m, oriented along the beam direction, an upper stream half of Fiducial-B. The fiducial
mass is 25 t.

7.2

Number of neutrino interactions in 1KT

In order to make a prediction for the number of neutrino events in SK, neutrino flux is measured
by counting the number of neutrino interactions in 1KT. A merit to use 1KT for this purposeis that most of systematic uncertainties are canceled out because of the same interaction target(water) and the same detection techniques. The description on the measurements of the numberof neutrino interactions in 1KT is provided in this section.

7.2.1

Outline to obtain the number of neutrino interactions in 1KT

At first, the number of neutrino events which are reconstructed in the fiducial volume Fiducial-C
is counted using data which passed all the reduction steps mentioned in Sec. 7.1.1. This number
1KT .
is referred as the number of observed events in 1KT, Nobs
Next, using pulse shape information measured by FADC, the number of spills which have1
total ) observed in FADC are
only one peak in FADC (Npeak) and the total number of peaks (Npeak
counted, which is shown in Fig. 7.5.
1KT , is calculated byThen, the total number of neutrino interaction in Fiducial-C, Nint
1KT
1KT
Nint
= Nobs
·

total
Npeak

1

1

· 1KT ·· Cmulti ( · C7→9 )1²νµ
1 + RB.G.
Npeak

,

(7.1)

where
²1KT
νµ

: detection and selection efficiency for muon neutrino interactions in 1KT.

RB.G. : fraction of background contamination into the selected events.
Cmulti : correction factor for multiple events in a spill which could not be identified as multiple events in the FADC peak search.
C7→9 : correction factor for 7-bunch analysis for the data taken during May andJune 2000, as described in Sec. 7.2.6.
1KT is used to predict the number of neutrino events expected to be observed
The number Nintin SK, as described in Sec. 7.3.

7.2.2

Event selection for neutrino interaction in the fiducial volume

Using the reconstructed information, further selections are imposed upon the data remaining in
the data reduction described in Sec. 7.1.1 in order to obtain the number of neutrino events in
1KT .
Fiducial-C, Nobs
Ph.D. Thesis by Issei Kato, July 2004

4000

Data
fiducial

3500

MC

3000

105
#events/ton#events/ton

7.2. Number of neutrino interactions in 1KT

3500
Data
fiducial

3000

MC

2500

2500
2000
2000
1500
1500
1000
1000
500

500

upstream
0

0

50

100

150

200

250

300

350
400
R (cm)

0
-400

-300

-200

downstream
-100

0

100

200

300
400
Z (cm)

Figure 7.12: The distributions of the reconstructed vertex in the radius direction (left) and thebeam directions (right). Red circles with error bars show
p data and black boxes show a Monte Carlosimulation. The events which vertex satisfies that R = x2 + y 2 < 200 cm and −200 cm < z < 0 cm
are selected as the events taking place inside the fiducial volume.

First, in order to ensure that events are correctly reconstructed, the events which haverings equal to or greater than one are selected. Furthermore, since event tends to be misreconstructed if its point-fit vertex is near the wall of the ID tank, the events which point-fit
vertex is settled more than 30 cm away from the wall are selected. Then fiducial volume cut
to select the events in Fiducial-C is imposed onto the remaining events. Fig. 7.12 shows thereconstructed vertex distributions in the radius direction and the beam direction. As shown in
the figure,pthe criteria on the fiducial volume is that the reconstructed vertex is inside FiducialC; R = x2 + y 2 < 200 cm and −200 cm < z < 0 cm, where x and y are the coordinatestransverse to the beam direction, and z is that along the beam direction as shown in Fig. 7.11.
Small discrepancy seen in the z distribution is taken into account for the systematic uncertainty
in the fiducial volume cut, which is described in Sec. 7.2.8.
By counting the number of events remaining after these cuts, the number of observed neutrino
1KT , is obtained. In total, 80,024 events are observed in Fiducial-C during theinteractions, Nobs
whole run period from June 1999 to July 2001. Table 7.1 summarizes month-by-month observed
number of neutrino events, separately.

7.2.3

Event selection efficiency

Fig. 7.13 shows the event selection efficiency for Fiducial-C as a function of R, z, and the incident
neutrino energy Eν . The averaged efficiency for all interaction modes is about 71% for runs in1999 and about 75% for runs in 2000 and 2001. The efficiency for each month is also summarizedin Table 7.1.

7.2.4

Background rate in the selected events

Expected source of backgrounds are cosmic ray muons and beam neutrino induced incoming
muons. In addition to them, we had reflection pulse in the signal cables in 1999 runs, which
made fake events. These background contaminations are estimated as follows.
Ph.D. Thesis by Issei Kato, July 2004

106

Chapter 7. Analysis in Near Detector

Table 7.1: Summary of the number of interactions measured in 1KT.
periodTarget diameter
Horn current
POT1KT (×1018 )total# total peaks (Npeak)
1
Single event (Npeak)
Efficiency (²1KT
νµ )Background rate (RB.G. )Multi-event corr. (Cmulti )7 to 9-bunch corr. (C7→9 )1KT# observed events (Nobs)
1KT# interaction (Nint)
Event rate (/1015 POT)

Jun.’992 cmφ
200 kA
2.60
109,119
89,782
0.706
0.031
1.008
—
4,282
7,206
2.77

Nov.’99

Jan.’00

2.62
118,32196,304
0.708
0.031
1.008
—
4,923
8,351
3.19

1.81
85,15567,678
0.743
0.015
1.008
—
3,576
6,013
3.32

periodTarget diameter
Horn current
POT1KT (×1018 )total# total peaks (Npeak)
1
Single event (Npeak)
Efficiency (²1KT
νµ )Background rate (RB.G. )Multi-event corr. (Cmulti )7 to 9-bunch corr. (C7→9 )1KT# observed events (Nobs)
1KT)# interaction (NintEvent rate (/1015 POT)

Jan.’01

Feb.’01

Mar.’01

2.92
136,372
11,0867
0.745
0.015
1.008
—
5,746
9,420
3.23

4.75
229,826
182,166
0.745
0.015
1.008
—
9,213
15,491
3.26

4.27
207,066
163,502
0.745
0.015
1.008
—
8,228
13,888
3.26

May.’00

Jun.’00

2.42
88,44574,227
0.742
0.015
1.008
1.282
3,705
7,573
3.13

3.17
114,688
95,888
0.742
0.015
1.008
1.283
4,933
10,130
3.20

Apr.’01
3 cmφ
250 kA
2.47
120,324
95,032
0.745
0.015
1.008
—
4,743
8,004
3.24

May.’01

Jun.’01

Jul.’01

1.60
75,864
60,113
0.745
0.015
1.008
—
3,113
5,236
3.27

5.79
27,597220,087
0.745
0.015
1.008
—
11,43019,1023.30

1.43
67,71953,606
0.745
0.015
1.008
—
2,759
4,645
3.26

1KT
Nobs

=

80, 024

1KT
Nint

=

137, 483 ± 486(stat.) ± 5, 971(syst.)

fiducial
0.8

1

Efficiency

1

Efficiency

Efficiency

In total :Feb.’00 Mar.’00
3 cmφ
250 kA
3.74
3.35
174,224 155,643
139,241 122,700
0.748
0.743
0.015
0.015
1.008
1.008
—
—
7,139
6,234
11,857
10,567
3.17
3.16

fiducial
0.8

1
0.8

0.6

0.6

0.6

0.4

0.4

0.4

(a)

0.2
0

0

100

200

300
R (cm)

(b)

0.2
0

-200

0

200
Z (cm)

(c)

0.2
0

0

1

2

3

4
5
Eν (GeV)Figure 7.13: Event selection efficiency for Fiducial-C as a function of R, z, and the incident neutrinoenergy Eν . These are estimated by the Monte Carlo simulation with the configuration since Jan. 2000.

Ph.D. Thesis by Issei Kato, July 2004

7.2. Number of neutrino interactions in 1KT

107

Cosmic ray muons
The rate of cosmic ray muon contamination is estimated by using randomly triggered data (offspill trigger). The data was analyzed by the same selection procedures as is done for on-spill
data. The contamination of cosmic ray muons into the beam neutrino candidates in Fiducial-C
is estimated to be 1.0%.
Beam neutrino induced incoming muonsOn-spill data contains neutrino induced incoming muons, which are generated by neutrino interaction in materials surrounding 1KT tank such as upstream concrete wall of the experimental
hall. Most of such muons are coming from upstream of 1KT and penetrate the front side outerdetector with making hits in OD-PMTs. Some of the selected neutrino candidates in Fiducial-C
were investigated by visually looking at OD hits with the event display (or “eye scanning”). The
contamination of beam induced incoming muons is estimated to be 0.5%.
Reflection pulse in 1999 runs
The reflection pulses in signal cables existed in June and Nov. 1999 runs, making fake events.
This problem was fixed by installing buffer amplifiers on ATM input in Jan. 2000 as mentioned
in Sec. 3.5.1. The fraction of fake events by reflection pulses during the period before installationof buffer amplifiers is estimated to be 2.6%
In total, background contamination RB.G. is estimated to be 3.1% and 1.5% for 1999 runs
and 2000−2001 runs, respectively, as is also summarized in Table 7.1.

7.2.5

Multi-event correction

1KT by using single peak events in FADC to the total number ofIn order to extrapolate Nobs
1KT , the correction factor N total /N 1
interactions in 1KT Nintpeak
peak is multiplied to the observed
number of events in Fiducial-C. However, since there are a small fraction of multiple events
which are not identified as multiple events by the FADC peak search, further correction isneeded. In a Monte Carlo simulation, multiple events are generated and the pulse shape of
PMTSUM recorded in FADC is also simulated. Then, by employing the same analysis method
as data, total number of neutrino interactions in Fiducial-C is estimated, and it is compared with
the number of neutrino interaction generated in the Fiducial-C; a fraction of 97.7% events arecorrectly counted. Among the total number of interactions, the fraction of multiple interactions
is estimated to be 0.34, and hence a fraction of mis-counted events is (1 − 0.977) × 0.34 = 0.0078.
Therefore the correction factor Cmulti is estimated to be 1/(1 − 0.0078) = 1.008.

7.2.6

Correction from 7 to 9-bunch for data in May and June 2000

Left figure in Fig. 7.14 shows the FADC peak timing distribution of each event spill observed in
May and June 2000 runs. As shown in the figure, the 8th and 9th bunches were sometimes lost.
This is due to that the stop-timing signal of FADC was unstable and drifted over a few 100 nsec
in this period. Neutrino events in the first 7 bunches are used to obtain the total number ofneutrino interactions during this period to avoid uncertainty of the gate window. This effect iscorrected by a correction factor, C7→9 . This factor is the ratio of the number of events in the
1−9th bunches to that in the 1−7th bunches, and is obtained using only the data taken during
the period when the stop-timing signal was not drifted. The stability of the correction factor
Ph.D. Thesis by Issei Kato, July 2004

Chapter 7. Analysis in Near Detector

Npeak(9)/Npeak(7)

108

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

10

20

30

40

50

60
70
80
Days from Jan.1

Figure 7.14: The distribution of FADC peak timing for each event spill observed from May 2000 toJune 2000 (left) and the correction factors for 7 to 9 bunches obtained in January to March 2000 (right).
In the left figure, Vertical axis is the peak time of FADC (or bunch number) and horizontal axis is thedate from 10 May to 24 June, 2000. The 8th and 9th bunches were sometimes lost due to the drift of thestop-timing signal of FADC. In the right figure, the correction factors C7→9 during Jan. to Mar. 2000
are stable within 0.4%.

had been confirmed to be within 0.4% during the run period as shown in the right figure of
Fig. 7.14.

7.2.7

Total number of interactions in 1KT

After all the correction factors and detection efficiency are substituted into Eq. (7.1), the total
total , is estimated to be 137, 483 ± 486(stat.). Monthnumber of interactions in Fiducial-C, Nintby-month total number of interactions is summarized in Table 7.1 together with the number ofprotons on target for the analysis POT1KT , total number of peaks in FADC, number of spills
with single peak, number of observed events, event rate, and so on.
Fig. 7.15 shows the stability of neutrino event rate measured in 1KT. The intensity of neutrino
beam was also lower in June 1999 than other period due to lower horn magnet current in June
1999. The event rate had been stable within 6%, which is used to estimate the error on thecorrection of the number of POT used in 1KT to that used in SK as expressed in Eq. (5.8) in
Sec. 5.2.3.

7.2.8

Systematic errors on the number of neutrino interaction in 1KT

Systematic errors on the total number of neutrino interaction in Fiducial-C in 1KT are explainedin this section, which are summarized in Table 7.2.
Uncertainty of fiducial volume cut
The performance of the vertex fitter in 1KT had been experimentally studied using cosmic
ray muons [44]. In this study, a pipe was installed into the 1KT tank which optically separates
Ph.D. Thesis by Issei Kato, July 2004

Rate (10-15)/pot

7.2. Number of neutrino interactions in 1KT

109

5
99

00

01

4

3

2

Jun Nov Jan Feb

Mar

May Jun

Jan

Feb

15

20

25

Mar

Apr May

30

35

Jun

Figure 7.15: Long term stability of the neutrino event rate measured in 1KT. In June 1999,
the event rate was lower than other period due tolower horn magnet current, and hence lower neutrino beam intensity. The stability is estimatedto be within 6% during the whole run period.

Jul

1

0

0

5

10

40

Integrated CT(1018 POT)

Table 7.2: Summary of systematic errors on the number of interactions measured in 1KT.
period1KT)# interaction (NintFraction
Fiducial volume
FADC threshold
Energy scale
Background rate
Multiple-events corr.
7 to 9-bunch corr.
Total

Jun.’99
7,206
5.24%

Nov.’99
8,351
6.07%

Jan.’00
6,013
4.37%

1.0%

1.4%

4.4%

4.5%

0.0%
4.3%

period1KT# interaction (Nint)
Fraction
Fiducial volume
FADC threshold
Energy scale
Background rate
Multi-events correction
7 to 9-bunch correction
TotalJan.’01
9,420
6.85%

Feb.’01
15,491
11.27%

Mar.’01
13,88810.10%

4.3%

4.3%

4.3%

Feb.’00
11,857
8.62%
4.0%

Mar.’00
10,567
7.69%

May.’00
7,573
5.51%

Jun.’00
10,130
7.67%

1.0%
1.0%

1.0%

0.5%
0.7%
1.2%
4.3%

4.3%

4.5%

4.5%

Apr.’01
8,004
5.82%
4.0%
1.0%
1.0%
0.5%
0.7%
0.0%
4.3%

May.’01
5,236
3.81%

Jun.’01
19,102
13.89%

Jul.’01
4,645
3.38%

4.3%

4.3%

4.3%

Ph.D. Thesis by Issei Kato, July 2004

MC
5

3.5
Data
3
MC
2.5

6

Data
MC

5
4

4

2

3

1.5

2

1

1

-200

South
-100

0

3
2

0.5

Horizontal
North

0
-300

×103 events/ton

Data

6

×103 events/ton

Chapter 7. Analysis in Near Detector
×103 events/ton

110

100

200
300
X profile (cm)1

Vertical
Lower

0
-300

-200

Upper
-100

0

100

200
300
Y profile (cm)Longitudinal
Upstream

0
-300

-200

Downstream
-100

0

100

200
300
Z profile (cm)Figure 7.16: Reconstructed vertex profile in horizontal (leftmost), vertical (middle), and longitudinal (rightmost) directions in 1KT. The events which vertex is inside Fiducial-A are used, and thedifference of target mass in each bin is corrected. In all figures, red crosses are data and black boxes
are estimated by a Monte Carlo simulation.

inside and outside the pipe. Cosmic ray muons going through inside the pipe were triggered. The
vertex of Cherenkov ring seems to be at the end of the pipe. Using this data, the reconstructedvertex was compared with the true one (end position of the pipe). It is also compared with thatin Monte Carlo simulation. The results show that the reconstructed vertex in the transverse
direction to the particle track is in good agreement with the true position within a few cm.
However the reconstructed vertex point along the particle track direction is shifted from thetrue position by a few 10 cm in both data and the Monte Carlo simulation, and the size of theshift disagrees detween data and the simulation by ∼ 10 cm.
In order to quote the error on the number of neutrino interaction due to the known uncertainty in the reconstructed vertex point mentioned above, following method was employed.
The profile of reconstructed vertex is analyzed using the selected events in Fiducial-A. Fig. 7.16
shows horizontal (x), vertical (y), and longitudinal (z) vertex profiles, in which the number of
events in each bin is corrected by the target mass due to the cylindrical shape of the fiducial
volume. Systematic difference between data and the Monte Carlo simulation is clearly seen inhorizontal and longitudinal direction, while there is small difference in vertical direction.
For longitudinal direction, by counting the number of events reconstructed in several cylindrical volumes with different lengths in z, the difference between data and MC is studied aslisted in Table 7.3.
For horizontal and vertical direction, there is difference in the center and the width of profiles.
The center of the profile in the horizontal direction is +9.8 cm in data and −3.7 cm in MC, andhence there is 13 cm difference between them, while that in the vertical direction is −12.3 cm indata and −16.5 cm in MC, and hence there is 4 cm difference between them. By changing thecenter of fiducial volume in MC by ±13 cm in the horizontal direction and ±4 cm in the verticaldirection, the difference of the number of events from the default fiducial volume is studied aslisted in Table 7.3. The width of profile also have discrepancy by about 13% between data andMC in x-direction. The same method as the case of the profile center is employed by changing
the radius of fiducial volume in MC.
The difference of event rate have settled within 4% in the all studies mentioned above, andhence 4% is taken as the systematic uncertainty of the fiducial volume.
Ph.D. Thesis by Issei Kato, July 2004

7.2. Number of neutrino interactions in 1KT

111

Table 7.3: Comparison of event rate in various fiducial volume in 1KT. First column is the definitionof fiducial volume, second and third columns are the number of events in each fiducial volume
normalized to the target mass of Fiducial-C for data and a Monte Carlo simulation, respectively,
and the last column is the ratio of the number of events for data and for the simulation relative tothat of Fiducial-C. In the table, z is the coordinate along the beam direction, xMC
is the center of0
defined fiducial volume in horizontal direction in MC, y0MC is that in vertical direction in MC, and
RMC is the radius of defined fiducial volume in MC.
Fiducial volume
Fiducial-C−300 < z < 0 cm
−200 < z < 100 cm−200 < z < 200 cm−200 < z < 300 cm
xMC= 0 ± 13 cm
0Data
62,77462,193
61,28460,02858,612—y0MC = 0 ± 4 cm

—

MC

—

R

= 200 ± 25 cm

MC
74,00070,65073,58972,74770,379Relative Data/MC
—
1.037
0.982
0.973
0.982

73,819(+13cm)
73,915(−13cm)
73,972(+4cm)
74,096(−4cm)
71,710(+25cm)
76,022(−25cm)

0.998(+13cm)
0.999(−13cm)
0.999(+4cm)
1.001(−4cm)
0.969(+25cm)
1.027(−25cm)

Uncertainty of FADC threshold
The threshold of FADC peak search is set at around 1000 photoelectrons, as shown in Fig. 7.4.
The fluctuation of the threshold is estimated to be about 10% for the whole run period. Thechange in FADC threshold by 10% yield the change in the event rate by 1%, therefore ±1% isquoted as the systematic uncertainty due to FADC threshold.
In addition, the selection efficiency decreased by 3.5% due to the disconnection of 1/4 partof PMTSUM signal in November 1999 run, as mentioned in Sec. 7.1.1. The uncertainty in the1KT .
efficiency during this period yields an additional 1% error on Nint
Uncertainty of energy scale
The uncertainty of absolute energy scale is estimated to be +2−3 % as described in Sec. 3.5.1. Thechange in the scale of the total number of photoelectrons detected in 1KT by +2−3 % yields thechange in the event rate by less than 1%, and hence error of ±1% on the number of the neutrino
interactions is assigned as the error due to the uncertainty of the absolute energy scale.

Uncertainty of background rate
The estimation of the background rate is described in Sec. 7.2.4. The statistical error on theestimation of the background rate is assigned as its systematic uncertainty, which is ±1.0% in1999 runs and ±0.5% in the other runs.

Uncertainty of multi-event correction
The treatment of multiple events in a spill is described in Sec. 7.2.5. The statistical error in theMonte Carlo study, ±0.7%., is assigned as the error on the multi-event correction Cmulti .
Ph.D. Thesis by Issei Kato, July 2004

112

Chapter 7. Analysis in Near Detector

Uncertainty of 7 to 9-bunch correction
As mentioned in Sec. 7.2.6, only the events in the first 7 bunches are used for the data taken in
May and June 2000 to estimate the number of interactions in 1KT. The statistical error in thecalculation of the correction factor C7→9 is 1%.
In order to validate the 7-bunch analysis method, the same method is applied to the datetake from January to March 2000. The stability of the correction factor C7→9 during this period
is shown in Fig. 7.14. The difference between the event rate estimated by 7-bunch analysis andthe standard method is found to be at most 0.4%.
Furthermore, the mis-fitting of vertex point caused by signals which belong to the masked
bunches is also considered. When FADC signals in the 8th and 9th bunches are masked, amulti-event may mis-identified as a single event. Even in these events, the data of each PMT isrecorded as usual since ATM gate is about 300 nsec which corresponds to 3 bunches. In suchcase, the vertex fitter failed to find the vertex point at correct position. Approximately 0.6% of
events selected by the 7-bunch analysis is estimated to be in this case, and this value is assigned
as the error on the event rate due to 7-bunch analysis.
In total, a systematic error of ±1.2% is quoted as the uncertainty of the 7-bunch analysis.
All the systematic errors above quadratically summed up, the total systematic error on thenumber of neutrino interaction in 1KT Fiducial-C during whole period is estimated to be 4.34%.

7.3

Expected number of neutrino events in Super-Kamiokande

The total number of interactions estimated in 1KT is extrapolated to the expected number of
events in SK. In this section, the method and the results of the extrapolation and the systematic
errors on the expected number of events in SK are described.

7.3.1

Extrapolation of the number of interactions in 1KT to SK

SK ) is derived using the number of neutrino
The expected number of neutrino events in SK (Nexp
1KT ) by following formula,interactions in 1KT (NintSK/1KTSK
1KT
Nexp= Nint· Rint·POTSK· ²SK · Cνe
POT1KT,(7.2)

where POTSK(1KT) is the number of protons on target used in the analysis in SK (1KT), ²SK isthe neutrino detection efficiency in SK averaged over the whole energy of the neutrino beam, Cνe
SK/1KTis a factor to correct the effect of the electron neutrino component in the beam, and Rintisthe ratio of number of neutrino interactions expected in SK to those in 1KT.
Far-to-near number of neutrino interaction ratio
SK/1KTThe F/N ratio Rintis expressed asZΦSK (Eν ) · σH2 O (Eν ) · MSK dEν
SK/1KT
Rint=Z
Φ1KT (Eν ) · σH2 O (Eν ) · M1KT dEν

,

(7.3)

where ΦSK(1KT) (Eν ) is the neutrino energy spectrum at SK (1KT), σH2 O (Eν ) is the cross-sectionof neutrino interaction with water, and MSK(1KT) is the fiducial mass of SK (1KT). The neutrino
Ph.D. Thesis by Issei Kato, July 2004

7.3. Expected number of neutrino events in Super-Kamiokande

113

spectrum at SK and 1KT and the cross-section of neutrino interaction are numerically estimatedby using Beam-MC and Neut-MC, while the fiducial masses of SK and 1KT are 22.5 kt andSK/1KT
25 t, respectively. Rintfor the run in K2K-Ia and K2K-Ib are estimated to be 6.81 × 10−4
−4
and 6.71 × 10 , respectively.
Correction for number of protons on target used in analysis
A factor to correct the difference of total number of protons on target used in 1KT and SK
1KT ;analyses is multiplied to NintPOTSK
POTSK − POT1KT=1+
POT1KT
POT1KT,(7.4)

which is already described in Sec. 5.2.4.
Correction for electron neutrino component
Since the effect of the electron neutrino component in the beam is not taken into account in
SK/1KT
the calculation of the F/N ratio Rint
and the selection efficiencies in 1KT (SK) ²1KT(SK) ,a factor to correct this effect is multiplied to the expected number of neutrino events in SK.
Using a Monte Carlo simulation, the correction factor (Cνe ) due to these effects is estimated to
SK , its uncertainty is ignored in thebe 0.996. Since this correction makes only tiny effect on Nexp
SK .
estimation of the systematic errors on Nexp
Expected number of neutrino events in SK
After all the corrections described above are taken into account, the expected number of neutrino
events in SK during the runs from June 1999 to July 2001 is estimated to beSKNexp= 80.6 ± 0.3(stat.)+7.3−8.0 (syst.)

for 4.79 × 1019 POT ,(7.5)

in the case of no neutrino oscillation. It is summarized on a month by month basis in Table 7.4
together with the number of neutrino interactions in 1KT, F/N neutrino interaction ratio, thecorrection factors, and so on. The statistical error on the expected number of neutrino events
1KT ). The
in SK comes from the statistics of number of neutrino events observed in 1KT (Nobssources of the systematic error are described in Sec. 7.3.2.
As references to the above number, it is also estimated using SciFi and MRD. The results
are
SK
Nexp
(SciFi) = 85.9 ± 1.0(stat.)+7.8−8.5 (syst.) ,SK
Nexp(MRD) = 87.4 ± 0.2(stat.)+12.7−13.9 (syst.) ,which are consistent with the estimation in 1KT.

7.3.2

Systematic errors on the expected number of neutrino events in SK

Systematic errors on the expected number of events in SK are described in this section, which
are summarized in Table 7.5.
Error on the measurements of the number of interactions in 1KT
The uncertainties of the measurements of the number of neutrino interactions in 1KT is as
described in Sec. 7.2.8.
Ph.D. Thesis by Issei Kato, July 2004

114

Chapter 7. Analysis in Near Detector

Table 7.4: Summary of the expected number of neutrino events in SK.
periodTarget diameter
Horn current
POTSK (×1018 )POT1KT (×1018 )1KT
Nint
SK/1KT
Rint(×10−4 )
²SK
Cνe
SK
Nexp

Jun.’99
20 mmφ200 kA
3.10
2.60
7,206
6.81
0.781

Nov.’99

Jan.’00

3.57
2.62
8,351

2.22
1.81
6,013

4.55

5.97

3.87

periodTarget diameter
Horn current
POTSK (×1018 )POT1KT (×1018 )1KT
Nint
SK/1KT(×10−4 )
Rint
²SK
Cνe
SK
Nexp

Jan.’01

Feb.’01

Mar.’01

3.20
2.92
9,420

5.04
4.75
15,491

4.60
4.27
13,888

5.42

8.63

7.87

In total :

SK
Nexp

=

Feb.’00 Mar.’00
30 mmφ250 kA
4.04
3.70
3.74
3.35
11,857
10,567
6.71
0.785
0.996
6.73
6.14

May.’00

Jun.’00

2.56
2.42
7,573

3.76
3.17
10,130

4.19

6.31

Apr.’01
30 mmφ250 kA
2.76
2.47
8,004
6.71
0.785
0.996
4.70

May.’01

Jun.’01

Jul.’01

1.75
1.60
5,236

6.12
5.79
19,102

1.54
1.43
4,645

3.00

10.59

2.63

80.6 ± 0.3(stat.)+7.3−8.0 (syst.)

Error on the correction of the number of protons on target
Error due to the difference of the number of protons on target used in 1KT and SK analyses is
as described in Sec. 5.2.3. Uncertainty of POT comes from only un-overlapped spills between
1KT and SK. Therefore, the error on the correction of POT is as follows;δPOT =POTSK − POT1KT· δS1KT
POT1KT,(7.6)

where the uncertainty of beam intensity is quoted from the instability of neutrino event rate in
1KT (δS1KT ), which is estimated to be 6% as mentioned in Sec. 7.2.2.
Uncertainty of neutrino energy spectrum at near and far sites
SK due to the uncertainties in neutrino energy spectrum and F/NHere, systematic errors on Nexp
ratio are considered. The extrapolation of the number of neutrino interactions in 1KT to the
expected number of neutrino events in SK is done by Eq. (7.2), where the selection efficiency ofneutrino events in SK (²SK ) is factorized out by using the efficiency averaged over the neutrinoenergy. When Eq. (7.2) is expressed in more strict form, it becomesZ
SK/1KT
Rflux(Eν ) · Φ1KT (Eν ) · σH2 O (Eν ) · ²SK (Eν ) · MSK dEν
SK
1KT
Z
Nexp = Nint ·
,
(7.7)
1KT
Φ
(Eν ) · σH2 O (Eν ) · ²1KT (Eν ) · M1KT dEν

Ph.D. Thesis by Issei Kato, July 2004

7.3. Expected number of neutrino events in Super-Kamiokande

115

where ²1KT(SK) (Eν ) is efficiency to detect neutrino interaction of the neutrino energy of Eν in
SK/1KT

1KT (SK), and Rflux(Eν ) is the ratio of the neutrino energy spectra at SK and 1KT as
explained in Sec. 5.1 (Eq. (5.4)). In this expression, other corrections such as POT and electron
neutrino component are ignored since they make no effect (or very small effect even if they do)on the discussion. For simplicity, we denote some quantities appeared in Eq. (7.7) as following;£ SK¤
SK/1KTnobs (Eν ) MC = Rflux(Eν ) · Φ1KT (Eν ) · σH2 O (Eν ) · ²SK (Eν ) · MSK£ 1KT¤
nobs (Eν ) MC = Φ1KT (Eν ) · σH2 O (Eν ) · ²1KT (Eν ) · M1KT ,Z£ 1KT(SK) ¤£ 1KT(SK)
¤
Nobs
=
nobs
(Eν ) MC dEν ,
MC

,

(7.8)
(7.9)
(7.10)£ 1KT(SK)¤where nobs
(Eν ) MC stands for the number of neutrino events with an energy of Eν in 1KT£ 1KT(SK) ¤(SK) and Nobs
stands for the total number of neutrino events in 1KT (SK) estimatedMCby a Monte Carlo simulation.
SK/1KT
SK/1KTIf Rflux(Eν ) is changed by ∆Rflux(Eν ) and Φ1KT (Eν ) is changed by ∆Φ1KT (Eν ), thenSK , ∆N SK , is expressed by following two different terms;
the change in Nexp
exp
SK
∆Nexp

≈

SK
Nexp
·

·Z ³
h nSK (E ) n1KT (E ) i ´ννdEν∆φ1KT (Eν ) · obs SK − obs1KT
MC
Nobs
Nobs
¸
Z ³
h nSK (E ) i ´ν
SK/1KT
obs
dEν
,
+
∆r
(Eν ) ·
SKMC
Nobs

(7.11)

where∆φ1KT (Eν ) =∆Φ1KT (Eν )Φ1KT (Eν )SK/1KTand ∆rSK/1KT (Eν ) =∆Rflux(Eν )SK/1KT
Rflux
(Eν )

,

(7.12)and only the first order corrections are considered. In Eq. (7.11), the first term corresponds tocorrelated error between 1KT and SK which comes from the uncertainty of energy spectrum
shape in 1KT, and the second term corresponds to uncorrelated error which comes from theSK due toextrapolation of 1KT measurements to SK by F/N ratio. Ths systematic errors on Nexp
the uncertainties in neutrino energy spectrum and F/N ratio are estimated by using Eq. (7.11).
In actual case, the neutrino energy is divided into the same bins as the binning of PIMON
described in Sec. 6.3, and the integration is replaced by the summation over 6 bins. Using theerrors estimated by PIMON measurements listed in Table C.1, C.2, and C.3 as ∆φ1KT (Eν ) andSK for K2K-Ib (K2K-Ia) are +3.8 % (+5.8 %) from the∆rSK/1KT (Eν ), the systematic errors on Nexp
−3.5
−7.0
+13.6
uncertainties of the neutrino energy spectrum and +5.6
%
(
%)
from
the
F/N
ratio.
−7.3−9.9
Uncertainty of neutrino interaction cross-section
Since there is small difference of detection efficiency between 1KT and SK for each neutrino
interaction mode, the uncertainties of the neutrino interaction cross-section causes some ambiSK . In order to estimate this systematic effect, the ratio of neutral current to charged
guity in Nexp
SK
current interaction cross-section (σNC /σCC ) is changed by ±30%, yielding a change in Nexp
by +0.2−0.3 %, and the ratio of inelastic to (quasi-)elastic interaction cross-section (σnonQE /σQE ) is
SK by +0.5 %.
changed by ±30%, yielding a change in Nexp
−0.8
Ph.D. Thesis by Issei Kato, July 2004

116

Chapter 7. Analysis in Near Detector

Table 7.5: Summary of the systematic errors on the expected number of neutrino events in SK.
periodSK
NexpJun.’99
4.55

Nov.’99
5.97

Jan.’00
3.87

Feb.’00
6.73

Mar.’00
6.14

May.’00
4.19

Jun.’00
6.31

Errors from 1KT
POT correction
Neutrino Spectrum
F/N ratio
σNC /σCC
σnonQE /σQE
SK efficiency

4.4%
1.0%
+5.8
−7.0 %+13.6−9.9 %

4.5%
1.6%

4.3%
1.1%

4.3%
0.5%

4.3%
0.6%
+3.8
−3.5 %+5.6−7.3 %
+0.2
%
−0.3
+0.5
−0.8 %
±3%

4.5%
0.3%

4.5%
1.0%

Total

+15.8
−13.3 %

+8.8
−9.9 %+8.6−9.7 %+8.6−9.7 %+8.6−9.7 %+8.7−9.8 %+8.7−9.8 %

periodSK
NexpJan.’01
5.42

Feb.’01
8.63

Mar.’01
7.87

Apr.’01
4.70

May.’01
3.00

Jun.’01
10.59

Jul.’01
2.63

Errors from 1KT
POT correction
Eν Spectrum
F/N ratio
σNC /σCC
σnonQE /σQE
SK efficiency

4.3%
0.5%

4.3%
0.3%

4.3%
0.4%

4.3%
0.6%
+3.8
−3.5 %+5.6−7.3 %+0.2−0.3 %+0.5−0.8 %
±3%

4.3%
0.5%

4.3%
0.4%

4.3%
0.3%

Total

+8.6
−9.7 %+8.6−9.7 %+8.6−9.7 %+8.6−9.7 %+8.6−9.7 %+8.6−9.7 %+8.6−9.7 %

Uncertainty of event selection in SK
The event selection in SK, which is described in Chapter 8, have some uncertainties, causing
the errors on the expected number of neutrino events in SK. Dominant uncertainty is in theselection of the events with vertex contained in the fiducial volume of SK. By applying two
different vertex fitters, TDC-fit and MS-fit, to the atmospheric neutrino data sample and MonteSK due to the uncertainty
Carlo simulation and comparing the results, the systematic errors Nexp
of fiducial cut is estimated to be ±2%.
SK come from the event selection for the neutrinos of
Other systematic uncertainties of Nexp
K2K beam (1%) and statistics of Monte Carlo simulation (1%). In total, 3% is quoted as the
SK due to the uncertainties of event selection in SK.
error on Nexp
By estimating the errors on the expected number of neutrino events in SK month-by-month,
+9.1
+7.3
SK
−9.9 % (−8.0 events) is quoted as the systematic error on Nexp in total.

7.4

Measurement of neutrino spectrum in near detectors

The neutrino energy spectrum at near site is measured using data taken by both 1KT and thefine grained detector (FGD). A momentum and angle with respect to the beam direction of
charged lepton produced in the interaction is used to estimate the energy of neutrino.
Events which have only one µ-like Cherenkov ring with the particle fully contained inside
the inner tank of 1KT (FC1Rµ) are used as a data sample from 1KT, while events with a vertex
contained in SciFi and an end point of scattered charged lepton contained inside MRD are used
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

117

as a data sample from FGD. FC1Rµ sample covers the muon momentum range below 1 GeV/cwith high efficiency and with 4π coverage in solid angle although 1KT has little efficiency toreconstruct muons with momentum above 1.5 GeV/c since they exit the detector. FGD, on theother hand, has high efficiency for measuring muons above 1 GeV/c, and hence 1KT and FGD
can complementarily cover the relevant energy range.
In addition, since ND, especially FGD, has sensitivity to separate the non-qe events from CCqe ones, a fraction of non-qe interactions (or cross-section ratio σnonQE /σQE ) is also measured
in ND, which can become a background in the measurements of the neutrino energy.
In this section, first, further event selections for the spectral analysis in 1KT are described.
Then event samples from FGD are briefly mentioned. Finally, the analysis to estimate theneutrino energy spectrum at ND as well as non-qe/qe ratio is described.
The spectrum in June 1999 (K2K-Ia) differs from that in the rest of the period (K2K-Ib)
since the horn current and target radius in K2K-Ia were different from the rest of the period. In
the oscillation analysis described in this thesis, we do not use the spectral information for thedata taken in K2K-Ia, and hence only the spectrum for K2K-Ib is estimated here.

7.4.1

Further event selections in 1KT

In order to reconstruct the neutrino energy in 1KT, events which have only one µ-like Cherenkov
ring with the charged particle fully contained inside the 1KT inner tank (FC1Rµ) are selected.
The criteria to select FC1Rµ are described in this section, which are corresponding to the selections (8)−(12) in the flow chart in Fig. 7.2. The data taken during the period from January 2000
to July 2001 are used in the spectral analysis in 1KT, since we had problem in the threshold of
FADC in October and November 1999, as described before (1/4 of PMTSUM was disconnected).
Events with a visible energy greater than 30 MeV
In order to eliminate the low energy background events, events are required to have a visibleenergy greater than 30 MeV. Since the threshold of FADC peak search is set around 1,000 p.e.,corresponding to 100 MeV visible energy, this cut does not reduce so many events; only 0.01%
of events in Fiducial-C are discarded.
Events with all the particles fully contained inside the inner tank of 1KT
In 1KT analysis, we classify the neutrino events into two categories; “fully contained (FC)” and“partially contained (PC)” events. Fig. 7.17 shows a schematic view of each event category. The
events in which all secondary charged particles are contained in the inner detector (ID) of 1KT
are referred as FC events, and those in which some of secondary charged particles are going out
of ID are referred as PC events.
In practice, the numbers of photoelectrons detected by individual PMTs are used to classify
each event into FC or PC category. The PMT which have the largest number of photoelectrons
among the PMTs inside a cone of 20◦ opening angle along the direction of the most energetic
ring (referred as “pomax20deg”) is selected in each event. Fig. 7.18 shows the distributionof pomax20deg. When a charged particle exits the inner tank, the ID PMTs near the exit
point receive intense Cherenkov light, and ATM channels of these PMTs tends to saturate. By
selecting the events with pomax20deg less than 200 p.e., PC events are effectively eliminated,and contamination of PC events into FC events is negligible. Among the events used in theestimation of the expected number of neutrino events in SK (events with vertex inside FiducialC), 74.8% are selected as FC events.
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118

Chapter 7. Analysis in Near Detectorνν

Fully contained (FC) event

Partially contained (PC) event

Figure 7.17: Categories of neutrino events in 1KT. Dashed lines show the trajectories of primary
neutrinos, and solid arrows show those of secondary charged particles. The events in which thesecondary charged particles are fully contained in the inner detector of 1KT are referred as “fully
contained (FC)” events, and those in which some of secondary charged particles are going outside
the inner detector of 1KT are referred as “partially contained (PC)” events.

Data
MC
5000
FC

PC

4000

3000

2000

1000

0

0

50

100

150

200
250
300
pomax20deg (p.e.)

Figure 7.18: The distribution of pomax20deg in
1KT. Red points show data and black boxes
show a Monte Carlo simulation. A peak around
250 p.e. corresponds to the saturated point ofreadout electronics (ATM), which is caused by intense Cherenkov light of exiting particle. Eventswith pomax20deg less than 200 p.e. are classified
as fully contained (FC) events, and events withpomax20deg equal to or greater than 200 p.e. areclassified as partially contained (PC) events.

Events with one Cherenkov ring
In order to enhance CC-qe events for which the energy of incident neutrino can be reconstructed,
events which have only one Cherenkov ring are selected, since the Cherenkov threshold for proton
in water is 1.07 GeV/c and recoil protons in CC-qe interaction typically have a momentum
below the threshold in the energy range of the K2K neutrino beam. A likelihood function F (orDLFCT ) for the separation between one and more than one ring is used to select one ring events,
which is described in Sec. B.2.2. Fig. 7.19 shows the distribution of the likelihood function F
and the number of ring distribution. Events with F < 0 are selected as one ring events (#ring= 1). By requiring the number of ring to be one, 55.3% of FC events with vertex in Fiducial-C
are remaining.
Events with a muon-like ring
In order to select the events with a muon type (µ-like) ring, the likelihood for particle identification for the single ring events, P1 , is used. The definition of P1 is described in Sec. B.3.2.
Fig. 7.20 shows the distribution of the likelihood P1 for FC 1-ring events. The events with P1
greater than 0 are selected as the events with a µ-like Cherenkov ring. By this selection, 9.8%
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

Data
3000

35000
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MC
single-ring

multi-ring119

selected
30000

MC

2500
25000
2000
20000
1500
15000
1000

10000

500

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5000

-30

-20

-10

0
10
20
30
Ring Count Likelihood (DLFCT)

0

1

2

3
4
5
Number of Cherenkov Rings

Figure 7.19: Distributions of the ring counting likelihood for single and multiple ring separation(left) and the number of ring distribution (right) in 1KT. Red points show data and black boxes
show a Monte Carlo simulation. In left figure, the ring counting likelihood F (DLFCT ) less than 0
is corresponding to event with only one Cherenkov ring.

of FC 1-ring events are rejected as e-like events.

Events with total photoelectrons greater than 1000 p.e.
Up to here, FC1Rµ events with the vertex in Fiducial-C are selected. In addition, a criterion
to select events with a total number of photoelectrons greater than 1000 p.e. is imposed onto
the sample in order to define a clear threshold of the detected charge and to make systematicstudies on the behavior of the threshold easier. Fig. 7.21 shows the distribution of total numberof photoelectrons for FC1Rµ sample. This cut reduces 0.7% of FC1Rµ events, and the remaining
events are used in the spectral analysis as a final data sample from 1KT.
The reduction rate in each selection step is summarized in Table 7.6. After all the selection
criteria are imposed, 23,254 FC1Rµ events with a vertex in Fiducial-C and a total photoelectrons
greater than 1000 are remaining. According to a Monte Carlo simulation, a fraction of about
53% events in FC1Rµ sample is induced by CC-qe interaction.

7.4.2

Neutrino event selection in FGD

Events which have one or two tracks with a reconstructed vertex point in the fiducial volume of
SciFi, at least one track penetrating into MRD and its end point contained inside MRD (SciFiMRD sample) are used in the spectral analysis. Fig. 7.22 shows a typical event of MRD sample.
Methods to reconstruct tracks in SciFi and MRD are described in [47] and [53], respectively.
Here, only criteria for event selection are briefly described, which are also described in [46, 47,115]. FGD data taken from November 1999 to July 2001 are used in the spectral analysis.
Ph.D. Thesis by Issei Kato, July 2004

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2500µ-likee-like
2000
Data
1500
MC

1000

500

0

-10

-8

-6

-4

-2

0

2

4
6
8
10
PID Likelihood P1

Figure 7.20: The distribution of the likelihoodfor particle identification for FC 1-ring sample
in 1KT. Red points show data and black boxes
show a Monte Carlo simulation. The likelihood P1 greater than 0 is corresponding to µlike Cherenkov ring, while P1 less than 0 is corresponding to e-like ring.

2500
used in analysis
Data

2000

MC
1500

1000

500

0

0

2000

4000 6000 8000 10000 12000 14000
Total number of photoelectrons (p.e.)

Figure 7.21: The distribution of the total number of photoelectron for the FC1Rµ sample in
1KT. Red points show data and black boxes
show a Monte Carlo simulation. The events witha total number of photoelectrons greater than
1000 p.e. are used in the spectral analysis.

Table 7.6: Summary of the event selections for FC1Rµ sample in data and a Monte Carlo simulation. The number of events remained after each selection step is listed. The numbers inside
the parentheses is the fraction of events which are remained from the previous selection step. The
reduction rate in data and a Monte Carlo simulation for each step agrees well.
Selection criteria
Fiducial-C
Visible energy > 30 MeV
Fully contained
1-ringµ-likeTotal # of p.e. > 1000
Final sample for analysis

Ph.D. Thesis by Issei Kato, July 2004

Data
62,77362,762 (∼100%)
46,950 (74.8%)
25,959 (55.3%)
23,426 (90.2%)
23,254 (99.3%)
23,254MC
74,00074,000 (100%)
54,641 (73.8%)
30,186 (55.2%)
27,927 (92.5%)
27,717 (99.2%)
27,717

7.4. Measurement of neutrino spectrum in near detectors

121

Figure 7.22: Event display of a typical SciFi-MRD 2-track events. Red points show hits in detectors
and a blue point in SciFi represents the reconstructed vertex point for this event.

Selection for SciFi-MRD 1-track and 2-track events
In the track reconstruction of SciFi, the most energetic track is taken as a first track of the event.
Events in which the first track starts from inside SciFi, penetrates the downstream TGC and LG
into MRD, and the track end is contained in MRD are selected as “SciFi-MRD events”. The first
track of a SciFi-MRD event is regarded as a muon scattered via a charged current interaction,
and an energy of the muon is reconstructed by using the range of the track. If protons or pions
scattered from a interaction penetrate at least three SciFi layer, second or more tracks are also
reconstructed. Events with no second track or only one second track are selected. Among the
SciFi-MRD events, the events which have only first track are referred as “1-track events” andthe events which have one first and one second tracks are referred as “2-track events”.
Fiducial volume cut
A vertex is taken to be the middle point of the closest upstream water tank in 1-track events,
and the intersection of the first and the second tracks is taken as a vertex in 2-track events. The
fiducial volume of SciFi is defined as following: Among the 19 layers of water tanks in SciFi, the
1st to 17th layers are used as a fiducial region along the beam (z) direction, and a square regionof 2.2 m × 2.2 m centered at the beam axis is used as a fiducial region in horizontal (x) andvertical (y) directions. Total fiducial mass is 5.9 t including aluminum structure of a fractional
weight of 15%. The events whose reconstructed vertex is inside the fiducial volume are selected.
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600

µ

500

ν
P
∆Θ exp.

400

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P

.
bs

Po

300

MC
(CCQE)

200

>30

o

100
0

-1

-0.8 -0.6 -0.4 -0.2

0

<25

o

0.2 0.4 0.6 0.8 1cos(∆ΘP)

Figure 7.23: The distribution of cosine of the angular difference between the expected and the observed
second track directions, cos ∆θp , in SciFi-MRD 2-track
events. Black points shows data and red histogram showsa Monte Carlo simulation. Blue hatched area indicate thefraction of CC-qe interaction in the Monte Carlo simulation. Events with ∆θp less than 25◦ (greater than 30◦ )are classified as QE (non-QE) sample.

Separation of 2-track into QE and non-QE enhanced samples
The direction of a scattered proton can be predicted by using the momentum and angle of thefirst track assuming the event is induced by CC-qe interaction;
p~p = ( −pµx , −pµy , prec
ν − pµ cos θµ ) ,(7.13)

where p~p is a predicted momentum vector of scattered proton, pµx and pµy are, respectively, x
and y component of the first track (muon) momentum vector, pµ and θµ are, respectively, thefirst track momentum and angle with respect to the beam direction, and prec
ν is the reconstructed
neutrino momentum calculated by assuming CC-qe interaction;
prec
ν =

1 m2p − m2n − m2µ + 2mn Eµ·2
mn − Eµ + pµ cos θµ.

(7.14)

If the second track of a 2-track event is reconstructed in the direction of (tan θxz , tan θyz , 1),
where θxz and θyz are projected angle of the second track onto x-z and y-z planes, respectively,
the angular difference (∆θp ) between the expected (~pp ) and the reconstructed directions can becalculated ascos ∆θp = q£−pµx · tan θxz − pµy · tan θyz + prec
ν − pµ cos θµ
¤ £
¤
2
2
2
2
rec
(prec
ν ) + pµ − 2 pν pµ cos θµ · tan θxz + tan θyz + 1.

(7.15)In the case of CC-qe interaction, ∆θp may become small, while the expected and the observed
second track directions are not correlated so much in the case of non-qe interactions. Fig. 7.23
shows the distribution of cos ∆θp for SciFi-MRD 2-track sample. As is expected, most of CC-qe
events are in the small ∆θp region. Using this kinematic information, SciFi-MRD 2-track sample
is further classified into two categories; if an event has ∆θp less than 25◦ , it is categorized into
QE sample, while if an event has ∆θp greater than 30◦ , it is categorized into non-QE sample.
After the selection criteria are imposed onto the FGD events, 5,963 1-track events, 764 2track QE events, and 1,288 2-track non-QE events are remaining. These are also used in the
spectral analysis together with FC1Rµ in 1KT. According to a Monte Carlo simulation, 60% of
2-track QE events come from CC-qe interactions, while 85.7% of 2-track non-QE events comefrom interactions other than CC-qe.
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

7.4.3

123

Basic distributions of FC1Rµ and SciFi-MRD samples

Fig. 7.24 show basic distributions for FC1Rµ sample in 1KT. The momentum and angular
distributions of the muon candidates are shown in upper left and right figures, respectively,
while the distributions of the reconstructed neutrino energy (Eνrec ) and 4-momentum transfer
2squared ( Q2rec = (pµ − precν ) ) calculated by assuming CC-qe interaction are shown in lower
left and right figures, respectively. In each figure in Fig. 7.24, a fraction of CC-qe interactions
estimated by a Monte Carlo simulation is shown by a blue hatched histogram.
The same figures for SciFi-MRD 1-track, 2-track QE, and 2-track non-QE samples are shownin Fig. 7.25, 7.26, and 7.27, respectively. Here again, the fraction of CC-qe interaction ineach distribution is indicated by the hatched histograms, which is estimated by a Monte Carlosimulation.
The model in the Monte Carlo simulation shown here is NEUT-0000 (the original NeutMC, see Sec. 4.2.7 and Table 4.4), where data and the Monte Carlo simulation have somediscrepancies in all figures. Several systematic studies had been done in 1KT detector against
these discrepancies.
As shown in Fig. 7.28, the discrepancies in the momentum and neutrino energy distributions
are found to be within the uncertainty of energy scale which is estimated to be +2−3 % in 1KT.
2
However the discrepancies in the angular distribution and also in the Q distribution cannot
be explained by any detector systematics such as angular resolution, angular bias, or a bias
in vertex reconstruction. Fig. 7.29 shows the results of several systematic studies on possible
angular biases. In the cosmic ray data, the Monte Carlo simulation shows about 2◦ better angularresolution than data [44]. Therefore, the effect of the difference in angular resolution had beenstudied by smearing the reconstructed angle of muons by 2◦ in the Monte Carlo simulation,
which is shown by the yellow histogram in Fig. 7.29. In the studies of cosmic ray data, it had
also been found that the vertex fitter tends to reconstruct the vertex to be at a point about
5−10 cm shifted toward the particle direction only in data [44]. Therefore, this effect had beenstudied by changing the z position and the radius of the fiducial volume by ±10 cm, which isshown by green and blue histograms in Fig. 7.29. Furthermore, a possible effect of angular shift
due to the vertex shift is also considered by adding +1◦ to the muon angle in the simulation,
which is shown by the purple histogram.
In conclusion, the deficit in the forward region and large angle scattering in data cannot
be explained in any cases of systematic biases. Therefore, we have modified the models in ourMonte Carlo simulations for our spectrum and oscillation analysis within their uncertainties,
which will be discussed in the next section. The descriptions on their modifications are alreadygiven in Sec. 4.2.

7.4.4

Choice of neutrino interaction models

As mentioned in the previous section, there exists a clear deficit in the forward region in ourdata compared with the model of NEUT-0000, and it is not due to the detector systematics.
Furthermore, the χ2 fitting to estimate the neutrino spectrum, which will be described in thefollowing sections, have been performed with the use of NEUT-0000, but it is found that theχ2 minimum does not settle at the reasonable size (χ2min = 290.8/197d.o.f., which probability
is 0.0015%) and the non-qe/qe ratio is found to be un-physically small value of about 0.66
relative to the initial value in MC. Therefore, we have concluded that the models employed in
our MC do not reproduce our experimental data due to the lack of the knowledge of neutrino
Ph.D. Thesis by Issei Kato, July 2004

4500
Data
4000
MC
3500

MC (CCqe)

3000

events / 10 degrees

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events / 0.1 GeV/c

124

3500
Data
3000

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2500

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2500

2000

2000

1500

1500
1000
1000
500

500
0

0.5

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0

1.5
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Pµ (GeV/c)

10000
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MC

8000

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6000

events / 0.1 (GeV/c)2

events / 0.25 GeV

0

0

50

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7000

150
θµ (degree)

Data
MC

6000

MC (CCqe)

5000
4000
3000

4000

2000
2000
1000
0

0

0.5

1

1.5

2
2.5
Rec.Eν (GeV)

0

0

0.5

1

1.5
2
2
2 2
Rec.Q (GeV /c )Figure 7.24: The momentum (upper left) and angular (upper right) distributions of scatteredmuons in FC1Rµ sample, and the distributions of the reconstructed neutrino energy (lowerleft) and the reconstructed 4-momentum transfer squared (lower right) for FC1Rµ sample. In
all figures, red points show data and black boxes show a Monte Carlo simulation. The fractionof CC-qe events in FC1Rµ estimated by MC is also shown by blue hatched histogram in eachfigure.

Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

125

600

700
1−track
600

1−track
500

500

400

400
300
300
200
200
100

100
0
0

0.5

1

1.5
2
2.5
3
Muon Momentum (GeV/c)

1−track

600
500

0
0

20

40

60
80
100
Muon Angle (degree)

1−track

1000

800

400
600
300
400
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200

100
0
0

0.5

1

1.5
2
2.5
3
3.5
4
Rec. Neutrino Energy (GeV)000.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8 2
Rec.Q 2 (GeV 2 /c 2 )Figure 7.25: The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 1-track sample, and the distributions of the reconstructed neutrino energy(lower left) and the reconstructed 4-momentum transfer squared (lower right) for SciFi-MRD
1-track sample. In all figures, red points show data and a black histogram show a Monte Carlosimulation. The fraction of CC-qe events in SciFi-MRD 1-track estimated by MC is also shownby a hatched histogram in each figure.

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126

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140
2−track QE
120
100

2−track QE

100

80

80

60

60
40
40
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0
0

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2
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3
Muon Momentum (GeV/c)2−track QE

140

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50 60 70 80 90
Muon Angle (degree)

120

120

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10

2−track QE

60

60
40
40
20

20
0
0

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3
3.5
4
Rec. Neutrino Energy (GeV)000.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8 2
Rec.Q 2 (GeV 2 /c 2 )Figure 7.26: The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 2-track QE sample, and the distributions of the reconstructed neutrinoenergy (lower left) and the reconstructed 4-momentum transfer squared (lower right) for SciFiMRD 2-track QE sample. In all figures, red points show data and a black histogram show aMonte Carlo simulation. The fraction of CC-qe events in SciFi-MRD 2-track QE estimated by
MC is also shown by a hatched histogram in each figure.

Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

350

2−track non−QE

127

2−track non−QE

120

300
100
250
80
200
60
150
40

100

20

50
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300

0
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60
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Muon Angle (degree)250
2−track non−QE

2−track non−QE
250

200

200
150
150
100
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50

50
0
0

0.5

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1.5
2
2.5
3
3.5
4
Rec. Neutrino Energy (GeV)000.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8 2
Rec.Q 2 (GeV 2 /c 2 )Figure 7.27: The momentum (upper left) and angular (upper right) distributions of scatteredmuons in SciFi-MRD 2-track non-QE sample, and the distributions of the reconstructed neutrino energy (lower left) and the reconstructed 4-momentum transfer squared (lower right) for
SciFi-MRD 2-track non-QE sample. In all figures, red points show data and a black histogramshow a Monte Carlo simulation. The fraction of CC-qe events in SciFi-MRD 2-track non-QE
estimated by MC is also shown by a hatched histogram in each figure.

Ph.D. Thesis by Issei Kato, July 2004

Data
default MC
Escale -2%
Escale +3%

3500
3000
2500

events / 0.25 GeV

Chapter 7. Analysis in Near Detector

events / 0.1 GeV/c

128

Data
default MC
Escale -2%
Escale +3%

8000
7000
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Rec.Eν (GeV)

Data
default MCvertex +10cm
vertex -10cm+2 deg. smear+1 deg. shift

2500

2000

1500

events / 0.1 (GeV/c)2

events / 10 degrees

Figure 7.28: Systematic studies on the effect of the uncertainty in the energy scale on the
momentum (left) and reconstructed neutrino energy (right) distributions in FC1Rµ sample.
In the Monte Carlo simulation, the momentum is scaled up and down by +3% and −2%
according to the size of the uncertainty, showing that the discrepancy in the reconstructed
neutrino energy distribution is within the size of the energy scale uncertainty.

4000

3000

1000

2000

500

1000

0

0

50

100

150
θµ (degree)Data
default MCvertex +10cm
vertex -10cm+2 deg. smear+1 deg. shift

5000

0

0

0.5

1

1.5
2
2
2 2
Rec.Q (GeV /c )Figure 7.29: Systematic studies on the effect of the angular biases in the reconstruction on the
angular (left) and reconstructed 4-momentum transfer squared (right) distributions in FC1Rµsample. See the text for the explanation of each histogram. Any systematic biases cannot
explain the deficit in the forward region and the hard scattering in data.

Ph.D. Thesis by Issei Kato, July 2004

4500
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NEUT-0000
3500

NEUT-1211

3000

events / 10 degrees

events / 0.1 GeV/c

7.4. Measurement of neutrino spectrum in near detectors

129

3500
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NEUT-0000

2500

NEUT-1211

2500

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1000
500

500
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Pµ (GeV/c)

0

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50

100

150
θµ (degree)

Figure 7.30: Comparison of the muon momentum and angular distributions between NEUT-0000 and
NEUT-1211 for FC1Rµ sample. Data is also superimposed in the figures.

interaction cross-section around 1 GeV region.∗ We have modified the models used in our Monte
Carlo simulation according to the existing models or within the size of uncertainties of existing
experimental data. The detailed descriptions for the modifications are given in Sec. 4.2. The
key point of the modifications is that the model for each interaction mode have been modified
to have harder scattering and suppression in low q 2 region.
For the interactions of (quasi-)elastic and single pion production, the existing experimental
values for MA are 1.0 GeV/c2 and have uncertainty of about 10% and 20%, respectively. In
our spectral analysis, we have decided to use 1.1 GeV/c2 for (quasi-)elastic interaction and
1.2 GeV/c2 for single pion production. For the deep inelastic scattering and the coherent pion
production, we employ the models by A. Bodek et al. [96] and J. Marteau et al. [105, 106],
respectively, both of which suppress the interaction cross-section in the low q 2 region. Fig. 7.30
show the comparison of muon momentum and angular distributions between NEUT-0000 and
NEUT-1211 as well as data for FC1Rµ sample, indicating that our data favors NEUT-1211 than
NEUT-0000 although data still has a little deficit in the small angle region.
In summary, we have employed the model NEUT-1211 in the spectral analysis described infollowing sections and the oscillation analysis described in Chapter 9. It is also found that the
choice of models make some biases on the measurement of the cross-section ratio of non-qe/qe,
and hence the effect of choice of different models has been also studied, which is described inSec. 7.4.6.

7.4.5

χ2 fitting to derive the neutrino spectrum at ND

An overview of the fitting method
A χ2 -fitting is employed to derive the neutrino energy spectrum at ND from the observed muon
momentum and angular distributions. The data sample used in the fitting is FC1Rµ, SciFi-MRD
1-track, 2-track QE, and 2-track non-QE samples. The fitting procedure is as follows.
∗

Actually, there exist no experimental data for the oxygen target in the low energy region, and hence we do
not understand well the behavior of the cross-section.

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1. The neutrino spectrum is divided into eight bins; 0−0.5 GeV, 0.5−0.75 GeV, 0.75−1.0 GeV,
1.0−1.5 GeV, 1.5−2.0 GeV, 2.0−2.5 GeV, 2.5−3.0 GeV, and above 3.0 GeV. The neutrino
interaction modes are also separated into two categories; (quasi-)elastic (qe) and inelastic
interactions (non-qe). The fitting parameters are, therefore, the weighting factors for eachenergy bin relative to the values estimated by Beam-MC (fiφ , i = 1, · · · , 8) and the crosssection ratio of non-qe to qe which is also relative to the value in Neut-MC (Rnqe ). In orderto make consistency between 1KT and FGD, the 4th bin (f4φ ) is fixed to be unity during
the fitting for the normalization, and another set of parameters is prepared to normalize
1KT and P FGD ).
the distributions separately in 1KT and FGD (Pnorm
norm
2. The 2-dimensional distributions of the muon momentum versus scattering angle with respect to the beam direction for four categories of event sample are compared in the χ2 fitting. For the Monte Carlo sample, this 2-dimensional distribution is prepared separately
for each of eight neutrino energy bin and each interaction mode, therefore, 8 × 2 distributions are made in MC. The example distributions for data and MC are shown in Fig. 7.31.
3. The χ2 functions for 1KT sample (χ21KT ) and for FGD samples (χ2FGD ) are separately
defined, and they are summed to build a combined χ2 function (χ2ND ). In addition to them,since the results of PIMON measurements can also restrict the neutrino energy spectrum,a χ2 function (χ2PIMON ) is added to χ2ND as a constraint on the weighting factors of thespectrum. Therefore, the final form of the χ2 function becomesχ2ND = χ21KT + χ2FGD + χ2PIMON.

(7.16)The details of each part of the χ2 function are described in the following sections.
4. Finally, a set of fitting parameters (fiφ and Rnqe ) are found by minimizing the χ2 function.
Same procedure is applied to the different sets of interaction models in the Monte Carlosimulation in order to estimate the dependence of fitting results on interaction models,
which is discussed in Sec. 7.4.6
Definition of χ2 function for FC1Rµ sample
The momentum versus angle 2-dimensional for FC1Rµ sample is binned with the interval of
0.1 GeV/c in momentum and 10◦ in angle. Bins above 90◦ are integrated into one angular bin,as shown in Fig. 7.31. The χ2 function is defined as
χ21KT =

data − N MC )2
X ( Nm,n
m,n
m,n

MC
1KT
Nm,n
= Pnorm·(σm,n )2
8
X+

1KT )2( 1 − Pe-scale
1KT )2(σe-scale,¡ MC[i,qe]¢MC[i,nqe]
fiφ · Nm,n
+ Rnqe · Nm,n,(7.17)(7.18)

i=1

where i represents the bin number of neutrino energy, m and n represent the bin number of thedata is the number of contents in the
2-dimensional distribution of momentum versus angle, Nm,nMC[i,qe(nqe)](m, n)-th bin in data, Nm,nis the same one as data but for the i-th energy bin and qe(non-qe) interactions in the Monte Carlo simulation, σm,n is the error associated to the (m, n)-th
1KT is overall normalization
bin including both statistical and systematic uncertainties, and Pnorm
factor for FC1Rµ sample. In the summation over (m, n), only the bins with contents in MC
greater than 20 are used in order to avoid a possible strange bias due to small statistics. The
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

Data
80

60

100

integretedMCEν<0.5 GeV
Int.Mode:QE

80

60

Muon Angle θµ (deg.)

100

integreted

Muon Angle θµ (deg.)

integreted

60

40

40

20

20

20

0.2

0.4

0

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)

0

0.2

0.4

Muon Angle θµ (deg.)

100
MC
0.5<Eν<0.75 GeV
Int.Mode:QE8060

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)

20

0

0.2

0.4

0

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)

MC
0.5<Eν<0.75 GeV
Int.Mode:non-QE

60

20

100

Muon Angle θµ (deg.)

0.4

80

40

0

0.2

0.4

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)100

integretedMC
0.75<Eν<1.0 GeV
Int.Mode:QE

8060

integreted

60

40

20

20

0

0.2

0.4

0

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)100

MC0.75<Eν<1.0 GeV
Int.Mode:non-QE

80

40

0

0.2

0.4

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)100

integretedMC
1.0<Eν<1.5 GeV
Int.Mode:QE

8060

integreted

60

40

20

20

0

0.2

0.4

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)

MC
1.0<Eν<1.5 GeV
Int.Mode:non-QE

80

40

0

0.2

integreted

40

0

0

100

integreted

0Muon Angle θµ (deg.)

0

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)
Muon Angle θµ (deg.)0Muon Angle θµ (deg.)0MCEν<0.5 GeV
Int.Mode:non-QE

80

40

Muon Angle θµ (deg.)

Muon Angle θµ (deg.)

100

131

0

0

0.2

0.4

0.6 0.81
1.2 1.4 1.6
Muon Momentum Pµ (GeV/c)

Figure 7.31: Two-dimensional distributions of the muon momentum versus scattering angle for data
(red plot) and for the Monte Carlo simulation for each energy bin and each interaction mode (blue plots).
These plots are of FC1Rµ sample, and same distributions are prepared for SciFi-MRD samples. The sizeof each box represents the number of contents in each bin. The corresponding energy bin and interaction
mode of each plot for MC is indicated in the plot. Here, only 8 distributions are shown for MC, although
there are 16 distributions in total.

Ph.D. Thesis by Issei Kato, July 2004

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Muon Momentum (GeV/c)
Energy Scale

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Muon Momentum (GeV/c)

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

20

Ring Counting

0

20

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

40
60
80 100
Muon Angle (degree)

40
60
80 100
Muon Angle (degree)

VertexRelative Error

Ring Counting

0

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

Relative Error

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Muon Momentum (GeV/c)

Statistics

Relative Error

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

Relative Error

Relative Error

Statistics

Relative Error

Chapter 7. Analysis in Near Detector

Relative Error

Relative Error

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

Relative Error

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

Relative Error

132

1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Muon Momentum (GeV/c)
Particle ID

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Muon Momentum (GeV/c)

Vertex

0

20

40
60
80 100
Muon Angle (degree)
Particle ID

0

20

40
60
80 100
Muon Angle (degree)

Angular Resolution

0

20

40
60
80 100
Muon Angle (degree)

Figure 7.32: Contributions of various uncertainties to the momentum and angular distributions in
FC1Rµ sample. Relative errors are shown. In all the figures, light blue region show the size of total
error and red region show the contribution of the error source specified in each figure. Statistical uncertainty is calculated to be the squared root of the number of events projected onto the momentum andangular axes.

systematic uncertainty in the energy scale is also incorporated into the χ2 function, which is
1KT
expressed by the last term in Eq. (7.17). Pe-scaleis the fitting parameter for the energy scale
uncertainty, which scales the (p, θ) distribution of data up and down in the momentum direction
1KT ), +2 % is used.
by varying its value. As the uncertainty in the energy scale (σe-scale−3
Systematic uncertainty on the (m, n)-th bin are estimated for the various sources as a functionof muon momentum and angle. Each contribution to the error on each bin are illustrated inFig. 7.32, where uncertainties on momentum and angular bins are separately shown. The method
to estimate the systematic uncertainty for each source is as follows;
Vertex reconstruction: As mentioned before, there exists discrepancy of about 5−10 cm inreconstructing the vertex between data and MC. The effect of such vertex shift is studied bychanging the size and the position of fiducial volume by ±10 cm, and the difference in the
distributions is quoted as the systematic error.
Ring counting: The uncertainty in the ring counting also makes effect on the momentum andangular distribution, since the goodness of the ring counting depends on the particle momentum.
By changing the selection criterion for single ring events, where the ring counting likelihood
F1 is used, the effect of single ring event selection is studied. As seen in Fig. 7.19, there issmall discrepancy around the cut position (F1 = 0), and hence two kinds of studies have been
performed. First, selection criterion is changed around F1 = 0 by ±2.5 only in data, and thedifference in the momentum and angular distribution is studied. Secondly, selection criterion is
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

133changed around F1 = 0 by ±5 in both data and MC simultaneously, and the difference of change
in the distributions between data and MC is studied. The effects of these two operations arequadratically summed and quoted as the systematic errors due to the ring counting uncertainty.
Particle identification: The performance of particle identification also depends on particle momentum. The difference in the momentum and angular distribution between with and withoutµ-like selection is studied, and is quoted as the systematic error.
FC/PC separation: The effect due to a variation in the criterion of FC/PC separation is studied
by changing the pomax20deg cut by ±5%, yielding a negligible effect on both momentum andangular distributions.
Angular resolution: As is also previously mentioned, the angular resolution has discrepancy of
about 2◦ between data and MC. The resolution in MC is smeared by this size and the effectis studied. Furthermore, in order to make the large angle region not affect on the fitting, wequoted additional 40% error on the bins greater then 90◦ , since the consistency check between
1KT and FGD can not be done due to that FGD has no acceptance in this region and we cannot
judge whether the discrepancy between data and MC in this region is really physical or not.
Energy scale: The uncertainty in the energy scale is estimated to be +2−3 % as mentioned before.
The momentum is scaled within this size and the difference in the momentum distribution isquoted as the systematic uncertainty. In this study, the behavior of the distribution around thethreshold (∼ 1000 p.e.) is also investigated by changing the criteria on the total photoelectroncut.
All the systematic uncertainties above are quadratically summed on a bin by bin basis
together with the statistical error, and the total error on each bin, σm,n , is obtained.
Definition of χ2 function for SciFi-MRD samples
The χ2 function for SciFi-MRD samples is built separately for 1-track, 2-track QE, and 2track non-QE samples. In the 2-dimensional distribution of muon momentum and angle foreach sample, momentum is binned into the same binning as that of neutrino energy, and angle
is binned into an interval of 10◦ . In order to calculate the χ2 , binned likelihood method is
employed;χ2FGD = −2 ln λ(f )
X Xh
MC
data
data
= 2
Nl;m,n(f ) − Nl;m,n+ Nl;m,n
· ln
l

m,n

data i
Nl;m,nMC (f )
Nl;m,n,(7.19)

where λ(f ) = L(N data ; N MC (f ))/L(N data ; N data ) is a ratio of a likelihood that a set of data
data }, is obtained when a set of MC bins, N MC (f ) = {N MC (f )}, is expected,
bins, N data = {Nl;m,nl;m,nand f is a set of fitting parameters such as the weighing factors for neutrino energy bins (fiφ ),non-qe/qe ratio Rnqe , and some systematic parameters. Poisson likelihood is used for L. The
summation in Eq. (7.19) is performed over all the event categories (l = 1-track, 2-track QE,
2-track non-QE) and all the (pµ , θµ )-bins (m, n). For convenience, l = 1, 2, and 3 represent
MC (f ) are calculated as
1-track, 2-track QE, and 2-track non-QE samples, respectively. Nl;m,nfollowing steps.

Ph.D. Thesis by Issei Kato, July 2004

134

Chapter 7. Analysis in Near Detector
First, content in each bins for each event category is calculated;
MC
FGD
N1;m,n= Pnorm·

8X£ MC[i,qe]MC[i,nqe] ¤fiφ · N1;m,n+ Rnqe · N1;m,n,(7.20)iMC
FGD
N2;m,n= Pnorm·

8X£ MC[i,qe]
fiφ · N2;m,n
+

i

MC
FGD
N3;m,n= Pnorm·

8X

MC[i,nqe] ¤MC[i,qe]+ Rnqe · N2;m,nMC[i,qe]+ Rnqe · N3;m,nRrescat · (1 − Prescat ) · N2;m,n,(7.21),(7.22)£ MC[i,qe]
fiφ · N3;m,n−i

Rrescat · (1 − Prescat ) · N2;m,nMC[i,nqe] ¤MC[i,qe(nqe)]

FGD is the normalization
where Nl;m,n
is the same meaning as the FC1Rµ case, and Pnorm
parameter for FGD samples. The second terms in Eq. (7.21) and (7.22) represent the migration
between QE and non-QE samples due to the effect that a proton scattered in CC-qe interaction
is re-scattered by the nucleons inside the nucleus, which makes a QE event to be identified as
non-QE one. Rrescat is a fraction of the number of QE events migrating into non-QE sample
when the proton re-scattering probability changes from 0% to 100%, and Prescat is a fitting
parameter which represents the uncertainty of the proton re-scattering probability. Rrescat is
estimated to be 0.33 by a Monte Carlo study. Since the default value of the proton re-scattering
probability in our Monte Carlo is set to 100%, Prescat is used to rescale it. The central value of
Prescat is set to be 0.87 in order for our Monte Carlo simulation to reproduce the results of themeasurements for the proton re-scattering in electron scattering on 12 C target [116]. The 10%
uncertainty on the probability is adopted according to its results.
Next, the detector systematics is considered as following. Migration between 1-track and2-track samples due to the ambiguity of the efficiency for the second track finding is taken into
account by following expression;
MC

MC
MC
MC
N 0 1;m,n = N1;m,n+ (1 − P2nd-eff ) · (N2;m,n+ N3;m,n) ,MC
N 0 2(3);m,n

=

MC
MC
N2(3);m,n+ P2nd-eff · N2(3);m,n,(7.23)(7.24)

where P 2nd-eff represents the uncertainty of the second track finding efficiency, which is also
incorporated in the fitting as a fitting parameter.
Finally the uncertainty of the first track finding efficiency is considered. This is taken into
account in the momentum dependent form;
MC

MC

N 00 l;m,n = P1st-eff(m) · N 0 l;m,n,(7.25)

where P1st-eff(m) is a fitting parameter representing the uncertainty of the first track finding
efficiency for the m-th momentum bin. In actual fitting, only the uncertainties in first threebins are treated as free parameters (the first momentum bin in SciFi-MRD samples is empty,
and hence the second and third ones are meaningful).
Then, each content of the weighted MC, N 00 MC
l;m,n , is normalized to data by total number of2
MC (f ) in Eq. (7.19).
events in all three samples, and used in χFGD as Nl;m,n
In order to constrain the systematic parameters within their uncertainties, constraint terms
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

135

Table 7.7: The central values and the uncertainties of systematicparameters incorporated in the χ2 function of FGD.
Systematic parameters
Proton rescattering Prescat
FGD
Energy scale Pe-scale
1st track efficiency P1st-eff(2)P1st-eff(3)2nd track efficiency P2nd-eff

Central values
0.87
1.0
1.0
1.0
1.0

Errors
0.1
0.027
0.5
0.5
0.05

are added to χ2FGD ;χ2FGD-syst =00(P2nd-eff − P2nd-eff)2(Prescat − Prescat)2+(σrescat )2(σ2nd-eff )20
FGD − P 0 FGD )2
X (P1st-eff(m) − P1st-eff(m) )2(Pe-scalee-scale
+
+
2
(σ
)
(σ
)2
1st-eff(m)e-scalem,(7.26)

where P 0 ’s and σ’s, respectively, represent the central values and the uncertainties of the systematic parameters. As is done in the FC1Rµ case, the uncertainty in the energy scale in SciFi-MRD
samples is also incorporated in the fitting, and the 2-dimensional distribution is scaled up anddown in the momentum direction. The last term in Eq. (7.26) represents the constraint on
the energy scale. The central values and the uncertainties of the systematic parameters are
summarized in Table 7.7.
Constraint of PIMON measurements on the energy spectrum
In addition to the χ2 functions from 1KT and FGD, since PIMON measures the neutrino spectrum above 1 GeV as mentioned in Chapter 6, the results can constrain the corresponding
weighting factors for the neutrino spectrum in the fitting, namely f4φ − f8φ . The χ2 function for
the PIMON constraint term is
χ2PIMON =7
X(f φ − f PIMON )2
i

i=5

i

(σiPIMON )2,(7.27)

where fiPIMON is the central value of the spectrum weighting factor of i-th bin derived from the
PIMON measurements and σiPIMON is its error. Since f4φ is fixed to be unity for a normalization in
the fitting and there is only one bin above 2.5 GeV in the PIMON measurements, the summationis performed from 5th to 7th bin. The central values of PIMON measurements, fiPIMON , in
Eq. (7.27) is calculated as follows;fiPIMON =ΦPIMON/ΦMCiiMCΦPIMON/Φ44( i = 5, 6, 7 ) ,(7.28)

where ΦPIMON
is the neutrino flux in i-th bin measured by PIMON and ΦMCis that estimatedii
MC , f PIMON , and σ PIMON are summarized in Table 7.8.
by Beam-MC. The values for ΦPIMON
,
Φ
i
i
i
i

Ph.D. Thesis by Issei Kato, July 2004

136

Chapter 7. Analysis in Near Detector

Table 7.8: Summary of the numbers used in the constraint term of PIMON in the χ2 function.
Neutrino energy(Bin number)
ΦPIMON
i
ΦMC
i
PIMON
fi
σiPIMON

1.0−1.5 GeV(i = 4)6.30 × 1011
6.19 × 1011——

1.5−2.0 GeV(i = 5)
3.21 × 1011
3.35 × 1011
0.941
+10.7
−9.9 %

2.0−2.5 GeV(i = 6)1.01 × 1011
1.05 × 1011
0.945
+12.1
−17.7 %

2.5 GeV−(i = 7)
4.27 × 1010
3.96 × 1010
1.059
+47.7
−34.0 %

Fitting results
By changing the weighting factors fiφ , non-qe/qe ratio Rnqe , and systematic parameters for eachdetectors, the best-fit point is searched for. MINUIT [117] is used to minimize the χ2 function.
The value of χ2 is 227.18/197 d.o.f at the best-fit point, for which the χ2 -probability is 6.91%.
The central values for the fitting parameters and their errors are summarized in Table 7.9. All
the parameters including the detector systematics are found to lie within their expected errors.
The error matrix for fiφ and Rnqe is shown in Table 7.10.
The resulting distributions of the muon momentum, the muon angle, the reconstructed
neutrino energy, and the reconstructed 4-momentum transfer squared for each sample are shownin Fig. 7.33 and Fig. 7.34. All the distributions show that the fitted results agree well with thedata. The behavior of χ2 value around the best-fit point as a function of each fitting parametervalue is shown in Fig. 7.35, indicating that the minimization of χ2 function have successfully
done to find the global minimum point.
The fitting using only 1KT sample and only FGD samples have also been performed, andthese results are summarized in Table 7.9 together with the results of the 1KT+FGD combined
fitting. They are also compared in Fig. 7.36. All the parameters, except for Rnqe , are inagreement within their errors not depending on the data sample used in the fitting.
Several studies have been done against Rnqe resulting in the inconsistent values between
1KT only and FGD only fitting. In the conclusion of the studies, the reason is due to thedifferent purity for CC-qe in each sample. It is quantitatively understood as follows: A deficit
in the forward region still remain even if NEUT-1211 is chosen as a model in MC, as shownin Fig. 7.30. In the case of 1KT only fitting, Rnqe is decreased in order to suppress the eventsin the forward region since there are more non-qe events than qe ones in the forward region in
FC1Rµ sample. Small Rnqe value also decrease the events in small momentum region since there
are a lot of low momentum events from non-qe interaction as shown in Fig. 7.31. In order tocompensate the suppression in the low momentum region, neutrino fluxes in low energy region
are increased which can be seen in Fig. 7.36. Then the fitting is settled. In fact, there is strong
correlation between the weighting factors for the low energy region and Rnqe , which is seen in
the covariance matrix of fitting parameters in Table 7.10. On the other hand, in the case of the
FGD fitting, there are three samples with different purities for CC-qe, making the constraint on
Rnqe , and Rnqe is settled at different value from the 1KT case.
Inferred from the behavior above, the choice of model in MC may bias the estimation ofneutrino energy spectrum. Therefore we have studied the dependence of the results on models,
which will discussed in the next section.
Finally, dominant contribution to the error size of the spectrum weighting factors (fiφ ) isinvestigated by turning on and off the systematic uncertainties one by one. Fig. 7.37 shows theresulting size of errors on the fitting parameters by a fitting with systematic uncertainties on
Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

137

Table 7.9: Summary of the χ2 fitting results. The central values for all the fitting parameters andtheir errors are listed. The results with only 1KT χ2 and only FGD χ2 fitting are also shown as well
as 1KT+FGD merged (ND) fitting results.

Fitting parameters
0−0.5 GeV
f1φ
0.5−0.75 GeV
f2φ
0.75−1.0 GeV
f3φ
1.0−1.5 GeV
f4φ
1.5−2.0 GeV
f5φ
2.0−2.5 GeV
f6φ
2.5−3.0 GeV
f7φ
3.0 GeV−f8φ
non-qe/qe
Rnqe
1KT
1KT normalization
Pnorm
1KT
1KT energy scale
Pe-scale
FGD
FGD normalization
Pnorm
FGD
FGD energy scale
Pe-scaleProton rescattering
Prescat
1st track efficiency (2nd Bin) P1st-eff(2)
1st track efficiency (3rd Bin) P1st-eff(3)2nd track efficiency
P2nd-eff
Minumum χ2 /d.o.f.
χ2 -probability

1KT+FGD
Values Errors
1.314
0.486
1.021
0.119
1.007
0.092
1.000 (fixed)
0.955
0.071
0.962
0.084
1.183
0.188
1.073
0.199
0.929
0.060
0.733
0.010
0.971
0.004
0.956
0.044
0.967
0.006
0.850
0.069
1.536
0.093
1.083
0.034
0.976
0.021
227.18/197
6.91%

1KT only
Values Errors
1.781
0.460
1.125
0.111
1.012
0.086
1.000 (fixed)
0.956
0.085
0.966
0.120
1.143
0.473
1.000 (fixed)
0.696
0.081
0.740
0.988
0.975
0.005
—
—
—
—
—
—
—
—
—
—
—
—
83.48/74
21.12%

FGD only
Values Errors
1.000 (fixed)
0.950
1.351
1.487
0.433
1.000 (fixed)
1.084
0.179
0.927
0.133
1.344
0.312
1.024
0.225
1.094
0.091
—
—
—
—
0.832
0.080
0.962
0.007
0.786
0.075
1.485
0.102
1.049
0.044
0.962
0.024
130.83/117
18.04%

Table 7.10: £Error matrix
for fiφ and Rnqe obtained in the χ2 fitting. The squared root of error¤ pmatrix ( sign {Mφ,nqe }ij · |{Mφ,nqe }ij | ) is written here in the unit of %.

f1φ
f2φ
f3φ
f4φ
f5φ
f6φ
f7φ
f8φ
Rnqe

f1φ
48.9
−11.4
6.60
—
0.926
2.12
−4.16
5.12
−8.22

f2φ
−11.4
11.9
−2.98
—
2.68
0.989
2.26
2.97
−4.10

f3φ
6.60
−2.98
9.17
—
4.68
−0.867
4.55
2.09
−2.35

f4φ
—
—
—
—
—
—
—
—
—

f5φ
0.926
2.68
4.68
—
7.07
−2.12
7.64
4.93
−1.88

f6φ
2.12
0.989
−0.867
—
−2.12
8.43
−7.58
8.17
−1.86

f7φ
−4.16
2.26
4.55
—
7.64
−7.58
18.8
−11.2
−1.68

f8φ
5.12
2.97
2.09
—
4.93
8.17
−11.2
19.9
−3.69

Rnqe
−8.22
−4.10
−2.35
—
−1.88
−1.86
−1.68
−3.69
6.04

Ph.D. Thesis by Issei Kato, July 2004

4000
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3500

MC

3000

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2500

events / 10 degrees

Chapter 7. Analysis in Near Detector

events / 0.1 GeV/c

138

Data
5000

MC
MC (CCqe)

4000

3000

2000
1500

2000

1000
1000
500
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0

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2
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9000
Data
8000
MC
7000
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6000
5000

events / 0.1 (GeV/c)2

events / 0.25 GeV

0

0

50

100

150
θµ (degree)

Data
5000
MC
MC (CCqe)

4000

3000

4000
2000

3000
2000

1000
1000
0

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1

1.5

2
2.5
Rec.Eν (GeV)

0

0

0.5

1

1.5
2
2
2 2
Rec.Q (GeV /c )Figure 7.33: Distributions of the muon momentum (upper left), the muon angle (upper right), thereconstructed neutrino energy (lower left), and the reconstructed Q2 (lower right) after the fittingfor FC1Rµ sample. Histograms for the Monte Carlo simulations are weighted by using the fitted
parameter values.

Ph.D. Thesis by Issei Kato, July 2004

7.4. Measurement of neutrino spectrum in near detectors

1500

1 Track

1000

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MC
(CCQE)

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139

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400

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MC
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75
(deg.)

2 Track o∆ΘP > 30

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4
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Θµ (deg.)

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MC
(CCQE)

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(GeV)

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150∆ΘP < 25

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500
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2
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(GeV/c)2 Track o100∆ΘP < 25

0

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1

400

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2
(GeV/c)22 Track o

300∆ΘP > 30

200

100
0

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MC
(CCQE)

1000

50

50
0

1 Track

1500

100
0

1

2

3
4
Eν (GeV)

0

0

0.5

1

1.5
2
q2 (GeV/c)2

Figure 7.34: Distributions of the muon momentum (upper left three figures), the muon angle(upper right three figures), the reconstructed neutrino energy (lower left three figures), andthe reconstructed Q2 (lower right three figures), after the fitting for SciFi-MRD samples. For
each set of the distributions, top figure shows 1-track sample, middle figure shows 2-track QE
sample, and bottom figure shows 2-track non-QE sample. Histograms for the Monte Carlosimulations are weighted by using the fitted parameter values.

Ph.D. Thesis by Issei Kato, July 2004

1.5

f2 : Eν=0.5-0.75 GeV

5

0.5

2.5
0

0.5

0

1
1.5
2
Parameter Value

×10

f6 : Eν=2.0-2.5 GeV

6

0.5

×10

2

1

1

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0

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0

1
1.5
2
Parameter Value

×10

2

×10

6

Rnqe : non-QE/QE

2

0.5

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1

0.5

0.5

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1
1.5
2
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×102

4

FGD Proton rescatter

3

1KT E-scale

0.5

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FGD Normalization

10

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6
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0.96 0.98 1 1.02 1.04
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FGD 1st track eff. (2)

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0.96 0.98 1 1.02 1.04
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FGD 2nd track eff.

1.5
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1KT Normalization

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∆χ2

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2
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∆χ2

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∆χ2

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f8 : Eν=3.0- GeV

1.5

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2
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×103

2

0

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2
Parameter Value

2

∆χ2

∆χ2

2

0

∆χ2

0

f3 : Eν=0.75-1.0 GeV

4
3

1

7.5

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∆χ2

f1 : Eν=0-0.5 GeV

10

×102

∆χ2

×100

∆χ2

Chapter 7. Analysis in Near Detector

∆χ2

∆χ2

140

2

0.5

0

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0

0.5

1
1.5
2
Parameter Value

1
0.5
0

0.5

1
1.5
2
Parameter Value

0

0

0.5

1
1.5
2
Parameter Value

Weighting Factor

Figure 7.35: Behavior of ∆χ2 around the best fit point as a function of each fitting parameter value.
In each figure, only one parameter specified in the figure is varied around the best-fit point, and χ2 iscalculated as a function of the parameter value with all other parameters fixed at the best-fit point.
Horizontal axis is the value of the varied parameter and vertical axis is the ∆χ2 , the difference between
current χ2 and the minimum (best-fit) χ2 . Red arrow shows the best-fit point of each fitting parameter.

2.5
1KT+FGD merged fit
1KT only fit

2

FGD only fit

1.5

1
fixed
fixed

fixed
0.5

0

f1

f2

f3

f4

f5

f6

f7

f8

Ph.D. Thesis by Issei Kato, July 2004

Rnqe

Figure 7.36: Comparison of the fitting results between 1KT only fitting and FGD only fitting, together with the results of the 1KT+FGD merged
fitting. All the fitting parameters except for Rnqe
agrees within their errors not depending on the data
samples used in the fitting.

141

0.5

Error Size

Error Size

7.5. Summary of ND analysis

1KT FC1Rµ sample
All syst. ON
All syst. OFF
Energy scale
Angular syst.
Ring Count
Particle ID
Vertex

0.4

0.3

1.4
FGD SciFi-MRD samples
1.2

All syst. ON
All syst. OFF
Proton rescatter
Energy scale
1st track eff. (2)
1st track eff. (3)2nd track eff.

1
0.8
0.6

0.2

0.4
0.1
0.2
fixed
0

f1

f2

f3

f4

fixed
f5

f6

f7

f8

fixed
Rnqe

0

f1

fixed
f2

f3

f4

f5

f6

f7

f8

Rnqe

Figure 7.37: Error size of the fitting parameters. Left figure is of 1KT, and right figure is of FGD.
Each color corresponds to the fitting with a certain systematic uncertainty specified in the figure
turned on. There is only small difference in the size of error between the fitting with and without
the systematic uncertainties turned on, indicating that the main contribution to the error size isstatistic errors.

and off. Even when all the systematic uncertainties are turned off, the size of errors do notchange so much compared to the fitting with all the systematic uncertainties on. This indicatesthat the dominating contribution to the errors is statistical one.

7.4.6

Dependence of fitting results on interaction models

We have tried the same fitting for several sets of neutrino interaction models in order to investigate the possible bias on the results due to the choice of model. As mentioned in Sec. 4.2, westudied following changes in the neutrino interactions as their uncertainties.
In qe scattering and single pion production, the axial vector masses in the dipole formula isvaried by 10% and 20%, respectively [91], while their central values are set to be 1.1 GeV/c2
and 1.2 GeV/c2 , respectively. This affects both the q 2 dependence of the cross-section and thetotal cross-section. For the coherent pion production, two different models are compared; one isa model proposed by J. Marteau et al. [105, 106] which is employed in the default fitting, andthe other is the Rein and Sehgal model [103]. For deep inelastic scattering, GRV94 [95] and its
corrected structure function by A. Bodek and U. K. Yang [96] are studied, among which thelatter is taken in the default fitting.
Several combinations of the interaction models mentioned above are studied and it is foundthat all the fitting parameters other than Rnqe do not change beyond the size of their fitting
errors. The dependence of fitted Rnqe value on the choice of modes is shown in Fig. 7.38, as
well as the χ2 values at their best-fit points. It indicates that our experimental data favor themodels with larger MA values and more suppression in low q 2 region. By varying the interaction
models, Rnqe values is changed by ∼ 20% in all the sets of data samples used in the fitting.
The systematical differences between 1KT only fitting and FGD only fitting are as discussed in
the previous section. Therefore, an additional systematic error of ±20% on Rnqe is added tothe original fitting error as well as to the corresponding elements of the error matrix. The final
values for the spectrum weighting factors (fiφ ) and non-qe/qe ratio (Rnqe ) and their errors are
summarized in Table 7.11, as well as their final error martix.
Ph.D. Thesis by Issei Kato, July 2004

Chapter 7. Analysis in Near Detector

Rnqe

142

1

0.5

χ min / d.o.f.

1KT+FGD merged fit
1KT only fit
FGD only fit
0

2

1.5

1411

1311

1111

1011

1400

1300

1200

1100

1000

0411

0311

0211

0111

0011

0400

0300

0200

0100

0

0000

0.5

1211

our model

1

Figure 7.38: Dependence of fitted Rnqe values on neutrino interaction models (top) and χ2 /d.o.f.
values at the best-fit points (bottom). The numbers such as “0000”, “0100”, etc. are the abbreviationof the combinations of models as listed in Table 4.4. Horizontal red lines show the fitted Rnqe andminimum χ2 values for the model we have adopted (model hatched with light blue color). Bychanging the neutrino interaction models within their uncertainties, fitted Rnqe value varies by
about 20%. The artificially added error on Rnqe , as described in the text, is illustrated by theyellow band in the top figure.

7.5

Summary of ND analysis

The expected number of neutrino events in SK and the neutrino energy spectrum at near site
have been estimated based on the measurements in the 1KT and FGD.
The number of neutrino interactions occurred in 1KT is estimated by counting the numberof events with their vertex inside the 25 t fiducial volume of 1KT. Then, it is extrapolated by
F/N ratio to SK. In the case of that neutrino oscillation does not exist, the number of neutrino
events expected to be observed in SK is estimated to beSKNexp= 80.6 ± 0.3 (stat.) +7.3
−8.0 (syst.)(7.29)

for the accumulated neutrino beam of 4.79 × 1019 POT.
The neutrino energy spectrum at near site is estimated using the (pµ , θµ ) 2-dimensional
distributions in FC1Rµ, SciFi-MRD 1-track, 2-track QE, and 2-track non-QE samples. The χ2
fitting is employed to derive the spectrum weighting factors and non-qe/qe cross-section ratio
relative to the values in our Monte Carlo simulation. The results of the spectrum measurements
is shown in Fig. 7.39 together with the prediction of our Beam-MC, showing a good agreementswith each other. The uncertainty due to neutrino interaction models is also studied. The choiceof models does not bias the estimation of energy spectrum beyond its fitted error, but only affects
on the value Rnqe by 20%, which is added to the error on it. The correlation between each energy
bin and Rnqe is estimated in the form of an error matrix, which is shown in Table 7.11 together
with their central values. It is used in the oscillation analysis described in Chapter 9.

Ph.D. Thesis by Issei Kato, July 2004

Flux (Arbitrary / 0.5 GeV)

7.5. Summary of ND analysis

143

ND measurements
Beam-MC

integrated

0

1

2

3
4
5
Neutrino Energy (GeV)

Figure 7.39: The neutrino energy spectrum
measured at ND. The spectrum estimated by
Beam-MC is overlaid by a black histogram. The
results of spectrum measurements in ND are inagreement with the expectation of Beam-MC.

Table 7.11: The central values, errors, and error
fiφ and Rnqe used in the oscillation£ matrix for¤ panalysis. The square root of error matrix ( sign {Mφ,nqe }ij · |{Mφ,nqe }ij | ) is writen here in theunit of %. As described in the text, an additional error of 20% is added to the matrix elements
corresponting to Rnqe .

Central Values
Errorsf1φ
f2φ
f3φ
f4φ (fixed)
f5φ
f6φ
f7φ
f8φ
Rnqe

f1φ
1.314
0.487
48.9
−11.4
6.60
—
0.926
2.12
−4.16
5.12
−15.0

f2φ
1.021
0.119
−11.4
11.9
−2.98
—
2.68
0.989
2.26
2.97
−7.50

f3φ
1.007
0.092
6.60
−2.98
9.17
—
4.68
−0.867
4.55
2.09
−4.31

f4φ
1.000
fixed
—
—
—
—
—
—
—
—
—

f5φ
0.955
0.071
0.926
2.68
4.68
—
7.07
−2.12
7.64
4.93
−3.45

f6φ
0.962
0.084
2.12
0.989
−0.867
—
−2.12
8.43
−7.58
8.17
−3.41

f7φ
1.183
0.188
−4.16
2.26
4.55
—
7.64
−7.58
18.8
−11.2
−3.08

f8φ
1.073
0.199
5.12
2.97
2.09
—
4.93
8.17
−11.2
19.9
−6.75

Rnqe
0.929
0.203
−15.0
−7.50
−4.31
—
−3.45
−3.41
−3.08
−6.75
20.3

Ph.D. Thesis by Issei Kato, July 2004

Chapter 8
Observation in Far Detector
The observation of neutrino events in Super-Kamiokande (SK) is described in this chapter.
K2K beam originated neutrino candidates in SK are selected from a large number of cosmic
ray, radioactive, and atmospheric neutrino backgrounds. First, the selections for the accelerator
neutrino events are given. Then, the number and some distributions of observed events areshown in following sections. The systematic uncertainties in the event selections are explained,
and finally, an error matrix for the selection of 1Rµ events are described in the last section ofthis chapter, which is used in the oscillation analysis in Chapter 9.

8.1

Event selection for beam originated neutrino candidates

In order to select the K2K beam originated neutrino candidates from a large number of backgrounds, GPS system is employed as is previously described. Two UTC time stamps from GPS
system are compared, one is for the start time of the beam spill at KEK-PS (TKEK ) and theother is for the observed time of events in SK (TSK ). The time difference ∆T is defined asfollows;∆T ≡ TSK − TKEK − T OF ,(8.1)
where T OF is the time-of-flight of neutrinos to travel the distance from KEK to SK (249.83 km),which is estimated to be 833 µsec assuming that neutrinos travel with the velocity of light. For
the beam originated neutrino events, ∆T should be distributed around the time window of
0−1.1 µsec matching with the beam spills.
Events with the vertex inside 22.5 kt fiducial volume of SK and all the particles fully contained
inside the inner detector (FC) are selected, for which events whole momenta of particles andtheir particle type can be reconstructed. The method of the event reconstruction in SK isalmost the same as that in 1KT. The detailed description on the event reconstruction is given
in Appendix B. Fig. 8.1 shows an event display for one of the K2K beam neutrino candidates
with FC1Rµ in SK.
Following reduction steps are applied to select the FC events, which are the same as that of
atmospheric neutrino analysis in SK. The selection criteria are optimized by using atmospheric
neutrino data. A flow chart of the reduction steps is shown in Fig. 8.2. The number of selected
events in each step is summarized in Table 8.1.
(1) Good beam spill selection
Among the data taken in SK, events with good beam spill condition and valid GPS status areused. The criteria for the good beam spills are described in Sec. 5.2.
145

146

Chapter 8. Observation in Far Detector

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 8.1: Event display for one of the K2K beam neutrino candidates with FC 1-ring µ-like
Cherenkov ring.

Table 8.1: Summary of the number of selected events in each reduction step in SK.
Selection Criteria
1 Analyzed number of spill(MC) generated in the tank(MC) generated in the fiducial volume
2 Rough timing cut
3 Decay electron cut
4 HE trigger
5 Total photoelectron cut
6 Flasher event cut
7 Outer detector cut
8 Fitting goodness cut
9 Visible energy cut
10 Fine timing cut
11 Fiducial volume cut

Ph.D. Thesis by Issei Kato, July 2004

Data
9,177,578——
161,763
107,892
36,56018,902
18,617
108
107
100
91
56

MC
370,607
167,677

227,476
220,753
192,117
191,924
186,445
131,530

8.1. Event selection for beam originated neutrino candidates

147(1) Good beam spill selection(2) Rough timing cut(3) Decay electron cut(4) High energy trigger selection(5) Total photoelectron cut(6) Flasher event cut(7) Outer detector cut (FC selection)(8) Goodness of vertex fitting(9) Visible energy cut(10) Fine timing cut(11) Fiducial volume cut
Total number of neutrino events(13) Single−ring event selection(14) Muon−like event selection
Reconstructed neutrino energy spectrum

Figure 8.2: A flow chart of the data reduction and the event selection in the SuperKamiokande analysis. The events remaining after the fiducial volume cut are counted in
the total number of observed neutrino events in SK, while the events with only one muon-like
Cherenkov ring is used to reconstruct the neutrino energy.

Ph.D. Thesis by Issei Kato, July 2004

Entries

148

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10

4

10

3

10

2

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selected

MC

10

1

10

2

10

3

10

4

10

5

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6

PE300

Figure 8.3: Distribution of the total number of photoelectrons in 300 nsec time window (PE300 ) for the
events after high energy trigger cut. Red points are fordata and black histogram is for a Monte Carlo simulation for the beam neutrinos normalized to the expected
number of events for 4.79 × 1019 POT in the case of no
oscillation.

(2) Rough timing cut
Among all the triggered events in SK, events matching to a good beam spill inside the time
window of |∆T | ≤ 500 µsec are selected at this stage.
(3) Decay electron cut
If a cosmic ray muon stops inside the tank, an electron emitted by the muon decay makes a
Cherenkov ring, which may be mis-identified as a neutrino event. In order to remove such kind of
possible fake events, events which have detector activity within 20 µsec before them are rejected.
A fraction of dead time caused by this selection is less than 1/1000 since the total trigger rateis typically ∼10 Hz.
(4) High energy (HE) trigger
Events taken by high energy (HE) trigger are used for the K2K analysis. The trigger thresholdfor HE trigger is 31 hit PMTs within 200 nsec time window as described in Sec. 3.6.3, which iscorresponding to 50−100 photoelectrons.
(5) Total photoelectron cut
Events with maximum number of total photoelectrons in a sliding time window of 300 nsec
(PE300 ) less than 200 p.e. (Fig. 8.3) are rejected in order to eliminate low energy backgrounds
such as radon and gamma rays from the surrounding rock. Corresponding momentum thresholdto this criteria is ∼ 20 MeV/c for electrons and ∼ 190 MeV/c for muons.
(6) Flasher event cut
There are some flashing PMTs called “flasher” in SK, which are caused by sparks inside PMTs.
They sometimes make hit pattern like Cherenkov light. In order to reject such fake events,
following three cuts are applied;
Ph.D. Thesis by Issei Kato, July 2004

Data
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4

10

3

10

2

selectedMC

Entries

Entries

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149

Data
10

2

selected

MC

10

10
1
1

0

0.1

0.2

0.3

0.4

0.5

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0.7

0.8 0.9 1
PEmax/PE300

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9 1
Goodness

Figure 8.4: Distributions of PEmax /PE300 for the events after total photoelectron cut (left) and the
goodness of vertex fitter for flasher cut for the events with the number of hit ID-PMTs less than 500(right). Red points are for data and black histogram is for a Monte Carlo simulation for the beam
neutrinos normalized to the expected number of events for 4.79 × 1019 POT in the case of no oscillation.

Maximum photoelectron cut: If a spark occurs in a PMT, this PMT produces a large charge
signal in itself. In order to eliminate such events, PEmax /PE300 ≤ 0.2 is imposed, where PEmax
is the number of photoelectrons of the PMT which have maximum charge among all the PMTs.

Hit timing distribution cut: Since most of the flasher events have broad hit timing distribution
compared to that of neutrino events, flasher events are removed by using the width of the hit
timing distribution. The minimum number of hit PMTs within 100 nsec sliding time window inmin ) is searched for, and if N min is greater
the range of 300 to 800 nsec after the event trigger (N100100than 14, the events are discarded. For the events with the number of hit ID-PMTs less than
min is greater than 10.
800, the events are discarded if N100

Goodness of the fit: For the events with the number of hit ID-PMTs less than 500, the goodnessof a vertex fitter is used to select the flasher events. This fitter searches for a vertex point withan assumption that all photons were produced at a point. Events with the goodness of the fitterless than 0.4 are rejected as flasher events.

(7) Outer detector cut
In order to reject incoming cosmic ray muons, cuts using outer detector (OD) information isapplied. Events which have more than 9 hit PMTs in the largest hit cluster in OD (Nhitac) arerejected (left figure of Fig. 8.5). Furthermore, events which have more than 50 hit OD-PMTs
within 800 nsec time window (Nhita800 ) is removed (right figure of Fig. 8.5). These criteria
effectively select the FC events.
Ph.D. Thesis by Issei Kato, July 2004

10

3

Data
selected
10

MC

Entries

Chapter 8. Observation in Far Detector

Entries

150

60
Data
selected

50

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2

40

30
10
20

1

10

0

5

10

15

20

25 30 35 40 45 50
Nhit in largest OD cluster

0

0

20

40
60
80
100
OD-Nhit in 800nsec time window

Figure 8.5: Distributions of the number of hit PMTs in the largest OD hit cluster (Nhitac) for the
events after flasher cut (left) and the number of hit OD-PMTs within 800 nsec time window (Nhita800 )for the events after Nhitac cut (right). Red points are for data and black histogram is for a Monte Carlosimulation for the beam neutrinos normalized to the expected number of events for 4.79 × 1019 POT in
the case of no oscillation.

(8) Goodness of vertex fitting
A vertex fitter, TDC-fit, is applied to define the vertex point of the interaction. The algorithmof TDC-fit is described in Sec. B.1.3. Small fraction of events are removed as badly fitted ones
if the goodness of the fit is less than 0 (Fig. 8.6).
(9) Visible energy cut
In order to avoid the uncertainty of the total photoelectron cut, more well-defined energy cut isapplied. Events with the visible energy (Evis ) greater than 30 MeV are selected (Fig. 8.7). The
visible energy is defined as a sum of energy of each ring assuming the Cherenkov light of eachring is produced by an electron. This cut corresponds to the momentum threshold of 197 MeV/c
for muons.
(10) Fine timing cut
Tighter timing cut is applied using UTC time stamps from GPS systems. Since the uncertainty
of two UTC time stamps are less than 0.2 µsec as described in Sec. 3.7.2, events inside the time
window of −0.2 µsec ≤ ∆T ≤ 1.3 µsec are selected as beam induced neutrino events. Fig. 8.8
shows the ∆T distribution. Beam neutrino events are clearly identified in the time window of
0 µsec ≤ ∆T ≤ 1.1 µsec which matches with the width of the beam spill.
(11) Fiducial volume cut
Finally, fiducial volume cut is imposed on the remaining events. The definition of the fiducial
volume is optimized by using the atmospheric neutrino event sample observed in SK. The left
figure in Fig. 8.9 shows the distribution of the distance between the reconstructed vertex point
and the nearest wall of ID tank (Dwall ) in the atmospheric neutrino sample after the visible
Ph.D. Thesis by Issei Kato, July 2004

Entries

8.2. The number of observed neutrino events in SK

151

60
Data
selected

50

MC

40

30

Figure 8.6: Distribution of the goodness of vertex fitting (TDC-fit) for the events after OD cut. Red points
are for data and black histogram is for a Monte Carlosimulation for the beam neutrinos normalized to the
expected number of events for 4.79 × 1019 POT in thecase of no oscillation.

20

10

Entries0-1-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6 0.8 1
Goodness

40
Data
35

selected

MC

30
25
20
15
10
5
0
1

10

10

2

10

3

10
Evis (MeV)

4

Figure 8.7: Distribution of the visible energy (Evis )for the events after fitting goodness cut. Red points
are for data and black histogram is for a Monte Carlosimulation for the beam neutrinos normalized to the
expected number of events for 4.79 × 1019 POT in thecase of no oscillation.

energy cut (Evis > 30 MeV). The discrepancy around the wall (Dwall < 200 m) is mainly due tothe events which take place in the insensitive volume between the ID and OD tank, the cosmic
ray muon events which remain due to the inefficiency of OD, or mis-fitted events which happened
very close to the wall. In order to avoid these events, the vertex of each event is required to be
farther than 200 cm from the wall of ID tank (the right figure in Fig. 8.9). This fiducial volume
corresponds to water mass of 22.5 kt.
The selection efficiency for muon neutrinos of K2K beam is estimated using a Monte Carlosimulation. Fig. 8.10 shows the efficiency as a function of incident neutrino energy. The averaged
efficiency for all the interactions is 77.9% for the beam configuration in K2K-Ia, and 78.4% for
the configuration in K2K-Ib.

8.2

The number of observed neutrino events in SK

In total, 56 FC events were observed in SK during the whole run period from June 1999 to July
2001; one event was in K2K-Ia, and the other 55 events were in K2K-Ib. Timing distribution
Ph.D. Thesis by Issei Kato, July 2004

events

152

Chapter 8. Observation in Far Detector

10

3

10

2

(a)

10
1
-500

-250

0

250

events

15

500
∆T µs

Figure 8.8: Distribution of the time difference(∆T ) between two UTC time stamps. (Top figure:) For the events within ±500 µsec time window after decay electron cut (blank histogram),
after flasher event cut (hatched histogram), andafter fiducial volume cut (dark hatched histogram). (Bottom figure:) Foe the selected
events in the fiducial volume. A clear clusterof events can be seen just within 1.1 µsec time
window synchronized with the beam spill.

Selection gate

(b)

10
5
0
0

5
∆T µs

2500
2250
Fiducial Volume

Atmospheric Neutrinos
Evis > 30 MeV

Entriesnumber of events-520

selected

2000

16

1750

14

1500

12

1250

10

1000

8

750

6

500

4

MC

2

250
0

Data

18

0
0

200

400

600

800

1000

1200 1400
Dwall (cm)

0

200

400

600

800

1000

1200 1400
Dwall (cm)Figure 8.9: Distribution of the distance from the vertex point to the nearest wall of inner tank (Dwall )for the events after visible energy cut for the atmospheric neutrino sample in SK (left) and for the K2K
event candidates (right). In the left figure, black points are for data and the histogram is for a Monte
Carlo simulation of atmospheric neutrino events. The Monte Carlo simulation is normalized to the databy the number of events in the region of Dwall > 200 cm. In the right figure, red points are for data
and black histogram is for a Monte Carlo simulation for the beam neutrinos normalized to the expected
number of events for 4.79 × 1019 POT in the case of no oscillation.

Ph.D. Thesis by Issei Kato, July 2004

efficiency

8.2. The number of observed neutrino events in SK

153

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

3

3.5

4

Eventsefficiency

4.5
5Eν (GeV)Figure 8.10: Selection efficiency in SK as a function ofincident neutrino energy, estimated by a Monte Carlosimulation.

50

40

30

20

10
KS probability = 43.1%
0
0

5

10

15

20

25

30

35 40 45
CT *1018 POT

Figure 8.11: Relation between the accumulated number of protons on target (POT) and the number ofobserved events in SK. Blue line represents a linear relation between them. The probability of KS test for
the hypothesis that the observation obeys the relationof blue line is 43.1%.

Table 8.2: Summary of observed events in SK. The ovservations in K2KIa and K2K-Ib are separately listed since the beam configurations between
these two periods are different.

Event categories
1-ring µ-like
1-ring e-like
multi-ring
In total

Number of observed events
June 1999 rest period
1
29
0
2
0
24
1
55

Expected # of events
44.0
4.4
32.2
80.6+7.3−8.0

Ph.D. Thesis by Issei Kato, July 2004

154

Chapter 8. Observation in Far Detector

beam direction
0

2 GeV

x

a)

y

z

b)

z

Figure 8.12: Distribution of the reconstructed vertex points (circles) and momentum of each ring in an
event (lines) observed in SK. Left figure shows the top view and right figure shows the side view. Inner
circle (left) or box (right) represent the boundary of the fiducial volume, and outer circle or box represent
the wall of the inner tank. Solid (open) circles represent the events with the vertex inside (outside) the
fiducial volume. Lines from the each vertex show the directions of particles in the interaction, and thelength of each line represents its momentum.

Ph.D. Thesis by Issei Kato, July 2004

8.4. Error matrix of selection efficiency for 1Rµ events

155for these 56 events are shown in Fig. 8.8. These events are clearly isolated from the other SK
events, and they are inside the 1.1 µsec time window synchronized with the beam spill timing,
showing that these are the events induced by K2K beam neutrinos.
The relation between the accumulated number of protons on target (POT) and the numberof observed events in SK is shown in Fig. 8.11. The Kolmogorov-Smirnov (KS) test has been
performed for a hypothesis that our observation in SK have a linear relation between accumulated
POT. The KS probability of 43.1% is obtained, indicating that the observation is consistent withthe linear relation and that the events have randomly taken place.
Number of rings in each event and the momentum of each ring are also reconstructed. The
event classification for observed FC events is summarized in Table 8.2. The vertex point foreach event is shown in Fig. 8.12 together with the momentum and direction of each ring.
In the FC events with only one µ-like Cherenkov ring (FC1Rµ), the neutrino energy can bereconstructed using the muon momentum and scattering angle with respect to the beam direction
as Eq. (2.2), assuming that the events are induced by CC-qe interaction. The muon momentum
and angular distributions for FC1Rµ events are shown in Fig. 8.13, and the distribution of
the reconstructed neutrino energy is shown in Fig. 8.14. Their expectation without neutrino
oscillation is also overlaid in each figure.
A source of possible background against our signal is the atmospheric neutrino interactions.
However, since its typical rate for FC events is about 8 events per day, an accidental contamination of atmospheric neutrinos into our event sample is order of 10−3 events through the entire
run period thanks to the 1.5 µsec time window cut. One event at ∆T = −122.7 µsec in the
top figure of Fig. 8.8 is consistent with the event rate of atmospheric neutrino background in±500 µsec time window.

8.3

Systematic uncertainty in the event selection

Systematic uncertainties in the event selection in SK are as follows.
Event selection
The systematic uncertainties in the event selections, except for the fiducial volume cut, is estimated by changing the following thresholds; a 10% change in the PE300 cut, a ±3 hits change
in OD cut, and ±10 MeV change in the Evis cut. Then effect of these changes on the numberof remained events is studied. In total, ±1% error is quoted as the uncertainty in the event
selection.
Fiducial volume cut
The performance of the vertex fitter is checked by comparing the results of two different vertex
fitters, “auto-fit” (Sec. B.1) and “MS-fit” (Sec. B.4). These two fitter were applied to atmospheric neutrino data and its Monte Carlo simulation, resulting 2% difference in data/MC ratio.
Statistics of Monte Carlo simulation
The statistical uncertainty of the Monte Carlo simulation is 1%.
In total, 3% is quoted as the uncertainty in the selection efficiency.
Ph.D. Thesis by Issei Kato, July 2004

20
Data

18

MC

16
14

integrated

12

Entries

Chapter 8. Observation in Far Detector

Entries

156

35
Data
30

MC

25
20

10
15

8
6

10

4
5
2
0

0

0.5

1

1.5

2

2.5
3
Pµ (GeV/c)0-1-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8 1
cosθKEK

EntriesFigure 8.13: The Momentum (left) and angular (right) distributions for FC1Rµ events in SK. The angle
in the right figure is taken with respect to the neutrino beam direction. The Monte Carlo simulation isin the case of no oscillation.

20
Data

18

MC

16
14

integrated

12
10
8
6
4
2
0

0

0.5

1

1.5

2

2.5
3
Rec. Eν (GeV)

Ph.D. Thesis by Issei Kato, July 2004

Figure 8.14: The distribution of the reconstructed
neutrino energy for FC1Rµ events in SK. The Monte
Carlo simulation is in the case of no oscillation.

8.4. Error matrix of selection efficiency for 1Rµ events

8.4

157

Error matrix of selection efficiency for 1Rµ events

The error on the selection efficiency for FC1Rµ events is estimated as a function of the incident
neutrino energy in order to use it in the oscillation analysis described in Chapter 9. The
neutrino energy is binned into six bins; 0−0.5 GeV, 0.5−1.0 GeV, 1.0−1.5 GeV, 1.5−2.0 GeV,
2.0−2.5 GeV, and above 2.5 GeV, which is the same binning as PIMON. Then, the error isprovided in the form of 6 × 6 error matrix, M²SK . Uncertainties due to the particle identification,
the ring counting, and the energy scale are estimated.
For particle identification, a study using a Monte Carlo simulation was employed. The
number of electron or gamma ray events which are mis-identified as µ-like and that of muon
events which are mis-identified as e-like are counted. The fractions of mis-identified µ-like ande-like events are calculated as a function of energy, quadratically summed, and used as thesystematic error on the selection efficiency for µ-like events.
The atmospheric neutrino data is used in order to estimate the uncertainty due to the ringcounting. Single-ring events are selected in both data and Monte Carlo simulation, and thedifference in the distribution of likelihood for the separation between single-ring and multiring (F1 described in Sec. B.2.2) are compared between data and Monte Carlo simulation. Bychanging the criteria to select single-ring events, its systematic uncertainty is estimated as afunction of energy.
Finally, the uncertainty in energy scale is propagated to the uncertainty in the selection
efficiency as a function of energy. As an error on the energy scale, ±3% is used as described inSec. 3.6.5.
All the errors above are quadratically summed, and the error matrix M²SK is obtained to be

sign(M²SK ) ·

p
M²SK


8.7 0
0
0
0
0
 0 4.3 0
0
0
0 


 0

0
8.9
0
0
0

= 
 0
0
0 10.0 0
0 


 0
0
0
0
9.8 0 
0
0
0
0
0 9.9

,

(8.2)

where six columns or raws are corresponding to the six energy bins, the values are written in
the unit of %, and the correlation between bins is ignored.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 9
Analysis for Neutrino Oscillation
Up to here, the measurements in ND, the extrapolation of ND measurements to the expectations
in SK, and the observations in SK are described. During the run period from June 1999 to July
2001, corresponding to the data of 4.79 × 1019 accumulated protons on target, the number ofobserved neutrino events in SK is 56 while the expectation from the ND measurements is 80.6+7.3−8.0
in the case of that no neutrino oscillation exists; a clear deficit in the number of neutrino events
can be seen. Furthermore, the neutrino energy distribution observed in SK seem to be distorted
compared to that without neutrino oscillation, as shown in Fig. 8.14. These facts indicate theexistence of neutrino oscillation.
In order to test the neutrino oscillation hypothesis and constrain its parameter space, ananalysis for two flavor oscillation with νµ disappearance (νµ → νx ) mode have been performedby using a maximum likelihood method. This chapter describes its procedure and results indetail. First, an overview of the analysis and the definition of likelihood to be maximized are
given. Next, the expected number of neutrino events and energy spectrum are re-estimatedusing the full information of the measurements in ND and far-to-near spectrum ratio (F/N )with given error matrix. Then, the best-fit point of oscillation parameters, the probability fornull oscillation, and constraint on oscillation parameter space from our observation are provided.

9.1

Overview

The signature of the neutrino oscillation with the νµ disappearance mode is a reduction in thenumber of neutrino events and a distortion in the neutrino energy spectrum. All the beam
induced neutrino events observed in the 22.5 kt fiducial volume of SK are used to study the
reduction of neutrino events. On the other hand, single-ring µ-like events (1Rµ) are used to
study the spectral distortion in order to enhance the fraction of CC-qe interactions in which theneutrino energy can be reconstructed using the momentum of muon produced in the reaction;
Eνrec =

1 m2p − m2n − m2µ + 2mn Eµ·2
mn − Eµ + pµ cos θµ

,

(9.1)

as described before.
In the estimation of expected number of events and energy spectrum in SK at each pointof oscillation parameter space, the correlation between energy bins are taken into account for
the errors on the neutrino spectrum and F/N ratio by quoting the errors in the form of error
matrix, which are obtained in Chapter 6 and Chapter 7.
As described in the next section, the likelihood function to be maximized is defined as a
product of three terms; a likelihood for the number of FC events Lnorm , a likelihood for the
159

160

Chapter 9. Analysis for Neutrino Oscillation

spectrum shape Lshape , and a constraint term for the systematic uncertainties Lsyst . Whole
data sample taken from June 1999 to July 2001 are used in the calculation of Lnorm . However
the data taken in June 1999 (K2K-Ia) is discarded in the calculation of spectrum shape part
(Lshape ) since, as is also mentioned in Sec. 3.1.2, the radius of pion production target and thecurrent of horn magnets in K2K-Ia were different from those in the rest of the period (K2K-Ib),
and hence the spectrum shape in K2K-Ia was different from that in K2K-Ib. The discarded datais corresponding to 6.5% of total POT. The number of observed FC (1Rµ) events are 1 (1) in
K2K-Ia and 55 (29) in K2K-Ib as summarized in Table 8.2. Therefore, in total, 56 FC eventsare used in Lnorm , while 29 1Rµ events are used in Lshape .

9.2

Likelihood function for the analysis

9.2.1

Definition of likelihood function

The definition of the likelihood function to be maximized is as following;
Ltotal (sin2 2θ, ∆m2 , f ) = Lnorm (sin2 2θ, ∆m2 , f ) × Lshape (sin2 2θ, ∆m2 , f ) × Lsyst (f ) ,(9.2)

where θ and ∆m2 are the mixing angle and mass squared difference in the two flavor oscillation
approximation as expressed in Eq. (1.14), and f is a set of parameters representing the systematic
uncertainties (f Ia,Ib , f φ,nqe , f F/N , f ² , and f Escale , which are described later).
Normalization term
The normalization term Lnorm is just Poisson probability to observe N obs (= 56) FC events in
SK when the expected number of events is N exp ;¡ exp ¢N obs
N
exp
· e−N
Lnorm =
obs
N !

.

(9.3)

exp
exp
The expected numbers of events for K2K-Ia (NIa
) and K2K-Ib (NIb
) are separately estimatedsince the spectra, F/N ratio, and their systematic errors are different between them. These two
numbers are summed up to obtain the total number of events;
exp
exp
N exp = NIa
+ NIb

.

(9.4)

The expected number of events for each period is calculated by extrapolating the observed
number of events in 1KT (nIa,Ib ) asi
X h Ia,Ib
2
2Φi· σij · ²SK
·
P
(
E
;
sin
2θ,
∆m
)
#
"
i
ij
POT
M
i,j
SK
SK
exp
X¡ Ia,Ib, (9.5)NIa,Ib·= f Ia,Ib ·nIa,Ib ×
·
¢
KT
M
POT
KT
KT
φ
· σij · ²
i

ij

i,j
SK(KT)

where Φi (φi ) is the neutrino flux in the i-th energy bin at far (near) site, σij and ²ij
are,respectively, the interaction cross-section of muon neutrino with water target and the detection
efficiency of SK (1KT) for the FC events of the i-th energy and the j-th interaction mode,
MSK(KT) is the fiducial mass of SK (1KT), and POTSK(KT) is the number of protons on target
corresponding to the amount of data analyzed in SK (1KT). f Ia,Ib is a factor relative to thecentral value of overall normalization for the period Ia and Ib, and it is constrained within its
error. Hereafter, sub(super)scripts “Ia” and “Ib” are omitted when it is not confusing.
Ph.D. Thesis by Issei Kato, July 2004

9.2. Likelihood function for the analysis

161

The oscillation probability P ( E ; sin2 2θ, ∆m2 ) is
1.27 · ∆m2 · L 1 − sin2 2θ · sin2
E
P ( E ; sin2 2θ, ∆m2 ) = 1(for CC interactions)
,

(9.6)

(for NC interactions)where L = 250 km is the neutrino flight distance.
The neutrino flux at near site, φi , is measured in ND detectors as described in Sec. 7.4, andthey are expressed as
φi = fiφ · φMC
,
(9.7)
i
where φMCis the flux in the i-th energy bin predicted by Beam-MC, and fiφ is the weightingifactor for the i-th energy bin measured in ND. fiφ make the energy spectrum vary around theresults of ND measurements being constrained within its error. The flux at SK in the case ofno oscillation is calculated as a product of the flux at ND and F/N flux ratio Ri ;F/NΦi = Ri × φi = fi

· RiMC × fiφ · φMC
i

,

(9.8)

F/N

where RiMC is F/N ratio predicted by Beam-MC, and fi
is a factor relative to RiMC , whichmake F/N ratio vary around its central value being constrained within the error estimated by
PIMON measurements.
For the neutrino interactions, the model “NEUT-1211” is employed in this analysis, which isthe same one as is used in the spectrum measurements in ND. The classification of the neutrino
interaction in the likelihood is also the same as that in ND analysis, i.e. j = qe (quasi-elastic
interaction) or nqe (non-quasi-elastic interactions, non-qe). The total cross-section for the i-thenergy bin, then, can be written asXMCMC
σij = f qe · σi,qe+ f nqe · σi,nqe,(9.9)
j=qe,nqe
MCwhere σi,qe(nqe)is the interaction cross-section of the model used in our Monte Carlo simulation

for qe (non-qe) interaction, and f qe(nqe) is a parameters to adjust overall cross-section ratio being
constrained within the errors estimated by ND measurements. Only the relative value between
f qe and f nqe is meaningful in our method, and hence f qe is fixed to be unity and only f nqe is
the free parameter in the likelihood fitting. Therefore, f nqe is equivalent to the non-qe/qe ratio(Rnqe ) in the spectrum measurements in ND.
Since f φ and f nqe are obtained in the ND analysis in a combined form, we denote them asφ,nqef, hereafter.
Spectrum shape term
The spectrum shape term Lshape is the product of the probability for each 1Rµ event to beobserved at the reconstructed neutrino energy of E rec ;N1RµLshape =Y

Prob(Eirec ; sin2 2θ, ∆m2 , f ) ,(9.10)

i=1

where N1Rµ (= 29) is the number of observed 1Rµ events. The probability density function, orthe normalized E rec distribution, Prob(E rec ; sin2 2θ, ∆m2 , f ), is expressed as
Prob(E rec ; sin2 2θ, ∆m2 , f )
Z h
X©
ªi t
t
rec
t
=
Φ(E t ) · P ( E t ; sin2 2θ, ∆m2 ) ·σj (E t ) · ²1Rµ
(E
)
·
r
(E
;
E
)
dE , (9.11)
jjj

Ph.D. Thesis by Issei Kato, July 2004

162

Chapter 9. Analysis for Neutrino Oscillation

where E t is the true neutrino energy, σj (E t ) is the cross section (= σij in Eq. (9.5)), ²1Rµ(E t ) isj
the detection efficiency for 1Rµ events in SK, and rj (E rec ; E t ) is the detector response functionof SK and is the probability density function to observe the reconstructed energy of E rec when
the the true neutrino energy is E t . ²1Rµ(E t ) and rj (E rec ; E t ) are estimated by a Monte Carlojsimulation for SK detector. In actual analysis, the E t and E rec are binned with an intervalof 50 MeV, and hence the integral over the true neutrino energy is replaced by a summation
over true energy bins. In order to incorporate the uncertainty in the energy scale in SK, thereconstructed neutrino energies for observed events are scaled by a scaling parameter f Escaleconstrained within the estimated uncertainty. In the similar way, the energy dependent uncertainty in the detection efficiency for 1Rµ events is taken into account by replacing ²1Rµ
by
j
²
1Rµ
²
f ² , where f is also a parameter adjusted within its uncertainty.
Systematic constraint term
The distribution of the parameters describing the systematic uncertainties, f , are assumed to
be Gaussian and the constraint term (Lsyst ) for the parameters is expressed as¢¡−1
Lsyst = exp −∆f φ,nqe · Mφ,nqe· ∆f φ,nqe¡¢−1
× exp −∆f F/N · MF/N
· ∆f F/N¡¢× exp −∆f ² · M²−1 · ∆f ²
³ ∆f Ib ´³ ∆f Escale ´³ ∆f Ia ´× exp − 2× exp − 2
(9.12)
× exp − 22σIa
2σIb
2σEscalewhere ∆f ≡ f − fc is the difference of the parameter from its central value fc , Mφ,nqe , MF/N ,and M² are the error matrices for the corresponding parameters, σIa and σIb are the errors on
the normalization for K2K-Ia and Ib period, respectively, and σEscale is the error on the energy
scale in SK. These systematic parameters are treated as fitting parameters in the likelihood
analysis.

9.2.2

Input values for systematic parameters

For the neutrino energy spectrum, the values listed in Table 7.11 are used for the central values
for f φ,nqe and the error matrix Mφ,nqe .
For F/N ratio, since the values estimated by Beam-MC are used as the central values of
F/N ratio as described in Sec. 6.3, the central values of f F/N are set to be unity. On the other
hand, the error matrix shown in Eq. (6.7) is used as MF/N , which is estimated by PIMON above
1 GeV and by Beam-MC below 1 GeV.
The error on the selection efficiency for 1Rµ events in SK is estimated in Sec. 8.4 and thematrix shown in Eq. (8.2) is used as M² . The central values for f ² are set to be unity.
The uncertainty in the energy scale in SK is estimated to be 3% as described in Sec. 3.6.5.
Therefore, σEscale is set to be 3%, while the central value of f Escale is set to be unity.
The normalization parameters for K2K-Ia and K2K-Ib are separately treated since special
treatment is needed for K2K-Ia as described before.
For the error on the normalization in K2K-Ib (σIb ), the contributing systematic errors is listed
in Table 7.5. Among them, uncertainties due to neutrino spectrum, F/N ratio, and interaction
cross-sections are already introduced into the parameters of the likelihood function. Therefore,
only uncertainties other than them are used to estimate the error on the normalization; 0.37%
from 1KT statistics, 4.34% from 1KT systematics, 3% from SK systematics, and 0.6% from
POT correction. In total, 5.34% is quoted as σIb .
Ph.D. Thesis by Issei Kato, July 2004

9.4. Best-fit point for neutrino oscillation

163

Since the amount of data taken in K2K-Ia accounts for only a small fraction of total amountof data (6.5% of total POT), the effect of uncertainty in the expected number of events in
K2K-Ia is inferred to be negligible. Therefore, a simplified and conservative method is employed
to estimate the error on the normalization in K2K-Ia (σIa ). Unlike in the case of K2K-Ib, all
the uncertainties listed in Table 7.5 are taken into account for σIa . The cancellation of theerrors between ND and SK due to the uncertainties in the neutrino spectrum and the crosssection ratio (σnonQE /σQE ) is already taken into account for the numbers in Table 7.5 with anassumption of no neutrino oscillation. However the cancellation is not expected in the oscillatedcase. Therefore, the raw errors (or errors without cancellation) are used for these two quantities.
The neutrino spectrum errors above 1 GeV is quoted from the PIMON measurements, while
those below 1 GeV is quoted from the ND spectrum measurements, yielding the ±9.3% errors on
exp
NIa. A ±30% change in σnonQE /σQE yields 1.6
2.4 % change in the detection efficiency in SK. Theseerrors are used instead of those listed in Table 7.5. Other uncertainties are treated in the same
way as K2K-Ib. In total, the expected number of neutrino events in K2K-Ia is re-estimated to
be 4.55+0.80−0.68 events. This number is expected to become smaller in the oscillated case, and hence
its error is also expected to become smaller accordingly. However, in this analysis, we neglect+0.80
this effect and σIa = −0.68
event is used as constant independent from the value of oscillation
parameters.

9.3

Re-estimation of expected number of neutrino events andspectrum at SK in the case of no oscillation

Before performing the oscillation analysis with likelihood, we re-estimate the expected number ofneutrino events (N exp ) and the reconstructed neutrino energy spectrum at SK without neutrino
oscillation, using the results of spectrum analysis in ND. Here, Eq. (9.4), (9.5) and (9.11) areused. Many sets of parameters f are randomly generated around their central values assuming
Gaussian distribution with the energy correlation taken into account, and N exp and Prob(E rec )are calculated for each set of f with sin2 2θ = 0 (no oscillation).
Resulting distributions for N exp and Prob(E rec ) are shown in Fig. 9.1. By taking the peak
position and the standard deviation of the distribution in the left figure of Fig. 9.1, the expected
number of neutrino events in the case of no oscillation is estimated to be 80.1+6.2−5.4 . The error barof each point of Eνrec distribution in the right figure of Fig. 9.1 is corresponding to the standard
deviation of many trial.
The contribution of each systematic uncertainty to the errors on N exp and Prob(E rec ) is
estimated by turning each uncertainty on one by one. The errors on N exp are summarized in
Dominant contributions come from the uncertainties on the F/N ratio and the normalization.
The contribution of each uncertainty to the energy spectrum is shown in Fig. 9.2 as a functionof reconstructed neutrino energy. In low and high energy regions, the uncertainty in the energy
scale makes a dominant contribution, while all the uncertainties except for non-qe/qe ratio makesimilar contribution in the medium energy region. Table 9.1.

9.4

Best-fit point for neutrino oscillation

The likelihood is calculated at each point in (sin2 2θ, ∆m2 ) space to search for the point where
the likelihood is maximized. The best-fit point in the physical region of oscillation parameter
space is found to be( sin2 2θ, ∆m2 ) = ( 1.0, 2.8 × 10−3 eV2 ) .
(9.13)
Ph.D. Thesis by Issei Kato, July 2004

164

Chapter 9. Analysis for Neutrino Oscillation

4500
0.8
4000

80.14
0.7

3500

0.6

3000

0.5

2500
5.38 6.15

2000

0.4

1500

0.3

1000

0.2

500

0.1

0

55

60

65

70

75

80
85
90
95 100 105
Expected Number of Events

0

0

0.5

1

1.5

2

2.5

3

3.5

4
4.5
5
Rec. Eν (GeV)

Figure 9.1: The distribution of expected numbers of neutrino events (left) and the reconstructed neutrinoenergy (right) in SK for many trial of random number generation without neutrino oscillation. In theright figure, the error bar (size of box) for each point corresponds to the standard deviation of many trial,
indicating the size of error on each point.

Table 9.1: Summary of contribution of each systematic uncertainty to the expected number ofneutrino events in SK in the case of no oscillation. The third and fourth columns are errors in theunit of events and %, respectively.
Period
K2K-IaK2K-IbSource
Total
Neutrino spectrum
non-qe/qe
F/N ratio
Normalization
Subtotal in K2K-Ib

In total ( N exp = 80.1 )Ph.D. Thesis by Issei Kato, July 2004

Errors in events

Errors in %

+0.8
−0.7
+0.4
−0.5
+0.4
−0.9
+4.0
−4.1
+4.0
−4.0
+6.1
−5.3
+6.2
−5.4

+1.0
−0.9
+0.6
−0.6
+0.5
−1.1
+4.9
−5.0
+5.0
−5.0
+7.6
−6.7
+7.7
−6.7

0

2

4
Rec. Eν (GeV)

Far/near02

4Rec. Eν (GeV)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Relative Error

Spectrum165

nQE/QE

0

2

4Rec. Eν (GeV)
Relative Error

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Relative Error

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Relative Error

Relative Error

Relative Error

9.4. Best-fit point for neutrino oscillation

SK efficiency

02

4Rec. Eν (GeV)

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Spectrum and nQE/QE

02

4Rec. Eν (GeV)

SK energy scale

02

4Rec. Eν (GeV)

Figure 9.2: Contribution of various uncertainties to the reconstructed neutrino energy spectrum. Vertical axis is relative error of the spectrum. Source of uncertainty for each plot is written in the figure.
Black histogram is the total error and the blue filled histogram is the contribution from each source. The
red arrows in the plots indicate the reconstructed neutrino energies of 29 observed 1Rµ events.

Ph.D. Thesis by Issei Kato, July 2004

166

Chapter 9. Analysis for Neutrino Oscillation

Table 9.2: The Best-fit points for several conditions. “Global” means the fitting with the searchedregion extended to unphysical region, while “Physical region” means the fitting with the searchedregion constrained inside the physical ration. “1Rµ shape only” means the fitting with only theshape likelihood term and “Shape + Norm.” means the fitting with the total likelihood.

Global∆m2 [eV2 ]3.0 × 10−3
2.8 × 10−3
3.0 × 10−3
2.8 × 10−3

EventsPhysical region

1Rµ shape only
Shape + Norm.
1Rµ shape only
Shape + Norm.

sin2 2θ
1.09
1.03
1.00
1.00

12
10
8
6
4
2
0

0

1

2

3

4

5

Rec. Eν (GeV)

Figure 9.3: The reconstructed neutrino energy distribution for 1Rµ sample. Points with error bars are
our observation. The blue box histogram is the expected spectrum without neutrino oscillation. The
solid red histogram is the best-fit spectrum. These
histograms are normalized by the number of observed
1Rµ events (29). In addition, the black dashed line
shows the expectation with no oscillation normalized
to the expected number of 1Rµ events (44).

The best-fit points of fitting with the search region extended to unphysical region or with only
the use of shape likelihood term are summarized in Table 9.2.
The total number of neutrino events predicted at the best-fit point in the physical region is54.2, which is in good agreement with the observation (56) within statistical error. The observed
distribution of the reconstructed neutrino energy for 1Rµ events is shown in Fig. 9.3, in which
the expected distribution for no oscillation case and for the best-fit oscillation parameters areoverlaid. The consistency between the observed and the best-fit distributions are checked by
Kolgomorov-Smirnov (KS) test. A KS probability of 79% is obtained, indicating that the best-fit
spectrum shape agrees with the observation.

9.5

Null oscillation probability

The probability that the observations are only due to a statistical fluctuation instead of neutrino
oscillation is estimated by computing the likelihood ratio of no oscillation case to the best-fit
point. The probability for no oscillation is calculated to be only 0.7%. When only normalization(shape) information is used, the probability becomes 1.3% (16%).
The effect of each systematic uncertainty on the null oscillation probability is tested byturning each systematic uncertainty on one by one. The results are summarized in Table 9.3.
Ph.D. Thesis by Issei Kato, July 2004

9.8. Comparison with the results from atmospheric neutrino observation

167

Table 9.3: Effect of each systematic uncertainty on the null oscillation probability. The numbersin the table are null oscillation probabilities when only the uncertainty in the first column is turned
on, where “Statistics only” stands for all the systematic uncertainties turned off. “Norm. only”(“Shape only”) means the probability when only the normalization (spectrum shape) term is usedin the likelihood, and “Norm. + Shape” means that both likelihood terms are used.
Sources of uncertainty
Statistics only
Neutrino spectrum
non-qe/qe ratio
F/N ratio
SK 1Rµ efficiency
SK energy scale
K2K-Ia norm. σIa
K2K-Ib norm. σIb
All uncertainties

Norm. only
0.35%
0.36%
0.73%
—
—
0.35%
0.75%
1.27%

Shape only
8.2%
8.4%
8.2%
8.4%
8.3%
15.5%
—
—
15.7%

Norm. + Shape
0.14%
0.15%
0.24%
0.14%
0.24%
0.14%
0.28%
0.70%

The dominant contributions to make the probability large are the uncertainties in the F/Nratio and the normalization in K2K-Ib period in the case of using only normalization term,
while the uncertainty in the energy scale is the dominant contribution in the case of using only
spectrum shape term. For the probability with whole likelihood, these three sources make similar
contribution.

9.6

Constraint on the neutrino oscillation parameters

The allowed region for oscillation parameters are evaluated by calculating the likelihood ratio ofat each point to at the best-fit point, which is shown in Fig. 9.4. The 90% C.L. line intersects
the axis of sin2 2θ = 1 at ∆m2 = 1.5 × 10−3 and 3.9 × 10−3 eV2 . The behaviors of log-likelihood
difference (−∆ ln L) as a function of ∆m2 along the axis of sin2 2θ = 1 and as a function ofsin2 2θ along ∆m2 = 2.8 × 10−3 eV2 are shown in Fig. 9.5. In addition, the 68% allowed regionsin the case of that only the normalization term or only the spectrum shape term is used areshown in Fig. 9.6, indicating that the flux reduction alone and the spectrum distortion alone
favor the same oscillation parameter region.

9.7

Dependence of results on neutrino interaction models

The dependence of our results on the choice of neutrino interaction models is studied by adopting
several models to the likelihood fitting. It is found that the change in the null oscillation
probability is negligibly small when model is changed. As an example of change of models,Fig. 9.7 shows the difference in the reconstructed neutrino energy spectrum and the allowed
region is shown, where NEUT-1211 and NEUT-0000 (see Table 4.4 in Sec. 4.2.7) are compared.
As is seen in the figures, the difference is very small and within the estimated errors. The choiceof the interaction models does not affect so much on the results of oscillation analysis, as is seenin Fig. 9.7.
Ph.D. Thesis by Issei Kato, July 2004

∆m2(eV2)

168

10

10

10

Chapter 9. Analysis for Neutrino Oscillation

-1

-2

-3

68% C.L.
90% C.L.
99% C.L

2

Best fit (1.0,2.8x10 eV )

-4

0

0.2

0.4

0.6

0.8

1
2
sin 2θ

8
7
6
5

Figure 9.4: Allowed region of oscillation parameter constrained by K2K experiment. Black, red, andblue lines are 68%, 90%, and 99% contours, respectively. The best-fit point is indicated by a black “F”
mark.

-∆ln(L)-∆ln(L)

10

-3

5

99%

4
99%
3

4

90%
3

2

90%
2
1

68%
1

68%

0 -4
10

10

-3

10

-2

10
2
∆m (eV )
2

-1

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
2

sin 2θ

Figure 9.5: Behaviors of the log-likelihood difference, −∆ ln L, as a function of ∆m2 along the axis ofsin2 2θ = 1 (left) and as a function of sin2 2θ along ∆m2 = 2.8 × 10−3 eV2 (right). Green lines show the
68%, 90%, and 99% C.L. lines for −∆ ln L.

Ph.D. Thesis by Issei Kato, July 2004

10

-1

-∆ln(L)∆m2(eV2)

9.8. Comparison with the results from atmospheric neutrino observation

169

8
sin22θ = 1.0

7Shape+Norm
6
10

Shape Only

-2

Norm Only
5

99%

4

10

3

-3

90%
Shape only 68% C.L.

2

Norm. only 68% C.L.
10

-4

0

0.2

0.4

68%

1

0.6

0.8

0

1
2
sin 2θ

0

1

2

3

4

5
6
2
-3
2
∆m (10 eV )14

NEUT-1211

12∆m2(eV2)

EventsFigure 9.6: The 68% allowed regions of oscillation parameter space in the case of using normalization
term only or spectrum shape term only (left) and their behavior of the log-likelihood difference, −∆ ln L,
as a function of ∆m2 along the axis of sin2 2θ = 1 (right). In both figures, blue line shows the results ofnormalization term only and red line shows the results of shape term only. In left figure, the point where
the normalization (shape) likelihood function is maximized along the axis of sin2 2θ = 1 is indicated byblue (red) “F” mark.

10-1

NEUT-0000

10

10

-2

8
6
10

-3

4
NEUT-1211 90%C.L.
NEUT-1211 99%C.L.
NEUT-0000 90%C.L.
NEUT-0000 99%C.L.

2
0

0

0.5

1

1.5

2

2.5

3

3.5

4 4.5 5Rec. Eν (GeV)

10

-4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1
2
sin 2θ

Figure 9.7: Comparison of different neutrino interaction models for the reconstructed neutrino energy
and allowed parameter region. In the left figure, red hatched boxes are for NEUT-1211 and blue histogram
is for NEUT-0000. The error bars for NEUT-1211 is the same as in Fig. 9.1. In right figure, solid lines
show NEUT-1211 and dotted lines show NEUT-0000.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 9. Analysis for Neutrino Oscillation∆m2 (eV2)

170

10

10

10

-1

-2

-3

68% C.L.
90% C.L.
99% C.L.
10

K2K results
SK atmospheric ν

-4

0

0.2

0.4

0.6

0.8

1
2
sin 2θ

Figure 9.8: The allowed region of oscillation parameters constrained by K2K experiment together withthat constrained by the atmospheric neutrino observation in SK [118]. The solid lines show the our results
and dash-dotted lines show the results from atmospheric neutrino observation in SK. Black, red, and bluelines are for 68%, 90%, and 99% contours, respectively. The best-fit point of the K2K (SK) observation
is indicated by red (blue) “F” mark.

9.8

Comparison with the results from atmospheric neutrino observation

Finally, Fig. 9.8 compares the allowed region estimated by our analysis with the recent results of
the atmospheric neutrino observation in SK [118]. The best-fit point of the atmospheric results
is at ( sin2 2θ, ∆m2 ) = ( 1.0, 2.0 × 10−3 eV2 ), and the 90% C.L. region of ∆m2 along thesin2 2θ = 1 axis is (1.0−3.0) × 10−3 eV2 . Our results are also consistent with that favored by
the atmospheric neutrino observation pointing the same region of the oscillation parameters.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 10
Discussions and Prospects
Up to the previous chapter, we have developed the analysis to obtain the information on theneutrino oscillation and its results. We have successfully probed the neutrino oscillation withstrong indications: The probability to obtain our observation only due to the statistical fluctuation with no neutrino oscillation is only 0.7%, and the squared mass difference ∆m2 has been
constrained in the region of 1.5−3.9 × 10−3 eV2 at the mixing angle of sin2 2θ = 1, and sin2 2θ
has been constrained to be greater than 0.3 with the confidence level of 90%. However, there
are still several issues to be improved to make our sensitivity to the neutrino oscillation better.
In this chapter, some prospects to make our measurements of the oscillation parameters betterare discussed.
First of all, our sensitivity is statistically limited in the current situation, and hence much
more statistics is needed. For this point, our data will be doubled at the end of K2K experiment.
At the same time, enlarging the fiducial volume for the analysis in SK can also increase available
statistics. In the current analysis, we impose a cut on the distance between the reconstructedvertex point and the nearest wall (Dwall ) to be greater than 2 m, which makes the fiducial
volume 22.5 kt while the whole ID volume has 32.5 kt. Therefore there is another 45% volume
which potentially increases the statistics for analysis. In order to enlarge the fiducial volume,
understanding of the behavior of detection efficiency for the events which occur near the ID wall,
the rejection efficiency for the incoming cosmic ray muons, and behavior of the events whichhappen in the insensitive region between the ID and OD tanks is needed. After these studies,
it is expected to enlarge the fiducial volume for K2K analysis.
In the case of our statistics for the analysis is doubled, the systematic uncertainty in thecurrent analysis will become comparable with the statistical uncertainty. According to Table 9.3,
main contributions of the uncertainties to make the sensitivity to the neutrino oscillation worse
are as followings: The error on the F/N ratio and the normalization are dominant in thenormalization term in the likelihood function, while the error on energy scale in SK is dominant
in the spectrum shape term.
The F/N ratio in our analysis is estimated by Beam-MC, while its error is estimated basedon the uncertainties in the PIMON measurements for the neutrino energy of above 1 GeV andbased on ambiguities in the hadron production models for the neutrino energy of below 1 GeV.
They yield about 5−10% errors on the F/N ratio. In order to reduce these errors, HARP
experiment [119] was performed at CERN, which was the experiment to measure the hadronproduction cross-sections on various target materials with various incident beam momenta. In
this experiment, we had took data with the same condition as K2K experiment; the same
production target (aluminum) with the same dimensions (65 cm in length and 3 cm in diameter),and the same beam momentum (12.9 GeV/c). The data is under analysis and close to obtain
the results [120, 121]. Using this measured cross section, we expect to reduce the error on F/N
171

172

Chapter 10. Discussions and Prospects

ratio down to about 3% level.
The uncertainty in the normalization, the dominating errors are comes from the definitionof the fiducial volume both in 1KT (4%) and SK (2%). Currently, several calibration works
are being done to understand the behavior of the vertex reconstruction. Hopefully, it will be
expected to become a half size of the errors.
For the energy scale uncertainty, SK has 3% uncertainty. It also should be reduced to bearound 1% level in order not to affect the sensitivity of K2K experiment.
Furthermore, the energy information of the multi-ring events in SK is also available to makeour analysis more sensitive to the neutrino oscillation although we do not use them in the analysis
described in this thesis. These events mainly come from the non-qe interactions, and hence thedetailed understanding of the neutrino interaction is indispensable. For this purpose, a full
active tracking detector, SciBar [122], was installed in the near detector system in the summerof 2003. With this detector, we can study the neutrino interactions precisely down to the low
energy region of about a few 100 MeV. These studies also help us to reduce the uncertainties inspectrum measurements at ND, which is secondly dominating error on the spectrum shape in
SK as seen in Fig. 9.2. By feeding these studies back into the analysis in SK, we may be able tointroduce the multi-ring events into the spectral shape analysis with a reasonably small error.
For the spectral studies in ND, the error on the energy spectrum around 0.5−1.0 GeV should
be reduced, where maximum effect of the neutrino oscillation is expected according to our results.
In this thesis, the size of the error is about 10%. Here again, SciBar will be helpful since its
detection threshold is as low as about 100 MeV/c in muon momentum, and hence it can measure
the low energy neutrinos. Furthermore, as mentioned above, the understanding of the neutrino
interactions will also reduce the error on spectrum in the low energy region since non-qe/qe
ratio has strong correlation with the low energy neutrinos. At the same time as these studies
being done, the uncertainty in the energy scale of the detectors should also be understood at
the level of about 1%, since the current size of the energy scale uncertainty (∼ 3%) yields thelargest errors among the detector systematics as shown in Fig. 7.32.
With the studies mentioned above, the sensitivity of K2K experiment will still become better
even in the case of that the statistics will be doubled.

Ph.D. Thesis by Issei Kato, July 2004

Chapter 11
Conclusion
In order to investigate the neutrino oscillation discovered in the atmospheric neutrino observation, the first long baseline neutrino experiment, the K2K experiment, have been performed withthe use of accelerator produced neutrinos and their flight length of 250 km. Data taking wasstarted in June 1999, and up to now, the experiment have been successfully operated. Based on
the data taken from the beginning of the experiment to July 2001, the first oscillation analysis
for the νµ disappearance is performed with the use of both the number of observed events andthe observed energy spectrum. The corresponding number of protons on target is 4.79 × 1019
POT, which is about a half data of our goal.
First, the flux and the energy spectrum of the neutrino beam are measured in the neardetector system. The flux is measured by counting the number of neutrino interactions occurredin 25 t fiducial volume of 1KT, while the energy spectrum is derived from the muon momentum
distributions measured in both 1KT and FGD. The neutrino interaction itself is also studied in
ND and a parameter which describes the cross-section ratio of non-quasi-elastic to quasi-elastic
interactions is obtained at the same time. The measurements of neutrino energy spectrum
described in this thesis is done for the first time in the K2K experiment.
Then, these measurements are extrapolated to the expected observables in Super-Kamiokande
using Beam-MC which is validated by PIMON measurements. The expected number of events
fully contained in the 22.5 kt fiducial volume of SK is estimated to be 80.1+6.2−5.4 , while 56 events
are observed; a clear deficit in the number is found. The energy spectrum for 29 observed
single-ring µ-like events also shows a distortion in its spectral shape.
In order to estimate the significance of the reduction in number of events and the distortionin the spectrum shape, and in order to constrain the oscillation parameters, an oscillation
analysis have been performed by using a maximum likelihood method. Both information fromthe number of events and the spectrum shape are included in the likelihood function. The bestfit values for the neutrino oscillation is found to be ( sin2 2θ, ∆m2 ) = ( 1.0, 2.8 × 10−3 eV2 ).
The probability that the deficit in the number of events and the distortion in the spectrum
shape are only due to a statistical fluctuation is estimated to be 0.7%, strongly disfavoring theabsence of neutrino oscillation. Allowed region for the oscillation parameters are also evaluated.
At maximum mixing, sin2 2θ = 1, the mass squared difference is constrained to be within∆m2 = (1.5 − 3.9) × 10−3 eV2 with the confidence level of 90%. The deficit in the numberof events and the distortion in the spectrum shape both favor the same oscillation parameterregion. Our results are consistent with the results from atmospheric neutrino observations.
In conclusion, we have obtained strong indications for the neutrino oscillation with thedisappearance of muon neutrinos.

173

Appendix A
Neutrino oscillation measurements before
K2K experiment
Up to now, a number of experiments and observations to search for neutrino oscillation havebeen performed around the world. They are categorized into four types according to theirsource of neutrinos; atmospheric neutrino observations, solar neutrino observations, reactor
neutrino experiments, and accelerator neutrino experiments. This classification is also roughly
corresponding to the one based on the sensitive region to ∆m2 , except for the case of long
baseline experiments. The accessible regions of L/E for those experiments are
Atmospheric neutrino:
Solar neutrino:
Reactor neutrino:
Accelerator neutrino:

10−104 km/GeV
1010 −1011 km/GeV
1−102.5 km/GeV
10−2 −10 km/GeV

in the case of vacuum oscillation. In this section, the status of the measurements on neutrino
oscillation are briefly summarized. The results described here are basically what had been
published at the point when the results of the K2K experiment which is the main subject of thisthesis became public in the middle of 2002.

A.1

Atmospheric neutrino observations

Protons and α particles flying about in the universe always pour onto the Earth as primarycosmic rays. Atmospheric neutrinos are produced in the atmosphere of the Earth in such waythat these high energy protons and α particles collide and interact with the atmospheric components such as oxygen and nitrogen and create a number of secondary mesons, mainly pions
and kaons, then subsequently these mesons emit neutrinos in their decay processes, as shown in
the following diagram;p, αcosmic + Natmosphere →π + (K + )π − (K − )↓π + (K + )π − (K − )

175

+

N0

→ µ+ + νµ→ µ− + ν µ↓µ+ → e+ + ν µ + νeµ− → e− + νµ + ν e

(A.1)

176

Appendix A. Neutrino oscillation measurements before K2K experiment

Table A.1: Summary of the observed R values in atmospheric neutrino experiments. In SuperKamiokande, Kamiokande, and IMB experiments, R is evaluated in the low energy and highenergy samples separately. The R values in some experiments differ from that defined in thetitle column. See notes given below the table for details.
Experiment
Super-Kamiokande
Kamiokande
IMB
Soudan-2
MACRO
Fréjus
NUSEX

Energy Range
sub-GeVmulti-GeV
sub-GeVmulti-GeV
Evis < 0.95 GeV
Evis > 0.95 GeV————

Exposure Time[ kton·year ]
33
33
8.2
8.2 (FC)
6.0 (PC)

7.7
7.7
3.9
4.68 years
2.0
0.740

³
R

(Nµ /Ne )obs
(Nµ /Ne )M.C.

´

0.61 ± 0.03 ± 0.05 [123]0.66 ± 0.06 ± 0.06 [124]0.60+0.06−0.05 ± 0.05 [128]0.57+0.08−0.07 ± 0.07 [128]0.54 ± 0.05 ± 0.12 [129]a1.1+0.07−0.12 ± 0.11 [130]0.64 ± 0.11 ± 0.06 [132]0.74 ± 0.036 ± 0.046 ± 0.13b [136]1.00 ± 0.15 ± 0.08 [138]b0.96+0.32−0.28 [139]aThis value is the double-ratio of muon to total neutrino flux between the observation and the expec(Nµ /Ntotal )obs
tation;.
(Nµ /Ntotal )MCb
These values are only the ratio of the observed to expected muon neutrino flux; Nµobs /NµMC .

The energy spectrum of these neutrino has a peak about 1 GeV, and extends to the order of
100 GeV. The main production process of neutrinos with the energy of about GeV region is thesubsequence of pion decays, which results in the flux ratio of (νµ + ν µ )/(νe + ν e ) to be ideally 2.
In the simulation, this ratio is predicted with the uncertainty of 5%, whereas the absolute flux
have the uncertainty of 20%.
The ratio (νµ +ν µ )/(νe +ν e ) has been measured in several experiments: Super-Kamiokande [54,123, 124], Kamiokande [125, 126, 127, 128], and IMB [129, 130], which use water-Cherenkov typedetectors, and Soudan-2 [131, 132], MACRO [133, 134, 135, 136], Fréjus [137, 138], and NUSEX [139] which use iron-calorimeter type detectors. Both types of detector have the capabilities
to identify a event as neutrino induced event by the containment of the vertex, and to identify
the particle type as µ-type or e-type by the Cherenkov ring pattern in the water-Cherenkov
type detectors or by the hit distribution in the iron-calorimeter type detectors. In each experiment, the number of µ-like neutrino events Nµ and the number of e-like neutrino events Ne arecounted, and the ratio (Nµ /Ne )obs is taken and compared to that estimated by Monte Carlosimulation;(Nµ /Ne )obs
R≡
.
(A.2)
(Nµ /Ne )MC
Instead of R, only the ratio of observed to expected muon neutrino flux, (Nµ )obs /(Nµ )MC , isevaluated in MACRO and NUSEX experiment, and the double-ratio of muon to total neutrino
flux between observation and expectation, (Nµ /Ntotal )obs /(Nµ /Ntotal )MC , is calculated in themulti-GeV analysis of IMB experiment. The value R observed in each experiment is summarizedin Table A.1.
Historically, Kamiokande and IMB experiments observed the significantly small R values
away from unity [126, 127, 128, 129, 130], which was called “atmospheric neutrino anomaly”.
On the other hand, Fréjus and NUSEX experiments observed R to be consistent with unity [138,Ph.D. Thesis by Issei Kato, July 2004

A.1. Atmospheric neutrino observations

177

Figure A.1: The zenith angle distribution of the µ-like and e-like events in Super-Kamiokande [140].
The upward-going particles have cos Θ < 0 and the downward-going particles have cos Θ > 0. The
sub-GeV samples are the events with visible energy Evis of less than 1.33 GeV, while the multi-GeV
samples are the events with Evis of greater than 1.33 GeV. In sub-GeV samples, the events with thereconstructed momentum of less than and greater than 0.4 GeV/c are separately shown. The multi-GeV
e-like samples are also shown for the events with the reconstructed momentum less than and greaterthan 2.5 GeV/c, separately. The multi-GeV µ-like samples are shown for the FC and PC events. The
expectations of the Monte Carlo simulation without oscillation and with νµ → ντ oscillation for thebest fit are also drawn in each figure by hatched boxes and solid histograms, respectively.

139],though with poor statistics. Later, Super-Kamiokande and Soudan-2 experiments have been
carried out with higher statistics, and they provided the consistent results with Kamiokande
experiment.
The evidence of neutrino oscillation was clearly shown by the dependence of R on the zenith
angle in Super-Kamiokande experiment [140]. The upward-going neutrinos are originally produced in the atmosphere of the opposite side of the globe and travel more than 10,000 km
distance through the Earth, whereas the downward-going neutrinos are created in the upper air
and travel the distance of only several 10 km to the detector. Therefore, the zenith angle inwhich neutrino is coming have a good correspondence to the distance neutrino travels after its
production, which is the oscillation baseline L in Eq. (1.11). The direction of incoming neutrino
have correlation with the that of lepton produced by its charged-current interaction such thatthe lepton has a trend to be scattered in the same direction as the incoming neutrino travels.
Therefore, the zenith angle of the scattered lepton observed by the direction of Cherenkov ringin the water-Cherenkov type detector is also corresponding to the oscillation baseline L. If
neutrino oscillation actually exists with the oscillation parameters being in a certain region, thevalue R should have some dependence on the zenith angle of scattered lepton in the manner ofcharacteristic of neutrino oscillation.
Fig. A.1 shows the zenith distributions of scattered lepton for µ-like and e-like events observedin Super-Kamiokande [140]. The event samples of four energy regions are separately figured forboth µ-like and e-like events. “Sub-GeV (multi-GeV)” is the event sample with the visible
Ph.D. Thesis by Issei Kato, July 2004

178

Appendix A. Neutrino oscillation measurements before K2K experiment1∆ m 2 (eV 2 )10Atomosphericallowedregions

2

10

Super
Kamiokande

3

10

Figure A.2: Allowed regions of the oscillation parameters forνµ → νx mode. The results obtained in Kamiokande, SuperKamiokande, MACRO, and Soudan-2 are shown. In each experiment, the region inside the contour line is allowed by the
results of atmospheric neutrino observations with the confidence level of 90%.

Kamiokande
Soudan2
MACRO

4

10

0

0.5
2

1

sin (2 θ )energy Evis less (greater) than 1.33 GeV. Sub-GeV events with the reconstructed momentumof less than and greater than 0.4 GeV/c are separately shown. In the multi-GeV samples, elike events are shown for the reconstructed momentum less than and greater than 2.5 GeV/c,
separately, and µ-like events are also shown for the events fully contained (FC) and partiallycontained (PC) in the detector, separately. The results of Monte Carlo simulations without
neutrino oscillation and with νµ → ντ oscillation are also shown in Fig. A.1 by hatched boxes
and solid histograms, respectively. Since the zenith angle distributions in µ-like sample show
clear deficit in upward-going events whereas those in e-like sample are almost consistent with thecase of no oscillation, these results indicate that the scenario of νµ → ντ oscillation is strongly
favored rather than either νµ → νe or no oscillation. Analyzed with the assumption of neutrino
oscillation, the observation gave the allowed region of the mixing angle and the mass squared
difference to besin2 2θµτ > 0.88 ,1.5 × 10−3 eV2 < ∆m2 < 5 × 10−3 eV2(A.3)

in the two flavor oscillation case, and
0.4 < sin2 θ23 < 0.7 ,sin2 θ13 < 0.35 ,1.5 × 10−3 eV2 < ∆m223 < 5 × 10−3 eV2(A.4)

in the three flavor oscillation case with the confidence level of 90%.
In addition to the Super-Kamiokande observation, the flux of upward-going muons was analyzed in the Kamiokande and MACRO experiments. They also showed the deficit in the verticaldirection compared to the horizontal direction, giving the parameter regions for νµ → ντ oscillation to be consistent with Super-Kamiokande results. The allowed regions obtained in several
experiments are shown in Fig. A.2. Furthermore, it is another possible scenario to explain the
deficit of the muon neutrino flux that νµ oscillates into a sterile neutrino, νs , which does not interact with matter at all. However, according to the analyses of the upward-going muon sample
with the matter effect, or so-called the MSW effect [141, 142] in the Earth taken into account,
this mode is disfavored with 99% C.L. with respect to νµ → ντ oscillation in Super-Kamiokande
and MACRO experiments [143, 144]. Therefore, again, the results from the atmospheric neutrino observations strongly favor the oscillation mode νµ → ντ to explain the deficit and thezenith angle distribution of muon neutrino flux.
Ph.D. Thesis by Issei Kato, July 2004

Flux at 1 AU (cm-2 s-1 MeV -1)[for lines,cm-2 s-1]

A.2. Solar neutrino observations

1012

Gallium

1010

pp
±1%

108

106

13N
15O

17F

7Be

±10%

179

Chlorine

SuperK, SNO

pep
±1.5%
+20%
-16%

8B

104
hep

102
0.1

A.2

0.2

±?

2
0.5
1
Neutrino energy (MeV)

5

10

20

Figure A.3: The solar neutrino spectrum
predicted by the standard solar model. The
spectra for the pp chain are shown by solid
curves, while the spectra for the CNO chain
are shown by dotted curves. The neutrino
fluxes from continuum sources are given inunits of number cm−2 s−1 MeV−1 at one astronomical unit (1 AU). The spectra is calculated by J. N. Bahcall et al., which is often
referred to as BP2000 [145].

Solar neutrino observations

The Sun is a main-sequence star at a stage of stable hydrogen burning. It produces an intense
flux of electron neutrinos as a consequence of nuclear fusion reactions in the Sun. The energy ofthe neutrinos distributes from about 100 keV up to 15 MeV, as shown in Fig. A.3. The distance
between the Sun and the Earth is 1 AU, i.e. 1.5 × 108 km. Therefore, the sensitive region tothe ∆m2 of the oscillation νe → νx reaches down to the order of 10−11 eV2 .
There are two detection methods to observe solar neutrinos; the radiochemical techniqueand the water-Cherenkov technique.
The radiochemical experiments exploit electron neutrino absorption on nuclei, and theamount of the produced isotopes are counted after a certain period of exposure. The Homestake
chlorine experiment [146] uses the reaction
νe 37 Cl → e− 37Ar

(threshold 814 keV) ,(A.5)

while CALLEX [147], GNO [148], and SAGE [149] experiments uses the reaction
νe 71 Ga → e− 71 Ge(threshold 233 keV) .

(A.6)

According to the standard solar model (SSM), the dominant contribution in the chlorine experiment comes from 8 B neutrinos, but 7 Be, pep, 13 N, and 15 O neutrinos also contribute. In
addition to them, the most abundant pp neutrinos can be detected in gallium experiments. The
results from these experiments are summarized in Table A.2. All the experiments observed significantly less capture rate than the SSM predictions; it is only about 1/3 of the SSM predictionin Homestake experiment, and is about 60% in GALLEX, GNO, and SAGE experiments. Thiswas historically called “solar neutrino deficit problem”.
Kamiokande and Super-Kamiokande experiments use the detectors of water-Cherenkov type.
They can detect solar neutrinos via νe elastic scattering;ν x e− → ν x e−

,

(A.7)

where νx is νe , νµ or ντ , i.e. all active neutrinos. The energy threshold of Kamiokande and SuperKamiokande experiments are 7 MeV and 5 MeV, respectively. Therefore, they detect pure 8 B
neutrinos because the contribution of hep neutrinos is negligibly small according to SSM. Both
Ph.D. Thesis by Issei Kato, July 2004

180

Appendix A. Neutrino oscillation measurements before K2K experiment

Table A.2: Summary of the results from solar neutrino experiments and a comparison
with the SSM predictions. The first four experiments use the radiochemical technique,and the others use the water-Cherenkov technique to observe solar neutrinos. The first
and the second errors in the experimental results are statistical and systematic errors,
respectively.
37

ExperimentHomestake [146]GALLEX [147]
GNO [148]
SAGE [149]Kamiokande [150]Super-Kamiokande [151]
SNO [152]

BP2000 prediction

Cl → 37 Ar(SNU)a2.56 ± 0.16 ± 0.16
—
—
—
—
—
—
—
—
7.6+1.3−1.1

71

Ga → 71 Ge(SNU)a—77.5 ± 6.2+4.3
−4.7
+3.4
65.8+10.2−9.6 −3.6+3.5
67.2+7.2−7.0 −3.0
—
—
—
—
—
128+9
−7

8
B ν flux(106 cm−2 s−1 )————2.80 ± 0.19 ± 0.33bb2.32 ± 0.03+0.08
−0.07
+0.06
1.76−0.05 ± 0.09cb
2.39+0.24−0.23 ± 0.12
+0.44 +0.46 d
5.09−0.43 −0.43
5.05+1.01−0.81a

SNU (Solar Neutrino Unit) = 10−36 captures per atom per second.
b
Flux measured via the neutral-current reaction.
cFlux measured via νe elastic scattering.
dFlux measured via the charged-current reaction.

experiments observed significantly less neutrino fluxes than what SSM predicts [150, 151], as
well as the radiochemical experiments above. It was about a half flux of the prediction as shownin Table A.2.
SNO [153] is another experiment using water-Cherenkov type detector, started in 1999. Theenergy threshold in SNO is 5 MeV, as same as that in Super-Kamiokande. Therefore, SNO alsomeasures the fluxes of 8 B solar neutrinos. However, since SNO uses heavy water (D2 O) insteadof normal one (H2 O), it can take advantage of measuring charged-current and neutral-current
events as well as νe elastic scattering events, separately. The detectable reactions in SNO areν e d → e− p p−

νe d → e p n(charged-current)(A.8)(neutral-current)(A.9)

in addition to the reaction of Eq. (A.7). The charged-current reaction is sensitive only to electron
neutrinos, while the neutral-current reaction and elastic scattering are sensitive to all active
neutrinos. The fluxes of charged-current (φCC ), neutral-current (φNC ), and elastic scattering(φES ) are separately measured using the differences of cos θ¯ distributions among them, whereθ¯ is the angle of events with respect to the direction from the Sun to the Earth. The resultsof SNO are as follows [152];
+0.06
6
−2 −1
φCC
SNO = φ(νe ) = (1.76−0.05 ± 0.09) × 10 cm s

φES
SNO
φNC
SNO

=
=

,

6
−2 −1
φ(νe ) + 0.154φ(νµ,τ ) = (2.39+0.24−0.23 ± 0.12) × 10 cm s
+0.46
6
−2 −1
φ(νe ) + φ(νµ,τ ) = (5.09+0.44.
−0.43 −0.43 ) × 10 cm s

(A.10),(A.11)(A.12)

The fluxes φ(νe ) and φ(νµ,τ ) deduced from these results are shown in Fig. A.4, as well as theES
SSM prediction. Here, if only each of φCC
SNO and φSNO is considered, these fluxes are significantly less than the SSM prediction, as observed in other experiments. However, when φNC
SNO
Ph.D. Thesis by Issei Kato, July 2004

A.3. Reactor neutrino experiments

181

8

φESSNOφµτ (10 6 cm -2 s -1 )7

φCCSNO

6
5
4

φSSM

3

φNCSNO

2
1
0

0

1

2

3

φe (10 6 cm -2 s -1 )

4

5

6

Figure A.4: The fluxes of 8 B solar neutrino, φ(νe ) and φ(νµ,τ ), deduced from SNO
measurements. The bands show the resultsof flux measurements for charged-current(CC), elastic scattering (ES), and neutralcurrent (NC) with 1σ error. The band of
SSM prediction is also presented. The contours show the 68%, 95%, and 99% joint
probability for φ(νe ) and φ(νµ,τ ).

is considered, this flux represents the total flux of active neutrinos, and is remarkably consistent with the SSM prediction. These three fluxes together taken into account, the resultant
+0.48
6
−2 −1
φ(νµ,τ ) = (3.41+0.45−0.45 −0.45 ) × 10 cm s , providing the direct evidence for solar νe flavor transition.
In addition to these flux measurements, the energy spectrum of recoil electrons and the fluxes
were measured in the daytime and nighttime, separately. They are affected by the matter effectin the Earth, although no evidence of its effect has been found, so far [151, 154]. The global
analysis combining the all results from the solar neutrino observations together strongly favorsthe νe → νx oscillation with the MSW effect in the Sun. The allowed region of the νe → νxoscillation parameters lies in (sin2 2θ, ∆m2 ) = (0.64−0.97, (3−19) × 10−5 eV2 ) in the Large
Mixing Angle (LMA) region with 95% C.L. [155], as shown in Fig. A.5.

A.3

Reactor neutrino experiments

Nuclear reactors are abundant sources of electron anti-neutrinos, which are created in nuclear
β-decay of neutron rich fission products. The energy spectrum of reactor neutrinos is wellcalculated. The average energy of the neutrinos is about 3 MeV, and the distribution extends
up to about 8 MeV. The detectors are located at the distance of a few 10 m to 1 km from thereactor core, depending on experiments. Therefore, the sensitive region to ∆m2 differs from10−3 to 1 eV2 , depending on its distance.
Up to now, several experiments such as CHOOZ [156], Palo Verde [157], Bugey [158], and soon, were performed using reactor neutrinos. These experiments used detectors filled with liquid
scintillator∗ . They measured reactor electron anti-neutrino via the inverse β-decay reaction;
ν e p → e+ n.

(A.13)The neutrino events were identified by the prompt signal of two 511 keV γ-rays from the positron(e+ ) annihilation followed by a delayed coincident signal of γ-ray from neutron (n) capture onto
a nuclear. The signal-to-background ratio was estimated by comparing the data with reactor-on
and with reactor-off.
∗Krasnoyarsk experiment [159] used a detector of hexagonal prism filled with granulated polyethylene.

Ph.D. Thesis by Issei Kato, July 2004

182

Appendix A. Neutrino oscillation measurements before K2K experiment

Table A.3: Summary of the results from reactor neutrino experiments. The limits on ∆m2 andsin2 2θ in the table are obtained by the analysis of the ν e → ν x oscillation. The values of ∆m2
and sin2 2θ are respectively corresponding to those at sin2 2θ = 1 and at large ∆m2 region with
90% C.L. In the Bugey experiment, the ratio of observed to expected ν e events ((ν e )obs /(ν e )exp )are evaluated for each distance, while the limits on ∆m2 and sin2 2θ are derived from the data ofall distance combined.
Experiment
CHOOZ [156]Palo Verde [157]
Bugey [158]Gösgen [160, 161]
Rovno [162, 163]
Krasnoyarsk [159]
Savannah River [164]Distance from Reactor
1.1 km0.75, 0.89 km
15, 40, 95 m
15 m
40 m
95 m
37.9, 45.9, 64.7 m
18.3, 25.3 m
57.0, 57.6, 231.4 m
18, 24 m(ν̄e )obs /(ν̄e )exp
1.01 ± 0.028 ± 0.027
1.01 ± 0.024 ± 0.053—
0.988 ± 0.004 ± 0.05
0.994 ± 0.010 ± 0.05
0.915 ± 0.132 ± 0.05
1.05 ± 0.02 ± 0.05
0.985 ± 0.018 ± 0.034—
0.987 ± 0.006 ± 0.037∆m2 [eV2 ]< 0.0007< 0.0011< 0.01———< 0.019< 0.04< 0.0075—

sin2 2θ
< 0.10< 0.17< 0.02———< 0.21< 0.2< 0.15< 0.24

No experiment have found the evidence of ν e disappearance, so far† . The excluded regions of∆m2 and sin2 2θ provided by these experiments are shown in Fig. A.5 and also summarized inTable A.3. The most sensitive results around ∆m2 ∼ 10−3 −10−2 eV2 are obtained by CHOOZ
experiment. Assuming Eq. (1.16), CHOOZ provided the upper limit on ν e → ν x oscillation tobe ∆m213 < 7 × 10−4 eV2 at sin2 2θ13 = 1, and sin2 2θ13 < 0.10 in large ∆m213 region.

A.4

Accelerator neutrino experiments

Accelerator-produced neutrinos are also available to explore neutrino oscillation. The advantageof the use of accelerator neutrinos is that the energy of neutrino is controllable. Several experiments were performed using neutrino beams with various energies. The experiments which givethe most stringent results at present are briefly summarized below, as well as in Table A.4. The
resulting excluded/allowed regions are also shown in Fig. A.5.
CHORUS [165] and NOMAD [166] experiments at CERN-SPS have searched for ντ events
which is oscillated from νµ . The baseline of both experiments is about 800 m. Almost pure νµbeam with the average energy of about 25 GeV is used. Corresponding sensitive region to ∆m2
is above about 1 eV2 . CHORUS experiment used the emulsion target to identify the τ decay by
event topology, while NOMAD experiment used drift chambers and calorimeters to analyze τevents by kinematic distributions. Both experiments found no evidence for the oscillation signal.
The NOMAD experiment provided a constraint on νµ → ντ oscillation to be ∆m2 < 0.7 eV2 atsin2 2θ = 1 and sin2 2θ < 3.3 × 10−4 for large ∆m2 . The CHORUS experiment also gave similar
constraint to what NOMAD gave.
The region of ∆m2 between 0.3 and 100 eV2 was explored by two old experiments, CDHSW [171]and CHARM [172], using νµ beam at CERN-PS. The average neutrino energy was 1 to 1.5 GeV.
Each of them used two similar detectors. One was placed at 130 m downstream the production
target, and other was placed at 770 m further downstream. The observed fluxes at near and†Recently, at the end of 2002, KamLAND experiment, a reactor neutrino experiment with a baseline of about
180 km, provided the first evidence for the reactor electron anti-neutrino disappearance with the oscillation
parameter of around ∆m2 ≈ 6.9 × 10−5 eV2 [25]. This result is consistent with the solar LMA solution.

Ph.D. Thesis by Issei Kato, July 2004

A.4. Accelerator neutrino experiments

183

Table A.4: Summary of the results from accelerator neutrino experiments. The table isroughly sorted by sensitive regions of experiments to ∆m2 in the upper, middle, and lower
columns. The values for sin2 2θ is expressed in the unit of 10−3 . All the limits are withthe confidence level of 90%. The CDHSW and CHARM experiments have two detectors at
different distance, which corresponds to the two numbers of distance in the table.
Distance from
Neutrino Source
CHORUS (CERN) [165]hEν i = 27 GeV
L = 0.82 km
Neutrino Energy

NOMAD (CERN) [166]hEν i = 24 GeV
L = 0.836 km
CCFR (FNAL) [167, 168, 169]hEν i = 140 GeV L = 1.4 km
NuTeV (FNAL) [170]hEν i = 140 GeV L = 1.4 km
CDHSW (CERN) [171]hEν i = 1.5 GeV
L = 0.13, 0.9 km
CHARM (CERN) [172]hEν i = 1.5 GeV
L = 0.13, 0.9 km
BNL-E776 (BNL) [173]Eνpeak = 1 GeVb L = 1 km
KARMEN (Rutherford) [174, 175]Eν < 52.8 MeVc L = 0.018 km
LSND (LAMPF) [176, 177]
Eν < 52.8 MeVc L = 0.030 km∆m2 [eV2 ]sin2 2θ
[×10−3 ]νµ → ντνe → ντ

< 0.6
< 7.5

< 0.68< 52

νµ → ντνe → ντ

< 0.7
< 5.9

< 0.33< 15

νµ (ν̄µ ) → νe (ν̄e )νµ (ν̄µ ) → ντ (ν̄τ )νe (ν̄e ) → ντ (ν̄τ )

< 1.6
< 1.4
< 17

< 1.8
< 8.1
< 210

νµ (ν̄µ ) → νe (ν̄e )

< 2.6

< 1.1

Oscillation Modeνµ → νµ< 0.23 or > 100a < 100νµ → νµνµ → νe< 0.29 or > 22a< 0.19< 170< 80

νµ (ν̄µ ) → νe (ν̄e )< 0.075< 30

ν̄µ → ν̄e
νe → ντ< 0.055< 0.77

< 1.7
< 338

ν̄µ → ν̄e
νµ → νe0.03 − 0.05
0.03 − 0.3

3.8 − 14
0.5 − 30aSince the near detector, as well as far detector, sees the effect of neutrino oscillation for large∆m2 , and the difference of the flux between near and far detectors becomes smaller, suchanalysis that compares observations in near and far detectors usually lose the sensitivity inlarge ∆m2 region.
b
The energy spectrum of neutrino in BNL-E776 is wide band and it extends up to about 10 GeV,
having a peak around 1 GeV.
c
Neutrinos are created in the decay of pions and muons at rest. Therefore, neutrinos from thepion decay have a monochromatic energy of 29.8 MeV, and neutrinos from the muon decay
have energy described by Michel spectrum which have a endpoint at 52.8 MeV.

Ph.D. Thesis by Issei Kato, July 2004

184

Appendix A. Neutrino oscillation measurements before K2K experiment

far sites were compared to each other, and no evidence for νµ disappearance was found. The
region excluded by CDHSW is 0.23 < ∆m2 < 100 eV2 at sin2 2θ = 1 and sin2 2θ > 0.05 at∆m2 = 0.3 eV2 with the confidence level of 90%, as shown in the lower left figure of Fig. A.5.
KARMEN [174, 175], and LSND [176, 177] experiments explored rather lower ∆m2 region,
down to around 0.1 eV2 , in ν µ → ν e mode. They used neutrinos produced in the decay ofmuons at rest. Therefore, neutrino energy distributes in the region less than 52.8 MeV, which is
described by well-known Michel spectrum. The baseline of KARMEN and LSND was 18 m and
30 m, respectively. They both had the capability to identify ν e events by looking at the signals ofe+ from ν e p → e+ n and subsequent γ-ray from neutron capture. The LSND reported the positive
evidence for ν e appearance with an oscillation probability of (0.264 ± 0.067 ± 0.045)% [177].
This result provided the allowed region of oscillation parameters for ν µ → ν e mode to be
0.03 < ∆m2 < 0.05 eV2 at sin2 2θ = 1 and 0.0038 < sin2 2θ < 0.14 for large ∆m2 region with
90% C.L., as shown in Fig. A.5. On the contrary, KARMEN found no indication of oscillation
signal, and excluded large part of allowed region given by LSND. CCFR [167] and NuTeV [170]also performed the oscillation analysis in νµ (ν µ ) → νe (ν e ) mode for little bit larger ∆m2 region.
However they could not find any evidence for oscillation to result in excluding almost all part of
LSND allowed band above ∆m2 = 60 eV2‡ . All the experimental results above combined, theremaining allowed (sin2 2θ, ∆m2 ) space of LSND for νµ → νe is a slanting narrow band region
which lying between about (4 × 10−2 , 0.2 eV2 ) and (3 × 10−3 , 1 eV2 ) with the confidence levelof 90% [179].

‡

Recently, NOMAD experiment also performed νµ → νe analysis. No evidence for oscillation was found, anda part of the LSND allowed band above ∆m2 = 10 eV2 has been excluded [178].

Ph.D. Thesis by Issei Kato, July 2004

185

100

100

KARMEN2

A.4. Accelerator neutrino experiments

10

NOMAD

1

1

LS

ND

BNL E776

0.1

10∆m 2 [eV2]

10
10

−2

Buge

0.1

y

10

rde

oVe
Pal

−3

Z

OO

CH
−4

10
10

LMA
∆m 2 [eV2]

10

−5

SMA
10
10

CHORUS

−6

10

10

10

−4

LMA

−5

−6
−7

10

10

10

Super−Kamiokande
Zenith Angle Spectrum
Exclusion

VAC

10νe − ν µ

−11

10

−12
−4

−3

10 3
10 2

−2

10

NOMAD

10

10

0.1
tan2 θ

1

10

10∆m2 [eV2 ]

10

−10

CHORUS

10

LOW

−8

−9

1

CD

HS

W

−1

10

−2

νµ−ντ

10

−3

10 −4
10

10 −3

Z

OO

CH

LOW
10

rde

oVe

Pal

−3

SMA
10

−7

Buge
y

−2

Super−Kamiokande
atmospheric neutrino
10 −2
10 −1
1
2
sin 2θ

2

10

10

−8

Super−Kamiokande
Zenith Angle Spectrum
Exclusion

−9

VAC

−10

νe − ντ

−11

−12
−4

10

10

−3

−2

10

0.1
tan2 θ

1

10

2

10

Figure A.5: The allowed/excluded regions for νe ↔
νµ (upper left), νe ↔ ντ (upper right), and νµ ↔ ντ(lower left) oscillation parameters. Only the resultsof experiments which provided the most stringent limits are figured. The CPT invariance is assumed andneutrinos and anti-neutrinos are both shown together.
Filled regions are the allowed ones derived from positive results, while blank regions are excluded by measurements with negative results. The allowed/excluded
regions below ∆m2 = 10−3 in the upper two figures are
given by solar neutrino observations. Bugey, CHOOZ,
and Palo Verde are reactor neutrino experiments, andothers are accelerator neutrino experiments. Currently,
three allowed regions are sitting, which are labeled by
LMA, Super-Kamiokande atmospheric neutrino, and
LSND in the figures. The figures are quoted from [20].

Ph.D. Thesis by Issei Kato, July 2004

Appendix B
Event Reconstruction in Water Cherenkov
Detectors
In the analysis of 1KT and SK, selected events are reconstructed by following procedures inorder, which are almost the same in 1KT and SK.
(1) Vertex finding (auto-fit)(2) Ring counting(3) Particle identification (PID)(4) Precise vertex finding (MS-fit)(5) Momentum determination(6) Correction to the number of rings (ring correction)(7) Correction to the number of rings for the events in 1KT (ring correction II)
The procedures above are applied to all the event remaining after the event reduction, and thenumber of Cherenkov rings, and the direction, the particle type, and the momentum of eachring in each event are obtained.

B.1

Vertex finding (auto-fit)

First, the vertex position is reconstructed using the timing information of hit PMTs. The vertex
finding of this step is called “auto-fit”. The vertex finding algorithm of auto-fit consists of threesteps.

B.1.1

Point-fit

Vertex position of each event is roughly estimated in the first step assuming all the photons are
emitted from a point source at the same time. The time of flight of photon is subtracted fromthe hit timing of each PMT. The residual time of each PMT ti is calculated byti = t0i −n~ ,× |P~i − O|
c

(B.1)

where t0i and P~i is the hit timing and the position of i-th PMT, n is the refractive index of water,~ The position O~ is searchedc is the velocity of light, and the vertex point is assumed to be O.
187

188

Appendix B. Event Reconstruction in Water Cherenkov Detectors

so that the distribution of ti becomes sharp peak since all the hit PMTs should have similar ti~ is at the true vertex. This vertex reconstruction algorithm is called “point-fit”.
values when O
The estimator for the goodness of the fit is defined as
¶
µ
N
1 X
(ti − t0 )2
Gp =
exp −
N
2(1.5 × σ)2

,

(B.2)

i

where N is the number of hit PMTs, t0 is the mean value of ti , and σ is the time resolution of
PMT taken to be 2.5 nsec. The numerical factor 1.5 is chosen to optimaze the fitter performance.
~ is determined so that it gives the maximum value of Gp .
The vertex point O
The particle direction is also roughly estimated by summing up the charge weighted vector
over all hit PMTs:
NX~0
P~i − O
d~0 =
qi ×
,
(B.3)
~ 0|
|P~i − Oi~ i is the vertex point obtained by the point-fit, andwhere d~o is the estimated particle direction, O
qi is the detected charge by i-th PMT.
The vertex point and the particle direction obtained here are used in the next step.

B.1.2

Ring edge search

The direction of particle and the outer edge of the dominant Cherenkov ring is estimated in thisstep. In order to determine them, an estimator Q(θedge ) is defined as follows:Z θedgeQ(θedge ) =ÃPE(θ) dθ0sin θedge

×

!2
¯
¶
µ
(θedge − θexp )2d PE(θ) ¯¯× exp −dθ ¯θ=θedge
2σθ2

,

(B.4)

where θexp and σθ are the opening angle of Cherenkov ring expected from the charge within thecone and its resolution, respectively, and PE(θ) is the distribution of the observed charge as afunction of the opening angle θ with respect to the particle direction. THe effect of the watertransparency and the PMT acceptance on the observed charge are corrected in this expression.
The direction of particle is changed around d~0 so that the Q(θedge ) is maximized. The angle ofring edge θedge is determined to satisfy the following two conditions:(1) θedge > θpeak , where θpeak is the angle at which the PE(θ) takes its maximum.
¯
d2 PE(θ) ¯¯= 0.
(2)dθ2 ¯θ=θedge
Fig. B.1 shows a typical distribution of PE(θ) and its second derivative. The edge of thedominant Cherenkov ring in a event is found as pointed in the figure.

B.1.3

TDC-fit

The vertex point and the particle direction are determined more precisely in this step by TDCfit. Here the track length of the charged particle and the scattered Cherenkov photons are taken
into account in the TDC-fit, while a point-like light source is assumed in the point-fit.
Ph.D. Thesis by Issei Kato, July 2004

number of p.e.

B.1. Vertex finding (auto-fit)

189

150
100
50

second derivative

0

10

0
detected edge

-10
o

0

10

o

o

20

o

30

o
o
o
40
50
60
opening angle

o

70

o

80

o

90

Figure B.1: A typical distribution of PE(θ) (upper figure) and its second derivative (lower figure).
The edge of dominant Cherenkov ring is found as
pointed in the lower figure.

The time residual of the i-th PMT, ti , is defined by

1
n
0

~
~
~
~

 ti − c × |Xi − O| − c × |Pi − Xi | for PMTs inside the Cherenkov ringti = t0 − n × |P~i − O|~
for PMTs outside the Cherenkov ring
i
c

(B.5)

~ is assumed vertex point which is fitted in this step, X~ i is the position at which Cherenkov
where O
photons are emitted toward the i-th PMT. The definition of other symbols are the same as before.
The estimator of the TDC-fit is consist of three different estimators. Depending on thelocation of hit PMTs and their hit timing, one estimator is chosen to be used for each PMT.
For the hit PMTs located inside the Cherenkov ring, the estimator GI is defined byµ¶X 1(ti − t0 )2
GI =
exp −
,
(B.6)
2(1.5 × σ)2σi2iwhere σi is the time resolution of the i-th PMT depending on the detected number of photoelectons, σ is the time resolution for the average number of photoelectrons of all hit PMTs, andt0 is the mean time residual.
For the hit PMTs outside the Cherenkov ring, the definition of the estimator changes depending on the time residual of each PMT. In the case of the hit timing is later than t0 , thecontribution of scatterd photons are also considered in addition to the direct Cherenkov light.
The definition of estimators is as follows:
µ
¶
¸
X 1 ·
(ti − t0 )2
GO1 =
exp −
×2−1
for ti ≤ t02(1.5 × σ)2
σi2
i
¶
¶
¸
µ
µ
(B.7)
X 1 ·
(ti − t0 )2GO2 =, Gscat (ti , t0 ) × 2 − 1 for ti > t0
max exp −2(1.5 × σ)2σi2iwhere the estimator for the scattered photons, Gscat (ti , t0 ), is
µ
¶ µ
¶
µ
¶
Rq
Rq
(ti − t0 )2
ti − t0
Gscat (ti , t0 ) =
·
exp
−
+
1
−
·
exp
−
1.52
2(1.5 × σ)2
1.52
60 nsec.

(B.8)

Ph.D. Thesis by Issei Kato, July 2004

190

Appendix B. Event Reconstruction in Water Cherenkov Detectors

Cherenkov ring

600
most probablering center

400
200
0
150

hit PMTpossible ring center
estimated by each PMT

θ( 100
de
gr
ee 50
s)

00

100

200

300

es)

re
φ(deg

Figure B.2: The basic idea of the ring candidate search (left) and a typical charge of Cherenkov rings
derived by Hough transformation. Left figure: The point where the most of the circles for possible centerare intersecting is recognized as the direction of a Cherenkov ring. Right figure: Peaks in the charge map
is corrsponding to the possible Cherenkov ring direction with respect to the vertex point.

In this expression, Rq is the fraction of the charge detected inside the Cherenkov ring, and thenumerical factors are chosen to optimize the performance of the fitter.
Then the whole estimator of the TDC-fit is defined as
GTDC =

GI + GO1 + GO2
X 1
σi2
i

.

(B.9)

The vertex point and the direction of particle are determined to maximize this estimator.

B.2

Ring counting

With the knowledge of the vertex point found in the auto-fit, the ring counting algorithm
determines the number of Cherenkov rings and the direction of each ring.

B.2.1

Ring candidate search

The algorithm starts the ring candidate search. First, the expected charge from the Cherenkov
ring found in the vertex fitting is subtracted from the charge of each PMT. Then we use a petternrecognition method called “Hough tracsformation” [180]. Left figure in Fig. B.2 illustrates thebasic idea of the ring candidate search. A sperical coordinate centered on the vertex point is
considered so that the direction of each Cherenkov ring or PMT is considered to be a point on
the sphere. Assuming the opening angle of Cherenkov ring to be 42◦ , possible ring direction
is estimated using a certain hit PMT by drawing the virtual circle with its center being at the
PMT and its radius corresponding to 42◦ opening angle (thin circles in Fig. B.2). The point
Ph.D. Thesis by Issei Kato, July 2004

B.2. Ring counting

191

where the most of the circles estimated by all hit PMTs are intersecting is recognized as the
direction of a Cherenkov ring.
In the practical case, a Hough space is defined using the polar angle Θ and the azimuthal angle
Φ with respect to the reconstructed vertex. Instead of drawing the virtual circles, the expectedcharge distribution f (θ) weighted with the observed charge of each hit PMT is mapped onto the(Θ, Φ) space, where θ is the angle between the direction to the PMT under consideration andto each (Θ, Φ) point seen from the vertex. This operation is applied to all the hit PMTs. As aresult of this Hough transformation, a possible ring center becomes visible as a peak of charge
on the map. Right figure in Fig. B.2 shows a typical charge map derived by this operation,
where two peaks can be seen as candidates of ring direction.

B.2.2

Ring candidate test

Next, the ring candidates are tested using a likelihood method. Supposing N rings are alreadyfound in an event, the test for the (N +1)-th ring candidate is carried out by comparing two
likelihoods; the likelihood LN +1 for the assumption that the event has N +1 rings including thiscandidate and the likelihood LN for the assumption that the event has only N rings which are
already found. The likelihood function for the assumption of N +1 rings is defined as
LN +1 =

X
i

µ
N
+1
³
´¶
X
exp
obs exp
log prob qi , qi =αn · qi,n,(B.10)

n=1

exp
where qiobs is the observed number of photoelectron in i-th PMT, αn ·qi,nis the expected numberof photoelectron in i-th PMT which photon originates from the n-th Charenkov ring, and thesummation for i is performed over the PMTs inside the (N +1)-th Cherenkov ring. The scale
factors αn (n=1, · · · , N +1) are selected to maximize the LN +1 . The probability function,prob(qiobs , qiexp ), is defined asµ¶(qiobs − qiexp )2
1


√
exp −
(for qiexp > 20 p.e.)2 2π σ2σ(B.11)
prob(qiobs , qiexp ) =convolutionofsinglep.e.
distributionexp(for qi < 20 p.e.)
and a Poisson distribution

where σ is the resolution for qiexp .
In the case of that there is no candidate which satisfies LN +1 ≥ LN , the number of rings inthis event is determined to be N . For the ring candidate with LN +1 ≥ LN , the following four
estimators for the goodness of the ring are calculated:
F1: The difference L(N + 1) − L(N ) corrected for the total photoelectrons.

F2: The average of the expected photoelectrons in PMTs located around the edgeof (N +1)-th ring, Qedge , where the PMTs overlapped with other N rings are
not taken into account to make Qedge .

F3: The average of the expected from (N +1)-th ring, Qout , calculated over the
PMTs located outside the (N +1)-th ring and off the others N rings. The
difference Qedge − Qout is used in the estimator.

F4: The residual photoelectrons from the expected photoelectrons with the N rings
assumption are used. The total amount of the residual p.e.s is calculated as
Ph.D. Thesis by Issei Kato, July 2004

192

Appendix B. Event Reconstruction in Water Cherenkov Detectors

NUM
1
RUN
999999SUBRUN
0EVENT
1DATE 2002-Dec-16
TIME
22: 4:39
TOT PE:
6147.0MAX PE:
24.1
NMHIT : 2869
ANT-PE:
81.4
ANT-MX:
12.2
NMHITA:88

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

Comnt;

RunMODE:MonteCarloTRG ID :00000011
T diff.:0.
us
FEVSK :80000003
nOD YK/LW: 2/ 1
BAD ch.: masked
SUB EV : 0/ 0
Dec-e: 0( 0/ 0/ 0)CT16:0.00000e12
RN:
0SP:
0
GPSDIF:**********us
NHITAC:
1

NUM
3
RUN
999999SUBRUN
0EVENT
4DATE 2002-Dec-16
TIME
21:53:36
TOT PE:
4625.1
MAX PE:
28.4
NMHIT : 1524
ANT-PE:
70.7
ANT-MX:
4.6
NMHITA:83

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : GOOD
0.00: 0.00: 0.00:0.000
CANG : RTOT : AMOM : MS

Comnt;

RunMODE:MonteCarloTRG ID :00000011
T diff.:0.
us
FEVSK :80000003
nOD YK/LW: 1/ 1
BAD ch.: masked
SUB EV : 0/ 0
Dec-e: 0( 0/ 0/ 0)CT16:0.00000e12
RN:
0SP:
0
GPSDIF:**********us
NHITAC:
1

Figure B.3: Typical Cherenkov ring images for an electron event (left) and a muon event (right). The
ring produced by an electron have diffuse edge while that produced by an muon have sharp edge. These
events are generated by the Super-Kamiokande detector simulation, in which an electron and an muonwith their momentum of 700 MeV/c is injected horizontally from the center of the detector.

P| qires · ~ei |, where ~ei is a unit vector from the reconstructed vertex to the i-th
PMT.
These estimators have large values if the candidate is probable. The final estimator to test thering candidate is made as the linear sum of F1 , F2 , F3 , and F4 with some weight:
F = w1 · F1 + w2 · F2 + w3 · F3 + w4 · F4

(B.12)

where the weights wi (i=1, 2, 3, 4) are optimized to have the good performance. If there are no
candidate which satisfies F ≥ 0, the number of rings in this event is finally determined to be N .
If there exists the candidate satisfying F ≥ 0, it is regarded to be the (N +1)-th ring, and thecandidate search for the (N +2)-th ring starts.

B.3

Particle identification (PID)

The particle identification (PID) algorithm classifies Cherenkov rings into two types, a showering
type (e-like) and non-showering type (µ-like). Fig. B.3 shows typical Cherenkov images for anelectron event and for a muon event. As shown in the figure, the Cherenkov ring from anelectron or a gamma-ray has a diffuse edge since such a ring is made of Cherenkov photons
from multiple particle produced in an electro-magnetic showering process. On the other hand,a muon or a pion produces a sharper ring caused by single charged particle. The PID algorithm
uses this feature of Cherenkov ring patterns. In addition, since a muon or a pion with a lower
momentum has its velocity (β) smaller apart from unity, the opening angle of its Cherenkov ringgets smaller, whereas it does not occur down to very low energy in the case of an electron or a
gamma-ray. The PID algorithm also uses this difference in the opening angles. The observed
pattern of the photoelectron distribution is compared with the expected ones for an electron
and a muon, and then one of two types which matches better is selected for the PID of the ring.
Ph.D. Thesis by Issei Kato, July 2004

B.3. Particle identification (PID)

B.3.1

193

Expected charge distribution

Expected charge distribution for an electron
The expected charge distribution for an electron is made by the Monte Carlo simulation. In
practical case, we create the angular distribution of the expected photoelectrons reaching thecircular area of 50 cm diameter on the virtual surface of a sphere of 16.9 m radius centered on
the vertex point, which distribution is given as a function of the opening angle and the electron
exp
momentum, Qexpe (p, θ). Using Qe (p, θ), expected photoelectrons for the i-th PMT from then-th ring is calculated asµ ¶1.5
1
R
exp
exp
×
qi,n (e) = αn (e) × Qe (pn , θi,n ) ×× f (Θi ) ,(B.13)ri
exp(ri /L)
where
exp
qi,n
(e)

: expected p.e.s for the i-th PMT from the n-th ring with assumption thatthe particle producing the n-th ring is an electron.

αn (e): normalization factor.

θi,n: opening angle between the i-th PMT direction and the n-th ring direction.

ri: distance from the vertex to the i-th PMT.

R

: radius of the virtual sphere, 16.9 m.

L: light attenuation length in water.

f (Θi )

: correction function for the PMT acceptance as a function of the photon
incident angle Θi .

The factor (R/ri )1.5 comes from the distance dependence of the light intensity.
Expected charge distribution for a muon
The expected distribution of photoelectrons for a muon is analytically calculated asÃ!
sin2 θi,n
1
exp
knock
¯
qi,n (µ) = αn (µ) × ³
× f (Θi ) ,
+
q
×
´
i,n
dθ ¯¯
exp(ri /L)ri sin θi,n + ri ·dx ¯x=xi(B.14)

where
exp
qi,n
(µ)

: expected photoelectrons for the i-th PMT from the n-th ring with assumption that the particle producing the n-th ring is a muon.

αn (µ): normalization factor.

knock
qi,n

: expected photoelectrons for the i-th PMT from knock-on electrons.

x: distance from the initial vertex position along the muon trajectory.

xi,n: distance from the initial vertex position to the muon position where
Cherenkov photons are emitted toward the i-th PMT
Ph.D. Thesis by Issei Kato, July 2004

dθ

dx

⋅sin
θ

Appendix B. Event Reconstruction in Water Cherenkov Detectors

r⋅d
θ

194

r
Figure B.4: A schematic view of the Cherenkov radiation from a muon. Cherenkov photons are emitted to thearea of 2πr sin θ(dx sin θ + rdθ) while a muon travels the
distance of dx.

θ
dx

muon

θ

: Cherenkov opening angle of the muon traversing at x.

θxi,n: Cherenkov opening angle of the muon traversing at x = xi,n .

In this expression, the term sin2 θ comes from the angular dependence of the Cherenkov lightintensity, and the therm r(sin θ + r(dθ/dx)) comes from the area to which the Cherenkov photons are emitted. As shown in Fig. B.4, a muon emits Cherenkov photons toward the area of
2πr sin θ(dx sin θ + rdθ) while it travels the distance of dx with decreasing the Cherenkov angle
due to the ionization energy loss of muon in the water.

B.3.2

Estimation of the particle typeThe estimation of the particle type for each ring by the Cherenkov ring pattern information is
performed using likelihood functions defined as³
Y
X exp ´exp
Ln (e or µ) =prob qiobs , qi,n(e or µ) +qi,n0,
(B.15)in0 6=nexp
where qiobs is the observed photoelectrons in i-th PMT, qi,n(e or µ) is the expected photoelectrons of i-th PMT from the n-th ring with an assumption that the particle producing the ringexp
is an electron (Eq. (B.13)) or a muon (Eq. (B.14)), qi,n0 is the expected photoelectron of ith PMT from the n0 -th ring without particle type assumption, and the probability function
prob(q obs , q exp ) is the same one as is used in Eq. (B.11) in the ring counting algorithm. The
product in Eq. (B.15) is done over the PMTs inside the n-th ring. The expected photoelectrons
exp
exp
qi,n
(e) and qi,n(µ) are selected to maximize Ln (e) and Ln (µ), respectively, by changing thedirection and the opening angle of the n-th Cherenkov ring. Then the likelihood using the ringpattern information is translated into a χ2 parameters as

χ2n (e or µ) = −2 log Ln (e or µ) − constant ,(B.16)and the probability to detect qiobs in each PMT is calculated by
¢2 ¶
µ ¡ 2
χn (e or µ) − min[χ2n (e), χ2n (µ)]
patternPn(e or µ) = exp −,(B.17)2σχ2 2n√where the resolution of the χ2n distribution is approximated to be χ2n = 2N using the numberof PMTs (N ) used in the likelihood calculation in Eq. (B.15).
Ph.D. Thesis by Issei Kato, July 2004

B.4. Precise vertex finding (MS-fit)

195

10000
e-like8000

6000µ-likeνe CC q.e.
νµ CC q.e.

Figure B.5: The distribution of the PID estimator for
fully-contained (FC) single-ring events. The hatched(blank) histgram is for the CC-qe events of electron(muon) neutrinos in which event only an electron (amuon) is expected to be visible. Clear separation between the electron events and the muon events can be
seen. These histograms are estimated by a Monte Carlosimulation used in Super-Kamionande.

4000

2000

0

-10

-5
0
5
PID parameter10

The probability using the information of the opening angle of the Cherenkov ring is calculated
by

¢2 ¶
µ ¡ c
θn − θnexp (e or µ)−,
2 (δθn )2

Pnangle (e or µ) = exp(B.18)

where θnc ± δθn is the reconstructed opening angle of the n-th ring, and θnexp (e or µ) is the
expected Cherenkov angle of the n-th ring calculated from the estimated momentum with anassumption that the particle producing the ring is an electron or a muon.
Finally, the total probability is defined as
P1 (e or µ) = P1pattern (e or µ) × P1angle (e or µ) for single-ring eventsPn (e or µ) = Pnpattern (e or µ)
for multi-ring events(B.19)

where the probability estimated by only the pattern information (Pnpattern ) is used for multi-ring
events since the estimation of the opening angle works relatively worse in the case of multi-ring
events.
We usually use the estimator of the particle identification in the following form;pp
Pn = − log Pn (µ) − − log Pn (e) ,(B.20)
where Pn < 0 (Pn > 0) stands for e-like (µ-like) ring. Fig. B.5 shows the PID likelihood
distribution for single ring events (P1 ) estimated by a Monte Carlo simulation, where muon
events and electron events are clearly separeted at P1 = 0.

B.4

Precise vertex finding (MS-fit)

The auto-fit algorithm gives a relatively worse vertex resolution in the longitudinal direction
for single-ring events since a vertex shift along the ring direction changes the time of flight ofphotons evenly for all PMTs and hence the estimator of the fitting does not change so much.
In order to obtain more precise vertex point, the fitting using the ring pattern information,so-called “MS-fit”, is applied to single-ring events. The result of auto-fit is left to be used for
multi-ring events.
Ph.D. Thesis by Issei Kato, July 2004

196

Appendix B. Event Reconstruction in Water Cherenkov Detectors

In the algorithm of the MS-fit, the observed photoelectron distribution is compared with the
expected one by a likelihood method in which an estimator is maximized by changing the vertex
point and the direction of the Cherenkov ring. The definition of the likelihood is the same asthat used in the PID algorithm, in which the particle type and the Cherenkov opening angle aredetermined. After the modification of the vertex point and the ring direction, the vertex position
is further adusted perpendicularly to the ring direction to maximize the goodness GTDC definedin TDC-fit (Eq. (B.9)). These processes are iterated until the changes in the vertex position
and the ring direction become less than 5 cm and 0.5◦ , respectively.

B.5

Momentum determination

The momentum of each particle is estimated by the observed number of photoelectrons inside thecone with a half opening angle of 70◦ with respect to the direction of the corresponding Cherenkov
ring. In order to determine the momentum for individual rings, the observed photoelectrons inhits PMTs are separeted into the contribution from each ring. The separation of the observed
photoelectrons is done based on the expected photoelectron distribution of each ring as a functionof the opening angle θ and uniform in azimuthal angle φ. The observed number of photoelectrons
in the i-th PMT contributed from the n-th ring is estimated as
exp
qi,n
obs
qi,n
= qiobs × X exp
qi,n0

,

(B.21)

n0
obs is the fractional
where qiobs is the observed number of photoelectrons in the i-th PMT, qi,nexp
number of photoelectrons from the n-th ring in the i-th PMT, qi,n is the expected number ofphotoelectrons from the n-th ring in the i-th PMT, and the summation in the expression is done
over all the rings.
To calculate the total number of photoelectrons inside the 70◦ cone, the number of photoelectrons in each PMT is corrected for the light attenuation in water and the acceptance of the
PMT as follows;
"
#
µ
³r
´¶
X
X
GMC
cos
Θ
i
i
obs
α × qi,n
× exp
RT OTn =×−
Si,(B.22)GdataL
f (Θi )
◦
◦
θ
<70
i,n
ti ∈[−50,250]nsec

θi,n <70

whereα: normalization factor.

Gdata , GMC: relative PMT gain parameter for data and MC.

obs
qi,n

: observed number of photoelectrons in the i-th PMT contributed form
the n-th ring.

θi,n: opening angle between the i-th PMT direction and the n-th ring
direction.

ti: time of flight subtracted hit time of the i-th PMT.

L

: light attenuation length in water.

ri: distance from the vertex position to the i-th PMT.

Ph.D. Thesis by Issei Kato, July 2004

B.7. Correction to the number of rings for the events in 1KT (ring correction II)
f (Θi )

: correction function for the PMT acceptance as a function of the photon incident angle into PMT (Θi ).

Si: expected number of photoelectrons in the i-the PMT contributed
from scattered light.

197

The summation is restricted inside the time window of from −50 nsec to +250 nsec around thepeak of the time of flight subtracted hit timing distribution in order to reject the effect of theelectron from muon decay. The relations between RT OT and the momentum of an electron anda muon are estimated by the Monte Carlo simulation, and using these relationship, the value of
RT OT is translated into the momentum of an electron for a e-like ring and that of a muon fora µ-like ring.

B.6

Correction to the number of rings (ring correction)

Finally, the number of rings is corrected in this stage. Mis-fitted rings tend to have low momentum and overlapped with other energetic rings. There are two cuts to reject the mis-fittedrings. The first rejection criteria are(1-a) EA < EB : EA and EB are the visible energy of ring-A and ring-B, respectively,
and(1-b) |θA − θB | < 30◦ : the angle between the direction of the ring-A θA and thatof ring-B θB ,
and
(1-c)

EA cos(θA − θB ) < 60 MeV.

The second rejection criteria areP(2-a) EA / i Ei < 0.05
and(2-b) EA < 40 MeV.
If one of two criteria is satisfied, the ring-A is descarded as a fitting mistake.

B.7

Correction to the number of rings for the events in 1KT(ring correction II)

In addition to the ring correction above, further ring correction is done only in the 1KT reconstruction algorithm, called “ring correction II”. Some events in 1KT contain a few noise hit
PMTs with large charges, in which the ring counting algorithm makes mis-fitting resulting infinding the additional fake ring. A typical event for this kind of mis-fitting is shown in Fig. B.6.
There are two hit PMTs with large charges around the center of the figure, which clearly seemto be noise hits, and the fake ring illustrated by an ellipse of blue thin line had been found dueto the existence of these hits. In order to eliminate such fake rings, the following procedures areapplied to the events with 2 rings in 1KT.
Ph.D. Thesis by Issei Kato, July 2004

198

Appendix B. Event Reconstruction in Water Cherenkov Detectors

NUM
43
RUN
2256
SPIL
42693
SUBRUN
6
EVENT
18523
DATE **-Jan-20
TIME
0:29:51
TOT PE:
894.3
MAX PE:
111.2
NMHIT :
283
ANT-PE:
0.8
ANT-MX:
0.8
NMHITA:
1

1

1

NUM
43
RUN
2256
SPIL
42693
SUBRUN
6
EVENT
18523
DATE **-Jan-20
TIME
0:29:51
TOT PE:
894.3
MAX PE:
111.2
NMHIT :
283
ANT-PE:
0.8
ANT-MX:
0.8
NMHITA:
1

1

1

1

1

1

1

1

1

1

1

90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet**/09/22:;R= 2:NoYet
R :Z : PHI : GOOD
0.99: -1.93: 2.89:0.780
CANG : RTOT : AMOM :MS(pat):AMOME:AMOMM
36.1:
332:
47: 21.3:
18:
180
V= 0.879:-0.247:-0.408
24.0:
119:
17: -2.7:31:205
V= 0.748:-0.389: 0.537
Comnt;
1

1

1

1

1

TRG ID :00000001
TMC Ch1:TMC Ch2:TMC Ch3
0.22: 0.27: 0.89
0.83: 0.89: 1.50
1.61::
T diff.:0.
us
Q thr. :0.0
SUB EV : 0/ 0

1

90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet
90/00/00:NoYet:NoYet**/09/22:;R= 1:NoYet
R :Z : PHI : GOOD
0.99: -1.93: 2.89:0.780
CANG : RTOT : AMOM :MS(pat):AMOME:AMOMM
36.1:
413:
58: 21.3:
58:
244
V= 0.879:-0.247:-0.408
1

1

1

1

TRG ID :00000001
TMC Ch1:TMC Ch2:TMC Ch3
0.22: 0.27: 0.89
0.83: 0.89: 1.50
1.61::
T diff.:0.
us
Q thr. :0.0
SUB EV : 0/ 0

Comnt;

Figure B.6: A typical event in which the ring correction II is applied to and the fake ring is removed
in 1KT. The left figure shows the results of the ring counting before the ring correction II is applied, inwhich the large isolated charge around the center of the display makes a fake ring. However, it is removed
after ring correction II is applied as shown in the right figure.

First, the number of the isolated hit PMTs with large charge, NILQ , is counted. The definitionof “isolated hit PMT with large number of photoelectrons” is(1) the PMTs with the charge of larger than 60 photoelectrons,(2) the PMT which satisfies the condition (1) is located outside the 60◦ cone with respect tothe 1st ring direction,(3) the PMT which satisfies the condition (1) is located inside the 60◦ cone with respect tothe 2nd ring direction,(4) within two neighboring PMT layers, there is only one or two PMTs which satisfies above
three conditions.
Then follwoing cuts are imposed to reject the fake ring.
(3-a) NILQ > 0 in the event.
and(3-b) p2 (e) < 50 MeV/c, where p2 (e) is the reconstructed momentum of 2nd ringwith the assumption that the 2nd ring is e-like.
The 2nd ring of the event which satisfies both of these condition is eliminated as a fake ring due
to isolated hit PMTs with large charge.

Ph.D. Thesis by Issei Kato, July 2004

Appendix C
Systematic Uncertainties in PIMON
Analysis
Systematic errors on the neutrino spectra at ND and SK and F/N ratio due to various sources
are estimated in the PIMON analysis. Here, they are briefly explained. The errors on the
spectra at ND and SK in June 1999 and in Nov. 1999 are separately summarized in Table C.1,
and Table C.2, and the errors on F/N ratio are summarized in Table C.3.
Fitting error
Three errors are quoted on the each data point of the Cherenkov light distributions: The error(R.M.S. of ADC distribution)√. The uncertainty
due to spill-by-spill fluctuation is estimated bynumber of spillsof the PMT gain adjustment is estimated to be 10% and 5% for June 1999 and Nov. 1999 runs,
respectively, as described in Sec. 3.3.1. The uncertainty of lower gain operation in Nov. 1999
run is estimated by the difference between data with gain of 20 and 50 at the same refractive
index n = 1.00129. These errors are fed to the fitting, and hence they are included in the fitting
error.
Mirror reflectivity
The calibration using laser system have confirmed that the mirror reflectivity have no radiation
damage within 6% during the PIMON runs. A few percent of deterioration of the reflectivity
around the beam center considered, the difference of the results are quoted as the systematic
error of the mirror reflectivity.
Refractive index uncertainty
The major contribution to the uncertainty of the refractive index of freon gas is from its wavelength dependence. Two situations are compared: One is that the refractive index calibrated byprimary proton beam is used in the MC, and the other is that the wavelength dependence of therefractive index is included in MC. In both case, the fitting has been performed to reconstruct
the pion kinematics, and the difference between these resules are quoted as the systematic error.
Difference between the low and high beam intensity
As mentioned before, the PIMON data had been taken with the lower beam intensity than in
the normal run. A main difference between the low and high beam intensity is the profile anddivergence of the proton beam. During PIMON runs, the beam profile was about 30% narrower
199

200

Appendix C. Systematic Uncertainties in PIMON Analysis

than that in the normal runs. Using Beam-MC, the difference between the normal and thenarrower beam profile is quoted as the systematic error.
Injection point of the proton beam onto the target
The injection point of the proton beam onto the target during the PIMON runs was the sameas that in the normal runs within 1 mm. The Beam-MC study had been performed in order toestimate the effect of the difference of the beam injection point.
Beam stability during the PIMON run
Proton beam was monitored using V39out- and TGT-SPICs. The fluctuation of the center of the
proton beam during the PIMON runs was about 0.1−0.2 mm. The yield of secondary muons
was monitored by MUMON. It was also stable within 4.6% and 1.4% in June 1999 run andNov. 1999 run, respectively. In order to estimate the systematic errors from them, the proton
injection point was fluctuated at several points and their relusting differences are quoted as theerrors.
Beam stability during the normal run
The uncertainty from the instability of the injection point and the profile of proton beam during
the normal runs is also estimated by employing the MC simulation.
Azimuthal symmetry of the magnetic field inside the horn magnets
In the analysis of PIMON measurements, the azimuthal symmetry of the magnetic field inside
the horn magnets is assumed. As mentioned in Sec. 3.1.2, we had observed asymmetry of
the magnetic field of about 15%, although the measurement of the magnetic field have large
uncertainty. The fitting results with no asymmetry and 15% asymmetry are compared and thedifference is quoted as the systematic errors.
Alignment of the PIMONPIMON is well aligned with respect to the center of the beam line. The results of an opticalsurvey ensures that the height of the mirror is aligned with the precision of within 1 mm, andthe horizontal position is adjusted to the designed beam axis within a few hundred µm. The
systematic errors from the incorrect alignment is negligibly small.
Background subtraction using the mirror-off data
The data with the mirror rotated up to 14.5◦ off from the nominal direction were taken, which
proved that the background components are uniform. The systematic errors from the backgroundsubtraction using the mirror-off data is negligible.
Subtraction of the electro-magnetic components
The shape of the Cherenkov light distribution contributed from the electro-magnetic components
is well reproduced by Beam-MC. Therefore, the error on absolute normalization of the electromagnetic components in the χ2 -fitting is used to estimate the systematic errors on the neutrino
spectrum. It makes only negligibly small effect.
Ph.D. Thesis by Issei Kato, July 2004

201
Fitting method
Different MC are used to make the template histgrams of Cherenkov light distribution to study
the effect of fitting method: Cho-CERN and GCALOR hadron packages and different horncurrents. This difference makes the secondary pion profile and divergence. It had been studied
whether the fitting settled down at the same results even in the case of that the different MC’s
were used. The difference of results is quoted as the systematic errors from the fitting method.
Contrigution of pions decaying before PIMON
The uncertainty of the contribution of the pion decay before PIMON is estimated by comparing
two different hadron models, Cho-CERN and GCALOR.
Radial distribution of pions
Difference of radial distribution of pions affects to the decay probability of pion since some partof pions is absorbed in the wall of the decay volume. This makes the change in the energy
spectrum of the neutrino beam. Using two different hadron models, Cho-CERN and GCALOR,
the effect of the different radial distribution of pions is studied.
Bin size of pion kinematics (p , θ )Flat population inside each (pπ , θπ ) bin is assumed in the PIMON analysis, whereas there is
the structure inside the bin in the actual case. The systematic bias from this assumption isestimated by comparing the full Beam-MC and the Beam-MC with flat bins of (pπ , θπ ).
Uncertainty of neutrino flux below 1 GeVPIMON cannto predict the neutrino flux below 1 GeV. As mentioned in the previous section,
the errors on the neutrino flux in the region below 1 GeV are estimated using the Beam-MC byvarying the value of parameters in Eq. (4.4) within 90% C.L.

Ph.D. Thesis by Issei Kato, July 2004

202

Appendix C. Systematic Uncertainties in PIMON Analysis

Table C.1: Summary of systematic errors of the PIMON measurements on the spectra at ND and SK
in June 1999. Upper table shows the errors at ND and lower table shows those at SK. In the table,“—” means negligibly small error.
Errors on neutrino spectrum at near detector in June 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0 1.0−1.5
1. Fitting error±11.7%
2. Mirror reflectivity−1.4%
3. Refractive index—
4. PMT saturation correction±0.5%
5. Low/high beam intensity−5.5%
6. Beam injection point−1.5%
7. Beam stability (PIMON run)
±1.9%
8. Beam stability (normal run)—
9. φ asymmetry of horn field−2.9%—
10. PIMON alignment
11. Subtraction of background—
12. Subtraction of EM component—
13. Fitting method+6.8%
14. Pion decay before PIMON±0.9%
15. Radial distribution of pions±0.2%
16. Binning of pion kinematics+2.0%+13.9%
Total−13.6%

1.5−2.0
±9.2%
+4.2%
—
±1.2%
±1.0%
+6.8%
±4.3%
—
−0.9%
—
—
—
−7.7%
±1.9%
±0.4%
−2.7%

2.0−2.5±17.2%−3.5—±1.4%+10.0%−10.0%±5.0%+0.8%+32.6%———−15.3%
±2.8%
±2.3%
−7.2%

2.5−
+25.1%−8.7%—+30.0%+7.0%+8.9%±12.7%+13.2%−13.3%+39.0%−27.0%+49.0%−88.0%

Errors on neutrino spectrum at Super-Kamiokande in June 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0 1.0−1.5
1. Fitting error±14.7%
2. Mirror reflectivity−1.6%
3. Refractive index—
4. PMT saturation correction±0.8%
5. Low/high beam intensity−7.0%
6. Beam injection point−2.5%
7. Beam stability (PIMON run)
±3.2%
8. Beam stability (normal run)
+1.2%
9. φ asymmetry of horn field−2.4%—
10. PIMON alignment
11. Subtraction of background——
12. Subtraction of EM component
13. Fitting method+11.0%
14. Pion decay before PIMON±2.3%
15. Radial distribution of pions—−1.4%
16. Binning of pion kinematics+18.8%
Total−17.2%

1.5−2.0
±9.6%
+3.1%
—
±1.2%
±6.5%
+9.1%
±3.7%
−1.9%
−7.5%
—
—
—
−10.2%
±5.7%
±0.2%
−2.7%

2.0−2.5±19.3%
−0.7
—
±2.0%
+4.5%
−10.0%±5.0%

2.5−+26.7%−9.0%—+20.0%+6.5%+3.6%±12.8%

+1.8%
−1.0%

+38.8%———−12.3%
±6.3%
±1.4%
−7.4%

+4.2%
−4.3%

−10.7%——−60.0%+15.2%−18.8%+44.4%−27.1%+42.3%−77.5%

Ph.D. Thesis by Issei Kato, July 2004

+3.8%
−3.2%

−19.0%——−74.0%+12.0%−21.0%±1.3%±20.0%
−1.3%

+1.6%
32.0%

±0.4%
±21.0%−13.0%

203

Table C.2: Summary of systematic errors of the PIMON measurements on the spectra at ND and SK
in Nov. 1999. Upper table shows the errors at ND and lower table shows those at SK. In the table,“—” means negligibly small error.
Errors on neutrino spectrum at near detector in Nov. 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0 1.0−1.5
1. Fitting error±6.2%
2. Mirror reflectivity−2.0%
3. Refractive index−5.1%
4. PMT saturation correction—
5. Low/high beam intensity−1.2%
6. Beam injection point—
7. Beam stability (PIMON run)—
8. Beam stability (normal run)
±1.0%
9. φ asymmetry of horn field−3.6%—
10. PIMON alignment
11. Subtraction of background—
12. Subtraction of EM component—
13. Fitting method+6.8%
14. Pion decay before PIMON±0.2%
15. Radial distribution of pions±0.5%
16. Binning of pion kinematics
+2.7%
+9.2%
Total
−9.6%

Errors on neutrino spectrum at Super-Kamiokande in Nov. 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0 1.0−1.5
1. Fitting error±8.1%
2. Mirror reflectivity−3.1%
3. Refractive index−8.6%
4. PMT saturation correction—
5. Low/high beam intensity−2.1%
6. Beam injection point—
7. Beam stability (PIMON run)—
+1.6%
8. Beam stability (normal run)
−2.1%
9. φ asymmetry of horn field−5.7%—
10. PIMON alignment
11. Subtraction of background——
12. Subtraction of EM component
13. Fitting method+11.0%
14. Pion decay before PIMON±0.5%
15. Radial distribution of pions
±0.5%
+0.5%
16. Binning of pion kinematics
Total±13.8%

1.5−2.0
±4.8%
+2.9%
+7.3%
—
+0.6%
−2.0%
—

2.0−2.5
±7.7%
+3.4
+4.6%
—
+4.0%
—
—

2.5−
±12.0%+0.6%+37.0%
—
+5.0%
−4.8%
±5.5%

+1.0%
−1.9%

+4.4%
−1.1%

+6.3%
−3.4%

+5.2%
—
—
—
−7.7%
±0.8%
±1.0%
−2.4%

+0.7%
—
—
—
−15.3%
±0.5%
±4.3%
−7.0%

−10.6%———+10.7%−9.9%+12.1%−17.7%+47.7%−34.0%

1.5−2.0
±4.9%
+1.8%
+5.4%
—
−1.5%
—
—

2.0−2.5
±7.6%
+4.0
+1.1%
—
+3.1%
—
—

2.5−
+12.0%
+0.3%
33.0%
—
+7.8%
4.9%
4.8%

+0.3%
−1.5%

+4.1%
−1.6%

+16.0%−0.2%+12.0%−21.0%±0.4%±20.0%−10.0%+2.5%———−10.2%
±1.5%
±0.5%
−2.4%

+0.7%
—
—
—
−12.3%
±1.1%
±3.1%
−5.4%

+9.8%
—
—
—
—
±10.0%−15.4%+8.1%−11.9%+10.6%−15.8%+42.1%−39.5%

+1.6%
32.0%

Ph.D. Thesis by Issei Kato, July 2004

204

Appendix C. Systematic Uncertainties in PIMON Analysis

Table C.3: Summary of systematic errors of the PIMON measurements on the far-to-near spectrum
ratio in June 1999 and Nov. 1999. Upper table shows the errors in June 1999 and lower table shows
those in Nov. 1999. In the table, “—” means negligibly small error.
Errors on far-to-near spectrum ratio in June 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0
1. Fitting error
2. Mirror reflectivity
3. Refractive index
4. PMT saturation correction
5. Low/high beam intensity
6. Beam injection point
7. Beam stability (PIMON run)
8. Beam stability (normal run)
9. φ asymmetry of horn field
10. PIMON alignment
11. Subtraction of background
12. Subtraction of EM component
13. Fitting method
14. Pion decay before PIMON
15. Radial distribution of pions
16. Binning of pion kinematics
+5.1%
+7.3%
17. Hadron production model (MC)
−9.5%
−2.5%
+5.1%
+7.3%
Total
−9.5%
−2.5%

Errors on far-to-near spectrum ratio in Nov. 1999
Energy bins [GeV] 0.0−0.5 0.5−1.0
1. Fitting error
2. Mirror reflectivity
3. Refractive index
4. PMT saturation correction
5. Low/high beam intensity
6. Beam injection point
7. Beam stability (PIMON run)
8. Beam stability (normal run)
9. φ asymmetry of horn field
10. PIMON alignment
11. Subtraction of background
12. Subtraction of EM component
13. Fitting method
14. Pion decay before PIMON
15. Radial distribution of pions
16. Binning of pion kinematics
+5.1%
+7.3%
17. Hadron production model (MC)
−9.5%
−2.5%
+5.1%
+7.3%
Total
−9.5%
−2.5%

Ph.D. Thesis by Issei Kato, July 2004

1.0−1.5

1.5−2.0

2.0−2.5

2.5−

+3.2%
−4.5%

+6.2%
−4.9%

+2.0%
−5.7%

+8.5%
−5.8%

−0.1%
—
±0.6%
−6.0%
−1.0%
±1.0%

±3.8%
—
—

±3.4%
±1.0%
—

−0.3%
—
±4.2%
±0.5%
−4.8%
±1.1%
−3.4%
+4.9%
—
—
+72.0%−14.5%±1.6%±7.2%−13.0%

+5.5%
−7.8%

+7.8%
−11.3%+8.7%−11.2%+73.6%−22.8%

1.0−1.5

1.5−2.0

2.0−2.5

2.5−

+2.2%
−2.9%

+2.2%
−2.1%

+3.2%
−2.9%

+1.0%
−0.9%

+0.7%
−0.3%

+0.5%
—
—
—
+4.0%
±1.4%
—
−0.6%

+0.4%
—
±0.5%
−5.3%
+2.1%
±1.5%
−2.3%
−6.7%
—
—
—

+3.5
—
±1.3%
−6.6%
−0.6%
±3.4%

+1.4%
−3.0%

+3.2%
−4.6%

+0.9%
−1.5%

+4.7%
—
—
—

−1.2%
−3.7%
—
−1.9%
—
—

−1.1%
−1.8%
—
−3.7%
+1.2%
—

+0.5
−3.3%
—
−1.9%
—
—

−2.6%
—
—
—
+4.0%
±0.7%
—
−2.1%

−2.4%
—
—
—

−2.4%
—
—
—

+1.4%
−3.0%

±0.7%
±0.5%
—

+3.2%
−4.6%

±1.7%
±1.3%
+1.7%

−0.3%
−2.6%
—
+2.9%
—
±0.5%
+9.0%
−1.0%
—
—
—
−14.5%
±0.5%
±8.5%
−7.1%

+1.6%
−1.8%

+1.5%
−2.1%

+1.2%
−1.4%

+4.9%
−6.5%

+3.3%
−6.5%

+5.4%
−7.5%

+12.8%−18.5%

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