K U

S  νµ → νe   -  A              

D  P

B
S Y
K, J
J 2006

Abstract
We report a search for νµ → νe oscillation with the KEK to Kamioka (K2K)
long-baseline neutrino oscillation experiment.
The evidence for neutrino oscillations has been provided by a series of experiments. In our current knowledge of the three-flavor framework, the neutrino flavor mixing is described by two parameters of mass-squared difference(∆m2solar , ∆m2atm ), three mixing angles (θ12 , θ23 , θ13 ) and a CP phase (δ). As yet,there is no measurement of the mixing angle θ13 but just a limit of < 12◦ .
In the K2K experiment, we search for νµ → νe oscillation in an acceleratorproduced muon neutrino beam which results from non-zero value of θ13 . The
neutrino beam is produced by KEK’s proton synchrotron and directed toward
the Super-Kamiokande detector (SK) 250 km away. We analyzed the entire data
sample of 9.2 × 1019 protons on target. In the search for νe appearance, the background events from a neutral pion are the most significant in SK. We developed
a new reconstruction algorithm to reject a neutral pion more efficiently. With thenew π0 rejection cut, we have achieved the background suppression by 70% andimproved the sensitivity to νµ → νe oscillation.
We have searched for a signal of νµ → νe oscillation among one hundred andtwelve beam neutrino events observed in SK. We observe one single candidate
event, which is consistent with the background expectation of 1.7 events. Since
we find no evidence of νµ → νe oscillation, we set the limit on the νµ → νeoscillation parameters. In a two-flavor approximation, we set a constraint on
νµ → νe neutrino oscillation as sin2 2θµe < 0.13 [90% confidence level (C.L.)] at the∆m2 region of 2.8 × 10−3 eV2 . For the higher ∆m2 region, the more stringent limitof sin2 2θµe < 0.10 is obtained. Further, we set the upper limit of sin2 2θ13 < 0.26
(90% C.L.) on the assumption of the relation sin2 2θ13 ' 2 sin2 2θµe . Our result is
consistent with the results from the reactor ν̄e experiments over a few km baselinethat show the lack of observed disappearance of ν̄e .

Acknowledgment

I am most grateful for the support and encouragement of many people. I realizethat my research have relied on their joint efforts, therefore, this thesis is humbly
dedicated to them.
First of all, I would like to express my great appreciation to Prof. Koichiro Nishikawa
for the opportunity to do research with the K2K experiment. His encouragement was always a boost to my research and carried me through. I give my
special thanks to Prof. Tsuyoshi Nakaya for his guidance on various occasions.
His wise advices during my Ph.D. experience led me to a new perspective on
physics. I also give my special thanks to Prof. Kenji Kaneyuki. He gave me
advisory opinions on my study with the Super-K data. I am deeply thankful to
Dr. Masashi Yokoyama for his unstinting support. He guided me in my researchand kindly worked as a proofreader for my articles every time. I thank a special colleague, Dr. Masaya Hasegawa, for useful discussions, keen humor andfriendship. I look forward hopefully to the day when we collaborate again.
The years spent at KEK have been an incredible part of my life. I received
an excellent education as well as a great pleasure. I address my thanks to
Dr. Hirokazu Maesaka for his considerable efforts to the construction and operation of the SciBar detector. I was pleased at having a wonderful time withhim. I owe Dr. Makoto Yoshida a debt of gratitude for his strong support.
He generously served as assistant to me any number of times. I would liketo thank Prof. M. Tanaka for giving me hard but stimulating works on the development of electronics at the SciBar detector. I also thank Mr. T. Murakami;
without his support, I would never have completed them. I would be gratefulto Dr. A. K. Ichikawa for her considerable efforts to the construction of SciBar. I
also learned the basic skills in experimental physics from her. I give thanks to
Dr. K. Nitta for his support, encouragement and all the good times. I am mostiii

thankful to Dr. Y. Takubo. I received a lot of surprises and pleasures when weclosely cooperated. I am also thankful to Mr. T. Morita and Mr. T. Sasaki for theircooperation and friendships. I often had a pleasant dinner with Prof. Y. Hayato, Dr. M. Yoshida, Dr. H. Yokoyama and Mrs. M. Sekiguchi; I would like tothank them a lot. I again thank Prof. Y. Hayato for his support and passing theinteresting information about my favorite pastimes on to me.
In addition, my research is supported by many colleagues in the K2K collaboration. I express my thanks to the directors of Prof. Y. Totsuka, Prof. K. Nakamura,
Prof. Y. Suzuki, Prof. C. K. Jung and Prof. R. J. Wilkes, and the devoted membersof Prof. T. Kobayashi, Prof. M. Sakuda, Dr. T. Iwashita Dr. T. Ishida, Dr. T. Ishii,
Dr. J. H. Choi, Dr. Y. Ooyama, Dr. T. Nakadaira, Prof. Y. Itow, Prof. M. Shiozawa,Dr. M. Miura, Dr. Y. Obayashi, Dr. J. Kameda, Dr. S. Nakayama, Dr. S. Yamada,
Dr. S. Mine, Dr. T. Hasegawa and Dr. T. Maruyama. I address special thanks to
Prof. K. Sholberg, Prof. D. Kielczewska and Ms. J. Zalipska for their useful suggestions in the paper publication committee. I offer additional thanks to Mr. R. Terrifor his help in proofreading the thesis.
I must extend thanks to all of the past and present staffs and colleagues in
the high energy physics group at Kyoto University for memorable days and theirkindnesses: Prof. K. Nishikawa, Prof. N. Sasao, Prof. T. Nakaya, Prof. H. Sakamoto,
Dr. R. Kikuchi, Dr. T. Nomura, Dr. H. Nanjo, Dr. M. Yokoyama, Dr. H. Tanaka,
Dr. H. Sato, Mr. M. Suehiro, Mr. T. Fujiwara, Dr. T. Inagaki, Dr. H. Sakai, Dr. Y. Ushiroda, Dr. S. Nishida, Dr. I. Kato, Dr. Y. Honda, Dr. H. Maesaka, Dr. K. Mizouchi,
Ms. K. Uchida, Mr. M. Hasegawa, Mr. T. Sumida, Mr. S. Tsuji, Mr. K. Maeda,
Mr. K. Hayashi, Mr. H. Morii, Mr. T. Morita, Mr. S. Ueda, Mr. T. Sasaki, Mr. K. Hiraide, Mr. J. Kubota, Ms. T. Taniguchi, Mr. T. Shirai, Ms. K. Takezawa, Mr. H. Yokoyama,
Mr. K. Ezawa, Mr. Y. Kurimoto, Mr. Y. Kurosawa, Mr. Y. Nakajima, Mr. T. Nobuhara,
Mr. K. Matsuoka, Mr. M. Taguchi, Mr. S. Gomi, Mr. H. Kawamuko, Mr. H. Kubo,
Mr. K. Shiomi, Mr. T. Usuki and the secretary Ms. A. Nakao. Dr. I. Kato kindly
initiated me into experimental physics with his encouragement. I spent a happy
academic career with Mr. T. Sumida, and hope to work together before long.
I am afraid that I cannot include every single person who significantly contributed to my research life, but I wish to thank everyone equally.
Finally, I gratefully acknowledge a lot of support from my immediate family
for years.
iv

Contents
Abstracti

Acknowledgmentii

Contentsiv

pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp 1

2

Introduction
1.1 Physics of neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Massive neutrinos . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Neutrino oscillations in a vacuum . . . . . . . . . . . . . . .
1.2 Search for neutrino oscillation . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Mixing parameters measured by various neutrino oscillation experiments. . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Unsettled subjects on neutrino flavor mixing . . . . . . . . .
1.3 Motivation for νµ → νe search . . . . . . . . . . . . . . . . . . . . . .

6
8
10

The K2K experiment
2.1 Experimental goal and design . . . . . . . . . . . . . . . . . . . . . .
2.2 Experimental components . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Primary proton beam . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Neutrino beam and monitors . . . . . . . . . . . . . . . . . .
2.2.3 Near detector complex . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Super-Kamiokande, the far detector . . . . . . . . . . . . . .
2.2.5 Timing synchronization system . . . . . . . . . . . . . . . . .

11
11
13
14
16
18
22
24

v

1
1
2
3
5

CONTENTS
2.3

Experimental phases and data sample . . . . . . . . . . . . . . . . .

24

3

Simulations
3.1 Neutrino flux calculation . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Primary proton beam . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Pion production in the aluminum target . . . . . . . . . . . .
3.1.3 Particle tracking in the neutrino beam line . . . . . . . . . .
3.1.4 Neutrino energy spectrum . . . . . . . . . . . . . . . . . . . .
3.2 Neutrino interaction simulation . . . . . . . . . . . . . . . . . . . . .
3.2.1 Nuclear effects . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Water Cherenkov Detector simulation . . . . . . . . . . . . . . . . .

29
29
29
30
30
31
33
33
36

4

Outline of analysis
4.1 Signature of νµ → νe oscillation . . . . . . . . . . . . . . . . . . . . .
4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Search for νµ → νe oscillation . . . . . . . . . . . . . . . . . . . . . .

39
39
39
41

5

Expected number of beam neutrino events at SK
5.1 Neutrino interaction rate at the 1KT detector . . . . . . . . . . . . .
5.1.1 Event selection in the 1KT detector . . . . . . . . . . . . . . .
select5.1.2 Corrections on N1KT
. . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Event rate summary . . . . . . . . . . . . . . . . . . . . . . .
5.1.4 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . .
5.2 νµ energy spectrum measurement at the near site . . . . . . . . . . .
5.2.1 Measured neutrino energy spectrum at near site . . . . . . .
5.3 Near-to-far spectrum extrapolation . . . . . . . . . . . . . . . . . . .
5.3.1 The HARP experiment . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Neutrino flux prediction . . . . . . . . . . . . . . . . . . . . .
5.3.3 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . .
5.3.4 Estimated neutrino energy spectrum at SK . . . . . . . . . .
5.4 Prediction of the number of neutrino events at SK . . . . . . . . . .

43
43
44
45
46
46
48
49
52
52
53
55
56
58

6

Selection of beam neutrinos in SK
6.1 Selection of beam neutrino events in SK . . . . . . . . . . . . . . . .
6.1.1 Selection of neutrino events in SK . . . . . . . . . . . . . . .
6.1.2 Reconstruction of neutrino event . . . . . . . . . . . . . . . .

61
61
61
63

vi

CONTENTS
6.1.3

Selection of fully-contained events in the fiducial volume of
SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Beam neutrino selection with GPS information . . . . . . . .
6.1.5 Observed FCFV events . . . . . . . . . . . . . . . . . . . . . .
Selection of electron signal candidates in the fully-contained events
6.2.1 Single-ring event selection . . . . . . . . . . . . . . . . . . . .
6.2.2 Shower-type ring selection . . . . . . . . . . . . . . . . . . .
6.2.3 Visible energy cut . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 No decay electron . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64
66
66
68
69
70
71
71
74

7

Rejection of neutral pion background
7.1 Characteristics of π0 background event . . . . . . . . . . . . . . . . .
7.2 Reconstruction algorithm of the π0 fitter . . . . . . . . . . . . . . . .
7.2.1 Expected charge distribution . . . . . . . . . . . . . . . . . .
7.2.2 Finding the best-fit ring configuration . . . . . . . . . . . . .
7.3 Performances of π0 reconstruction . . . . . . . . . . . . . . . . . . .
7.4 e/π0 separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 Validation of π0 fitter with atmospheric neutrinos . . . . . . . . . .
7.6 π0 rejection for the K2K data sample . . . . . . . . . . . . . . . . . .
7.7 Summary of data reduction . . . . . . . . . . . . . . . . . . . . . . .

77
77
79
80
81
84
85
87
93
94

8

Estimate of systematic uncertainties
101
8.1 Expectation of the number of events in SK . . . . . . . . . . . . . . . 101
8.2 Uncertainties of normalization . . . . . . . . . . . . . . . . . . . . . 103
8.3 Uncertainties of neutrino interaction cross-sections . . . . . . . . . . 105
8.4 Uncertainties of selection efficiency . . . . . . . . . . . . . . . . . . . 107
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

9Constraint on neutrino oscillation parameters
115
9.1 Calculation of upper limits . . . . . . . . . . . . . . . . . . . . . . . . 115
9.1.1 Confidence interval with the unified method . . . . . . . . . 117
9.2 Handling of systematic uncertainties . . . . . . . . . . . . . . . . . . 118
9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.3.1 Check with an alternative approach . . . . . . . . . . . . . . 120
9.3.2 Effect of the systematic uncertainty . . . . . . . . . . . . . . . 120

6.2

6.3

vii

CONTENTS
9.4

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.4.1 Comparison with past experimental results . . . . . . . . . . 122
9.4.2 Future prospect of mixing angle θ13 . . . . . . . . . . . . . . 124

10 Conclusions127

pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp 

A Neutrino interaction simulation
129
A.1 Neutrino interaction simulation . . . . . . . . . . . . . . . . . . . . . 129
A.1.1 CC quasi-elastic scattering and NC elastic scattering . . . . 129
A.1.2 Resonance production of single meson . . . . . . . . . . . . 132
A.1.3 Multi-meson production . . . . . . . . . . . . . . . . . . . . . 132
A.1.4 Coherent pion production . . . . . . . . . . . . . . . . . . . . 135
B Verification of the νe flux prediction with SciBar
137
B.1 The SciBar detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B.2 νe flux measurement by SciBar . . . . . . . . . . . . . . . . . . . . . . 140
B.2.1 Comparison with the beam MC prediction and the LG measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
C Comment on the far/near flux ratio
145
C.1 Shape of the far/near flux ratio . . . . . . . . . . . . . . . . . . . . . 145
C.2 Possibility of employing near detectors which cover the same geometrical acceptance as SK . . . . . . . . . . . . . . . . . . . . . . . . 147
D Decay-electron identification

149

E Comment on the surviving events before the π0 rejection

151

References

153

viii

Chapter 1
Introduction
1.1

Physics of neutrinos

The Standard Model of particle physics has been extremely successful in describing the interactions and properties of fundamental particles. However, up tonow, we recognized that some experimental results cannot be explained within
the framework of the current theory. Neutrino oscillation is one such subject.
The Standard Model defines a neutrino to be a spin 1/2 fermion; it is colorlessand caries zero electromagnetic charge and weak isospin of +1/2. Therefore, theneutrino can only interact via the weak current. It is a lepton, and exists in threeflavors: νe , νµ and ντ . Up to now, various experiments have been performed
to measure the masses of neutrinos directly [1, 2, 3, 4]. Currently, there is noevidence for a finite neutrino mass, but the smallness of their masses is indicated.
However, there were disagreements between the measured neutrino fluxes andthe theoretical predictions in the observations of neutrinos produced in the sun
and the earth’s atmosphere. One possible solution to these anomalies is drawn
up with the phenomenon of flavor mixing in neutrinos, which is caused by finite
neutrino masses. In 1967, Pontecorvo first considered the consequences of thisphenomena which describes quark mixing. He advocated that neutrinos havea finite mass, where the weak and mass eigenstates are not identical and thenformulated a mixing between neutrinos as well as quarks.
In this section, we introduce massive neutrinos as an extension to the Standard
Model and explain neutrino oscillations.
11.1. PHYSICS OF NEUTRINOS

1.1.1

Massive neutrinos

Massive neutrinos can be introduced with only a minor extension to the Standard
Model. Neutrino masses can appear in two ways: as the Dirac mass term in the
Lagrangian or introducing the Majorana mass term.
The Dirac term assumes that a particle and its antiparticle are different, which
involves transitions between right- and left-handed states. That is, the righthanded neutrino νR is different from its charge conjugation νCR which is the CPT
partner of νL . The Dirac mass term (LD ) is formulated as
LD = mD νν(1.1)= mD (νL νR + νR νL ),(1.2)

where the Dirac field ν is defined as ν ≡ νL + νR . Thus, Dirac neutrinos have four
components, νL , νCR , νR and νCL , and conserve the lepton number.
Alternatively, a neutrino can be its own antiparticle as (νL )C = νCR because
neutrinos are neutral particles. Such a particle is called a ”Majorana” particle. A
Majorana neutrino causes a transition between a neutrino and an anti-neutrino,
which violates lepton number conservation. The form of a Majorana mass term(LM ) isLM = mM χχ
=

(1.3)

C
mM (νL νCR + νR νL )(1.4)

where χ is the self conjugate field χ = νL + νCR satisfying χ = χC .
In order to incorporate the neutrino mass into the Standard Model, we introduce a SU(2) singlet νR . Since the right-handed neutrino does not interact (sterile
neutrino), it is possible to describe a scenario in which both Dirac and Majorana
mass terms are present. Expressing νL and νR in terms of the self-conjugate fields
χ and ω as χ = νL + (νL )C and ω = νR + (νR )C , we can write the Lagrangian forneutrino masses as follows:
L = nL MnL + h.c.,

(1.5)

!
χ
,
ω

(1.6)

where
nL =
M =

!
mL mD /2,
mD /2 mR
2

(1.7)

CHAPTER 1. INTRODUCTION
mL and mR are the Majorana masses associated with the left and right handed
neutrinos, respectively, and h.c. means the Hermite conjugate of the first term.
Diagonalizing M to diag(m1 , m2 ) yields:
m1,2 =q1(mR + mL ) ± (mR − mL )2 + m2D ,
2
χ
ω

!
=

cos θ sin θ− sin θ cos θ

!

η1
η2

(1.8)

!
,

(1.9)

D
where η1,2 is the mass eigenstate and the mixing angle θ is given by tan 2θ = mRm−m.
L

Seesaw mechanism
Considering the case where mL = 0 and mR  mD , we obtain mass eigenstates as
m1 ∼

m2D
mR

,

m2 ∼ mR .

(1.10)

This indicates that a Dirac mass due to νL and a heavier mass due to νR can cause
a very light mass state m1 and a very heavy m2 . This special case is known as
the seesaw mechanism [5, 6], and it provides an explanation to the small neutrino
masses.

1.1.2

Neutrino oscillations in a vacuum

Introducing massive neutrinos to the Standard Model, we can consider the mixingof flavors between them. Assuming that neutrinos have the Dirac mass with threemass eigenstates νi , i = 1, 2, 3, each with a mass mi , the neutrino flavor eigenstates
can be written as linear combinations of them:Xνα =Uαi νi ,(1.11)

i=1,2,3

where α and i are the indexes of the flavor eigenstates (νe , νµ , ντ ) and the mass
eigenstates (ν1 , ν2 , ν3 ), respectively. Uαi is an unitary matrix known as the MakiNakagawa-Sakata (MNS) matrix, which can be parametrized in the same way as3

1.1. PHYSICS OF NEUTRINOS
the Cabibbo-Kobayashi-Maskawa matrix for quark mixing:




s13 e−iδ   c12 s12  c13
 1
 

 







U = 
c23 s23  1  −s12 c12




 


1
−s23 c23−s13 eiδc13
c13 c12c13 s12s13 e−iδ =  −c23 s12 − s13 s23 c12 eiδ c23 c12 − s13 s23 s12 eiδ c13 s23  ,s23 s12 − s13 c23 c12 eiδ −s23 c12 − s13 c23 s12 eiδ c13 c23(1.12)

where ci j ≡ cos θij , sij ≡ sin θi j , θi j is the mixing angle for each flavor, and δ is acomplex phase which causes the CP violation.
Now we consider the time evolution of a state that is in a flavor eigenstate να
at t = 0. The initial state is represented asX
Uαi |νi i .
(1.13)|να (t = 0)i =i

The time evolution of the state depends on its energy eigenvalues, and is represented asX
Uαi e−iEi t |νi i ,(1.14)|να (t)i =i

E2i = p2 + m2i ,(1.15)

where p and m1,2,3 are the neutrino momentum and masses, respectively. Here,the probability that a neutrino in a flavor eigenstate να at t = 0 is observed as νβ attime t, (Pα→β ), is formulated asDE2
Pα→β =(1.16)νβ (t)|να (0)
X D
E2
†
=
νβ (0)|Uβi e−iEi t Uαi|να (0)
i

X
=

2

X

Uαi Uβi +i∗
Uαi UβiUα∗ j Uβ j e−i(Ei −E j )t .

i, j

As a consequence of flavor mixing for massive neutrinos, the flavor transition
phenomenon, called ”neutrino oscillations,” could take place.
It is instructive to describe the probabilities in the framework of two-flavor
mixing. Considering two flavors of να and νβ , the matrix U is given as follows:!
cos θ sin θU=.
(1.17)− sin θ cos θ
4CHAPTER 1. INTRODUCTION
The probability for να → νβ oscillation is given as2P(να → νβ ) = sin 2θ sin

2!
(Ei − E j )t.
2

(1.18)

Making an approximation of Ei ∼ p + m2i /2p and including the factors of ~ and c,
the probability is formulated as

2P(να → νβ ) = sin 2θ sin

2!
1.27∆m2 [eV2 ]L[km],
E[GeV](1.19)

where ∆m2 ≡ m2j − m2i is the mass-squared difference and L is the flight length ofneutrino.
If the neutrino mass states mix together and their eigenvalues are different,
that is θ , 0 and ∆m2 , 0, neutrinos can change their flavor during travel. Thus,
the observation of neutrino oscillation gives an evidence for the finite neutrino
mass. The oscillation amplitude is characterized by the mixing angle θ and themass-squared difference ∆m2 , and expressed as a function of L/E. The oscillation
effect is enhanced to the maximum when the following condition is satisfied:
L [km]π=.
E [GeV] 2.53 · ∆m2 [eV2 ]1.2(1.20)

Search for neutrino oscillation

Currently, there is no theoretical prediction on neutrino masses, and many experiments have been performed to probe the masses of neutrinos. Up to now, theevidence for neutrino oscillations has been discovered by various experiments.
The neutrino oscillation experiments measure the sizes of the squared-mass differences and the mixing angles; these are called ”oscillation parameters”. Figure 1.2
shows the regions of neutrino oscillation parameter space allowed or excluded
by various experiments. In this chapter, we introduce neutrino oscillation experiments and summarize our current knowledge of the oscillation phenomena.
51.2. SEARCH FOR NEUTRINO OSCILLATION

Figure 1.1: The regions of ∆m2 andmixing angle allowed or excluded byvarious experiments.

1.2.1

Mixing parameters measured by various neutrino oscillation experiments.

∆m2solar region (10−5 ∼ 10−4 eV2 ) :The electron neutrinos created in the sun have been measured by several experiments: Homestake [7], Kamiokande [8], SAGE [9], GALLEX [10], GNO [11],SK [12] and SNO [13]. All of these experiments observed a deficit of solar neutrino fluxes compared with the prediction of the standard solar model. Because
the energy of solar neutrinos is in the range from 0 to 15 MeV and the flight lengthis ∼ 1018 km, a small ∆m2 region (down to 10−11 eV2 ) can be probed according toEquation 1.20.
Thanks especially to the flux measurements by SNO and SK, we understoodthat the solar neutrino oscillation is described by the LMA-MSW solution [14].
The solar neutrino results have been also confirmed with the spectral distortionand the flux reduction of reactor ν̄e measured by the KamLAND experiment [15].
Combining the KamLAND result with solar neutrino measurements, the param6

CHAPTER 1. INTRODUCTION
eters of neutrino oscillation νe → νx are constrained to be
7.4 × 10−5 < ∆m2solar < 8.6 × 10−5 [eV2 ],(1.21)

0.37 < tan2 θsolar < 0.54,(1.22)

at 95% confidence level (C.L.).
∆m2atm region (∼ 10−3 eV2 ) :High energy primary cosmic-rays interacting with the atmosphere produce a cascade of secondary particles, mostly pions and kaons, whose decay chains resultin a high flux of neutrinos called ”atmospheric neutrinos”. In the ∆m2 regionof 10−3 ∼ 10−2 eV2 , evidence for neutrino oscillations has been given in the atmospheric neutrino experiments [16, 17]. The energy spectrum of atmospheric
neutrinos is in the range 0.1 − 100 GeV, and the flight length of neutrinos detected on the surface of the earth ranges from 101 km to 104 km. Due to thesecharacteristics, we can probe neutrino oscillations with the sensitivity down to∆m2 ∼ 10−5 eV2 . The SK collaboration found that the zenith angle distributionsof muon neutrinos are asymmetric [16]. The SK collaboration also reported theobservation of an oscillatory signature with L/E dependence [17]. It is well described by the hypothesis that νµ oscillates to ντ with a probability of nearly 100%.
Long-baseline experiments with a muon neutrino beam, such as K2K [18] andMINOS [19], also confirmed the SK results by measuring the spectral distortionand the reduction of νµ flux during travel. In the two-flavor mixing framework,
the neutrino oscillation parameters of νµ → ντ are constrained to be
1.9 × 10−3 < ∆m2atm < 3.1 × 10−3 [eV2 ],(1.23)

sin2 2θatm > 0.90,(1.24)

at 90% C.L.
The results from atmospheric neutrino experiments imply the probability ofνµ → νe oscillation is small. The null results of disappearance of reactor ν̄e by
CHOOZ [20] and Palo-Verde [21] also limit the probability of νµ → νe oscillation,
assuming CPT invariance P(ν̄e → ν̄µ ) = P(νµ → νe ).
7

1.2. SEARCH FOR NEUTRINO OSCILLATION∆m2LSND region (∼ 1 eV2 ) :There is another report on neutrino oscillation from LSND. LSND is an accelerator
experiment with ν̄µ and observed an excess of ν̄µ → ν̄e signal events. In thethree-flavor framework, there are only three mass-squared differences and thesum of them is zero. Up to now, two of three are measured by solar neutrino,
atmospheric neutrino and long-baseline experiments experiments as describedabove; these results indicate that the maximum one (= ∆m2solar + ∆m2atm ) is nearto ∆m2atm considering ∆m2atm  ∆m2solar . The LSND result indicates that ∆m2 of∼ 1 eV2 (, ∆m2atm ), which is inconsistent with our expectation. This result requires
the extension of the neutrino mixing framework with more than three neutrinos
where a sterile neutrino is added to three active ones. However, the KARMEN
experiments [22], which has a similar experimental sensitivity as LSND, showednull results on ν̄µ → ν̄e oscillation. This issue is being addressed by the MiniBooNE
experiment [23], whose purpose is to confirm or reject the LSND result.

1.2.2

Unsettled subjects on neutrino flavor mixing

If we assume the framework of three active neutrinos, solar neutrino oscillation
occurs mainly with a small mass-squared difference:∆m2solar ≡ m22 − m21 = ∆m221 (> 0).

(1.25)

Results from atmospheric neutrino experiments imply that there is a small component of νe in the ν3 mass eigenstate, and the observed mass-squared differenceis larger than that of solar neutrinos (∆m2atm  ∆m2solar ). Because the states of m1
and m2 are closely spaced, ∆m2atm is represented as∆m2atm ≡ m23 − m22 = ∆m232 ∼ ∆m231 .

(1.26)The sign of ∆m232 (or ∆m231 ) is still unknown, and there is two possibilities ofmass hierarchy: m1 < m2 < m3 (called normal hierarchy) or m3 < m1 < m2 .
Figure 1.2 show the current understanding of the squared-mass spectrum in theframework of three active neutrinos and the normal mass hierarchy. We use theparameterized form of MNS matrix to identify the measured mixing angles asθ12  θsolar , θ23  θatm .
Up to the present, the unsettled subjects on the neutrino flavor mixing are:• Size of the mixing angle θ13 ,8

CHAPTER 1. INTRODUCTION

ν3∆m2atm

m2
ν2
ν1

-3

∆m2solar
νe

νµ ντ

2

(2~3×10 eV )-52(~8×10 eV )Figure 1.2: Squared-mass spectrum in three-neutrino framework. For each mass
eigenstate, the fractions of neutrino flavors are shown. The fraction of νe is shownwith cross-hatching, the νµ fraction with right-leaning hatching, and the ντ fraction
with left-leaning hatching.
• Determination of the mass hierarchy,• Size of CP phase δ.
A goal in neutrino physics is to measure the mixing angle θ13 ; this mixing angle
is yet to be measured. As mentioned before, the reactor neutrino experiments
reported null results on ν̄e → ν̄x oscillation. The survival probability of ν̄e (Pν̄e →ν̄e )in the reactor experiments can be writtenPν̄e →ν̄e ' 1 − sin2 2θ13 sin2 (∆m231 L/4E)(1.27)+α2 (∆m231 L/4E)2 cos4 θ13 sin2 2θ12 ,where α = ∆m221 /∆m232 . Thanks to the smallness of α, the third term is negligible
and the probability is formed by two parameters, sin2 2θ13 and ∆m231 . Currently,
a limit of sin2 2θ13 < 0.13 (θ13 <∼ 12◦ ) [20] at the ∆m2atm region of 2.8 × 10−3 eV2is set on this mixing angle at 90% C.L. The search for neutrino oscillations with abaseline of several hundred km, such as K2K and MINOS, also have a potential
to measure θ13 . The probability that νµ oscillates to νe (Pνµ →νe ) can be given as
Pνµ →νe = sin2 2θµe sin2 (∆m2µe L/4E)(1.28)' sin2 2θ13 sin2 θ23 sin2 (∆m231 L/4E)
1'
sin2 2θ13 sin2 (∆m231 L/4E).
2
In the above expression, we suppose sin2 2θ23 ' sin2 2θatm ∼ 1.0. Considering∆m231 ∼ ∆m2atm , these accelerator experiments can probe the mixing angle θ13 in
the mode νµ → νe .
9

1.3. MOTIVATION FOR νµ → νE SEARCH

1.3

Motivation for νµ → νe search

The recent discovery of neutrino oscillations by several experiments are full of
surprise and have provided a new window into physics beyond the Standard
Model. In the three-flavor framework, neutrino mixing is described by two
parameters of mass-squared difference (∆m2solar , ∆m2atm ), three mixing angles (θ12 ,θ23 , θ13 ) and a CP phase (δ). As yet, we know very little about the mixing angle
θ13 , although the null results of disappearance of reactor ν̄e by CHOOZ and Palo
Verde indicate that θ13 should be smaller than 12◦ .
Motivated by such situations, we have performed a search for θ13 in an experiment with a muon neutrino beam and a baseline of 250 km. We probe θ13
in the νµ → νe appearance mode, which provides a complementary result towhat the reactor neutrino measurements concluded. If θ13 has a non-zero value,
we will investigate the CP violation in lepton sector by comparing νµ → νe to
its CP-mirror image ν̄µ → ν̄e in the future. In the see-saw model, the neutrinomass eigenstates are identical to their anti-particles and νµ → νe and ν̄µ → ν̄e aredifferent processes. Demonstrations of CP violation in the interactions of lightneutrinos could enhance the feasibility of the production of the matter anti-matterasymmetry, known as leptogenesis.
In this thesis, we report the results of the search for νµ → νe oscillation in theK2K experiment using the entire data sample. For the νe appearance signal search,
the neutral pion production is the most significant background at the SK detector.
We have studied this π0 background and applied a new π0 rejection algorithm.
In this chapter, we summarized neutrino physics and the experimental searches
for neutrino oscillations as the introduction. We will begin with an overview
of the K2K experiment in Chapter 2. The following chapters (Chapter 3-9) givedescriptions of the analysis: Monte Carlo (MC) simulations, predictions of theneutrino event rate and energy spectrum at SK, the signal selection, and theconstraint on νµ → νe oscillation parameters.

10Chapter 2
The K2K experiment

2.1

Experimental goal and design

The KEK to Kamioka long-baseline neutrino oscillation experiment (K2K) uses
an accelerator-produced neutrino beam of nearly pure νµ . The neutrino beam is
produced by a 12 GeV proton synchrotron accelerator in KEK [24] and directed
toward the Super-Kamiokande detector 250 km away. In the proton collisions on
an aluminum target, positive pions are produced and their decays consist of νµ ’s.
With a mean neutrino energy of 1.3 GeV and a baseline of 250 km, the experimenthas the maximum sensitivity to neutrino oscillations with∆m2 =πE[GeV]∼ 6 × 10−3 eV2 .
2.53 · L[km](2.1)

The sensitivity of K2K covers the parameter region ∆m2 = 2 ∼ 3 × 10−3 eV2indicated by the atmospheric neutrino anomaly.
The goals of the K2K experiment are:11

2.1. EXPERIMENTAL GOAL AND DESIGN— Confirmation of the muon neutrino deficit in atmospheric neutrinos (νµ →νx ),— Search for electron neutrino appearance (νµ → νe ).
Neutrino oscillations cause the reduction of the total number of νµ events at SK.
In addition, the wide-band νµ spectrum is distorted at SK due to the energydependent oscillation probability, as shown in Figure 2.1. To confirm the resultsof atmospheric neutrinos, we evaluate these characteristics by comparing theobservation with the predictions without oscillation. Moreover, we probe theνµ → νe oscillation in K2K. The sub-dominant contribution of νµ → νe oscillation
is not completely excluded yet, although the νµ oscillation is the dominant contribution. We look for the excess of νe events at SK and set a constraint on νµ → νeoscillation parameters. Both measurements of νµ → ντ and νµ → νe oscillation
are the first experimental approach using an accelerator-produced νµ beam witha long baseline over a few hundred km.

probability(sin22θ=1.0,∆m2=3×10-3eV2)
1

0.75
0.5
0.25
0

1

2

3

4

5
Eν(GeV)8

4

10 /cm

2

0

6
4
2
0

0

1

2

3

4

5
Eν(GeV)

Figure 2.1: Oscillation probability (upper) and νµ energy spectrum (lower) at
SK. In the lower figure, the solid histogram shows the energy spectrum without
neutrino oscillation while the hatched one shows the energy spectrum on theassumption of oscillation parameters ∆m2 = 3 × 10−3 eV2 and sin2 2θ = 1.0.
In order to study neutrino oscillations, the K2K experiment has some key
components in its design as described below.
12CHAPTER 2. THE K2K EXPERIMENT
Beam direction monitoring:
In K2K, the variation of the beam direction affects the neutrino flux and theenergy spectrum at SK. In the Monte Carlo (MC) simulation, a change inthe beam direction by 3 mrad reduces the neutrino flux by 1%. Thus, we
require the beam to be controlled with an accuracy of 1 mrad as a guarantee
of beam stability at SK. For this purpose, several beam monitors and neardetectors are employed in KEK.
Measurements at the near detectors:
The absolute neutrino flux has a large uncertainty due to difficulties inthe estimation of the primary proton beam intensity, the proton targeting
efficiency, and hadron production cross-sections. There are also a large
uncertainty in the neutrino-nucleus interactions in water. To avoid these
uncertainties, we predict the neutrino event rate at SK by using the measured
event rate and the energy spectrum at the near detectors.
Neutrino flux extrapolation from the near site to SK:
Due to the difference of beam acceptances between the near detectors andSK, the neutrino energy spectra at the near site and SK are different. In orderto account for this difference, we evaluate the energy-dependent ratio of theνµ flux at SK to the near site (far/near flux ratio) with the in situ measurementof pion production in p − Al collisions. Then, we derive the the expected
neutrino event rate and energy spectrum at SK without oscillation from thenear detector measurements transformed using the far/near ratio.
Timing synchronization between near site and SK:
With the K2K neutrino beam, we expect the event rate at SK to be 0.4 per
day in the case of no oscillation. On the other hand, atmospheric neutrinos
are detected with a rate of about 8 events per day; that could be a crucial
background. Therefore, we adopt the time synchronization between theaccelerator and SK by using the Global Positioning System (GPS).

2.2

Experimental components

A schematic view of the K2K experiment is shown in Figure 2.2. An overview ofthe experiment is as follows:132.2. EXPERIMENTAL COMPONENTS(i) Protons are accelerated by KEK’s proton synchrotron and hit the aluminumtarget. In proton collisions, positive pions are produced and focused toward
SK by the magnetic horns (Figure 2.2(a)).
(ii) The νµ beam is produced in positive pion decays, and its direction is monitored (Figure 2.2(b)).
(iii) The near detectors measure the neutrino interaction rate and the energy
spectrum (Figure 2.2(c)).
(iv) After traveling 250 km, beam neutrinos are detected in SK (Figure 2.2(d)).
(v) The SK event times are synchronized with the accelerator (Figure 2.2(e)).
We will describe each experimental component in this section.
(e) GPS Sattelites
(a)
12GeV
PS

(d) Super−Kamiokande(b) Neutrino Beamline
Pion
Muon
Al
MonitorMonitor  
Target
 

P
SPIC
CT

 
 

     

π 

 π

Magnetic
Focusing
HORNs(c) Near DetectorsµµDecay Pipe
(200m)

ν



1kt waterC

0m






 
 

ν       

Fine−Grained
Detector(FGD)

300 m

250km

Figure 2.2: Schematic overview of the K2K experiment.

2.2.1

Primary proton beam

KEK 12 GeV proton synchrotron
The primary proton beam is provided by the 12 GeV proton synchrotron at KEK[25]. The accelerator is composed of a 750 keV Cockcroft-Walton pre-accelerator,
14

CHAPTER 2. THE K2K EXPERIMENT
40 MeV drift-tube LINAC injector, 500 MeV booster synchrotron and the main
ring of the synchrotron accelerating protons up to a kinetic energy of 12 GeV. In
operation, approximately 6 ∼ 7 × 1012 protons are accelerated in every repetition
cycle of 2.2 seconds. Accelerated protons are extracted in one turn; this is called“fast extraction”. Then, protons are transported to the primary proton beamline. The proton beam has the micro structure of nine bunches inside a spill,corresponding to the harmonic number of the main ring. The duration of the spillis 1.1 µsec.
Proton beam monitors
The extracted proton beam is transported in the primary beam-line, bent by 90
degrees toward SK (downward by 1.075 degrees), and hits the aluminum target.
Figure 2.3 shows a schematic view of the beam-line.
Neutrino

Pion monitor
Decay pipeHorn & Target

Beam dump
Muon monitor
Primary beam line

12GeV PS

Figure 2.3: Schematic view of the beam-line. The points along the beam-line
indicate the locations of the CTs and the SPICs.
In order to monitor the beam intensity and profile, current transformers (CTs)and segmented plate ionization chambers (SPICs) [26] are installed in multiple
places along the beam-line. The CT is a beam intensity monitor consisting of a
toroidal coil. The CT picks up the induced current from the beam spill by spill.
The efficiency of the beam transportation is measured by the CTs and estimated tobe approximately 85%. A CT placed just upstream of the target (called ”TGT-CT”)
is used to estimated the number of delivered protons on the target (POT).
15

2.2. EXPERIMENTAL COMPONENTS
SPICs are used for the monitoring of the beam profile. The information measured by two SPICs (V39-SPIC and TGT-SPIC) located upstream of the target isused as the input into our simulation for the neutrino beam.
Hadron production target and magnetic horns
In proton collisions on the aluminum target, mainly pions are produced. To
focus positive pions toward the direction of SK, two toroidal magnetic horns are
employed [27]. A schematic view of the magnetic horns is shown in Figure 2.4.
To enhance the focusing effect of positive pions, the aluminum target rod withdimensions of 3 cm in diameter and 66 cm in length is inserted into the first horn.
This plays the role of inner conductor of the horn current. Supplying pulsed
electric current of 250 kA to the horns, the maximum magnetic field of 3.3 T
is achieved at the surface of the target rod. Thanks to the magnetic horns, theneutrino flux is 22 times higher than that without the horn current, as shown in
Figure 2.5.
2.8m
2.5m

π+
p

1.7m

π+

0.6m

π

−

1st HORN

2nd HORN

Figure 2.4: Schematic view of aluminum target and magnetic horns. The electricalcurrent of 250 kA is supplied to the horns, making a toroidal magnetic field inside
the horns. The aluminum target is inserted into the first horn.

2.2.2

Neutrino beam and monitors

Pion monitor
A gas Cherenkov imaging detector, called a pion monitor, is employed downstream the magnetic horn system to measure the secondary pions. The schematic16

Arbitrary unit of neutrino flux

CHAPTER 2. THE K2K EXPERIMENTwithHORN current

without
HORN current
0

1

2

3

4

5

Neutrino energy (GeV)

Figure 2.5: Neutrino flux at SK with and without horn current.
view of the pion monitor is shown in Figure 2.6.
The two-body decay kinematics of a pion is well-understood, and the neutrinoenergy spectrum at any location can be predicted from the measurements ofpion momentum and direction. Thus, we can predict the neutrino spectra andthe fluxes at the near and far sites; we derive the far/near flux ratio from thesepredictions. The results of this measurement validate the calculation of far/near
flux ratio computed by the beam MC simulation (Section 5.3).

Figure 2.6: Schematic view of the pion monitor.

17

2.2. EXPERIMENTAL COMPONENTS
Decay volume
Positive pions focused by the magnetic horns enter a decay volume. The decay
volume is a cylindrical pipe and its length is 200 m. Inside this volume, thepositive pions decay to µ+ ’s and νµ ’s, π+ → µ+ + νµ , with a fraction of almost
100%. To avoid the hadronic interactions of pions, the decay volume is filled witha helium gas of 1 atm.
At the end of the decay volume, there is a beam dump composed of 3.5mthick iron and 2.0m-thick concrete. All the particles except for neutrinos andhigh-energy muons above 5.5 GeV/c are stopped there.
Muon monitor
There is a pit just downstream of the beam dump. The muon flux at the pit isestimated to be ∼ 104 muons/cm2 . Since the parent particles of both muons andneutrinos are pions, we can measure the neutrino beam direction by measuring
the direction of muons. The direction of muons is defined as the center of thespacial profile measured by two detectors called the ”muon monitor [28]”: one
is a segmented ionization chamber (ICH) and the other is an array of silicon
pad detectors (SPDs). Figure 2.7 shows the center of muon profile as a functionof running time measured by the ICH. The beam direction has been controlled
within 1 mrad as required.

2.2.3

Near detector complex

The near detector (ND) complex is located 300m downstream of the target. It is
formed by two neutrino detector systems: a 1kt water Cherenkov detector and afine-grain detector (FGD) system. Figure 2.8 shows a schematic overview of the
ND complex. They are located in a cylindrical hole with dimensions of 24 m indiameter and 16 m in depth, set on the axis of the neutrino beam. Each detector
has a different capability to measure the neutrino beam. Detailed descriptions ofeach detector are given below.
1kt water Cherenkov detector
A 1kt ring-imaging water Cherenkov detector (1KT), a miniature of the SuperKamiokande detector, is installed as the most upstream detector at the near de18

CHAPTER 2. THE K2K EXPERIMENT

Figure 2.7: Stability of the center of muon profile measured by the ICH of themuon monitor. The upper figure shows the stability in the horizontal direction
and the lower shows that in the vertical direction. The horizon black lines show
the beam direction to SK measured by GPS, and red ones are off to the center by±1 mrad.

Figure 2.8: Schematic view of the near detector complex.
192.2. EXPERIMENTAL COMPONENTS
tector complex. Figure 2.9 shows a schematic view of the 1KT detector. The watertank is a cylinder with the dimensions of 10.8 m in diameter and 10.8 m in height,
and filled with 1 kton of pure water. The inside of the tank is optically separated
into two parts: the inner detector (ID) with a cylindrical volume of 8.6 m in diameter and 8.6 m in height, and the outer detector surrounding the ID. There are
680 20-inch photomultipliers (PMTs) facing inward, providing the photo-cathodecoverage of 40%. The thickness of the OD part is 1 m for the barrel and 0.6 m
for the bottom. There are 68 8-inch PMTs facing outward on the support frame:
42 PMTs are attached to the upstream 1/3 of the barrel and the rest are attachedto the bottom. They work as the veto of incoming particles induced by neutrinos interacting outside. It also provides triggers to record cosmic-ray events forcalibration.

Figure 2.9: Schematic view of the 1kt detector.
The PMTs in the 1KT detect Cherenkov photons emitted from a charged particle traveling in the water. The refractive index of water is 1.33–1.36 dependingon the wavelength. The momentum thresholds of Cherenkov radiation for anelectron, a muon, a pion, and a proton are 0.58, 120, 159, and 1070 MeV/c, respectively. A particle with β = 1 emits approximately 340 photons per 1 cm in the
wavelength 300–600 nm, where a 20 inch PMT is sensitive. The opening angle of
Cherenkov radiation is 42 degrees.
In the 1KT detector, both charge and timing information of PMT signals isdigitized by a front-end module, called an ATM [29]. One ATM processes 1220

CHAPTER 2. THE K2K EXPERIMENT
PMTs. The ATM generates an analog sum of PMT signals (PMTSUM) and a
hit-sum signal whose pulse height is proportional to the number of hit PMTs
(HITSUM). The analog sum of all PMTSUM signals from ID is recorded by 500
MHz flash-ADCs (FADCs) and a 100 MHz one. Since the ATM cannot separate
multiple events within 1.2 µsec, we used the FADC data of the PMTSUM signal
to select the single-interaction events. Then, we estimate the fraction of multiinteraction events by counting the number of peaks in the PMTSUM signal.
We use the 1KT data to measure the neutrino event rate at the near site, which
is used to predict the event rate at SK. The neutrino energy spectrum is alsomeasured combining with the data taken by the FGDs.
Fine-grain detectors
The FGD system consists of a scintillation fiber tracker (SciFi), a fully-active scintillator detector (SciBar), a lead glass calorimeter (LG) and a muon range detector(MRD). We measure the neutrino energy spectrum with the FGD system. For
these studies, we analyze the data in which neutrinos interact with the SciFi and
the SciBar. SciFi and SciBar are designed to have the tracking capability for all
charged particles and particle identification. We use the MRD to measure the energy of a muon coming from SciFi and SciBar. With the LG detector, we measurethe νe contamination in the beam.
The SciFi [30] consists of 20 scintillating fiber modules of 2.6×2.6m2 in which 19
aluminum tanks filled with water are inserted between the modules as the targetof neutrino interaction. Each module contains double layers of scintillating fiber
sheets in both the horizontal and vertical directions. The scintillating fiber is 3.7 mlong, 0.692 mm in diameter, and made of polystyrene. The water target tank iscomprised of 15 rectangular pipes, each of which has dimensions of 16×6×240 cm3and a 1.8mm-thick aluminum wall. In total, the water target of SciFi is 6 tons.
The SciBar [31] was constructed as an upgrade of the near detector complex,
replacing the LG in summer 2003. The main part of the SciBar detector consistsof an array of plastic scintillator strips to realize a fully active detector with finesegmentation. Scintillators are coated with TiO2 as the reflector, each of whichhave dimensions of 1.3 × 2.5 × 300 cm3 . There are 14848 scintillator strips, andthey are arranged into 64 layers. These features of the detector allows us toreconstruct all the charged particles produced in a neutrino interaction. With atracking threshold of 8 cm, we can reconstruct protons (muons) with a momentum
21

2.2. EXPERIMENTAL COMPONENTS
greater than 450 MeV/c (100 MeV/c). The details of the SciBar detector are given
in Appendix B. In the downstream part of SciBar, an electromagnetic calorimeter(EC) is installed. We analyze the EC data to study the electron neutrino fractionin the beam which contributes to the background of the νµ → νe search. The
measurement of the νe flux is described in Appendix B.
The MRD [32, 33] is located as the most downstream detector of the neardetector complex. It consists of 12 iron absorbers sandwiched with 13 verticaland horizontal drift chamber layers. We employ the upper four iron plates of
10cm thickness to make the energy resolution of low energy muons better, while
the other plates have a thickness of 20cm. The total thickness of iron is 2 m,corresponding to the range of 2.8 GeV/c muons.

2.2.4

Super-Kamiokande, the far detector

The Super-Kamiokande detector is a cylindrical 50 kton water Cherenkov detector
located at Kamioka Observatory in Gifu Prefecture, 250 km from KEK. It is in themine under Mt. Ikenoyama, where the mean rock overburden is 1000 m. This
depth is equivalent to 2700 m of water, and the flux of cosmic rays is reduced by
five orders of magnitudes compared to that on the surface of the earth.
The SK detector started taking data in April 1996, aiming for nucleon decay
searches and studies of atmospheric and solar neutrinos. The running period of
the first five years is referred to as SK-I. After being suspended for maintenance,
an accident occurred in November 2001, which shattered 60% of the PMTs. The
detector was rebuilt with a half of PMTs in December 2002 and the running period
after the accident is called SK-II.
A schematic view of the detector is shown in Figure 2.10. The size of thewater tank is 41.4 m in height and 39.3 m in diameter, which contains 50 ktonsof pure water. The tank is optically separated into two concentric cylindricalregions by the support structure for the PMTs. The inner region, referred to as
the inner detector (ID), contains 32 ktons of water and 11146 20-inch PMTs areattached inward on the support structure uniformly at intervals of 70 cm in the
SK-I period. In SK-II, the number of PMTs was 5182. The photo-cathode coverageof the ID PMTs is 40% and 19% for SK-I and SK-II, respectively. A schematic viewof a 20-inch PMT is shown in Figure 2.11. In SK-II, the PMT is covered by anacrylic cover around the photo-cathode and a fiber reinforced plastic (FRP) casefor the rest. This is for prevention of damage through a chain reaction caused
22

CHAPTER 2. THE K2K EXPERIMENTby an implosion. The transparency of the acrylic cover in water is 98% for the
wavelength longer than 400 nm and 95% for a 350 nm wavelength.
The outer region surrounding the ID is called the outer detector (OD). The
thickness is 2.05 m on top and bottom and 2.2 m along the barrel. In this region,
1885 8-inch PMTs are mounted outward on the frame to veto incoming particles
such as cosmic-ray muons. Furthermore, this 2 m thick water acts as a selfshielding against gamma-rays and neutrons entering from the rock. To enhance
the light collection in OD, each PMT is equipped with a wavelength shifter plate.
The water in the tank is continuously circulated through the water purification
system to keep the water properties stable. With this system, the attenuation
length of the water has been kept at roughly 100 m. The system removes theradioactive materials, such as radon, from the water.

Figure 2.10: Schematic overview of the Super-Kamiokande detector

232.3. EXPERIMENTAL PHASES AND DATA SAMPLE

_

136

276

600
540

~ 70000

cable length

R 160

φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

R 325
M8-3

water proof structure

FRP( 610 20 )~ 720

acrylic cover

(mm)

168

Figure 2.11: Schematic view of 20-inch PMT (left). The drawing of a PMT with anacrylic cover and a FRP case for SK-II is also shown (right).

2.2.5

Timing synchronization system

The timing synchronization between the accelerator and SK separates the beam
neutrinos from atmospheric neutrino and cosmic-ray muon events in SK. For that
purpose, the global positioning system (GPS) is employed. Figure 2.12 shows aschematic view of GPS system in the K2K experiment; it consists of GPS receivers,
a VME receiver and a 50 MHz 32-bit local time clock (LTC). Receiving satellites’
timing and position information, the GPS receiver provides the VME receiverand LTC with a time stamp every second. The VME receiver decodes the timestamp to universal time coordinate (UTC). The number of counts in the LTC is
recorded simultaneously with receiving an event trigger signal. Identical setsof this system are located at KEK and at SK. For the stability monitoring of thesystem, two independent GPS receivers are employed at the near site.

2.3

Experimental phases and data sample

In the K2K experiment, there are two phases: K2K-I and K2K-II.
K2K-I corresponds to dates from June 1999 to July 2001 in which SK was
instrumented with the full 11146 inner PMTs. K2K-I is further divided into twophases: K2K-Ia and K2K-Ib. For the K2K-Ia phase in June 1999, the horn current
and the target diameter were different from the subsequent phases of experiment,
24

CHAPTER 2. THE K2K EXPERIMENT

GPS receiverTime stamp(every 1 s)

Event trigger

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

LTC count

OnlineComputerevery 1 s

GPS receiver
VME receiver

UTC = Tn−1

UTC = Tn

LTC = N n−1

LTC = N n

LTC (50MHz)
LTC = N ev

SK event trig.
recorded DATA

LTC & UTC

LTC & UTCLTC

SK event time = Tn + (Nev −Nn ) x

UTC
LTC

Figure 2.12: Schematic view and timing diagram of the GPS system. The time ofan event in SK is estimated by linear interpolation with the UTC and LTC counts,
as given in the formula.

25

2.3. EXPERIMENTAL PHASES AND DATA SAMPLE
which results in differences in the neutrino flux, far/near flux ratio, and systematic
uncertainties.
K2K-II corresponds to dates with SK-II (January 2003 to November 2004).
In the analysis of the FGDs for K2K-II, the phase is divided into two. The LG
calorimeter was replaced by the SciBar detector, and correspondingly the period
without the LG is called K2K-IIa (January 2003 to June 2003) and K2K-IIb (October2003 to November 2004) with SciBar.
Figure 2.13 shows the number of delivered protons on the target. We achieved
10.5 × 1019 POT in total, of which 9.2 × 1019 with the good beam condition are used
for analysis. The good beam condition is defined as follows:• Data in normal experimental configurations except for the accelerator study,
the beam tuning and the pion monitor measurement.
• All the beam-line components and the data acquisition are in good operation.
• A proton intensity is greater than 1.0 × 1012 protons/pulse, as a guarantee ofthe beam monitors’ accuracy.
• Horn current is greater than 240 kA (190 kA) for K2K-Ib and K2K-II (K2K-Ia).
• Good GPS status both in KEK and SK.
• SK is in operation.
Experimental configurations of each phase are summarized in Table 2.1.
Table 2.1: Summary of the experimental configurations.
Phase
K2K-I
K2K-IaK2K-Ib
K2K-II
K2K-IIa
K2K-IIb

periodPOT [1019 ]1999.6-2001.7
4.79
1999.60.31
1999.11-2001.7
4.48
2003.1-2004.11
4.43
2003.1-2003.6
2.26
2003.10-2004.11
2.17

Target/hornLG—set
φ20 cm/200 kA ↓φ30 cm/250 kA ↓
↓
—
↓
—
↓
—

26

SciBar
SK
—
SK-I
—
↓
—
↓
—
SK-II
4 layers↓
64 layers↓

CHAPTER 2. THE K2K EXPERIMENT

120
K2K-IaK2K-Ib

K2K-II

Accumulated POT (10^18)

100
80
60
40
20
0

Protons/Pulse (10^12)

200kA
6
5
4
3
2
1
0
-1
Jan/99250kA (horn current)

Jan/00

Jan/01

Jan/02

Jan/03

Jan/04

Jan/05

Date

Figure 2.13: The integrated number of protons delivered to the target.

27

Chapter 3
Simulations
We use the Monte Carlo (MC) simulations to derive the expectations of neutrino
events. Features of neutrino interactions, the methods of event reconstruction
and the effects of systematic uncertainties are studied with the MC simulations.
The MC predictions of neutrino events are given by the following procedure:(i) Neutrino flux calculation (beam MC),(ii) Simulation of neutrino interactions with nuclei (NEUT),(iii) Simulation of particle tracking in the detectors.
The detailed descriptions of each step are given in this chapter.

3.1

Neutrino flux calculation

The beam MC simulation reproduces the proton beam injection on the aluminumtarget, the secondary meson production and focusing by magnetic horns, and thetracking of secondary mesons until their decay to neutrinos.

3.1.1

Primary proton beam

To incorporate the beam properties into the beam MC simulation, we measure
the profile of the primary proton beam with two SPICs located between the final
focusing magnet and the target (V39-SPIC and TGT-SPIC). Based on this measurement, we estimate the beam profile and divergence at the target. The horizontal
29

3.1. NEUTRINO FLUX CALCULATION
beam spread of 1mm in standard deviation and the vertical spread of 6mm are
estimated for the runs in June 1999 (K2K-Ia). In the period after November 1999
(K2K-Ib and K2K-II), the values of 3.4mm and 7.2mm are estimated for the horizontal and vertical spread, respectively. We use these values as the input to thebeam MC simulation.

3.1.2

Pion production in the aluminum target

To predict the pion yield in p − Al collisions, we adopt an empirical formula ofSanford-Wang which provides a quantitative description of the secondary particle
production. This formula has eight parameters, and calculate the differential
d2 n) per interacting proton as
particle yield ( dΩdp!
 C3 pC4

p
d2 n
C2
C
= C1 p 1 −exp − C − C6 θ(p − C7 pB cos 8 θ) ,dΩdp
pB − 1
p 5

(3.1)

B

where θ is the angle of the secondary particle with respect to the beam axis in
the laboratory frame, p and pB are the momenta of the secondary particle and theprimary proton, respectively, and C1 , C2 , · · · , and C8 are the parameters to be set.
In this thesis, we adopt the pion production cross-section measured by the HARP
experiment, described in Section 5.3. We fit the measured cross-section with the
HARP measurement by the Sanford-Wang formula, and obtain the parameters of
C1,2,··· ,8 . For the flux predictions of the K2K-Ia period, we apply the compilation
result given by Cho et al.(called Cho-CERN model [34, 35]). Adopting alternativemodels of GCALOR/FLUKA [36, 37, 38] and Sanford-Wang [39] or other available
data [40, 41, 42, 43, 44, 34, 44], we estimate the systematic uncertainty.
For the kaon production, the Sanford-Wang formula with the parameter set
described in Reference [39] is employed.

3.1.3

Particle tracking in the neutrino beam line

Survived primary protons and secondary particles are traced though the twomagnetic horns down to the decay volume by using GEANT with the GCALOR
hadron simulator. The effect of the magnetic field is also simulated.
The neutrino beam is made up via the decays of pions, kaons and muons. In
the simulation, the following decay channels and their kinematics are simulated30

CHAPTER 3. SIMULATIONS
for the νµ (ν̄µ ) yield:
π+(−) → µ+(−) + νµ (ν̄µ )K+(−) → µ+(−) + νµ (ν̄µ )K+(−) → π0 + µ+(−) + νµ (ν̄µ )

+(−)
[πµ2
],

+(−)
[Kµ2
],
+(−)
[Kµ3
],

0
],
KL0 → π−(+) + µ+(−) + νµ (ν̄µ ) [Kµ3−(+)µ−(+) → e−(+) + ν̄e (νe ) + νµ (ν̄µ ) [µe3].

For the νe (ν̄e ) flux, the following decays are simulated:+(−)],µ+(−) → e+(−) + νe (ν̄e ) + ν̄µ (νµ ) [µe3
+(−)
+(−)
0
+(−)
K
→ π +e+ νe (ν̄e )[Ke3 ],
0
KL0 → π−(+) + e+(−) + νe (ν̄e ) [Ke3
].

3.1.4

Neutrino energy spectrum

Figure 3.1 shows the neutrino energy spectra at the near site and SK. Due tothe difference of beam acceptance, the energy spectra are different between nearand far sites. Figure 3.2 shows the energy spectrum for each neutrino type. The
fraction of νµ , νe , ν̄µ , and ν̄e are 97.9%, 0.9%, 1.2%, and 0.02%, respectively, at SK,
in the case of no oscillation. The composition of each decay process in νµ and νeis also shown in Figure 3.3. The main contributions to νµ is the decay of π+ (π+µ2 ).
For the νe flux, the main contribution comes from the muon decay µ+e3 (∼ 85%) and+,0
the rest comes from the kaon decays Ke3(∼ 15%).

Figure 3.1: Neutrino energy spectra at the near site (left) and SK (right).

31

3.1. NEUTRINO FLUX CALCULATION-1(0.1GeV ) (1020POT ) -1 ]

10

10

9

10

8

10

7

10

6

µ±e3

10

5

0

1

-2

ΦνFD [cmνµπ+µ 2νµtotal

K+µ 2
K+µ 3
K0µ 3

2

3

10

10

4

5

6

νe

9

µ+e3

8

K+e3
10

7

10

6

10

5

7
8
Eν [GeV ]νetotal

K0e3

-2

10

11

ΦνFD [cm10-1(0.1GeV ) (1020POT ) -1 ]Figure 3.2: Neutrino energy spectra at the near site (left) and SK (right) for eachneutrino type with 250 kA horn setting. Black, green, red, and blue lines show νµ ,
νe , ν̄µ , and ν̄e , respectively.

0

1

2

3

4

5

6

7
8
Eν [GeV ]Figure 3.3: Composition of each decay process in νµ (left) and νe (right). The fluxes
at the near site, according to the beam-MC simulation, are shown.

32

CHAPTER 3. SIMULATIONS

3.2

Neutrino interaction simulation

In the K2K experiment, neutrinos interact with nuclei and electrons in the water.
The neutrino interactions are treated by the NEUT program library [45].
This library was originally developed for studies of atmospheric neutrinos in
the Kamiokande experiment. In the code of the library, neutrino interactions withthe target material are simulated. It provides the four-momentum of recoil orproduced particles in the interaction.
In NEUT, the following charged current (CC) and neutral current (NC) interactions are taken into account:• CC quasi-elastic scattering ν + N → l− + N0(∼ 28%)• NC elastic scattering
ν+N →ν+N(∼ 13%)−0• CC resonance production
ν + N → l + N + (∼ 29%)meson
• NC resonance production ν+N → ν+N0 +meson (∼ 10%)• CC multi-pion production ν + N → l− + N0 + (∼ 14%)
hadrons• NC multi-pion production ν + N → ν + N0 +(∼ 4%)
hadrons• NC coherent-pion produc- ν + 16 O → ν + 16 O + π0(∼ 1%)
tion
where N and N0 are nucleons and l− is a charged lepton. The fraction of eachmode, in the energy region of K2K neutrino beam, is also shown in parentheses.
The details of neutrino interactions are given in Appendix A. The total crosssection of CC interactions consisting of quasi-elastic scattering (QE), single-meson
productions and deep-inelastic scattering are shown in Figure 3.4. Figure 3.5
shows the cross-section of each interaction mode with water, calculated by NEUT.

3.2.1

Nuclear effects

Hadrons produced in a nucleus often interact with nuclear medium inside the nucleus, which results in the different final state or alters the kinematics of particles.
These phenomena are called “nuclear effect”. The nuclear effects of pions, nucleons, and ∆ resonances are simulated in NEUT. The neutrino interaction position33

3.2. NEUTRINO INTERACTION SIMULATION

1.4
CC single π

CCQE
ANL
GGM 77
GGM 79Serpukhovσ/Eν (10-38 cm-2GeV-1)

1.2
1

Total σANL 82
BNL 86CCFR 90
CDHSW 87
IHEP-JINR 96
IHEP-ITEP 79
CCFRR 84
BNL 82

0.8
0.6
0.4
0.2
0
-1
10

1

Eν (GeV)10

σ per one nucleon (× 10

-38

2

cm )

Figure 3.4: Total cross-section of CC interaction as a function of neutrino energy.
Solid line shows the calculated total cross-section. The dashed, dotted and dashdotted lines show the calculated cross-sections of QE, single-meson production
and deep-elastic scattering, respectively. Data points are taken from various
experiments.
6

Total cross section (H2O)
5

4

3

NC

2

CC multi-π1

CC single-meson

0

0

1

2

CC quasi-elastic
3
45Energy (GeV)

Figure 3.5: The cross-section of each neutrino interaction mode with water asa function of incident neutrino energy. The CC resonance production and CC
coherent pion production modes are assorted in “CC single-meson”.

34

CHAPTER 3. SIMULATIONS
in a nucleus is calculated using the Wood-Saxon type density distribution:Zr − c −1
ρ(r) = ρ0 1 + exp
,
(3.2)
A
a
where we choose ρ = 0.48m3π , a = 0.41 fm, and c = 2.69 fm.
Pioncross section for π + + 16 O (mb)

The nuclear effects for pions are classified into inelastic scattering, charge exchange
and absorption. The cross-section is calculated by the model of L. L. Salcedo etal. [46]. The Fermi motion and the Pauli blocking effect of nucleons are taken into
account in the similar way as CC-QE interaction. Figure 3.6 shows the calculated
π+ -16 O interaction cross-section together with experimental data [47], which agree
well with each other.
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 3.6: Cross-sections of π+ -16 O interactions. The lines show the results ofour calculation of nuclear effect in NEUT based on [46], and the symbols show
the experimental data [47]. Each interaction channel is illustrated in the figure.

Nucleon
The nucleon-nucleon elastic scattering cross-section implemented in NEUT isbased on the measurement by H. W. Bertini [48], which is also used by GCALOR.
We rescale the nuclear effect for nucleons by multiplying 0.9 to the measured crosssection by H. W. Bertini, which better reproduces the yield of scattered protons ine − 12 C interaction [49]. The pion production by nucleon is also taken into account,according to the isobar production model of S. J. Lindenbaum et al. [50].
35

3.3. WATER CHERENKOV DETECTOR SIMULATION∆ resonance
The absorption of a ∆ resonance [51] is taken into account. Approximately 20%of the ∆ resonances are lost by this effect.

3.3

Water Cherenkov Detector simulation

The particles generated in NEUT are traced by a detector simulation. The detector
simulation is based on GEANT-3.2.1 package [52]. For the tracking of pionswith momentum below 500 MeV, we refer the experimental data from π − 16 O
scattering [53] and π − p scattering [54].
In the water Cherenkov detector simulation, Cherenkov photons are generated
according to the following equations of the half opening angle θC and the numberof photons (N):1cos θC =
(3.3)
nβ
!
d2 N
2πα
1
= 2 1− 2 2 ,
(3.4)
dxdλ
λ
nβ
where n, β, x, λ and α are the refractive index of water, velocity (= v/c), thepath length of a charged particle, the wavelength and the fine structure constant,respectively. For the propagation of Cherenkov photons, Rayleigh scattering,
Mie scattering and absorption are taken into account. Attenuation coefficientsused in the simulation are shown in Figure 3.7, which are tuned to reproduce
the in situ measurement by a laser system and using cosmic-ray muons [55]. The
quantum efficiency of PMT is implemented based on the measurement of single
photoelectron distribution. Properties of the electronics system, timing width of
ADC gate and signal threshold, are also simulated.

36

-1

attenuation coefficient (m )CHAPTER 3. SIMULATIONS-1

10

Dec.-3,4-96
Dec.-17-96
Jan.-18-97

Dec.-14-96
Dec.-27-96
Mar.-6-97

total
absorption-2

10
Mie scattering
Rayleigh scattering-3

10

200 250 300 350 400 450 500 550 600 650 700
wavelength (nm)Figure 3.7: Attenuation coefficients as a function of wavelength in water. The data
points are obtained from the light scattering measurement. The solid line showsa model in the simulation. The lines indicate the contribution of each process.

37Chapter 4
Outline of analysis
We describe the signature of νµ → νe oscillation signal events and background
events in this chapter. We also describe the outline of the analysis procedure to
extract the mixing parameter of νµ → νe oscillation.

4.1

Signature of νµ → νe oscillation

Our search for νµ → νe oscillation is based on detection of charged current interaction of νe in an oxygen nucleus. Supposing that ∆m2µe is nearly ∆m2atm , the νµoscillation probability is maximum with the neutrino energy of 0.6 GeV in K2K. In
this energy region, quasi-elastic scattering νe + n → e + p is the dominant processof interaction, in which the momentum of recoil proton is typically below theCherenkov threshold in water. Therefore, only an electron is visible in SK. Electron events can be separated from muon events by the Cherenkov ring pattern.
After the Cherenkov ring reconstruction, we select the single-ring events as a νesignal candidate because the separation between an electron and a muon becomesworse for multi-ring events mainly due to the overlapping of Cherenkov photons
from multiple particles.

4.2

Background

After the neutrino event selection, the background originates from the beam
neutrino interactions. Background of atmospheric neutrinos is negligible dueto the good timing synchronization between the near and far sites by GPS. The
39

4.2. BACKGROUND
dominant source of background comes from the π0 production in neutrino-16 O
interactions. When one gamma-ray from π0 decay is not reconstructed, the eventis classified as a single-electron event, which is a signature of νµ → νe oscillation.
The typical event displays of νe CC-QE interaction and π0 production backgroundare shown in Figure 4.1. Supposing that θ13 is near the current limit of ∼ 0.1 at∆m2 = 2.8 × 10−3 eV2 , we obtain an oscillation probability for νµ → νe in K2K of∼ 10−2 , which gives the expectation of a few νe signal events in our entire data
sample. Thus, the understanding of π0 background and the reduction are quite
critical. For this purpose, we have developed a new reconstruction algorithm of
π0 .We apply the π0 rejection cut to the K2K data sample using the π0 reconstruction
algorithm.
The remaining background events originate from the contamination of νe in
the beam (beam νe ). This is not intrinsically reducible. The beam-νe contaminationin the beam at SK is estimated to be 1.2%.

1
1

1

1
1

1

1

1

1

1
1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Figure 4.1: Typical event displays of νe CC-QE interaction (left) and π0 production
background (right). The solid lines show the reconstructed Cherenkov rings. In
the right figure, the two dashed lines show the expected ring projections according
to the vertices and directions of gamma-rays from a π0 decay.

40CHAPTER 4. OUTLINE OF ANALYSIS

4.3

Search for νµ → νe oscillation

To search for νµ → νe oscillation, we look for the excess of νe appearance signal
by comparing the observed number of signal candidate events with the expected
number of background events. Since the absolute neutrino neutrino flux and its
cross-section have large uncertainties, we derive the expected number of signal(background) events at SK from the total number of neutrino interactions (NSK )and the MC event rate predictions as:
NSK ×

MC event rate of νe signal (background).
MC total event rate without oscillation(4.1)

First, we estimate the total number of neutrino events in SK in the case of no
oscillation (Chapter 5). To calculate NSK , we perform the following measurements:• Neutrino interaction rate at the 1KT detector,• Neutrino energy spectrum at the near site,• Pion production cross-section in the p − Al collisions.
The in situ measurement of charged pions in p − Al collisions is performed in the
HARP experiment. Using the HARP results as the input to the MC simulation,
we calculate the far/near flux ratio. We then extrapolate the measured neutrino
interaction rate and energy spectrum at the near site to SK by multiplying the
far/near flux ratio.
Next, applying the event selection (Chapter 6, 7), we compare the observed
number of signal candidate events with the background expectation.
Finally, we give a constraint on the oscillation parameters of sin2 2θµe and∆m2 from the obtained νµ → νe oscillation probability with a statistical approach(Chapter 8, 9).

41

Chapter 5
Expected number of beam neutrino
events at SK
We predict the number of neutrino events at SK when there is no oscillation. For
the prediction, we use the neutrino interaction rate measured by 1KT. We alsomeasure the neutrino energy at the near site and extrapolate it to SK with the
far/near flux ratio.
In this chapter, we follow four steps as(i) Measurement of neutrino event rate at 1KT,(ii) Measurement of neutrino energy spectrum at near detectors,(iii) Near-to-far spectrum extrapolation,(iv) Prediction of the number of neutrino events at SK.

5.1

Neutrino interaction rate at the 1KT detector

In order to predict the number of neutrino events at SK, we measure the neutrino
interaction rate at the 1KT detector. The 1KT detector uses the same detector
technology as SK, and the event reconstruction algorithm of 1KT is also similar
to that of SK. Therefore, when we compare the observed number of events in SK
with the expected one from 1KT, most of the systematic uncertainties, such as
neutrino interaction cross-sections and the detection efficiencies, cancel out.
In the 1KT detector, multi neutrino interactions occur in a spill due to theintense neutrino beam; the fraction of multi-interaction events in the total spills
435.1. NEUTRINO INTERACTION RATE AT THE 1KT DETECTOR
is approximately 10%. Because we cannot reconstruct multi-interaction events
properly, we estimate the neutrino interaction rate from the number of singleinteraction events inside the fiducial volume by correcting the fraction of multiinteraction event. For this purpose, we count the number of peaks in the sum of
the pulse height information of all PMTs recorded by FADC. We then evaluate
singlesingletotal
total
the correction factor of Nint
/Npeak , where Nintand Nint are the total number of
FADC peaks of events and the number of single FADC peak events, respectively.
1KT
The number of neutrino events in 1KT (Nint) is expressed as
int
selectN1KT= N1KT
·

total
Npeak
single
Npeak

·

1
1KT

(5.1)

selectwhere N1KT
and 1KT are the number of single-interaction events and the event
selection efficiency, respectively. Descriptions of the event selection criteria andthe corrections are given in the following sections.

5.1.1

Event selection in the 1KT detector

The single-interaction neutrino events in 1KT are selected with the following
requirements:(i) There is no event 1.2 µsec before the beam timing,(ii) The total number of photoelectrons is greater than 200 (equivalent to approximately 20 MeV),(iii) Good beam condition (described in Section 2.3) is satisfied,(iv) FADC pulse height is greater than 1000 photoelectrons (equivalent to approximately 100 MeV),(v) Only one FADC peak in a spill is observed,(vi) The vertex is reconstructed in the fiducial volume.
Because the 1KT detector cannot record events properly when two events occur
within a short time interval, we apply the criterion (i). The criterion (ii) rejects lowenergy events which could not be reconstructed, and (iv) is applied to reject eventsof decay-electrons from stopped muons in the detector. Because the reconstruction
44

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK
algorithm cannot find the vertices of each event properly for the multi-interaction
event, we select the single-interaction event with the criterion (v). After the
event reconstruction, we select the events whose vertices are inside the fiducial
volume. Figure 5.1 shows the fiducial volume of the 1KT detector; it is defined asa cylindrical volume along the beam direction with a radius of 2 m and a heightof 2 m, and located 1 m upstream from the center of the tank. The fiducial mass
corresponds to 25 tons. Detailed descriptions of the event selection are given in
Reference [56].

200cm

Y

Z

X
200cm

Figure 5.1: Fiducial volume of the 1KT detector.
Figure 5.2 shows the event selection efficiency as a function of neutrino energy,
estimated by the MC simulation. The averaged efficiency is estimated to be 75%.

5.1.2

selectCorrections on N1KT

• Correction of background contamination:
There are background events from cosmic-ray muons and beam-induced
particles which are generated by neutrino interactions in the surrounding
materials. The fraction of background events due to the cosmic-ray muons
is estimated to be 1.0% with the data taken by the random trigger. The
beam induced background event has a PMT hit cluster in the OD region
originated from the incoming particle. We have performed a visual scanfor the OD-PMT hits to estimate the fraction of beam-induced background.
It is estimated to be 0.5 %. The total background contamination is estimated to be 1.5% by including small contributions from another backgroundsources [56]. The background events are subtracted from the number of selected events.
45

Efficiency

5.1. NEUTRINO INTERACTION RATE AT THE 1KT DETECTOR

1

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

1

2

3

4

5

Enu(GeV)Figure 5.2: Event selection efficiency of 1KT as a function of neutrino energy.
• Correction for multi-interaction events:
If neutrino interactions occur within one bunch, we cannot identify multiinteraction events by the FADC peak counting. To estimate the mis-identification
probability of multi-interaction events as single-interaction events, we employ the MC simulation which reproduces the FADC pulse-height distribution of multi-interaction events. Comparing the number of FADC peaks
with the MC events, we estimate the correction factor for multi-interaction
events happened in one bunch to be 1.008.

5.1.3

Event rate summary

We obtain the neutrino interaction rate at 1KT with the procedure describedabove. The numbers of neutrino interactions for each experimental period aresummarized in Table 5.1. The neutrino interaction rate as a function of running
time in the 1KT detector is shown in Figure 5.3. The event rate is stable within
the fluctuation of 6%.

5.1.4

Systematic uncertainty

The systematic uncertainty of the 1KT event rate is estimated to be 4.1%. The
dominant source comes from the uncertainty in the fiducial volume. To evaluate46

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK

Table 5.1: Summary of event rate measurements in the 1KT detector.
PeriodPOT1KT (1018 )K2K-IaK2K-Ib
K2K-II

selectN1KT

single

total
Npeak

Npeak

int
N1KT

2.6 4282
10911989782
7206
38.2 75973 1854781 1475799 130856
33.9 83529 2012446 1588669 140268(Normalized by CT)
1999

2000

2001

2003

2004

Month
(Normalized by SSD)
1999

2000

2001

2003

2004

Month

Figure 5.3: The event rate per month in the 1KT detector. The event rate isnormalized by POT measured by TGT-CT (upper) and SPD (lower). The middle
line shows the average and the interval between the lines shows the RMS of theevent rate, which is 2.0% (1.6%) for the upper (lower) figure. The full spread isapproximately 6%.

47

5.2. νµ ENERGY SPECTRUM MEASUREMENT AT THE NEAR SITE

SourceError (%)
Fiducial volume± 3.0
Energy scale± 0.3
FADC stability± 0.8
FADC cut position± 1.5
FADC error± 1.0
Event rate
± 1.6
Background± 0.5
Multi-interaction
± 0.7
Total
± 4.1
int
Table 5.2: Sources of systematic error on N1KT.

this uncertainty, we have studied the performance of the vertex reconstruction
using cosmic-ray muons [57]. We found a bias on the reconstructed vertices lessthan 4 cm, and estimate the uncertainty of the fiducial volume to be 3%. Other
sources of systematic uncertainty are the energy scale, the FADC gain stability and
1KT
the threshold, corrections on Nselect, the event rate stability and the beam profile.
All the uncertainties are summarized in Table 5.2. Details of all the sources aredescribed in Reference [56].

5.2νµ energy spectrum measurement at the near site

For the measurement of the neutrino energy spectrum before neutrinos oscillate,
we use the CC interaction events in 1KT, SciFi and SciBar. The neutrino energy isreconstructed from the muon momentum (pµ ) and angle with respect to the beam
direction (θµ ) by assuming QE interaction asEν =m2p − (mn − V)2 − m2µ + 2(mn − V)Eµ2(mn − V − Eµ + pµ cos θµ )

,

(5.2)

where mp , mn , mµ , Eµ and V are the proton mass, the neutron mass, the muon
mass, the muon energy and the nuclear potential energy (27 MeV for 16 O), respectively. The two-dimensional distributions of pµ versus θµ are used to measure theneutrino energy spectrum.
48

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS ATSKχ2 fitting
The observed pµ -θµ distributions are compared with the MC expectations by a
χ2 fitting method, treating the neutrino energy spectrum in the MC simulation
as fitting parameters. Here we give an example of the procedure in the 1KT
detector. The pµ − θµ distribution with the MC expectation is shown in Figure 5.4.
The neutrino energy in GeV is divided into eight bins: 0.0-0.5, 0.5-0.75, 0.75-1.0,
1.0-1.5, 1.5-2.0, 2.0-2.5, 2.5-3.0 and above 3.0. For the MC expectation, the pµ − θµdistribution is prepared for each Eν bin and separately for QE interactions andother than QE (non-QE); 8 × 2 distributions are prepared in total for each event
sample. The free parameters in the fit are the weighting factors of neutrino energyφφ
spectrum to the MC events for eight energy bins ( f1 , ..., f8 ) and a parameter RnQE
which represents the relative weighting of CC non-QE events to CC-QE events.
The χ2 functions are separately defined for each detector and then summed tobuild a combined χ2 function asχ2 = χ21KT + χ2SF + χ2SB ,(5.3)

where χ21KT , χ2SF and χ2SB are χ2 for 1KT, SciFi and SciBar, respectively. A set of thefitting parameters is found by minimizing the χ2 function. Details of the event
selection and the fitting procedure in each detector are given in References [56,58,
59, 60, 61]. Here only the results of measurement are given.

5.2.1

Measured neutrino energy spectrum at near site

The best-fit values of parameters given by the combined data sample are shownin Table 5.3. We have checked the results of the measurements with individual
detector data: all the fitting parameters are in good agreement within their errors
each other. The measured energy spectrum with the combined data shows a good
agreement with that with each detector sample. We also confirmed that the MC
simulation with the fitted parameters well reproduces all the distributions for eachdetector, such as pµ , θµ and momentum transfer squared q2 (≡ 2Eν (Eµ − pµ cos θµ ),assuming QE interaction). For the resultant RnQE , we evaluate the uncertainty of
RnQE to be 20% by comparing the combined result with the results of each detector.
The measured neutrino spectrum is shown in Figure 5.5. The error matrix
representing correlations between the spectrum parameters fiΦ and RnQE is also
shown in Table 5.4. The neutrino energy spectrum is used as the input to predict49

5.2. νµ ENERGY SPECTRUM MEASUREMENT AT THE NEAR SITE

Figure 5.4: pµ − θµ distributions.
the neutrino spectrum at SK, and the errors and correlations are used in νµ → νeoscillation analysis, which is described in Chapter 8 and 9.
Table 5.3: Results of the spectrum measurement. The best fit value of each parameter is listed for the fits with all the detectors data. The reduced χ2 (χ2total /DOF)
is also shown. (The parameters f1Φ , ·, f8Φ and RnQE are the weighting factors to theMC events.)
parameterf1Φ (0.00-0.50)
1.657 ± 0.437
Φ
f2 (0.50-0.75)
1.107 ± 0.075
Φ
f3 (0.75-1.00)
1.154 ± 0.061
Φ
f4 (1.00-1.50)≡1Φ
f5 (1.50-2.00)
0.911 ± 0.044
Φ
f6 (2.00-2.50)
1.069 ± 0.059
Φ
f7 (2.50-3.00)
1.152 ± 0.142
Φf8 (3.00- )1.260 ± 0.184
RnQE
0.964 ± 0.20
χ2total /DOF
1.17(=687.2 / 585)

50

arbitary unit

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK

0.7
0.6

Measurement

0.5

Beam MC

0.4
0.3

integrated

0.2
0.1
0

0

0.5

1

1.5

2

2.5

3

3.5

FD Spectrum shape (Beam MC)

4

4.5

5

(GeV)

Figure 5.5: The neutrino energy spectrum measured at near detectors (open circles). The expectation with the beam MC simulation is also shown (histogram).

Table 5.4: The error matrix for fiΦ and RnQE . The square root of error matrix isshown here in the unit of %.
f1Φ
f2Φ
f3Φ
f4Φ
f5Φ
f6Φ
f7Φ
f8Φ
RnQE
Φ
f1
43.86 -3.16 7.28
- -2.21 -0.76 -3.48
0.81
-8.62
Φ
f2
-3.16 7.51 1.97
1.90 0.62
1.29
2.43
-5.68
Φ
f3
7.28 1.97 6.00
3.38 1.63
3.44
1.71
-2.99
Φ
f4 (fixed)Φ
f5-2.21 1.90 3.38
4.04 -1.86 4.53
2.20
1.65
Φ
f6
-0.76 0.62 1.63
- -1.86 5.28 -5.85
5.11
0.94
Φ
f7
-3.48 1.29 3.44
4.53 -5.85 13.67 -10.14 4.09
Φ
f8
0.81 2.43 1.71
2.20 5.11 -10.14 18.35 -11.77
RnQE-8.62 -5.68 -2.99 1.65 0.94
4.09 -11.77 20.30

51

5.3. NEAR-TO-FAR SPECTRUM EXTRAPOLATION

5.3

Near-to-far spectrum extrapolation

Due to the finite size of the π decay volume and the detectors, the neutrino
flux is not simply proportional to L−2 , where L is the distance from the target(Appendix C). Therefore, we need to evaluate the energy-dependent flux ratioννµbetween SK and the near site, RF/N ≡ ΦSKµ /ΦND
, to extrapolate the near detector
measurement to SK, where ΦSK and ΦND are the neutrino fluxes at SK and thenear site, respectively. In the current analysis, we adopt a measurement of pion
production cross-section in p − Al collisions by the HARP experiment for the flux
prediction.

5.3.1

The HARP experiment

For the neutrino flux prediction in the previously published results [62, 63, 18],
we adopted the beam MC simulation based on the Cho-CERN pion production
model. It was validated by the in situ measurement of pions by the pion monitor [28]. However, in the uncertainty of νµ energy spectrum at SK, a dominant
contribution has originated from the uncertainty of RF/N which comes from theuncertainty of pion production in primary p − Al collisions.
For the precise measurement of pion production and the far/near flux ratio, the
HARP experiment was conducted at CERN. HARP comprises the same proton
beam momentum (12.9 GeV/c) as K2K and an aluminum target. The HARP detector consists of forward and large-angle detection systems, as shown in Figure 5.6.
In the large angle region, a time projection chamber (TPC) is located in a solenoid
magnet. The forward spectrometer is built around a dipole magnet with magnetic field of 0.66 T with large planar drift chambers (NDCs), a time-of-flight wall
(TOFW), a threshold Cherenkov detector (CHE) and an electromagnetic calorimeter (ECAL). The aluminum target is located inside TPC. A detailed description of
the HARP experiment is given in References [64, 65]. The forward spectrometercovers the angular range of produced pions from 30 mrad to 210 mrad and themomentum range from 0.75 GeV/c to 6.5 GeV/c, which agree with the dominant phase space of the pion production contributing to the K2K neutrino beam.
Therefore, in HARP, we measure the cross-section of pion production relevant to
the K2K far/near flux ratio.
52

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK
Drift Chambers
TOFW

NDC4
NDC5
ECAL

NDC3

NDC2
NDC1
TPC and RPCs insolenoidal magnet

CHE
Dipole magnet
FTP and RPCs

T9 beamyxzFigure 5.6: Schematic view of the HARP detector.

5.3.2

Neutrino flux prediction

The pion production cross-section is formalized by the Sanford-Wang formula as
expressed in Equation 3.1. The Sanford-Wang parameters for the Al target aremeasured by fitting the HARP data with the formula. The best-fit parameters andthe differential cross-sections of pions are shown in Table 5.5 and Figure 5.7. The
details of the HARP analysis are described in Reference [66].

Table 5.5: Parameters of the Sanford-Wang differential cross-section formula obtained by fitting the HARP data.
C1
4.4 × 102

C2C3−
8.5 × 10 1 5.1

C4 = C5
1.78

C6
4.43

C7
1.35 × 10−1C8
3.57 × 101

The production cross-section of pions measured by the HARP experiment isused to predict the neutrino fluxes in the beam MC simulation. Figure 5.8 and5.9 show the νµ flux predictions at the near site and SK, and the ratio of them,
respectively. The predictions based on the Cho-CERN pion production model arealso shown for comparison. The new predictions are in a good agreement withthe previous ones.
53

π30-210 mrad

2500

0.75-6.5 GeV/c

2000
1500
1000

π

80
70
60
50
40
30
20
10
0

dσ / dΩ (mb / sr)dσ / dp (mb / (GeV/c))

5.3. NEAR-TO-FAR SPECTRUM EXTRAPOLATION

0

2

4

500
0

6

0

50

p (GeV/c)

100

150

200

θ (mrad)Φnear (a.u.)

Figure 5.7: The differential cross-section of pions as a function of the pion momentum integrated over the pion angular range of 30 mrad < θ < 210 mrad, andas a function of θ in the pion momentum range of 0.75 GeV/c < p < 6.5 GeV/c.
The points show the HARP measurements. Also shown with the dotted lines are
the Sanford-Wang formula with the HARP best-fit parameters.

0.25
0.2
0.15
0.1
0.05
0
0

0.5

1

1.5

2

2.5

3

Φfar (a.u.)E ν (GeV)
0.25

0.2

0.15

0.1

0.05

0
0

0.5

1

1.5

2

2.5

3

E ν (GeV)

Figure 5.8: νµ fluxes at the near site (top) and SK (bottom) as a function of neutrino energy predicted by the beam MC simulation with the HARP measurement(circles with error bars) and the Cho-CERN model (dotted histograms). The
histograms are normalized to be unit in the integration.

54

2

SK

Φ /Φ

ND

-6

(10 )

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

1

2

3

Eν(GeV)

Figure 5.9: Ratio of νµ flux at SK to the near site predicted by the beam MC simulation. The HARP prediction and the prediction based on the Cho-CERN hadronicmodel are shown by the open circles with error bars and the dotted histogram,respectively. The arrow shows that the contents in last bin are integrated over all
neutrino energies above 2.5 GeV.

5.3.3

Systematic uncertainty

The systematic uncertainties in the νµ flux prediction for each neutrino energy bin
are estimated here, with the error matrix (MF/N ) including the correlation among
different energy bins.
We consider the uncertainties associated with the following objects:• primary beam optics,• primary hadronic interactions of protons,• secondary hadronic interactions,• horn magnetic fields.
For the beam optics parameters, we take into account the uncertainties in theimpact point at the target, the injection angle, the profile width and the angular divergence. They are evaluated from the beam profile measurement by theionization chambers of V39-SPIC and TGT-SPIC (Section 2.2.1).
Second, we consider the effect of the uncertainties in our understanding of primary hadronic interactions. In the p − Al hadronic interaction length, we assume55

5.3. NEAR-TO-FAR SPECTRUM EXTRAPOLATIONan uncertainty of 30% in the simulation. The uncertainty in the multiplicity andkinematics of pion production is estimated by using the uncertainties and correlations in the Sanford-Wang parameters given by the HARP result [66]. For the
production cross-section of charged and neutral kaons, we quote an uncertainty
of 50%.
Third, the effect of interactions of the secondary particles (e.g., inelastic scattering, absorption and charge exchange of pions) is estimated by adopting an alternative model. We evaluate the difference of fluxes between the GCALOR/FLUKA
model and GHEISHA model [67], and also compare them with the available
experimental data.
Finally, we consider the uncertainties due to the magnetic field in the hornsystem, field strength and field homogeneity in azimuth. The uncertainty of
the field strength and the azimuthal field perturbation is evaluated based on themeasurement of the magnetic field using inductive coils as in Reference [68]. We
estimate the uncertainties of 10% and 15% for the field strength and perturbation,
respectively.
Varying the parameters and cross-sections by their estimated errors in the
beam MC simulation, the uncertainty of the far/near flux ratio is estimated. The
estimated systematic uncertainties of RF/N is summarized in Table 5.6. We also
obtain the 6 × 6 error matrix MF/N as follows:
1/2

sign(MF/N ) · MF/N=
0.0 − 0.5 0.5 − 1.0 1.0 − 1.5 1.5 − 2.0 2.0 − 2.5 > 2.5  0.0 − 0.5
−0.6
−1.9
−1.7
1.4
0.2
1.6 



0.2
2.7
3.0
3.7
2.6 −3.7  0.5 − 1.0 1.0 − 1.5
0.6
3.0
3.6
4.6
3.2
4.5  .
 1.5 − 2.0
−1.9
3.7
4.6
6.5
4.7 −6.2  2.0 − 2.5
−1.7
2.6
3.2
4.7
4.2 −5.2 



> 2.5
1.6
−3.7
−4.5
−6.2
−5.2
8.5

(5.4)

The binning of neutrino energy is same as in Figure 5.9 and the values are in theunit of %.

5.3.4

Estimated neutrino energy spectrum at SK

Multiplying the measured energy spectrum at near detectors by the far/near flux
ratio, we obtain the expected νµ energy spectrum at SK in the case of no oscillation;
56

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK

Table 5.6: Summary of the systematic error sources in the far/near flux ratio
prediction. The errors are in %.
Category
Beam optics

Primary hadronic interaction

Secondary hadron interaction
Horn magnetic field

57

∆RF/N
Error source
0.03
Centering
0.03
Aiming0.75
Spread, divergence
0.76
Sub-total
0.63interaction rate
Kinematics of π pro1.43
duction
0.23
Multiplicity of kaons
1.58
Sub-total
0.71
0.52
Strength
Azimuthal field per0.34
turbation
0.62
Sub-total
1.99
Total

5.4. PREDICTION OF THE NUMBER OF NEUTRINO EVENTS AT SK

au

it is shown in Figure 5.10. The expected energy spectrum of νe oscillated from νµwith the oscillation parameters sin2 2θµe = 1.0 and ∆m2 = 2.8 × 10−3 eV2 is also
shown.

νµ w/o oscillation
oscillated νe (CC)

20

10

0

0

1

2

3

4
5
Eν (GeV)Figure 5.10: Expected neutrino energy spectrum at SK. The histogram shows theνµ energy spectrum without oscillation and the dashed one shows the νe energy
spectrum via CC interaction assuming sin2 2θµe = 1.0 and ∆m2 = 2.8 × 10−3 eV2 .

5.4

Prediction of the number of neutrino events at SK

We estimate the number of neutrino interactions in SK, which is used for normalization.
The expected number of neutrino events at SK (NSK ) without oscillation isderived from the 1KT event rate extrapolated by using the far/near flux ratio, live
time and fiducial mass of SK and 1KT. The formulation is expressed as
int
NSK = N1KT
· Rint ·R
Rint = RMSK POTSK·· Cνe · FCFVSK ,M1KT POT1KT
dEν ΦSK (Eν ) · σ(Eν )dEν Φ1KT (Eν ) · σ(Eν )

where
58

,

(5.5)

(5.6)

CHAPTER 5. EXPECTED NUMBER OF BEAM NEUTRINO EVENTS AT
SK
int
N1KT
ΦSK
Φ1KT
MSK
M1KT
POTSK

POT1KT
FCFV
SK
Cνe

:
:
:
:
:
:

The number of neutrino interactions in 1KT (Equation 5.1),
The neutrino flux at SK,
The neutrino flux at 1KT,
The fiducial mass of SK (22.5 ktons, described in Section 6.1),
The fiducial mass of 1KT (25 tons),
The number of protons on target which corresponds to theanalyzed data in SK,: The number of protons on target which corresponds to theanalyzed data in 1KT,
: The detection efficiency of beam neutrinos in SK,: The correction factor for the difference of νe contaminationin the beam at near detectors and SK.

The correction factor Cνe is estimated to be 0.996 with the beam MC simulation.
The measured neutrino energy spectrum at near detectors and the far/near flux
ratio are incorporated into Rint . In νµ → νe search, we use the SK events where thevertex is inside the fiducial volume and all the particles from the interaction are
fully contained in the inner detector. The selection criteria and detection efficiency
FCFV
are described later (Section 6.1). In total, we estimate the total number ofSK
neutrino events at SK without oscillation to be 158.4+9.4
for the entire period of−8.7
K2K. For each experimental phase, we estimate the number of neutrino events to
be 81.1 and 77.4 for K2K-I and K2K-II, respectively.

59

Chapter 6
Selection of beam neutrinos in SK
In this Chapter, we describe the selection criteria of beam neutrinos in SK. Then
we describe the selection criteria for νe signal candidates.

6.1

Selection of beam neutrino events in SK

In this section, we describe the selection criteria for the events originated from theK2K beam neutrinos.

6.1.1

Selection of neutrino events in SK

In SK, the beam neutrino events are stored in a large amount of recorded data.
The expected event rate of beam neutrinos is less than one event per day, while
approximately 106 other triggered events are recorded per day. Most of therecorded events are originated from the background events listed below:• cosmic-ray muons coming from outside of the detector,• decay-electrons emitted from stopping muons in the inner detector,• low energy gamma-rays (. 11 MeV) from radio activity (radon) in the wateror surrounding rock,• flashing light by a discharge of electricity at PMT dynodes,• solar neutrinos,
61

6.1. SELECTION OF BEAM NEUTRINO EVENTS IN SK• atmospheric neutrinos.
The background events except for atmospheric neutrinos are rejected by the data
reduction described below. This is the pre-selection of neutrino events to reduce
the amount of data to be processed, and the sophisticated selection cuts areapplied after the event reconstruction (Section 6.1.2). Considering the differenceof ID PMT density between SK-I and SK-II, some of the selection criteria aredefined separately for K2K-I and K2K-II.
High energy trigger event
In SK, beam neutrino events are selected with the high energy trigger. The trigger
threshold is set to be 31 (16) hit PMTs within 200 nsec time window, whichcorresponds to 50–100 (20–50) photoelectrons for SK-I (SK-II).
Decay-electron cut
When a cosmic-ray muon stops inside the tank, the subsequent decay-electron
could be misidentified as a neutrino event. To reject the decay-electron background, we require more than 30 µsec between the event and the preceding one.
Total photoelectron cut
To reject low energy background events such as gamma-rays from radon or surrounding rock, we require that the events should have more than 200 (94) photoelectrons in 300 nsec time window for SK-I (SK-II). This threshold corresponds toabout 20 MeV/c for electrons and about 190 MeV/c for muons.
Flashing PMT cut
There are sometimes PMTs that flash due to the discharge at dynodes (flashing
PMT events). Since the flashing PMT event is often recognized as a neutrino
event, we require the following criteria to remove it.
1. Maximum photo-electron cut :Since the signal from a flashing PMT is localized, we reject the event with
PEmax /PE300 > 0.2 (0.4) for SK-I (SK-II), where PEmax is the maximum numberof photo-electrons among the PMTs and PE300 is the number of total photoelectrons in 300 nsec time window.
62

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK
2. Timing distribution cut :Most of the flashing PMT events make relatively broad hit-timing distributions. We search for the minimum number of hits within 100 nsec (Nmin ) bysliding time window in the time range 300–800 nsec after the trigger timing.
We reject the events with Nmin ≥ 15 (20) for SK-I (SK-II). If the number of ID
hits is less than 800, we tighten the cut to reject the events with Nmin ≥ 10.
3. Goodness of fit :If the number of ID hits is less than 500 (250) for SK-I (SK-II), we use thegoodness of the vertex fitter to reject the flashing-PMT events. The goodness of fit becomes worse for flashing PMT events because the vertex of
Cherenkov ring is not reconstructed properly. We select the events with thegoodness of fit more than or equal to 0.4.

6.1.2

Reconstruction of neutrino event

Then, we reconstruct neutrino events and apply more strict selection criteria.
The reconstruction algorithm was originally developed for study of atmospheric neutrinos. Each reconstruction step is summarized below. More details
are described in Reference [69].

Vertex finding
The vertex position of an event is reconstructed using the timing information of
the PMTs. The vertex finding algorithm calculate the residual time defined ast0 − tTOF , where t0 and tTOF are the hit time of a PMT and the time of flight of
Cherenkov light from a given vertex to the PMT, respectively. Scanning vertex
points, the algorithm finds the point where the residual times of all the PMTs arein the best agreement. In this step, we also reconstruct the momentum vector andthe Cherenkov opening angle of the most energetic ring in the event.

Ring counting
After the vertex reconstruction, the number of rings and their directions arereconstructed. A description of the ring counting algorithm is given in Section 6.2.
63

6.1. SELECTION OF BEAM NEUTRINO EVENTS IN SK
Particle identification
The reconstructed rings are classified into two particle types of muon-like [minimumionization particle type (MIP-type)] and electron-like (shower-type), by using thering pattern and the Cherenkov opening angle. A description of particle identification is given in Section 6.2.2.
Precise vertex finding
With the particle identification information, another vertex finding algorithm (MSfit) is applied for single-ring events to improve the precision of the vertex position.
The momentum is also estimated from the total number of photoelectrons withina 70◦ half-angle cone relative to the particle direction.

6.1.3

Selection of fully-contained events in the fiducial volume
of SK

As the second step of the data reduction, we select the events where the vertex
is inside 22.5 kt fiducial volume of SK and all the particles are fully containedin the inner detector; these are called Fully-Contained Fiducial-Volume (FCFV)
events. For the FCFV events, we properly reconstruct the Cherenkov ring andmeasure the energy of the particles. The selection criteria are similar to those foratmospheric neutrinos as in Reference [16].
Outer detector cut
We select fully-contained (FC) events using outer detector (OD) information. We
require that the FC events should have the maximum number of hits in the OD
cluster less than 10. In addition, we also reject the event with the number of
OD hits greater than 50 within 800 nsec time window. The remaining cosmic-ray
events are also rejected with this cut.
Visible energy cut
Since the energy threshold is not well-defined in the total photoelectron cut, we
use the visible energy (Evis ). The visible energy is estimated from the sum of all
64CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK
ring energies in the inner detector, assuming all rings are originated by electrons.
We remove the events with Evis lower than 30 MeV.
Visual scan
The remaining events are visually scanned to confirm that the events are reallyneutrino events. A few flashing-PMT events surviving with the above cuts are
removed by this visual scan.
Fiducial volume cut
We require that the reconstructed vertex is within the fiducial volume defined as
Dwall ≥ 2.0 m, where Dwall is the distance from the vertex to the nearest surfaceof ID. This volume corresponds to the water mass of 22.5 kton. Figure 6.1 shows
the reconstructed vertex distribution after the beam timing cut described in Section 6.1.4. We find that the reconstructed vertices are distributed uniformly as acharacteristics of neutrino events. The boundary of the fiducial volume is shownin the figure.

z

z

r2

r2

Figure 6.1: Vertex distribution of beam neutrino events in r2 − z space for K2KI (left) and K2K-II (right), where r and z are the cylindrical coordinates whose
origin is defined as the center on the bottom of the inner detector. The verticesof events inside and outside the fiducial volume are shown by filled and open
circles, respectively. The fiducial volume is shown by the inner lines.

65

6.1. SELECTION OF BEAM NEUTRINO EVENTS IN SK

6.1.4

Beam neutrino selection with GPS information

Finally, to select beam neutrino events and reject atmospheric neutrinos, we apply
a cut based on timing synchronization between the KEK accelerator and SK using
the GPS information. We also require the data accumulated under the good beam
spill conditions.
Using the UTC stamps of the starting time of the beam spills (TKEK ) and theevent time in SK (TSK ), we define the time difference between the observed eventand the expected arrival time of the K2K neutrino beam (∆T) as∆T ≡ TSK − TKEK − TOF,

(6.1)

where TOF is the time-of-flight of neutrinos traveling from KEK to SK, which isapproximately 833 µsec with the assumption that the velocity of neutrino is sameas the light velocity. For the beam originated events, we expect they distributewithin the time range 0 . ∆ T . 1.1 µsec, corresponding to the beam spill width.
Considering the uncertainty of the UTC time stamp of < 0.2 µsec, we impose thetiming cut as−0.2 µsec < ∆T < 1.3 µsec.
Figure 6.2 shows the ∆T distributions for each reduction step within the time
windows of |∆T| < 500 µsec and |∆T| < 5 µsec. The selected events are clustered
within the time window of the beam spill, and they show the bunch structure ofbeam spill as shown in Figure 6.3. These indicate that we have properly selected
the beam neutrino events. Three events outside of the time window are consistent
with atmospheric neutrino events; we expect 2.3 background events originatedfrom atmospheric neutrinos in |∆T| < 500 µsec window.

6.1.5

Observed FCFV events

After the reduction described above, we obtain fifty five and fifty seven FCFV
events for K2K-I and K2K-II, respectively. The data reduction of the FCFV selection is summarized in Table 6.1. The selection efficiency for FCFV events in SK isestimated to be 0.772 and 0.779 for K2K-I and K2K-II, respectively, according to
the MC simulation. As described in Equation 5.5, we expect the number of FCFV
events without oscillation to be 81.1 and 77.4 for K2K-I and K2K-II, respectively.
The relation between the observed number of events and the accumulated
number of POT is shown in Figure 6.4. The observed number is proportional to66

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK

10 4

K2K-1+2 Jun1999 - Nov2004

10 3
10 2
10
1
-500 -400 -300 -200 -100 0 100 200 300 400 500
Tdiff(µs)

18
16
14
12
10
8
6
4
2
0
-5

-4

-3

-2

-1

0

1

2

3

4

5

Tdiff(µs)

Figure 6.2: ∆T distribution for each reduction step. Open, hatched and shaded
histograms in the upper figure are after the decay electron cut, the visible energy
cut and the fiducial volume cut, respectively. The lower is the ∆T distribution
after the timing cut. Data of K2K-I and K2K-II are combined.

SK event timing (1bin=125/2 (nsec))
20
125nsec
15
10
5
0

0

500
1000
event timing (nsec)

Figure 6.3: ∆T distribution in a narrow time window.
676.2. SELECTION OF ELECTRON SIGNAL CANDIDATES IN THE
FULLY-CONTAINED EVENTS

Table 6.1: Reduction of fully contained events in the fiducial volume.
K2K-I
Total number of spill 9177578|∆T| < 500µs
107892High energy trigger
36560
Total p.e. cut
18902
Evis > 30eV
103
Scanning
95
Fiducial volume cut
56−0.3µs < ∆T < 1.2µs
55

K2K-II
8214003
470469
29878
16623
88
87
59
57

the accumulated POT as we expect. The KS-test probability assuming the linear
correlation is 79%.

6.2

Selection of electron signal candidates in the fullycontained events

We have one hundred and twelve fully-contained events in the 22.5kt fiducial
volume of SK. We select the the νe appearance signal candidate events from the
FCFV events with the following requirements:(i) single-ring event,(ii) shower-type ring,(iii) visible energy above 100 MeV (rejection of low energy pions),(iv) no decay electron follows the event (rejection of muons),(v) non-π0 like event.
The selection criteria of each step are described in the following sections. The
selection (i)-(iv) use the standard reconstruction algorithm of atmospheric neutrinos. For the final selection (v), we developed a new reconstruction algorithm,
described in Chapter 7. The data reduction is also summarized after applying
this π0 rejection cut.
68events

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK

K2K-1 K2K-2

100

80

60

40

20

0

0

10 20 30 40 50 60 70 80 90 100
POT vs events18

CT *10 POT

Figure 6.4: Neutrino event rate at SK as a function of POT.

6.2.1

Single-ring event selection

We count the number of Cherenkov rings of the FCFV events, and select singlering events to enhance the fraction of νe CC-QE events. Single-ring events are
separated from multi-ring events based on an estimator using the charge pattern
distribution on the PMTs. A second ring is searched for by scanning possible ring
directions, and the assumption of two rings is compared with that of one ring.
To obtain the number of rings which is most consistent with the data, the ringcounting algorithm works iteratively and tries to find another ring. The estimatoris constructed to take a positive value when the second ring is detected: negativevalues indicate a single-ring event. We require the candidate events to havenegative values of the estimator. Distributions of the ring counting estimator for
K2K-I and K2K-II data, together with those of the MC simulation for the νe signal
events and νµ background events are shown in Figure 6.5. Unless we explicitly
state otherwise, the histograms of the MC events are normalized by the numberof expected νµ events (81.1 for K2K-I and 77.4 for K2K-II) at SK without oscillationin this chapter.
696.2. SELECTION OF ELECTRON SIGNAL CANDIDATES IN THE
FULLY-CONTAINED EVENTS

20
15
10

(single)(multi)2015νµνe(CC)

10

50(single)(multi)νµνe(CC)

5
-40

-20

0
20
40
ring count estimator

0

-40

-20

0
20
40
ring count estimator

Figure 6.5: Distributions of the ring counting estimator for K2K-I (left) and K2K-II(right). The open circles show the data. The solid histogram and the dashed one
show the νµ background MC events and the νe signal MC events on the assumptionof sin2 2θµe =1.0 and ∆m2 = 2.8 × 10−3 , respectively. Negative values indicate thesingle-ring events.

6.2.2

Shower-type ring selection

Next, we identify the particle type of a Cherenkov ring.
An electron or a gamma-ray make a ring with a diffused hit pattern due to theelectromagnetic shower and the multiple scattering. On the other hand, a muon ora charged pion make a ring with the sharp edge and they can be distinguished froman electron or a gamma-ray. In addition, for a given momentum, the difference inmass makes Cherenkov opening angle different for an electron and a muon. Thus,
we construct the estimators based on the ring pattern and the opening angle.
To identify the particle type, the observed charge pattern is compared withthe expectation of an electron or that of a muon based on the MC simulation. The
probability function of the charge for each PMT is assumed to be the Gaussian
distribution ( or Poisson distribution for small photoelectrons) using the numberof observed photoelectrons and the expected one assuming an electron or a muon[69]. The ring pattern likelihood for the electron (muon) ring (L) is constructedwith the product of the probabilities for the PMTs inside the 70◦ half-angle cone
relative to the particle direction. Then, the probability from the ring pattern forelectrons (muons) is given as  χ2 e(µ) − min(χ2 (e), χ2 (µ)) 

 ,
(6.2)
Probpattern e(µ) = exp −

2
2σχ2
70

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK
where χ2 (e(µ)) is translated from the ring pattern likelihood as χ2 (e(µ)) = −2 log L.
√
The resolution of the χ2 distribution, σχ2 , is approximated by σχ2 = N, where N
is the number of PMTs used in the calculation.
For the Cherenkov opening angle, the probability is similarly given as no2  θobs − θexp e(µ) 


 ,
Probangle e(µ) = exp −2
2 (δθ)
(6.3)

Where θobs ,δθ and θexp (e(µ)) are the reconstructed opening angle, the uncertaintyof the reconstruction and the expected opening angle with the reconstructed
momentum assuming an electron (a muon), respectively.
With these variables, two PID parameters of ring pattern (Ppattern ) and opening
angle (Pangle ) are defined as:
Ppattern(angle) =q
q−logPpattern(angle) (µ) − −logPpattern(angle) (e).

(6.4)

The distribution of single ring events in Ppattern −Pangle space is shown in Figure 6.6.
We select the events where both PID parameters are negative as the shower-type
events.

6.2.3

Visible energy cut

Some of νµ -originated background events are caused by low-energy charged pions
or muons. When a charged pion interacts in the water and it makes the Cherenkov
ring edge scattered, the event can be classified as single-ring shower-type by thereconstruction algorithm. In addition, for a muon with the momentum below
Cherenkov threshold, only an electron event from its decay is observed with theenergy of a few tens of MeV. These events have Evis below ∼ 100 MeV. Thus, we
reject the events to have the visible energy below 100 MeV as the background.
The distributions of the visible energy are shown in Figure 6.7.

6.2.4

No decay electron

After the selection cuts described above, a small fraction of muon or mis-identified
charged pion events still remains. To reject these events, we require that thesignal candidate events are not followed by an event of muon-decays within a71

6.2. SELECTION OF ELECTRON SIGNAL CANDIDATES IN THE
FULLY-CONTAINED EVENTS

4(e-like)νµν e(CC)(µ -like)

6
4

opening angle

203(e-like)νµν e(CC)(e-like)νµν e(CC)4(µ -like)

18
14
10
6
2

6

2

6

(e-like)νµν e(CC)2

10

2

opening angle

6

2
1
0

-2

-1

-4

-8

-10

0

-2

(µ -like)(µ -like)

-6

-3

10
ring pattern-5(a) K2K-I

0

5ring pattern(b) K2K-II

Figure 6.6: Distribution of single-ring events in the ring pattern and opening angle
parameter space for K2K-I and K2K-II. The open circles show the data. The open
boxes and the solid ones show the νµ background MC events and the νe signal MC
events on the assumption of sin2 2θµe =1.0 and ∆m2 = 2.8 × 10−3 , respectively. The
selection boundary for shower-type events are shown with lines. The events withnegative values of each PID parameters are classified as the shower like event.
The projections of each PID parameter are also shown, and the hatched region inthem represents the composition of νµ -NC interaction.

72

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK

0.3

0.3
νµ

νµ

νe(CC)0.2
0.1
0νe(CC)

0.2
0.1

0

500

1000
1500
2000
visible energy (MeV)(a) K2K-I

0

0

500

1000
1500
2000
visible energy (MeV)(b) K2K-II

Figure 6.7: Visible energy distribution of single-ring shower-type events. The
remaining events in the data are shown by arrows. The distribution of νµ background MC events are shown by a solid histogram. The contribution of lowenergy charged pion and muon in the νµ -originated background is shown by thehatched region. The νe signal MC events, on the assumption of sin2 2θµe =0.1 and∆m2 = 2.8 × 10−3 , is also shown by a dashed histogram. The selection boundary isdrawn with a line.

736.3. SUMMARY

5

5

4

νµ

4

νµ

3

νe(CC)3

νe(CC)

2

2

1

1

0

0

1

2

3

4
# decay-e0(a) K2K-I

0

1

2

3

4
# decay-e(b) K2K-II

Figure 6.8: Distribution of the number of decay electrons for single-ring showertype events. The remaining events in the data are shown by arrows. The distribution of νµ background MC events and the νµ -NC composition are shown by asolid and hatched histograms, respectively. The dashed histogram shows the νesignal MC on the assumption of sin2 2θµe =0.1 and ∆m2 = 2.8 × 10−3 .
30 µsec time window. Distributions of the number of decay-electrons are shownin Figure 6.8. The criteria of decay electron tagging is described in Appendix D.
With all the standard selection cuts described above, we obtain one signal
candidate for K2K-I and four for K2K-II. On the other hand, we expect that the
number of νµ -originated background events to be 4.1 for the entire data sample.
As shown in Figure 6.8, the νµ -originated background is dominated by the NC
interaction events in which most of them make up π0 ’s, according to the MC
simulation.

6.3

Summary

In this chapter, we described the selection criteria for the beam neutrinos andthe event reconstruction. We obtained one hundred and twelve fully-contained
events in the 22.5 kt fiducial volume of SK.
For the FCFV events, we applied the standard selection cuts to select the signalring shower-type events. We obtained one candidate event in K2K-I and four in
74

CHAPTER 6. SELECTION OF BEAM NEUTRINOS IN SK
K2K-II. However, we expect that the π0 background events are yet to be rejectedaccording to the MC simulation. For the final π0 rejection cut, we give detailed
descriptions in the next chapter. We also give the resultant number of surviving
events after the π0 rejection.

75

Chapter 7
Rejection of neutral pion backgroundIn the search for a signal of νµ → νe oscillation, a dominant source of background
events is originated from π0 production in neutrino-16 O interactions. In this chapter, we introduce a new reconstruction algorithm called ”π0 fitter” to improve theπ0 rejection. At first, we present the characteristics of π0 background events. We
then describe the π0 reconstruction algorithm. Second, we check the performanceof the π0 fitter by using atmospheric neutrinos. In the end, we apply the π0 fitterto the surviving events for the final selection of signal candidate events in K2K.

7.1

Characteristics of π0 background event

A dominant source of background comes from the events with a single π0 decaying into two gamma-rays, where one gamma-ray is missed by the standard
reconstruction algorithm described in Section 6.2. The π0 events are classified as
single-ring shower-type, the same signature of νe -CC interaction. The π0 background mainly originates from NC interaction where a single π0 and no othermesons are produced in the final state from the nucleus. We label this π0 background as ”NC1π0 ”. In the K2K beam energy, a single π0 is produced via ∆resonance of NC interaction as
ν+N → ν+∆,→ N0 + π0 ,where N and N0 are nucleons. In addition, π0 ’s could be produced by final stateinteractions of nucleons or mesons inside of nucleus. We estimate that 70% of
77

7.1. CHARACTERISTICS OF π0 BACKGROUND EVENT
background in the single-ring shower-type sample originate from NC1π0 process
after the standard selection described in Section 6.2. From now on, unless we
explicitly state otherwise, we define that the higher-energy gamma-ray is the”first” gamma-ray and the lower-energy one is the ”second” in π0 decay.
A gamma-ray from π0 decay could be missed with the following reasons.
• The energies of two gamma-rays are highly asymmetric and the energyof second gamma-ray (Eγ2 ) is too small to be reconstructed as a ring (Figure 7.1a).
• The two rings of gamma-rays are overlapped and reconstructed as one
ring when the opening angle between two gamma-rays (θγγ ) is small (Figure 7.1b).
The Eγ2 -θγγ and π0 momentum distributions of NC1π0 background events in the
single-ring shower-type sample are shown in Figure 7.2. Since the events clusterin the Eγ2 region below ∼ 50 MeV, we find the second gamma-ray with lower
energy is not properly reconstructed as a ring, as shown in Figure 7.1(a). We alsofind the events cluster in the region θγγ < 20◦ . To count the Cherenkov rings,
we search ring edges in the observed charge pattern. Therefore, due to the finite
image resolution, we cannot count over two rings for π0 events with θγγ <∼ 20◦
as shown in Figure 7.1(b).

not reconstructed

γ1

γ2
ν

π0

γ
Eγ1>>Eγ2π0ν(a) Highly asymmetric energy decay

θγγγ
θγγ: small(b) Small opening angle

Figure 7.1: Illustrations of π0 production background.

78

Eγ2 (MeV)

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

1000

400

generated

500

200

remaining

0

0

50

100

150
θγγ (degree)

0

0

500

1000
1500
Pπ0 (MeV)

Figure 7.2: Eγ2 − θγγ (left) and π0 momentum (right) distributions of NC1π0background events in the single-ring shower-type sample. In the right figure, thehistogram shows the all events produced via NC1π0 interaction, and the hatchedshows those classified as single-ring shower-type.

7.2

Reconstruction algorithm of the π0 fitterWe describe the new algorithm of the π0 fitter developed to improve the π0
reconstruction.
For the reconstruction of second gamma-ray, the fitter works on the assumptionthat two Cherenkov rings of gamma-ray must exist. The π0 fitter reconstructs two
gamma-rays by comparing the observed charge distribution on the PMTs withthe expected charge distributions of two gamma-rays.
In the fitter, two gamma-rays are supposed to be emitted at one point. Thenthe following variables given by the standard reconstruction algorithm are used
as input:• vertex,• direction of the shower-type ring,• visible energy (Evis ).
The vertex is assumed to be the point where two gamma-rays were emitted, andthe direction of the first gamma-ray is set to be that of the single ring found by
the standard reconstruction. Varying the direction of the second gamma-ray andthe fractions of energy shared among two gamma-rays, we obtain a combination
797.2. RECONSTRUCTION ALGORITHM OF THE π0 FITTERof two gamma-rays which matches with the observed charge distribution. The
estimation of charge distribution and the fitting method are described next.

7.2.1

Expected charge distribution

The expected charge distribution is calculated for the given vertex, momenta anddirections of two gamma-rays. On the assumption that the Cherenkov photon flux
is axially symmetric around the direction of gamma-ray, the Cherenkov photon
fluxes are estimated as a function of the angle θ with respect to the gamma-ray
direction. The shape of electromagnetic shower and its length depend on theinitial gamma-ray momentum (pγ ). Further, the Cherenkov photon flux depends
on the distance of the PMT from the vertex (r). Thus, the direct light distributions
are estimated as a function of θ, pγ and r in the MC simulation.
In this way, the expected photoelectrons for the i-th PMT from a gamma-rayexp(qi ) is given as




 


−ri
r
exp
i
exp


 · exp
qi = α · Q (θi , pγ , ri ) · 1 − q· f acc + qscatt
i

L


r2i + R2PMT 

(7.1)

where
α
exp
Qi

RPMT
L
ri
acc
f
qscatti: the normalization factor,: the expected photon flux from a gamma-ray, which is estimated as a function of θi , pγ and ri ,: the PMT radius of 25 cm,: the attenuation length of water,: the distance from the vertex to the i-th PMT,
: the correction of PMT acceptance as a function of incident
light angle to the PMT.
: the expected scattered light flux on i-th PMT.



q
2
2
The factors of 1 − ri / ri + RPMT and exp (−ri /L) represent the corrections ofsolid angle and light attenuation, respectively. The effect of the light scatteringis also taken into account based on the measurement using a laser as in Reference [55]. Finally, the expected charges are summed for two gamma-rays to obtainan expected charge distribution.
80

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

7.2.2

Finding the best-fit ring configuration

To determine the best-fit configuration of two gamma-rays, a χ2 fit is applied
to the charge distribution with the fitting parameters of gamma-ray momentum
vectors pγ1 and pγ2 . Supposing that the charge pattern is distributed according toPoisson statistics, the χ2 for a PMT (χ2i ) is given by
qobs
i

exp

obs
χ2i (pγ1 , pγ2 ) = 2(qi (pγ1 , pγ2 ) − qobsi ) + 2qi lnexp

qi (pγ1 , pγ2 )

,

(7.2)

exp

where qi is the expected charge on the i-th PMT for the given gamma-rays, andqobs
is the observed one. The fitting is performed by minimizing the overall χ2 , theisum of χ2i among all PMTs, using the simplex method [70, 71]. In the procedure,
we do not require any kinematical constraint of π0 decay.
The π0 events where two rings are almost overlapped have a narrow χ2 distribution in the direction of the first ring. To improve the fitting performance forsuch events, a second fit is performed with the finer stepping to look for the second gamma-ray near the first gamma-ray ring. The procedure of the second fit isidentical to the initial one except that the initial parameters of second gamma-ray
are set to be near the first gamma-ray ring. We choose the fitting result with asmaller χ2 between two fits.
Figure 7.3 shows the energy resolution of gamma-ray as a function of the
gamma-ray energy, estimated from the MC π0 events. The resolution of the firstgamma-ray energy (Eγ1 [GeV]) is estimated to be ∼ 20%, while the resolutionpp
for the second is estimated to be 3.1/ Eγ2 + 19.4(%) for K2K-I and 3.5/ Eγ2 +18.8(%) for K2K-II. The angular resolution of the gamma-ray direction and theopening angles between two gamma-rays are shown in Figure 7.4. The resolutions
are around 8◦ for the gamma-ray direction and ∼ 6.5◦ for the opening angle.
Figure 7.5 shows the distribution of the invariant mass (Minv ) reconstructed fromtwo gamma-rays found by the π0 fitter. The Minv is defined asq
Minv =

2Eγ1 Eγ2 (1 − cos θγγ ).

(7.3)

The resolution of π0 invariant for K2K-I and K2K-II is 22.4 MeV/c2 and 23.1 MeV/c2 ,respectively.
817.2. RECONSTRUCTION ALGORITHM OF THE π0 FITTER

100

75
σ~20%

50

resolution (%)

resolution (%)

100

25
0

100

200

300

400

resolution (%)

σ~20%

50
25
0

0

3.1/(Eγ2(GeV))0.5+19.4

0

50

100

150

100

75

P1
P2

100

200

300

400

200

250 300Eγ2 (MeV)

0.7079E-01/ 8
18.60
3.492

23.10
7.482

75
50
25

0

22.26
7.119

50

500 600Eγ1 (MeV)

100

0.3879E-01/ 8
19.36
3.150

75

25

resolution (%)

0

P1
P2

0

500 600Eγ1 (MeV)

3.5/(Eγ2(GeV))0.5+18.6

0

50

100

150

200

250 300Eγ2 (MeV)

Figure 7.3: Energy resolution of gamma-rays for NC1π0 events for K2K-I (upper)
and K2K-II (lower).

82

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

21.75

1000

σ=8.1˚1000

σ=8.8˚

750

/ 8
825.5
1.201
6.509

0

20

14.56
0.10390.1225

500

500

500

Constant
Mean
Sigma

250
0

0

5 10 15 20 25 30 35 40 45 50

00

5 10 15 20 25 30 35 40 45 50∆θγ1 (degree)

0-40∆θγ2 (degree)

-20

40

∆θγγ (degree)(a) K2K-I

32.69

σ=7.6˚σ=8.3˚

1000

1000

0

5 10 15 20 25 30 35 40 45 50

0Constant
Mean
Sigma

/ 8
1017.
0.16246.567

16.24
0.9550E-01
0.1145

0

20

40

500

500

500
0

1000

0

5 10 15 20 25 30 35 40 45 50∆θγ1 (degree)

0-40∆θγ2 (degree)-20∆θγγ (degree)(b) K2K-II

Figure 7.4: Angular resolution of gamma-rays for NC1π0 events. The angularresolution of gamma-rays is defined as the width in which 68% of the events areincluded.

21.30
Constant
Mean
Sigma

/ 5
1295.
138.0
22.40

15.40
21.16
0.33040.3566

Constant
Mean
Sigma

1500

/ 5
1563.
134.3
23.09

22.96
0.3286
0.3496

1000
1000
500
0

500

0

50

100

150

200

250

300

2

0

0

50

100

150

200

250

300

2

Minv (MeV/c )Minv (MeV/c )Figure 7.5: Reconstructed π0 invariant mass distribution of NC1π0 events for
K2K-I (left) and K2K-II (right).
83

7.3. PERFORMANCES OF π0 RECONSTRUCTION

7.3

Performances of π0 reconstruction

In order to check the performance of the π0 fitter, we use MC NC1π0 events
in SK with the K2K neutrino energy spectrum. We apply the π0 fitter for the
NC1π0 events. When the multiple rings are found in the standard reconstruction
algorithm, the ring with highest energy is used as the input to the π0 fitter.
At first, with the standard reconstruction algorithm, we select the single π0
events with the following selection criteria:(i) two-ring events,(ii) both rings are shower-type,(iii) no decay electron follows,(iv) 85 MeV/c2 < Minv < 185 MeV/c2 .
Criterion (iii) is used to reject invisible muons and charged pions whose momentum is below the Cherenkov threshold. The detection efficiency of NC1π0 event
is estimated to be 46% (44%) for K2K-I (K2K-II), for the standard algorithm.
Second, we select the π0 events by the π0 fitter to compare the performancewith the standard reconstruction algorithm. In this event selection, we only
require one ring with shower-type. So we remove the criteria (i) and (ii), andreplace them with(i’) single or multi-ring events with one shower-type.
Then, we apply the π0 fitter to find the two gamma-ray rings. In the calculationof invariant mass in criterion (iv), we use the momenta and the opening angle
between two gamma-rays reconstructed by the π0 fitter. Applying the criteria (i’),(iii) and (iv) with the π0 fitter, we improve the π0 detection efficiency of NC1π0
event to 76% (78%) for K2K-I (K2K-II). The detection efficiencies as a functionof π0 momentum and in Eγ2 -θγγ space with the MC-true information are shownin Figure 7.6 and 7.7, respectively. With the π0 fitter, we recover the π0 events
especially with high momentum in which the opening angle of two gamma-rays
is small or the energy of the second gamma-ray is low.
84

1efficiency

efficiency

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

0.8
0.6

1
0.8
0.6

0.4

0.4

0.2

0.2

0

0

500

1000
1500
π momentun (MeV/c)
0

0

0

500

1000
1500
π0 momentun (MeV/c)

Figure 7.6: π0 detection efficiency as a function of momentum for K2K-I (left) andK2K-II (right). The open circles show the efficiency with the standard reconstruction by criteria (i)-(iv) and the solid circles show that with the π0 fitter by criteria(i’)+(iii)+(iv).

7.4e/π0 separation

In this section, we study the performance of the separation between electrons andπ0 ’s.
For the separation between the electron events and the π0 events, we use theinvariant mass of two gamma-rays reconstructed by the π0 fitter. We note thatthe π0 fitter may find the second gamma-ray ring even for single-electron events.
The invariant mass distributions of νµ -originated background and νe signal events
for single-ring shower-type events are shown in Figure 7.8. The π0 background
events have a value of Minv close to the π0 mass, while a νe signal event has Minv
smaller than the π0 mass. This is explained as follows.
For νe signal events, there is no real second ring and the fitter could reconstruct
the second fake ring with hits around the first energetic ring. Because the electromagnetic shower and light scattering defuse the edge of the first ring and makescattered hits around it, the fitter recognizes these hits as a ring of gamma-ray.
Therefore, the angle between the second fake ring and the first ring is expected to
be close (∼ 20◦ ). Further, the visible energy is equivalent to the shower-type ringenergy (Ee ) for the single-ring shower-type events and the second gamma-ray energy tends to be small after sharing Ee with the two-ring configuration. Figure 7.9
shows distributions of the reconstructed opening angle and the energy fraction of
the first gamma-ray (Eγ1 /(Eγ1 + Eγ2 )). Considering that Ee is shared with two rings
85

400

6

22

13

29

8

32

100
80

36

200

0

60

46

81

37

69

27

72

74

14

53

74

75

72

16

42

66

68

68

66

64

64

1

9

13

21

26

20

20

0

40

50

100

Eγ2 (MeV)

Eγ2 (MeV)

7.4. E/π0 SEPARATION

400

74

68

62

87

65

73

68

73

77

100

74

83

68

84

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92

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79

40

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15

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θγγ (degree)

0

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20
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58

150
θγγ (degree)

0

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400

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2

0

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44

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62

65

47

5

11

16

26

24

18

17

50

40

100

Eγ2 (MeV)

Eγ2 (MeV)(a) K2K-I

400

200

20
11

7

150
θγγ (degree)

0

0

0

100

55

61

80

72

73

83

59

80

35

77

86

35

80

84

76

87

86

58

86

91

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92

35

63

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91

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51

48

52

57

67

66

62

57

80
60

50

40

100

20
48

47

150
θγγ (degree)

0(b) K2K-II

Figure 7.7: π0 reconstruction efficiency in Eγ2 -θγγ space. The left figures show theefficiency with the standard reconstruction and the right ones show that with theπ0 reconstruction.

86

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND
and the reconstructed opening angle and the energy fraction are assumed to beconstant (∼ 20◦ and ∼ 0.9), we expect a linear dependence of Minv on the electronpenergy as Minv = 2(0.9Ee )(0.1Ee ))(1 − cos 20◦ ) ∝ Ee , as shown in Figure 7.10.
As a result, for the νe signal event in the energy region of K2K neutrino beam,
Minv is reconstructed to be smaller than the nominal π0 mass. Then, by selecting
the low Minv events, we can separate the electron events from the π0 events.
We also find that the peak position of Minv for the π0 background events isslightly shifted lower from the nominal π0 mass as shown in Figure 7.8. We
reconstruct Minv less than the π0 mass when Evis (or Ee ) is smaller than the true π0energy (E0π ). Because the standard reconstruction algorithm defines the observed
charge within a 70◦ half opening angle of Cherenkov ring toward the particle
direction as Ee , the energy of the second gamma-ray is not included in Ee for the
events where the opening angle of two gamma-rays is large. Figure 7.11 shows
the difference between Ee and Eπ0 for the π0 background events with θγγ < 40◦and θγγ > 70◦ . Although Ee is equivalent to Eπ0 for the events with θγγ < 40◦ , Ee isslightly lower than Eπ0 for the events with a large θγγ . Consequently, we observe
Minv lower than the π0 mass when Ee is smaller than Eπ0 and it is shared with two
gamma-rays in the π0 fitter.

7.5

Validation of π0 fitter with atmospheric neutrinos

We apply the π0 fitter for the real data of atmospheric neutrinos to validate theperformance.
Using the standard reconstruction algorithm, we select the events with two
shower-type rings (two-ring shower-type events) by requiring the criteria (i)(iv) given in Section 7.3. Figure 7.12 shows the invariant mass distribution of
two-ring shower-type events for atmospheric neutrinos. The MC histograms arenormalized by the live time of 1492 days for SK-I and 627 days for SK-II. We thenapply the π0 fitter to these samples. The comparison of reconstructed gammaray energies and opening angle between the standard reconstruction and the π0
fitter is shown in Figure 7.13. We find a good agreement between the standard
reconstruction algorithm and the π0 fitter for the two-ring π0 events, and also finda good agreement between data and the MC events.
We also perform a check for e/π0 separation by using the single-ring eventsof atmospheric neutrinos. (These atmospheric neutrino events have the same87

au

7.5. VALIDATION OF π0 FITTER WITH ATMOSPHERIC NEUTRINOS

νµ
νe

10

5

0

0

100

200

300
Minv (GeV/c2)

30
νµ
νe

20

10

νµ
νe

5

10
0

au

au

Figure 7.8: Invariant mass distribution of π0 → γγ for single-ring shower-type
events. The solid line shows the νµ background MC events, and the dashed line
shows the νe signal MC events assuming ∆m2 = 2.8 × 10−3 eV2 .

0

50

100

150
θγγ (degree)

0
0.5

0.6

0.7

0.8
0.9
1
energy fraction

Figure 7.9: Opening angle (left) and energy fraction (right) distributions givenby the π0 fitter for single-ring shower-type events. The solid line shows theνµ background MC events, and the dashed line shows the νe signal MC events
assuming ∆m2 = 2.8 × 10−3 eV2 .

88

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

Minv (MeV/c2)

200
150
100
50
0

0

500

1000

1500
Ee (MeV)Figure 7.10: Profile histogram of Minv -Ee for νe signal events under the assumptionof ∆m2 = 2.8 × 10−3 eV2 .

150
100

17.71

θγγ < 40°

Constant
Mean
Sigma

/ 18
132.5
-3.315
30.78

32.14
5.202
0.98130.7371

200

/ 13
263.8
-21.3816.10

10.43
0.50350.4027

100

50
0
-200

θγγ > 70°

Constant
Mean
Sigma

0

200
Ee -Eπ0 (MeV)

0
-200

0

200
Ee -Eπ0 (MeV)

Figure 7.11: The difference between the shower-type ring energy and the π0energy for the π0 background events with θγγ < 40◦ (left) and θγγ > 70◦ (right).

89

7.5. VALIDATION OF π0 FITTER WITH ATMOSPHERIC NEUTRINOS

100
30

75

20

50

10

25
0

0

100

200

300

0

0

2

100

200

300

2

Minv (MeV/c )Minv (MeV/c )Figure 7.12: The invariant mass distributions for the atmospheric neutrino eventswith two shower-type rings for SK-I (left) and SK-II (right). The open circles andhistogram show the data and the MC events, respectively. The hatched histogramshows the contribution from NC interactions. The selection boundary is shownby lines. The MC histograms are normalized by the live time of the detector.
topology as νe signal or νµ -originated background in K2K.) In this sample, morethan 90% of events are originated from νe (ν̄e ) interaction, and the remaining
fraction comes from νµ (ν̄µ ). The π0 ’s are produced via NC interaction of νe (ν̄e ) andνµ (ν̄µ ), and have a ∼ 6% fraction of the events. Figure 7.14 shows the distributionof atmospheric neutrinos in Minv -Ee space. The MC event distributions for CC and
NC interactions are separately shown in the top and middle plots, respectively.
We can see the π0 events clustered around the π0 invariant mass for NC interaction.
In the distribution of the data, we can recognize the events around the π0 mass
expected by the NC interaction of the MC simulation. Figure 7.15 shows theinvariant mass distribution of single-ring shower-type events with the showertype ring energy below 250 MeV. The invariant mass distribution of electrons andπ0 ’s shows reasonable agreement between the data and the MC simulation. In
addition, the invariant mass peak of π0 is obtained by fitting with a combinationof the Gaussian function for the π0 events and the exponential function for theelectron events (Figure 7.16). The fitted peaks of data and the MC events for
SK-I (SK-II) are 122(118) MeV/c2 and 116(117) MeV/c2 , respectively. The data areconsistent with the MC simulation considering the energy scale uncertainty of
2% [60] and the statistical uncertainty of data; the estimated statistical errors are±2MeV/c2 and ±3 MeV/c2 for SK-I and SK-II, respectively.
90

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

100

50

0

0

200

400

600

800

100

80

75

60

50

40

25

20

0
1000 0200

Eγ1 (MeV)

400

0

0

50

100

150

θγγ (degree)Eγ2 (MeV)(a) SK-I

40

40

20

20

0

0

200

400

600

800

40

20

0
1000 0200

Eγ1 (MeV)

Eγ2 (MeV)

400

0

0

50

100

150

θγγ (degree)(b) SK=II

Figure 7.13: Comparison of reconstructed gamma-ray energies and opening angle
between the standard reconstruction and the π0 fitter for SK-I (upper) and SK-II(lower). The open boxes show the distributions for the standard reconstruction,and the open circles show that for the π0 fitter.

91

7.5. VALIDATION OF π0 FITTER WITH ATMOSPHERIC NEUTRINOS

Figure 7.14: Event distribution of atmospheric neutrinos in Minv -Ee space. The
upper and middle figures shows the CC and NC interaction in the MC simulation,
respectively. The lower shows the data. The boxes indicate the region where theπ0 events lie, expected by the MC simulation.

Data
MC
π0

100

50

0

60

Data
MC
π0

40
20

0

100

200
Minv (MeV/c2)

0

0

100

200
Minv (MeV/c2)

Figure 7.15: Invariant mass distribution of single-ring shower-type events foratmospheric neutrinos in SK-I (left) and SK-II (right). The open circles and histogram show the data and the MC events, respectively. The contribution of π0
events is shown by the hatched region.
92

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

60

Data
MC

100

Data
MC

40
50

0

20

0

100

200
Minv (MeV/c2)

0

0

100

200
Minv (MeV/c2)

Figure 7.16: Invariant mass distribution of single-ring shower-type events ofatmospheric neutrinos for SK-I (left) and SK-II (right). The distributions are fitted
by a combination of the Gaussian function with the exponential function. The
results are shown by the solid (dashed) lines for the data (the MC events).
We perform another check for e/π0 separation using the events with two rings
where one is MIP-type and the other is shower-type (two-ring µ − e sample). Thiskind of event topology is mainly attributed to the π0 production via CC interaction(νµ + N → µ + π0 + N0 ) where a muon and only one gamma-ray are reconstructed.
After masking the hits associated with the MIP-type ring, we obtain the sample
similar to the π0 background events. We applied the π0 fitter to this sample, andreconstructed the invariant mass as shown in Figure 7.17. We find the π0 events inthis two-ring µ − e sample by the π0 fitter. The Minv peaks of the data and the MC
simulation for SK-I (SK-II) are 120 ±7(117±8) MeV/c2 and 117 ±2(116±2) MeV/c2 ,respectively. The data and the MC events show a good agreement, and values ofthe Minv peaks are also consistent between the data and the MC events.
We checked the validity of the π0 fitter and confirmed the performance withthe real data as we expected in the MC simulation.

7.6

π0 rejection for the K2K data sample

In this section, we apply the π0 fitter in the selection criteria of νe signal candidate
events.
Using the invariant mass Minv of two gamma-rays given by the π0 fitter and the93

7.7. SUMMARY OF DATA REDUCTION

SK-I

20

SK-II
12

15

8

10

4

5
0

0

50

100

150

200

250

300

350

400

450

0

0

50

100

150

200

250

300

350

400

450

Minv(MeV/c2)

Minv(MeV/c2)

Figure 7.17: Reconstructed π0 invariant mass distributions of two-ring µ-e sample
for atmospheric neutrinos. The points with error bars and boxes show data andthe MC events, respectively. The hatched histogram shows the fraction of π0
production in the MC simulation. The left and right figure show SK-I and SK-II,
respectively. The fitted peaks of data and the MC events are 120±7(117±8) MeV/c2
and 117 ± 2(116 ± 2) MeV/c2 , respectively.
shower-type ring energy Ee as estimators, we separate the νe signal events fromthe π0 background events. The resultant Minv -Ee plot is shown in Figure 7.18. The
selection boundary is set to be 100 MeV/c2 . Here, we consider that the resolutionof invariant mass is poor for π0 events with low momentum, while the νe signal
events with a small Ee tend to have a small value of Minv , as shown in Figure 7.10.
Thus, in the region of Ee < 400 MeV, we apply a tighter Minv cut to the event. The
resultant selection cut is set to be

3Ee



Minv < 20 + 40 MeV for Ee < 400 MeV,
(7.4)



M < 100 MeV
for E ≥ 400 MeV.
inve

The signal region is optimized to maximize the sensitivity for the νµ → νe signal
with sin2 2θµe = 0.05 and ∆m2 = 2.8 × 10−3 eV2 , based on the MC study.
After the π0 rejection, we find one surviving event in K2K-II.

7.7

Summary of data reduction

The reduction of the data, the background and signal expectations according
to the MC simulation are summarized in Table 7.1 and 7.2. The MC events
are normalized by the expected number of FCFV events without oscillation, as
described in Section 5.4. In the table, we consider the small fraction of the νe94

Minv (MeV/c 2)

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

300

K2K-I
νµ

K2K-I
ν e(CC)

200
100
0

0

500

0

1000

500

1000
Ee (MeV)

Minv (MeV/c 2)

Ee (MeV)300

K2K-IIνµ

K2K-IIν e(CC)

200
100
0

0

500

1000

0
Ee (MeV)

500

1000
Ee (MeV)Figure 7.18: Distribution of candidate events in the Minv -Ee space for K2K-I (upper)
and K2K-II (lower). The left figures show the νµ background MC events, and theright ones show the νe signal MC events on the assumption of ∆m2 = 2.8 × 10−3 .
Surviving events before the π0 rejection in data are shown by open circles. The
selection boundary is also shown by a line with a bent.

957.7. SUMMARY OF DATA REDUCTION
contamination in the beam as shown in Figure 3.2. This beam-νe flux has beenchecked by the νe flux measurements of the near detectors (Appendix B).
The efficiency of νµ rejection and νe selection as a function of neutrino energy
with all the selection cuts are shown in Figure 7.19. The overall efficiency for theselection of νe via CC interactions for K2K-I and K2K-II is 47% and 51%, respectively. This selection efficiency of K2K-II is a little larger than K2K-I, however,the νµ background expectation is also larger for K2K-II. That is due to the poor
ring counting performance of SK-II for the second ring: SK-II has the lower PMT
density than SK-I and the finding efficiency of second ring is slightly worse dueto the lower image resolution. The overall νµ rejection factors are estimated tobe 0.55% and 0.74% for K2K-I and K2K-II, respectively. In Figure 7.19, the tightrejection of νµ in the lowest energy bin is due to the visible energy cut. The lower
νe selection efficiency above 1 GeV is due to the π0 rejection cut: the events witha high energy electron have a large value of Minv , and are rejected as π0 -like.
We have searched for a signal of νµ → νe oscillation among one hundred andtwelve beam neutrino events in SK. After all the selection cuts, we observed one
signal candidate event in the data. This is consistent with the total backgroundexpectation of 1.7 events. The statistical tests of distribution are described inAppendix E. Five events remain before the final selection of π0 fitter, and fourof them are rejected as π0 -like. This rejection capability is consistent with what
we expected: 70% of νµ -originated events are rejected by the invariant mass cut
according to the MC simulation. The rejection of νµ -originated background foreach interaction mode is summarized in Table 7.3.
Feature of the surviving event in the data
The event display of the single surviving event is shown in Figure 7.20. While
this event is categorized as a single-ring shower-type event by the standard reconstruction procedure, we recognize that the π0 fitter properly finds two possible
rings like a π0 event. With a manual examination of ring reconstruction, the surviving candidate event is revealed to have more than two rings. As a matter offact, we found it is inconsistent with the π0 mass with any combination of tworings. The CC and NC multi-meson production contributes to the classification ofmulti-ring event. The breakdown of the νµ -originated background expectation is
given in Table 7.4. The fraction of the multi-hadron background event is estimatedto be 12.7% for K2K-I and 15.7% for K2K-II, which results in the expectation of96

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND

Table 7.1: Reduction of events for νµ → νe search at SK. The MC events arenormalized by the expected number of FCFV events without oscillation. The firstcolumn lists each selection cut. The others give the number of observed events,
νµ -originated background in the case of no oscillation and beam-νe for K2K-I and
K2K-II, respectively. The νµ -originated background expectations with νµ → ντoscillation of sin2 2θµτ = 1 and ∆m2 = 2.8 × 10−3 eV2 are given in parentheses.

FCFV
single ring
shower likevisible energy cut
no decay electron
non-π0 like

K2K-I
data
νµ
55
81.1 (54.18)
33 50.92 (30.59)
3
2.66 (2.41)
22.47 (2.25)
1
1.90 (1.83)
00.58 (0.56)

beam-νe
0.81
0.47
0.40
0.40
0.35
0.17

K2K-IIdataνµ5777.4 (51.55)
34 49.41 (29.72)
5
3.21 (2.81)
5
2.93 (2.61)
4
2.17 (2.06)
10.74 (0.69)

beam-νe
0.86
0.52
0.44
0.44
0.39
0.21

Table 7.2: Reduction of νe signal MC events on the assumption of the oscillation
parameters of sin2 2θµe = 1.0 and ∆m2 = 2.8 × 10−3 eV2 . The MC events arenormalized by the expected number of FCFV events without oscillation. The firstcolumn lists each selection cut. The second and third give the expected number of
events for K2K-I and K2K-II, respectively. The efficiencies in each selection step
are given in parentheses.
K2K-I
FCFV
28.2 (97.3%)
single ring
22.7 (78.3%)
shower like20.3 (70.0%)
visible energy cut 20.1 (69.3%)
no decay electron 18.3 (63.3%)
non-π0 like13.7 (47.2%)

97

K2K-II
24.7 (98.6%)
19.8 (78.9%)
18.3 (72.8%)
18.1 (72.2%)
16.5 (65.7%)
12.9 (51.3%)

1.4

efficiency

efficiency (10-2)

7.7. SUMMARY OF DATA REDUCTION

K2K-I
K2K-II

1.2
1.0

1
K2K-I
K2K-II

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2
0

0

1

2

3

4
5
Eν (GeV)00(a) νµ rejection

1

2

3

4

5
Eν (GeV)(b) νe selection efficiency

Figure 7.19: Efficiencies of νµ -originated background rejection (a) and νe signal
selection (b) as a function of neutrino energy.

Table 7.3: νµ rejection factors after all the selection cuts for each interaction mode.
K2K-I
CC-QE
6.8 × 10−4
CC single meson 1.2 × 10−3
CC multi mesons 9.9 × 10−4NC
1.7 × 10−298

K2K-II
9.2 × 10−4
2.3 × 10−3
1.7 × 10−3
2.3 × 10−2

CHAPTER 7. REJECTION OF NEUTRAL PION BACKGROUND
0.2 event. Thus, we conclude the surviving event could be originated from themulti-hadron production and it is consistent with the background expectation.
As a result, we found no evidence for a signature of νµ → νe oscillation.

NUM
12
RUN
21858
SUBRUN57
EVENT
2240771
DATE 2003-Mar- 3
TIME
23:40:28
TOT PE:
1697.
MAX PE:
28.7
NMHIT :
773
ANT-PE:
24.1
ANT-MX:
3.5
NMHITA:
28

1

1

1

1
1

1

1

1

1
1

1

1

1

1

1

1

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**/04/12:;R= 1:NoYet
R :Z : PHI : G
GOOD
10.28: -3.18:-0.23:0-3.18:-0.23:0.818
CANG : RTOT : AMOM : M
MS
41.9:
1027:
409: -4.1
V= 0.436:-0.717: 0.5
0.544

RunMODE:NORMALTRG ID :00000011
T diff.: 360.
FEVSK :81022801
nOD YK/LW: 2/ 2
SUB EV : 0/ 2
Dcye: 0( 0/ 0/ 0
CT:1075273452
SKGPS: 104670242
94825782
RN: 7593SP:
PSGPS: 104670242
94743194
GPSDIF:
0.62

Comnt;

Figure 7.20: Single candidate event remaining after all selection cuts. The ringreconstructed by the standard fitter (solid line) and two rings by the π0 fitter(dashed lines) are drawn.

99

7.7. SUMMARY OF DATA REDUCTION

Table 7.4: Breakdown of νµ background events after all the selection cuts.

CC-QE
CC single π0
CC single meson
CC multi mesons
NC single π0
NC single meson
NC multi mesons
NC elastic

K2K-I K2K-II
2.9%
5.5%
2.5%
4.4%
2.2%
5.7%
2.2%
3.7%
71.6% 57.4%
6.0%
8.6%
10.5% 12.0%
2.1%
2.7%

100

Chapter 8
Estimate of systematic uncertainties
In the measurement of νµ → νe oscillation parameters, we compare the observed
number of events with the expectation in SK. In this chapter, we estimate thesystematic uncertainty of the expected number of events in SK.
The events in SK are classified into three categories: νµ -originated background,beam-νe background and νe appearance signal. We estimate the expected numberof events for each of them. Then, the systematic uncertainties of normalization,interaction cross-section and selection efficiency are evaluated. Summary tablesof the systematic uncertainties for each event category are given in the end of thechapter (Table 8.1, 8.2 and 8.3).

8.1

Expectation of the number of events in SK

The number of signal and background events are estimated based on the total
number of neutrino interactions in SK (NSK ) described in Section 5.4.
The expected number of νe signal events, Sνe , is derived by multiplying theratio of the expected signal event rate (rνe ) to the neutrino interaction rate without
oscillation (rnull ):rνe (sin2 2θµe , ∆m2 ),(8.1)
Sνe = NSK ·
rnull
Z
2
2
rνe (sin 2θµe , ∆m ) ≡dEν ΦνSKe (Eν | sin2 2θµe , ∆m2 ) · σ(Eν ) · νSKe (Eν ),(8.2)
Zrnull ≡

ν ,nulldEν ΦSKµ(Eν ) · σ(Eν ) · FCFV
SK (Eν ),

101

(8.3)

8.1. EXPECTATION OF THE NUMBER OF EVENTS IN SK
ν ,null

where ΦνSKe , ΦSKµ , σ, νSKe and FCFV
are the νe flux at SK with oscillation parametersSK22of sin 2θµe and ∆m , the νµ flux at SK without oscillation, the neutrino interaction cross-section with water, the νe detection efficiency after all the selection cutsand the νµ detection efficiency for the FCFV events without oscillation, respectively. The neutrino flux at near detectors (ΦND ) and the far/near flux ratio areincorporated into νµ flux at SK:
ν ,nullΦSKµ(Eν ) = RF/N (Eν ) · ΦND (Eν ).

(8.4)

ν

In a two-flavor approximation, ΦνSKe and the νµ flux ΦSKµ are written asν ,nullΦνSKe (Eν | sin2 2θµe , ∆m2 ) = Pνµ →νe (Eν | sin2 2θµe , ∆m2 ) · ΦSKµ (Eν ),
(8.5)
h
i
ν ,nullνΦSKµ (Eν | sin2 2θµe , ∆m2 ) = 1 − Pνµ →νe (Eν | sin2 2θµe , ∆m2 ) · ΦSKµ (Eν ), (8.6)
where Pνµ →νe is the probability for νµ → νe oscillation. To take into account thesystematic uncertainty in σ, we classify interaction modes into four categories:
CC-QE, CC other than CC-QE (CC non-QE), NC1π0 and NC other than NC1π0(NC-other).
Similarly, the expected numbers of background events originated from νµ andbeam νe , Bνµ and Bbeam−νe , are written as follows:Bνµ = NSK ·rνµ (sin2 2θµe , ∆m2 )
rnull

,

(8.7)

rbeam−νe
,
(8.8)
rnull
where rνµ and rbeam−νe are obtained by replacing the flux and the detection efficiencyof νe in Equation 8.2 with those of νµ and beam νe . The beam-νe flux at SK isestimated based on the beam MC simulation.
When we estimate the expected numbers of events and the uncertainties,
we take into account the differences of neutrino fluxes and detector systematics
between the experimental phases (K2K-Ia, K2K-Ib and K2K-II).
Bbeam−νe = NSK ·Effect of neutrino oscillations
When neutrino oscillations occur, the estimation of the event selection efficiency
and the number of events vary, which could affect the estimation of the systematic
uncertainty.
102

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIESFor the νµ -originated background, NC interaction dominates as shown in
Table 7.4. The number of background events is not so sensitive to νµ oscillationto ντ with parameters sin2 2θµτ = 1.0 and ∆m2 = 2.8 × 10−3 eV2 . It only affect the
reduction of the number of background events by ∼ 5% (Figure 9.1 in Section 9.1),
which is much smaller than the systematic uncertainty. The contribution of ντ CC
interactions is negligibly small. Thus, we do not account for the effect of νµ → ντoscillation.
The effect of beam-νe oscillation is also negligible.
For the νe appearance signal, the νe energy spectrum depends on ∆m2 and theselection efficiency could be varied with ∆m2 . Thus, we evaluate uncertainties byscanning ∆m2 and assign the maximum among them as the uncertainty.

8.2

Uncertainties of normalization

This section covers the systematic uncertainties related to the normalization: detector systematics of 1KT and SK, νµ energy spectrum, far/near flux ratio, neutrino
fluxes and accumulated POT.
Detector systematics
In the estimate of event rate in SK, systematic uncertainties could originate
from the event selection in the 1KT detector and SK.
For the 1KT detector, details are already described in Section 5.1 and theuncertainty is 4.1%.
For SK, a dominant contribution comes from the uncertainty of the fiducial
volume definition. We use two vertex fitters to analyze the SK events as
described in Section 6.1.2. Comparing the number of events in the fiducial
volume between two fitters by using atmospheric neutrino data, we obtain
the difference in the ratio of data to the MC events by 2%. This is assigned
as a systematic uncertainty of the fiducial volume.
Another contribution comes from the uncertainty by the OD cut. Comparing
the number of hits in an OD cluster between the data and the MC events
for the partially contained events of atmospheric neutrinos, we evaluate asystematic uncertainty. The difference of the number of OD hits between
the data and the MC events is estimated to be 15% (30%) for SK-I (SK-II).
A change of the OD cut threshold by this difference varies the expected1038.2. UNCERTAINTIES OF NORMALIZATION
number of events by 0.2% (0.4%) for K2K-I (K2K-II). We assign it as thesystematic uncertainty.
We estimate the total uncertainty of 3% on the expected number of events
due to the uncertainty of SK detector.
νµ energy spectrum
We estimate the νµ energy spectrum at SK by using the measured νµ energy
spectrum at near detectors. The uncertainty due to the νµ energy spectrum
is derived from the error of the spectrum measurement at near detectors
given in Table 5.4.
Far/near flux ratio
The uncertainty from the far/near flux ratio is estimated from the errors of
RF/N given in Equation 5.4.
Number of protons on target
In the normalization of SK events, the correction of POT (POTSK /POT1KT ) is
applied to account for the difference of live time between 1KT and SK. The
uncertainty due to the POT correction is estimated as
POTSK − POT1KT· δS,
POT1KT(8.9)

where δS is the stability of the 1KT event rate, evaluated to be ±6% considering the full spread of the event rate fluctuation (Figure 5.3). We estimate
the uncertainties in the number of events for K2K-Ia, K2K-Ib and K2K-II to
be ±1.0%, ±0.6% and ±0.3%, respectively.
Pion/kaon production in p − Al collisions
Muon and kaon decays contribute to the beam-νe flux as shown in Figure 3.3,
and we evaluate their uncertainties in the number of beam-νe events.
To estimate the uncertainty of the pion production, we adopt alternative
pion production models in its production [35]. Comparing between ourdefault model and alternative models, we evaluate the error on the flux
ratio of beam-νe to νµ at SK as shown in Figure 8.1. Varying the νe /νµ ratio by
its error, we estimate that the beam-νe flux uncertainty affects the number ofbeam-νe background events by +14.5%(+14.1%) for K2K-I (K2K-II).
−11.5
−11.2
104

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIES

Figure 8.1: Flux ratio of beam-induced νe to νµ at SK (left). The beam MC prediction
with our default pion production model is shown by circles. The error boxes show
the the maximal deviation from our default model for alternative pion production
models. The right figure shows the relative deviation.
For the kaon production, there is no available data. Therefore, a 100%
fraction of νe yield from kaon decays is conservatively treated as the systematic uncertainty, which results in an uncertainty of ±15.8% in the expected
number of beam-νe events.

8.3

Uncertainties of neutrino interaction cross-sections

In this section, we describe the uncertainties in neutrino interaction cross-section
which mainly affect the estimate of the number of νµ -originated background
events.
Neutral current cross-sections
The NC1π0 background has a 70% fraction in the total background events.
For understanding the cross-section in the water, we have measured thecross-section ratio of NC1π0 production to CC interaction (NC1π0 /CC) [72]with the 1KT detector. NC1π0 events are selected by extracting events with
two shower-type rings. Then, the events are required to have the invariant
mass within the range 85 − 215MeV/c2 . The CC interactions are selected in
the same procedure as the νµ energy spectrum measurement [56]. The 1KT
measurement of NC1π0 /CC gives 0.064 ± 0.001(stat.) ± 0.007(sys.), and ourMC simulation predicts the ratio to be 0.065. Taking into account the errors
on this measurement and the difference between the two central values, weevaluate the uncertainty of 12% to the NC1π0 /CC ratio.
105

8.3. UNCERTAINTIES OF NEUTRINO INTERACTIONCROSS-SECTIONSFor NC interaction other than NC1π0 , we quote an uncertainty of 20% in the
cross-section ratio to CC as in Reference [73].
Varying these cross-sections by their errors, we estimate the contributions
to the systematic uncertainty for the number of νµ -originated background
events. The estimated uncertainties are ∼ 8% and ∼ 2% from NC1π0 andNC-other, respectively. The contributions to the beam-νe prediction are
estimated in the same way.
NC coherent π0 production model
For the coherent NC π0 production, the model of Rein and Sehgal [74]with modification by Marteau et al. [75] is used in our MC simulation.
However, the measurement of CC coherent pion production cross-section
with SciBar [76] is consistent with no CC coherent pion signal; this indicatesthe possibility that the cross-section of the NC coherent π0 production is
also considerably smaller than the MC prediction assuming the isospin
relation. Considering that, the difference between the zero NC coherent
pion production case and the model of Rein and Sehgal is taken into accountas an systematic uncertainty, which affects the number of νµ -originatedbackground events by +3%.
−10
π0 spectrum in the water
Final state interactions of nucleons and mesons inside of nuclear matter
could substantially alter the π0 momentum, which affect the expected number of π0 background events. In order to account for the uncertainty of theπ0 spectrum in our simulation, we have checked the differences of the π0spectra between the 1KT data and the MC simulation. In the 1KT detector,
π0 events are selected as described in Section 7.3. Figure 8.2 shows the reconstructed π0 momentum distribution in 1KT. Reshaping the MC π0 spectra of
SK by the differences of π0 momentum between data and the MC events in
1KT, without changing the normalization, we estimate the contribution to
the number of νµ -originated background events. It is estimated to be 8.0%
and 9.6% for K2K-I and K2K-II, respectively.
CC non-QE cross-sections
The uncertainty in CC non-QE cross-section has an effect mainly on thenumbers of νe signal and beam-νe events. Varying this cross-section by its
106

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIES

Figure 8.2: Reconstructed π0 momentum distribution in the 1KT detector (upper).
The dots with error bars and the boxes show data and the MC events, respectively.
The ratio of data to the MC events is also shown (lower).
uncertainty from the near detector measurement of 20%, the uncertainty
in the expected number of events is estimated to be about 5% for both of
νe signal and beam-νe . The uncertainty in the νµ -originated background isestimated to be ∼ 1%.

8.4

Uncertainties of selection efficiency

We describe the uncertainty of the selection efficiencies in this section.
Ring counting
Most of the νµ -originated background events comes from π0 ’s. To estimate
the uncertainty due to the ring counting for the νµ -originated background,
we have compared the distributions of ring counting estimator for the atmospheric neutrino data and the MC events with two shower-type rings.
The selection criteria for π0 events is described in Section 7.3. The distribution of the ring counting estimator for the two-ring shower-type events isshown in Figure 8.3. We define the uncertainty of ring counting estimator forνµ -originated background events as the difference of the peak position (∆)
p
between data and the MC events: ∆ ≡| µdata − µMC | + (∆µdata )2 + (∆µMC )2 ,where µdata(MC) and ∆µdata(MC) is the peak position and its error for data (MCevents), respectively. The distribution is fitted with Gaussian function to107

8.4. UNCERTAINTIES OF SELECTION EFFICIENCY
find the peak position. Shifting the MC distribution of the ring counting
estimator by ∆, we estimate the change of the expected number of events.
We apply this change as the systematic uncertainty due to the ring counting,which results in ±4.3% (±3.5%) for K2K-I (K2K-II).
For the signal νe and beam-νe events, we have performed the similar procedure as described above. The MC shift value is evaluated by using singlering shower-type events of atmospheric neutrinos in the energy range up
to several GeV. We estimate the contributions to the beam-νe and νe signal predictions for K2K-I (K2K-II) to be ±3.1% (±1.3%) and +2.3
% (+1.3
%),
−6.9
−2.9
respectively.

60

Data
MC

20

Data
MC

40
10
20
0

0

20
40
ring counting estimator

0

0

20
40
ring counting estimator

Figure 8.3: Distribution of ring counting estimator for atmospheric neutrino
events with two shower-type rings. The open circles and boxes show the data andthe MC events, respectively. The peak position is estimated to be 7.5±0.3(7.1±0.7)
for the data and 6.8 ± 0.1(6.7 ± 0.1) for the MC events in SK-I (SK-II). The fitted
Gaussian functions for the data and the MC events are indicated by solid anddashed lines, respectively.
Shower-type ring identification
The systematic uncertainty due to the particle identification is estimatedwith a similar procedure to that for the ring counting, using atmospheric
neutrinos. The contribution to the expected number of events for K2K-I%) for the% (+3.6% (+7.2%) and +4.3%), +4.6(K2K-II) is estimated to be +2.4
% (+6.1
−5.0
−5.0
−6.9
−5.1
−4.9
−6.1
νµ -originated background, beam-νe and signal νe , respectively.
Decay-electron tagging
Figure 8.4 shows the detection efficiency of decay-electrons measured by108

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIES

0.8

efficiency

efficiency

using cosmic-ray muons which stop inside the inner detector. The uncertainty in the decay-electron tagging is estimated from the difference of theefficiency between data and the MC events. Varying the efficiency by thisdifference, we estimate the uncertainties of 1.7% and 1.1% in the number ofνµ -originated background events for K2K-I and K2K-II, respectively.

0.6

0.8
0.6

0.4

0.4

0.2

0.2

0

0

5000

0

10000
photoelectrons

2000

4000

6000
photoelectrons

Figure 8.4: Detection efficiency of decay-electrons for SK-I (left) and SK-II (right).
The open circles and boxes show the data and the MC events, respectively. The
efficiencies are shown as a function of observed photoelectrons.
π0 rejection cut
The uncertainty of π0 rejection comes from the nuclear effects(e.g., final stateinteractions and nuclear deexcitations [77]), the variations of water properties and other possible reconstruction biases. To account for these contributions, we have compared the Minv distributions of atmospheric neutrinos
between the data and the MC events; the in situ measurements of π0 eventswith only one reconstructed shower-type ring have been already describedin Section 7.5. In this sample, the difference of Minv peak position between
data and the MC events is estimated to be less than 10 MeV including statistical uncertainty. The other sample of π0 , two-ring µ − e events, also gives
an uncertainty of 10 MeV in the reconstructed invariant mass. We evaluate the uncertainty due to the Minv cut by changing the selection boundaryby 10 MeV. It is estimated to be +18.6% (+18.9%) for the νµ -originated back−18.4−18.7
ground in K2K-I (K2K-II). For both of beam-νe and signal νe , the uncertainty
is estimated to be about 6% (3%) for K2K-I (K2K-II).
109

8.5. SUMMARY

attenuation length (m)Stability of water properties
There is a possibility that variations of water properties, such as light absorption, scattering and reflection, could affect the finding efficiency of a
gamma-ray ring with small energy. These effects are estimated by changing
the water properties in the MC simulation. To check the stability of water properties, we have measured the light attenuation length in SK using
cosmic-ray muons during the entire running period. The attenuation lengthis measured from the observed photoelectrons corrected by the travel lengthof Cherenkov photons; the travel length is determined by the distance between a PMT and a muon track [78]. According to this measurement shownin Figure 8.5, the attenuation length is changed by ±20%(±15%) for SK-I
(SK-II), which results in systematic effects of ±11.3% (±5.7%) on the numberof νµ -originated events for K2K-I (K2K-II). The contributions to the signal νeand beam-νe predictions are estimated to be about 4%.
160
140
120
100
80
60
40
20
0

160
±20%

SK-II

140

±15%

120
100
SK-I
80

Super-Kamiokande Preliminary
A
P
R
9
6

J
A
N
9
7

J
A
N
9
8

J
A
N
9
9

J
A
N
0
0

J
A
N
0
1

J
A
N
0
2

J
A
N
0
3

J
A
N
0
4

60

0

200

400

600

800

days from 2003/1/1

Figure 8.5: Stability of light attenuation length for SK-I (left) and SK-II (right).

8.5

Summary

Contributions of each systematic uncertainty in νµ -originated background, beamνe background and νe signal expectations are summarized in Table 8.1, 8.2 and 8.3,
respectively.
For the expectation of νµ -originated background, the dominant uncertainties
are related to the π0 production cross-sections and its rejection. This is dueto the fact that the background is still dominated by the π0 production events.
Among those components, we have assigned the largest uncertainty on the π0
rejection cut. The pion/kaon yield at the aluminum target is the main contribution110

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIES

Table 8.1: Systematic uncertainties [%] in the expectation of νµ -originated background.

1KT systematics
SK systematics
νµ energy spectrum
Far/Near flux ratio
POT
NC1π0 /CC cross-section ratio
NC/CC cross-section ratio (for nonNC1π0 )NC coherent π0 production model
π0 energy spectrum
non-QE/QE cross-section ratio
ring counting
shower-type ring identification
decay-e tagging efficiency
π0 rejection
water properies
total

K2K-I
(K2K-Ia) (K2K-Ib)
±4.1
±4.1
±3
±3
+5.1
±13.6
−4.9
+14.7
±2.8
10.5
±1.0
±0.6
±8.4
±8.4

K2K-II
±4.1
±3
+5.1
−4.8
+2.9
−2.8

±0.3
±8.1

+3.9
−3.7

+2.4
−2.2

+2.4
−2.3

+2.8
−10.0

+2.8
−10.0

+2.6
−9.4

±8.0

±8.0

±9.6

+1.6
−2.1

+1.0
−0.9

+1.0
−0.8

±4.3

±4.3

±3.5

+2.4
−4.9

+2.4
−4.9

+6.1
−6.9

±1.7

±1.7

±1.1

+18.6
−18.4

+18.6
−18.4

+18.9
−18.7

±11.3

±11.3

±5.7

+33.8
−31.8

+37.3
−25.6

+39.3
−24.4

to the systematic uncertainty of the beam-νe flux. However, this uncertainty is
not significant because the fraction of beam-νe events in the total background issmall. For the expectation of νe signal events, the major sources originate from themeasurements of the νµ energy spectrum and the non-QE/QE cross-section ratio.
In total, the expected number of events for νµ -originated background, beam-νe, respectively. The numbers of total background, 0.38+0.12
background are 1.32+0.50
−0.08
−0.33
events for K2K-I, K2K-II and K2K-I+II are estimated to be 0.75+0.21, 0.95+0.30
and
−0.16
−0.19
+0.51
1.70−0.34 , respectively. When we incorporate all the systematic uncertainties in the
expected number of events, we take into account the correlations between neutrino flux ration, fluxes and cross-sections according to Equation 5.4 and Table 5.4.

111

8.5. SUMMARY

Table 8.2: Systematic uncertainties [%] in the expectation of beam-νe background.

1KT systematics
SK systematics
pion production
kaon production
POT
NC1π0 /CC cross-section ratio
NC/CC cross-section ratio (for nonNC1π0 )NC coherent π0 production model
non-QE/QE cross-section ratio
ring counting
shower-type ring identification
decay-e tagging efficiency
π0 rejection
water properies
total

112

K2K-I
(K2K-Ia) (K2K-Ib)
±4.1
±4.1
±3
±3

K2K-II
±4.1
±3

+14.5
11.2

+14.5
−11.2

+14.1
−11.5

±15.8
±1.0
±0.2

±15.8
±0.6
±0.2

±15.8
±0.3
±0.2

±0.1

±0.1

±0.1

±0.2

±0.2

±0.2

+5.2
−6.5

+4.7
−5.5

+5.7
−5.5

±3.1

±3.1

±1.3

+4.6
−6.1

+4.6
−6.1

+7.2
−5.1

±0.1

±0.1

±0.3

+5.9
−6.2

+5.9
−6.2

+2.6
−2.3

±3.7

±3.7

±4.5

+30.5
−20.3

+32.5
−20.8

+31.5
−22.8

CHAPTER 8. ESTIMATE OF SYSTEMATIC UNCERTAINTIES

Table 8.3: Systematic uncertainties [%] in the expectation of νe signal.

1KT systematics
SK systematics
νµ energy spectrum
Far/Near flux ratio
POT
NC1π0 /CC cross-section ratio
NC/CC cross-section ratio (for nonNC1π0 )non-QE/QE cross-section ratio
ring counting
shower-type ring identification
decay-e tagging efficiency
π0 rejection
water properies
total

113

K2K-I
(K2K-Ia) (K2K-Ib)
±4.1
±4.1
±3
±3
+6.8
±16.0
−6.3
+16.0
±2.1
−10.0
±1.0
±0.6
±1.4
±1.4

K2K-II
±4.1
±3
+6.7
−6.3
+2.1
−2.2

±0.3
±1.4

±1.0

±1.0

±1.0

+5.2
−6.5
+2.3
−6.9
+4.3
−5.0

+4.7
−5.5
+2.3
−6.9
+4.3
−5.0

+5.7
5.5
+1.3
2.9
+3.6
−5.0

±2.7

±2.7

±0.3

+5.7
−6.2

+5.7
−6.2

+2.2
−2.7

±3.7

±3.7

±4.5

+24.7
−21.2

+20.5
−13.6

+19.8
−11.6

Chapter 9
Constraint on neutrino oscillation
parameters
We obtained one signal candidate event in the data as described in Chapter 7. It
is consistent with the background expectation of 1.7, and no evidence for νµ →
νe oscillation signal was found. Then the constraint on the neutrino mixing
parameters is set by using one observed signal event with the MC backgroundexpectation. In this chapter, we calculate the upper limits on the oscillation
parameters. We also describe the statistical analysis method, the comparison
with the past experiments and the implication of our result for the future.

9.1

Calculation of upper limits

To set the upper limits on the νµ → νe oscillation parameters in a two-flavor
neutrino oscillation model, we adopt a confidence interval construction with
the Poisson distribution using the expected number of events and the observed
number. The expected number of events Nexp is represented by the sum of an
appearance signal and two background components as
Nexp (sin2 2θµe , ∆m2µe ) = Sνe (sin2 2θµe , ∆m2µe ) + Bνµ (sin2 2θµe , ∆m2µe ) + Bbeam−νe , (9.1)
where Sνe is the number of νe signal events, Bνµ is the number of background
events originated from νµ or oscillated ντ , and Bbeam−νe is the number of beam-νe
events. Sνe and Bνµ depend on the probability of νµ → νe oscillation (Pνµ →νe ).
115

9.1. CALCULATION OF UPPER LIMITSPνµ →νe is expressed as

2
2
2


sin 2θµe · sin (1.27 · ∆m · L/Eν ) (for CC),Pνµ →νe (Eν | sin2 2θµe , ∆m2 ) = 0(for NC),(9.2)

where Eν is neutrino energy in GeV and L is the flight distance of 250 km. Since
the oscillation signature in the K2K experiment is smeared in the large ∆m2 region,
we take an average of oscillation probability for CC interactions in ∆m2 region
above the third oscillation maximum:Pνµ →νe (Eν | sin2 2θµe , ∆m2 ) =

2
2
2


sin 2θµe · sin (1.27 · ∆m · L/Eν ) 1 sin2 2θµe
2(9.3)
(for 1.27 · ∆m2 L/Eν < 11π)
4(for 1.27 · ∆m2 L/Eν ≥ 11
π).
4

Number of events

Number of events

When we estimate the contribution of νµ → ντ oscillation to Bνµ , we assume
the best-fit parameters of the K2K νµ disappearance analysis: (sin2 2θµτ , ∆m2 ) =(1.0, 2.8×10−3 eV2 ). The effect of beam-νe oscillation is negligible. The formulationsof Bνµ , Bbeam−νe and Sνe are given in Equation 8.7, 8.8 and 8.1, respectively. The
dependence of the number of events on the oscillation parameters is shown in
Figure 9.1. The number of background events is not sensitive to the νµ → νeoscillation parameters. The number of νe signal events becomes maximum around∆m2 = 5 × 10−3 eV2 .
1.8
ν µ +beam-ν e

1.7

1.6

1.5
-4
10

30
ν e signal(sin22θ µ e =1)

20

10

10

-3

10

-2

∆m2 (eV2)

0
-4
10

10

-3

10

-2

∆m2 (eV2)

Figure 9.1: The expected number of events as a function of ∆m2 . The left shows
the total background, and the right shows the νe signal assuming sin2 2θµe = 1.

116

CHAPTER 9. CONSTRAINT ON NEUTRINO OSCILLATIONPARAMETERS

9.1.1

Confidence interval with the unified method

We consider the Poisson distribution for the expected number of events to construct a confidence interval. In our case, the probability of getting a measured
value of n events for a given set of oscillation parameters P(n | sin2 2θµe , ∆m2 ) is
simply expressed as

n
Nexp
P(n | sin2 2θµe , ∆m2 ) =e−Nexpn!
nSνe + Bνµ + Bbeam−νe=e−(Sνe +Bνµ +Bbeam−νe ) .
(9.4)
n!
For each value of ∆m2 , a probability α (β) to observe n event more than (less than)
the number of observed events nobs is written asXα=P(n| sin2 2θloµe , ∆m2 ),(9.5)
n≥nobsX

β=up

P(n| sin2 2θµe , ∆m2 ),(9.6)

n≤nobsup

Then, we obtain the confidence interval [sin2 2θloµe , sin2 2θµe ] which contains afraction 1 − α − β.
For the construction of the confidence interval, the Bayesian approach is often
applied. However, the Bayesian approach has the following issues:• It do not cover the case when we measure a parameter near the physicalboundary or null parameter.
• The true value of the parameter is treated as a random variable, and it does
not provide a statistically exact confidence interval.
When we have a number of nobs smaller than the expected background events, we
obtain an anomalously low upper bound. In order to avoid these issues, we apply
the unified method of Feldman and Cousins proposed in Reference [79]. It covers
the treatment of the confidence interval for both of null and non-null results, andnaturally provides two-sided intervals.
The Feldman and Cousins method introduces the ratio of likelihoods as an
unified ordering principle when we select the values of n to place in the confidence
interval, that isP(n|T),(9.7)
RT (n) =P(n|Tbest )117

9.2. HANDLING OF SYSTEMATIC UNCERTAINTIES
where T is the set of oscillation parameters (sin2 2θµe , ∆m2 ), and Tbest gives thehighest probability for P(n|T) in the physically allowed region of sin2 2θµe and∆m2 . The interval of Nexp is determined by adding values of n in decreasing orderof RT , until the sum of P(n|T) exceeds the required confidence level (C.L.) as{Nexp ; RT (Nexp ) ≥ CT }.

(9.8)

where CT is the lower bound on RT for the required C.L. The notation {A; B}
represents a conditional ensemble of A satisfying B. Then, the unified intervals of
oscillation parameters are defined as{T; RT (Nexp ) ≥ CT }.

9.2

(9.9)

Handling of systematic uncertainties

In order to implement the systematic uncertainties listed in Chapter 8, we convolute the Poisson probability with functions representing their probability densitiesof the expected number of events as follows:(i) Suppose a certain set of oscillation parameters,(ii) Define a toy model of the experiment with randomly generated systematicparameters listed in Table 8.1, 8.2 and 8.3,(iii) Perform the virtual experiment for a case which the oscillation parameters
is set above, and obtain the number of events in the Poisson regime,(iv) Repeat the virtual experiment with various systematic parameters,(v) Estimate the probability of observing n events from many virtual experiments.
The simple Poisson probabilities of Equation E.1 are replaced by the obtained
probability densities. When we generate the systematic parameters, we supposethat each of them distributes as a Gaussian or an asymmetric Gaussian with thestandard deviations of errors. For the near-to-far flux extrapolation, we take
into account the correlations between the neutrino fluxes and cross-sections byadopting the error matrices given in Equations 5.4 and Table 5.4.
The probability densities as a function of the expected number of events arecomputed numerically in that way, and their distributions with some oscillation
parameters are shown in Figure 9.2.
118

Probability

CHAPTER 9. CONSTRAINT ON NEUTRINO OSCILLATIONPARAMETERS

0.3

null oscillation22-3
sin 2θ µe = 0.1, ∆m =2.8×102
2-3
sin 2θ µe = 0.5, ∆m =2.8×102
2-3
sin 2θ µe = 1.0, ∆m =2.8×10

0.2
0.1
0

0

10

20

30

40

50
Nobs

Figure 9.2: Probability density functions for K2K-I+II.

9.3

Results

Scanning along the oscillation parameter space and calculating the confidence
intervals, we set the upper bound on the νµ → νe oscillation parameters. We
search a series of oscillation parameters where the confidence interval of 90%(99%) coverage probability would exclude the case of observing one event or
below, as shown in Figure 9.3. Figure 9.4 shows the obtained upper bounds andexperimental sensitivities at 90% and 99% C.L. for K2K-I, K2K-I and K2K-I+II.
Here, the sensitivity is defined as the average of upper limits calculated froman ensemble of virtual experiments with the expected background and no truesignal. The formulation is given asXupνs (n | sin2 2θµe , ∆m2 ) × P(n | sin2 2θµe = 0, ∆m2 ),(9.10)
nup

where the νs (n | sin2 2θµe , ∆m2 ) is the upper limit of sin2 2θµe with the observationof n events, and P(n | sin2 2θµe = 0, ∆m2 ) is the probability that one would observe nevents in the case of no oscillation, respectively. At the ∆m2 region of 2.8×10−3 eV2 ,the neutrino oscillation from νµ to νe is constrained assin2 2θµe < 0.13

(90%C.L.),< 0.27(99%C.L.).

119

9.3. RESULTS

probability

The most strict limit of sin2 2θµe < 0.10 (90% C.L) is set at the region of ∆m2 ∼5 × 10−3 eV2 . Upper bounds with independent data sets of K2K-I and K2K-II arealso shown in Figure 9.4.

99% C.I.
90% C.I.

0.2

2

sin 2θµe=0.13

0.1

0

2

sin 2θµe=0.27

0

5

10

15

20

25
Nobs

Figure 9.3: Confidence intervals at 90% and 90% coverage probabilities. The
probability density functions are calculated assuming ∆m2 = 2.8 × 10−3 eV2 .

9.3.1

Check with an alternative approach

As a check of the obtained result, we perform an alternative approach of constructing the confidence intervals. Figure 9.5 shows the comparison of upperbounds between the Feldman and Cousins method and the classical limit calculation with the single-sided interval. The classical method gives slightly strict
limits, however, it is consistent with the result of Feldman and Cousins.

9.3.2

Effect of the systematic uncertainty

We estimate the uncertainty of ∼ 30% in the expected numbers of background
events. Figure 9.6 shows the comparison of the upper bounds obtained with andwithout the systematic uncertainty. We found that the systematic uncertainty
little affect the limit on sin2 2θµe with the current statistics. Figure 9.7 showsthe expected sensitivities of sin2 2θµe as a function of POT with and without thesystematic uncertainties. We suppose that the neutrino beam properties and the120CHAPTER 9. CONSTRAINT ON NEUTRINO OSCILLATIONPARAMETERS-1∆m2 (eV2)∆m2 (eV2)

-1

10

-2

-2

10

10

-3

-3

10

10
excluded (99% C.L.)

sensitivity (99% C.L.)

excluded (99% C.L.)

sensitivity (99% C.L.)

excluded (90% C.L.)

sensitivity (90% C.L.)

excluded (90% C.L.)

sensitivity (90% C.L.)

-4

10

0

10

-4

0.2

0.4

0.6

0.8
1
sin22θµe

10

0

0.2

(a) K2K-I

0.4

0.6

0.8
1
sin22θµe(b) K2K-II∆m2 (eV2)

-1

10

-2

10

-3

10

excluded (99% C.L.)

sensitivity (99% C.L.)

excluded (90% C.L.)

sensitivity (90% C.L.)

-4

10

0

0.2

0.4

0.6

0.8
1
sin22θµe(c) K2K-I+II

Figure 9.4: Upper bounds of νµ → νe oscillation parameters at 90% and 99% C.L.
for K2K-I (a), K2K-II (b) and K2K-I+II (c). The sensitivities for each C.L. are also
drawn with dashed (90%) and dot-dashed (99%) lines.

1219.4. DISCUSSION∆m2 (eV2)

10-1

10-2

10-3

10

99%C.L.(F&C)

99%C.L.(classical)

90%C.L.(F&C)

90%C.L.(classical)

0.2

0.6

-4

0

0.4

0.8
1
sin22θµe

Figure 9.5: Comparison of upper bounds on νµ → νe oscillation parameters
between the Feldman and Cousins method (solid lines) and the classical limit
calculation (dashed lines).
performances of the SK detector are similar to those of K2K-Ib in the calculation.
The systematic uncertainty could become a dominant effect on the sensitivity if
we collect more than 10 times statistics.

9.4

Discussion

We describe the comparison of our result with the past experimental results. Then
we present our prospects of further neutrino oscillation searches.

9.4.1

Comparison with past experimental results

K2K-I published result
We have previously reported the search for νµ → νe oscillation with the K2K-I data
set [63]. We observed one signal candidate with the background expectation of
2.4 events. In the previous search, we applied the event selection without the π0
fitter and found that the π0 background events dominate. In fact, we concluded
122

CHAPTER 9. CONSTRAINT ON NEUTRINO OSCILLATIONPARAMETERS∆m2 (eV2)

10-1

10-2

10-3

10

99%C.L.

99%C.L.(w/o syst. error)

90%C.L.

90%C.L.(w/o syst. error)

-4

0

0.2

0.4

0.6

0.8
1
2
sin 2θµe

sin22θµe

Figure 9.6: Upper bounds of νµ → νe oscillation parameters with (solid line) andwithout (dashed line) systematic uncertainties.

0.5
90% sensitivity (stat.+syst.)
99% sensitivity (stat.+syst.)
90% sensitivity (stat. only)
99% sensitivity (stat. only)

0.4
0.3
0.2
0.1
0

K2K entire sample

1

10
POT (x1020)

Figure 9.7: Expected sensitivities at 90% and 99% C.L. as a function of POT. The
sensitivities for each C.L. with or without the systematic uncertainties are drawn
by solid and dashed lines, respectively. The numbers of νe signal events arecalculated on the assumption of ∆m2 = 2.8 × 10−3 eV2 .

123

9.4. DISCUSSION
that the observed event could be the π0 production background by the visual
examination.
In the new search, we have analyzed the entire K2K data sample which corresponds to almost the double statistics of our published results of K2K-I. We
revised the signal selection by applying the π0 fitter. The background events aresuppressed by 70% and the signal candidate of K2K-I is rejected by the new cut.
Consequently, we improved the sensitivity of νµ → νe oscillation. The sensitivityof sin2 2θµe is 0.17 at ∆m2 = 2.8 × 10−3 eV2 for the entire data sample; this is twotimes as strict as the previous one.
Results from reactor ν̄e experiments
As mentioned in Chapter 1, we can probe the neutrino mixing angle θ13 from ourresult on the assumption:sin2 2θµe '1
sin2 2θ13 .
2(9.11)The limit on sin2 2θ13 is set assin2 2θ13 < 0.26 (90%C.L.)(9.12)

at ∆m2 = 2.8 × 10−3 eV2 . Currently, this is most strict result on this mixing anglein νµ → νe appearance experiments.
Further, the reactor ν̄e experiments with a few km baseline provide complementary results to the search for non-zero value of θ13 in K2K. In the ∆m2
region of 2.8 × 10−3 eV2 , the most stringent limit from the reactor experiments
is sin2 2θ13 < 0.13 by CHOOZ [20] and a weaker limit of < 0.20 is reported by
Palo-Verde [21], showing a good agreement with our result. Constraints on ∆m2 sin2 2θ13 space by various experiments are shown in Figure 9.8. The allowed
region given by Kamiokande [80] and the indicated space by SK [81] using atmospheric neutrinos, on the assumption of the three-flavor framework and thenormal mass hierarchy, are also shown in the figure.

9.4.2

Future prospect of mixing angle θ13

Measurement of the mixing angle θ13 is important to resolve the leptonic mixing
and probe CP violation in the leptonic sector. The CP asymmetry ACP is inversely124∆m2 (eV2)

CHAPTER 9. CONSTRAINT ON NEUTRINO OSCILLATIONPARAMETERS

10-1

10

-2

10-3

10

-4

0

– )
CHOOZ 90%C.L. (ν–e→ν
x–
Palo Verde 90%C.L. (νe→ν– x)
K2K 90%C.L. (νµ→νe)
Kamiokande 90%C.L. (νµ→νe)
SK 3-flavor 90%C.L. (3-flavor, NH)

0.2

0.4

0.6

0.8
1
2
sin 2θ13

Figure 9.8: Constraints on ∆m2 -sin2 2θ13 space by various experiments.

1259.4. DISCUSSION
proportional to sin θ13 as
ACP =Pνµ →νe − Pν̄µ →ν̄ePνµ →νe + Pν̄µ →ν̄e=∆m212 L sin 2θ12
4Eν

!
×

sin δ
.
sin θ13(9.13)We believe the measurement of θ13 is the most important issue in neutrino physics
for several years or a decade. Currently, no experiment shows the evidence of
non-zero value of θ13 , and our resulting upper bound on the mixing parameters
are still limited by statistics as shown in Figure 9.6. The experimental sensitivityof sin2 2θ13 reaches < 0.1 with ∼ 10 times statistics in K2K, while the systematic
uncertainty in the expectation of background events prevents us to improve thesensitivity. The π0 production is still the dominant background and has a large
contribution to the systematic uncertainty. For a further search, we need to reducethe π0 background and improve the statistics.
In near future, some projects with nuclear reactors and high-intensity accelerators are planed or going to start to measure θ13 with large statistics; their
sensitivity on sin2 2θ13 is expected to be O(10−3 ). Especially, an accelerator experiment of T2K [82] is scheduled to start in a few years. T2K has some advantages
in beam intensity and spectrum: the statistics is expected to become ∼ 50 times
as much as K2K for five years, and the neutrino beam energy is tuned to theoscillation maximum with a narrow spread to enhance the oscillation signature.
However, T2K uses SK as the far detector. The NC π0 production background is
crucial as well as K2K, although the narrow band neutrino beam with averagedenergy 0.8 GeV suppresses the resonance production of π0 . To settle this issue,
we took the initiative in rejecting the π0 background events and demonstrated thesearch for νµ → νe oscillation in this thesis.
Hopefully, the mixing angle θ13 is not zero and will be addressed in the future
experiments.

126

Chapter 10
Conclusions
We reported the results of the search for νµ → νe oscillation in the K2K longbaseline neutrino oscillation experiment with the entire data sample of 9.2 × 1019
protons on target.
Our search for νµ → νe signal is based on detection of charged current quasielastic interaction of νe in the Super-Kamiokande detector. The signature of νeappearance is the event with one shower-type Cherenkov ring generated by anelectron. With this classification, the dominant background comes from π0 ’s induced by νµ NC interactions. A single π0 decaying into two gamma-rays can
be classified as a single-ring shower-type event, when one gamma-ray is notreconstructed. To improve the π0 rejection capability, we developed a new π0
reconstruction algorithm and validated its performances using atmospheric neutrino data. We revised the signal selection imposing the π0 rejection cut andachieved the π0 background suppression by 70%. As a result, we have improved
the experimental sensitivity for νµ → νe oscillation.
We search for a signal of νµ → νe oscillation among one hundred and twelve
beam neutrino events observed in SK. We find one signal candidate event, whichis consistent with the background expectation of 1.7 events. We conclude thatthe event is consistent with the multi-hadron production background and there
is no evidence for νµ → νe oscillation. Then, we set the limit on the oscillation
parameter space. In a two-flavor approximation, we set a constraint on sin2 2θµeassin2 2θµe < 0.13 (90%C.L.)at ∆m2 = 2.8 × 10−3 eV2 . For the higher ∆m2 region, we set the more stringent limitof sin2 2θµe < 0.10. Currently, our result is the most strict result on this mixing
127

angle in νµ → νe appearance experiments.
Further, we can derive a constraint on θ13 from νµ → νe oscillation. On theassumption of the relation sin2 2θ13 ' 2 sin2 2θµe , we give a constraint on sin2 2θ13
assin2 2θ13 < 0.26 (90%C.L.)at ∆m2 = 2.8 × 10−3 eV2 . Our result is consistent with the results from the reactor ν̄e experiments of CHOOZ and Palo-Verde that show the lack of observed
disappearance of ν̄e .

128

Appendix A
Neutrino interaction simulation
A.1 Neutrino interaction simulation
In the K2K experiment, we adopt the NEUT library to simulate the neutrino interactions with the target material. In NEUT, the following CC and NC interactions
are considered: (quasi-)elastic scattering, resonance production, multi-pion production and coherent-pion production. In this chapter, we give descriptions ofeach interaction mode.

A.1.1

CC quasi-elastic scattering and NC elastic scattering

The charged current quasi-elastic (CC-QE) and neutral current elastic (NC-el)interactions are two-body scatterings of neutrino on a nucleon. The simulationsof their cross-sections are based on Llewellyn Smith’s formula [83]. Its amplitudeis described as a product of hadronic and leptonic weak currents as
GF
T = √ ū(k2 )γµ (1 − γ5 )u(k1 ) hN0 (p2 )|Jµhad |N(p1 )i,
2

(A.1)

where GF is the Fermi coupling constant, p1 (p2 ) is the initial (final) nucleon fourmomentum, and k1 (k2 ) is the initial (final) lepton four-momentum. The hadronic
current, hN0 |Jhad |Ni, can be expressed as a function of four-momentum transfer(Q2 ≡ −q2 = −(p1 − p2 )2 ) as
"
0 had

hN |J

0

|Ni = cos θc ū(N )γλ F1V (Q2 ) +iσλν qν ξF2V (Q2 )

129

2mN

#
2

+ γλ γ5 FA (Q ) u(N), (A.2)

A.1. NEUTRINO INTERACTION SIMULATION
where θc is the Cabbibo angle, and mN is the nucleon mass. The vector form
factors, F1V and F2V , are represented as follows:
!−1 "
#
Q2
Q2 V 2
1
2V
2FV (Q ) = 1 +GE (Q ) +G (Q ) ,(A.3)
4m2N
4m2N M
ξF2V (Q2 ) =GVE (Q2 ) = 

Q2
1+
4m2N
1

Q2
1+ M
2
V

!−1

2 ,

h

i
GVM (Q2 ) − GVE (Q2 ) ,GVM (Q2 ) = 

1+ξ
Q2
1+ M
2
V

2 ,

(A.4)
(A.5)

where ξ ≡ µp −µn (= 3.71) is the difference of anomalous magnetic dipole moments
between a proton and a neutron, and the vector mass in the dipole parametrization(MV ) is set to be 0.84 GeV/c. The axial form factor (FA ) is given by
FA (Q2 ) = 

−1.23
Q2
1+ M
2
A

2 ,

(A.6)

where MA is the axial vector mass. In NEUT, MA is referred to electron-nucleon andneutrino-nucleon scattering experiments; they result in 1.0 − 1.1 GeV/c2 [84]. On
the other hand, our measurement favors larger value of MA around 1.11 GeV/c2 .
Thus, in the current simulation, we set the standard value of MA to 1.11 GeV/c2 .
Finally, the differential cross-section is expressed as follows:#"2
m2N G2F cos2 θcdσ
2 (s − u)2
2 (s − u)=+ C(Q )
(A.7)
A(Q ) ∓ B(Q )
dQ2
8πE2ν
m2N
m4N
where Eν is the incident neutrino energy, (s − u) ≡ 4mN Eν − Q2 − m2l , ml is the lepton
mass, and"!
!
!
(m2l + Q2 )
Q2
Q2
Q2
Q2
2
2
1 2
2 2
A(Q ) =
4 + 2 |FA | − 4 − 2 |FV | + 2 |ξFV | 1 −
4m2N
mN
mN
mN
4m2N
#

4Q2 F1V ξF2V m2l  1
2 2
2
|F
(A.8)
+
−
+
ξF
|
+
|F
|
,
A
V
V
m2N
m2N

Q2 
B(Q2 ) = − 2 FA F1V + ξF2V ,
(A.9)
mN


2
2 ξF2 

Q
1
V 
 .
C(Q2 ) = |FA |2 + |F1V |2 + 2(A.10)
4
mN 2 
130

APPENDIX A. NEUTRINO INTERACTION SIMULATIONThe sign of B(Q2 ) in Equation (A.7) is − for neutrino and + for anti-neutrino.
Figure A.1 shows the cross-section for the CC-QE interaction as a function ofneutrino energy. They are consistent with various bubble chamber measurements
around 1 GeV [85, 86, 87, 88].
For the NC-el interaction, the cross-section is derived from following relations[89]:
σ(νp → νp) = 0.153 × σ(νn → e− p),(A.11)σ(νn → νn) = 1.5 × σ(νp → νp).

(A.12)The Fermi motion and the Pauli blocking effect are considered for the target
nucleons bound in 16 O. In NEUT, the Fermi gas model is adopted to reproduce
the Pauli blocking effect. The final nucleon momentum is required to be larger
than the Fermi surface momentum, which is estimated to be 225 MeV/c for 16 O,
based on an electron-12 C scattering experiment [90].

Figure A.1: Cross-section of CC-QE interaction on a free neutron in NEUT, together with the results of measurements by bubble chamber experiments. Horizontal axis is the incident neutrino energy. Solid, dashed, and dotted lines
show the calculations of the cross-section in NEUT with MA = 1.01, 1.11, and0.91 GeV/c, respectively. Data points are from ANL [85], BNL [86], GGM [87], and
Serpukhov [88].

131A.1. NEUTRINO INTERACTION SIMULATION

A.1.2

Resonance production of single meson

The resonance production interaction produces one lepton and one pion via anintermediate baryon resonance state (N∗ ):ν + N → l− + N∗
N∗ → N0 + π (η, K),(A.13)

where N (N0 ) is a nucleons in initial (final) state. In the simulation, this production
is based on the model of Rein and Sehgal [91]. The differential cross-section of theresonance production with the mass M is written by
d2 σ
1
1 X
=
· ·
|T(νN → lN∗ )|2 · δ(W 2 − M2 ),22
dQ dEν 32πmN Eν 2 spins(A.14)

where W is the invariant mass of the hadron system, and the width of the resonance decay is neglected. The amplitude of the resonance production, T(νN →lN∗ ), is calculated based on the FKR (Feynman-Kislinger-Ravndal) baryon model[92]. This model includes vector and axial-vector form factors using dipole
parametrization with the same values of MV and MA as CC-QE interaction. The
differential cross-section for the resonance, with a finite decay width Γ, is derived
by replacing the δ-function in Equation (A.14) with a Breit-Wigner formula:δ(W 2 − M2 ) →Γ
1.
2π (W − M)2 + Γ2 /4(A.15)In the simulation, ∆(1232) and other seventeen resonance states with W < 2.0 GeV/c2
are taken into account. Figure A.2 shows the the cross-section for each final
state with MA = 1.01 GeV/c2 and experimental data [93, 94, 95]. In the case of
MA = 1.11 GeV/c2 , the cross-section is approximately 10% higher than that with
MA = 1.01 GeV/c2 . The cross-section is consistent with past experiments, nomatter which MA value is employed.
The decay kinematics of ∆(1232) is calculated by the model of Rein and Sehgal. For the other resonance states, the meson direction is determined under theassumption that it is isotropic in the rest frame of the resonance state.

A.1.3

Multi-meson production

In order to calculate the cross-sections of deep inelastic scattering, which is responsible for multi-pion production, we adopt the GRV94 [96] parton distribution132

APPENDIX A. NEUTRINO INTERACTION SIMULATION

mass cut M(pπ)<1.4GeV
NEUT M A = 1.01 GeV/c2+30% scaledσ (10−38cm2)

1.2

CC−singleπ

0.8

0.2

CPS−GGM, 1979

0

0

µpπ0

2

+

0.4

BNL−7ft, 1986

νn

µpπ

0.6

ANL−12ft, 1982

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

νp

1

4
Energy (GeV)

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0

2

νn

0

4
Energy (GeV)

µnπ+

2

4
Energy (GeV)

Figure A.2: The figuring of CC resonance production in NEUT program library
and, experimental results. Solid lines show the calculation by NEUT, and dashedlines show the the cross-section scaled by ±30%, where MA = 1.01 GeV/c2 . The
experimental results from ANL [93], BNL [94], and GGM [95] are plotted here.

133

A.1. NEUTRINO INTERACTION SIMULATION
function with modifications by Bodek and Yang [97]. Its differential cross-section
is given by integrating the following equation [98]:
G2 mN Eν 
d2 σ
1
1
= F
· (1 − y + y2 + C1 )F2 (x) + y(1 − y + C2 )[xF3 (x)]
dxdy
π
2
2
m2 (y − 2) mN xy m2l
C1 = l−− 2
4mN Eν x
2Eν
4Eν
2
ml
C2 = −
4mN Eν x(A.16)

where x = Q2 /(2mN (Eν − El ) + m2N ) and y = (Eν − El )/Eν are the Bjorken scaling
parameters, and El is the energy of the final state lepton. The nucleon structure functions, F2 and xF3 , are taken from GRV94. In the calculation, the hadronic
invariant mass, W, is required to be larger than 1.3 GeV/c2 . The Bodek-Yang modification of the functions effectively changes the cross-section by a Q2 -dependent
factor as
Q2
d2 σ
d2 σ
→ 2
·
.
(A.17)dxdy
Q + 0.188 dxdy
This reduces the cross-section in low Q2 region, which is favored by our previous
analysis [62, 56].
In the simulation of the kinematics of the hadronic system, two methods are
adopted according to the invariant mass W. In the region of 1.3 < W < 2.0 GeV/c2 ,only pions are considered. The mean multiplicity of pions is estimated from theresult of Fermilab 15-foot hydrogen bubble chamber experiment [99]:hnπ i = 0.09 + 1.83 ln W 2 .

(A.18)The number of pions for each event is determined using KNO(Koba-NielsenOlesen) scaling [100]. Since the range of W overlaps with that in the resonanceproduction mode, nπ is required to be larger than or equal to two in this W region.
The forward-backward asymmetry of pion multiplicity is also taken into accountto be [101]:hnFπ i 0.35 + 0.41 ln W 2=.
(A.19)
hnBπ i 0.50 + 0.09 ln W 2
In the region of W above 2.0 GeV/c2 , JETSET/PYTHIA package [102] is adopted.
134

APPENDIX A. NEUTRINO INTERACTION SIMULATION
For the NC deep inelastic scattering, the ratio of NC to CC is assumed to be(Eν < 3 GeV)0.26
σ(NC) =
0.26 + 0.04(Eν /3 − 1) (3 < Eν < 6 GeV) ,σ(CC) 
0.30
(Eν > 6 GeV)

(A.20)

which is based on the experimental results of Ref. [103].

A.1.4

Coherent pion production

The coherent pion production is the neutrino interaction with a whole nucleus
instead of an individual nucleon. In such interaction, the charge or isospin of thenucleus does not change. This reaction produces one pion with the same charge as
the intermediating weak boson. Since the transferred momentum to the nucleus
is small, the angular distribution of the recoil leptons and pions are peaked in theforward direction, and the nucleus does not break up due to the small momentum
transfer.
The cross-section and the kinematics of coherent pion production is calculated
based on the model of Rein and Sehgal [74]. The differential cross-section of theRein & Sehgal model is expressed by
2

G mN E νdσ(πN → πN)
d3 σ1= F 2 fπ2 A2 (1− y)·
·
2
2
2
2
dQ dydt2πdqq2 =0 1 + Q /MA!2e−bt Fabs , (A.21)

where fπ is the pion decay constant of 0.93mπ , A is the atomic number, b =(R0 A1/3 )2 /3 is of the order of the transverse dimension of the nucleus taken to
be 80 GeV−2 for oxygen, and t is the square of the four-momentum transfer tothe nucleus. Fabs is a factor coming from the pion absorption in the nucleus.
However, Marteau et al.have recently pointed out that the nuclear medium can
modify widths of resonances, thus we make modifications on the cross-section
calculation based on their proposal [75]. Figure A.3 shows the comparison of thecross-sections between the Rein & Sehgal model and its modification by Marteau
et al.The model of Rein and Sehgal gives the sightly higher value of cross-section
around the neutrino energy of 1 GeV.
In our simulation, we set the cross-section for CC coherent pion production
to zero based on the measurement with SciBar [76, 61]. For NC coherent pion
production, we adopt the model of Rein and Sehgal with the corrections reported
135

A.1. NEUTRINO INTERACTION SIMULATION
by Marteau. We have measurements of NC coherent pion production cross-sectionin the energy region of a few GeV, but there is a possibility that the cross-sectionis also considerably smaller than the MC prediction in the K2K beam energy
assuming the isospin relation σ(CC) = 2σ(NC). Thus, we evaluate the uncertaintyof cross-section considering the differences between alternative NC coherent pion
production models.

Figure A.3: Cross section of the coherent pion production off the 16 O nucleus.
Solid lines show the cross-section of CC coherent pion production, and dashedlines show that of NC. Blue and red lines show the model of Rein & Sehgal [74]and Marteau et al. [75], respectively.

136

Appendix B
Verification of the νe flux prediction
with SciBar
In order to validate the νe flux prediction by the beam MC simulation, we have
performed the measurements of νe composition in the neutrino beam with twonear detectors, LG [104] and SciBar. Here, we describe the details of the SciBar
detector and present the result of the νe flux measurement with SciBar.

B.1

The SciBar detector

A fully active scintillator detector, SciBar, was constructed as an upgrade of thenear detector complex, replacing the LG detector in summer 2003. A schematic
views of the detector and the readout system are shown in Figure B.1. The detector
is designed to measure the neutrino energy spectrum and study of neutrino
interaction with good detection efficiency for low momentum particles.
The main part of the SciBar detector consists of an array of plastic scintillator
strips to realize fully active detector and fine segmentation. The SciBar detector
consists of 14848 scintillator strips arranged into 64 layers. Each layer consists of
two planes, with 116 strips to give horizontal and vertical position. The scintillator
strips are produced with TiO2 reflector coating and a hole of 1.8 mm in diameterat the point of production (called extruded scintillator [105]). Each strip havedimensions of 1.3 × 2.5 × 300 cm3 . In total, the detector weights about 15 tons andthe dimensions are 3 × 3 × 1.7 m3 . The scintillation light is guided by wavelength
shifting (WLS) fibers, inserted into the holes of scintillator strips, to 64-channel
137B.1. THE SCIBAR DETECTOR

front−end board
scintillator

MA−PMT 
 
































 
 


WLS fiber
VA/TA

Figure B.1: Schematic views of the SciBar detector (left) and the readout system(left).
multi-anode photomultipliers (MAPMTs). A bundle of 64 WLS fibers is glued to
an attachment for precise alignment between fibers and the photo-cathode of the
MAPMT.
The readout system for MAPMT consists of two components: a front-end
electronics board attached to the MAPMT and a back-end VME module [106, 107,108]. At the front end, a circuit board with self-triggering readout using VA/TA
ASIC (VA32HDR11 [109] and TA32CG [110]) was newly developed. VA has 32channel pre-amplifier followed by a slow-shaper and a multiplexer, and serialize
the outputs from the MAPMT. TA has a fast-shaper with a comparator, which
provides the timing information of OR-ed signal of 32 channels. The output from
the MAPMT is serialized by front-end electronics and digitized by FADCs on
the back-end VME modules. Charge and timing information are digitized by
FADCs on the back-end VME modules and the multi-hit TDCs, respectively. The
noise level and the timing resolution for MIP signal are about 0.3 photoelectrons(p.e.) and 1.3 nsec, respectively. The back-end module also newly developed as astandard VME-9U module, and controls readout of the front-end boards.
These features of the detector allows us to reconstruct all the charged particles
produced in neutrino interaction. A typical event display of CC-QE interaction isshown in Figure B.2.
138

APPENDIX B. VERIFICATION OF THE νE FLUX PREDICTION WITHSCIBAR

Figure B.2: A typical event display of CC-QE interaction in the SciBar detector.
The longer track is muon and the shorter is proton. The area of hit circle is
proportional to energy deposit in a scintillator strip.
In the downstream part of the SciBar, an electromagnetic calorimeter (EC) is
installed to study the νe contamination in the beam and π0 production in neutrino
interaction. The calorimeter modules are originally built for CHORUS neutrino
experiment at CERN [111]. A module of EC consists of scintillating fibers and lead
sheets. The dimensions of the module are 4.0 × 8.2 × 262 cm3 . A vertical plane (32modules) and a horizontal plane (30 modules) are installed between the scintillator
tracker and the MRD detector, providing an additional eleven radiation lengths(11X0 ) to the main tracker part (about 4X0 ). The energy resolution of the EC ispabout 14/ E(GeV)% with linearity better than 10%.
To reconstruct charged particles in SciBar, track projections in each of two
dimensional view are looked for using a cellular automaton algorithm [112, 113].
Then, track candidates from two views are combined based on matching of the
track edges in the beam direction and timing information. Reconstructed tracks
are required to have hits in more than three consecutive layers. The minimum
length of reconstructible track is 8 cm, corresponding to 450 MeV/c for protons.
The reconstruction efficiency for an isolated track longer than 10 cm is 99%.
The track finding efficiency as a function of the number of traversed layers formuons, protons and charged pions according to the MC simulation are shown in
Figure B.3. In the measurement of νµ energy spectrum, we select muons in CC
interactions. The muon is identified by requiring corresponding track or hits in
MRD, which imposes a threshold of 450 MeV/c on muon momentum. The pµ scale
uncertainty, pµ resolution, and θµ resolution are 2.7%, 80 MeV/c, and 1.6 degrees,139B.2. νE FLUX MEASUREMENT BY SCIBAR

0

10

20

30

40

50

60

the number of layers

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

track finding efficiency

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

track finding efficiency

track finding efficiency

respectively.

0

10

20

30

40

50

60

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0

10

20

30

the number of layers

40

50

60

the number of layers

Figure B.3: Track finding efficiency of the SciBar detector as a function of thenumber of traversed layers for muons (left), protons (center) and charged pions(right).

B.2

νe flux measurement by SciBar

The measurement of the νe contamination in the beam has been performed by
SciBar with a statistics corresponding to 2.1 × 1019 POT.
In order to measure the νe flux, we select the νe events interacting with SciBarin CC interactions and separate recoil electrons from muons with EC. Since the EC
detector has a radiation length of 11X0 , electrons in the energy range of ∼ 1 GeV
are almost fully contained. On the other hand, the averaged energy loss in
EC for penetrating muons and charged pions is small, which is estimated to be∼ 100 MeV. Thus, we look for the event with a large signal of electromagnetic
shower in a restricted region of EC. A typical event display of νe interaction isshown in Figure B.4.
In EC, the hits are clustered within a 20 cm width centered in the modulewith the maximum signal. We estimate the energy deposit in EC from the totalenergy of the cluster (cluster energy). Using the cluster energy for each plane, theelectron event candidates are selected with the following criteria:(i) The maximum hit energy of the first plane is greater than 100 MeV,(ii) The cluster energy of the first plane (E1 ) is greater than 350 MeV,(iii) The ratio E2 /E1 lies in the range 0.2–1.1, where E2 is the cluster energy of thesecond plane,140

APPENDIX B. VERIFICATION OF THE νE FLUX PREDICTION WITHSCIBAR

Figure B.4: Event display of νe interaction in SciBar.
(iv) The event with any track starting in the fiducial volume of SciBar (9.38 ton)
is matched with the position of the EC clusters.
(v) The energy outside of the cluster for each EC plane is less than 30 MeV.
With criteria (i) (ii), the events with single MIP track or multi tracks are rejected.
The criterion (iii) selects the electron events efficiently: the fraction of electron isestimated to be 95% according to the MC simulation. Rejecting the remaining νµmulti-hadron production events with the criterion (v), we enhance νe CC events.
After the selection cuts, we observed 42 electron candidate events. The visual
examination of the events allows us to discard 9 events; they are identified as
background events of the beam-induced particles generated by neutrino interactions outside SciBar, or as π0 production events. In this sample, we expect there
is a fraction of background originated from the π0 production in the νµ interactions. For the π0 production background, we estimate the contamination withthe visual examination described above, by correcting the detection efficiency
based on the MC simulation. Finally, we obtain 33 evens with the backgroundexpectation of 3 ± 2 events. The purity of electron is 90 %. The characteristicsof the selected events are compared to those of MC events resulting from a full
simulation of νe interactions in the SciBar and including also a 10% backgroundfrom νµ interactions.
Figure B.5 shows the electron energy spectrum for the surviving events with
the MC expectation. In the MC events, the 10% fraction of background events
is taken into account. The electron energy is reconstructed by correcting theenergy loss in SciBar and the longitudinal leakage; the average correction is of the141B.2. νE FLUX MEASUREMENT BY SCIBAR
order of 20%. The data and the MC events are in good agreement except for thehigher energy region. The discrepancy in the higher energy region indicates ourunderestimate of kaon production in p − Al collisions at the target, however, wecannot give any conclusion with a small statistics.

16
14
12
10
8
6
4
2
0

0

1000
2000
3000
E(electron) (MeV)

8000

Figure B.5: Electron energy spectrum for the νe candidate events. The open circles
and the histogram show the data and the MC events, respectively. The MC events
are normalized to the data separately for the signal and background events.
In the νµ → νe search, the contribution of beam-νe background is estimatedbased on the MC simulation including its flux and cross-section. Thus, to validate the MC prediction, we estimate the interaction ratio of νe to νµ . The total
number of νµ interactions is calculated by correcting the number of observed
events with the detection efficiency estimated by the MC simulation. The total
νµ interactions are estimated from the νµ CC event sample used in the measurement of νµ energy spectrum in SciBar. The resultant νe /νµ interaction ratio is
1.6 ± 0.3(stat.) ± 0.2(syst.)%.

B.2.1

Comparison with the beam MC prediction and the LG measurement

The measurement of beam-νe contamination has been also performed with the LG
detector. The event selection and the result are given in Reference [104, 63].
142

APPENDIX B. VERIFICATION OF THE νE FLUX PREDICTION WITHSCIBAR
The resulting νe /νµ interaction ratios by SciBar and LG, and the MC predictionare:
SciBar: 1.6 ± 0.3(stat.) ± 0.2(syst.)%LG: 1.6 ± 0.4(stat.)+0.8(syst.)%−0.6
Beam MC: 1.3% (at near site)
These are in a good agreement each other and give a validity of the νe flux
prediction in the beam MC simulation.

143

Appendix C
Comment on the far/near flux ratio
In the K2K experiment, the νµ beam is produced via decays of positive pions
generated in p − Al collisions. If we assume the neutrino source to be a point like,the intensity of neutrino beam is proportional to 1/L2 , where L is the distance fromthe source to the detector location. The SK detector is located 250km far from theπ production target and the neutrino source is regarded as a point like. However,the near detectors are close to the target (L = 300 m) and the neutrino flux is notproportional to 1/L2 due to the finite size of decay volume in which π+ ’s decay
to µ+ ’s and νµ ’s. In addition, there is a difference of geometrical acceptance forneutrinos between the near detectors and SK. The detector acceptance is proportional to the solid angle to the target and the covering angles of 1KT and SK are±20 mrad and ±0.1 mrad, respectively. Therefore, we predict the event rate at SK
with the near detector measurements by multiplying the far/near flux ratio. The
predicted neutrino fluxes at the near site and SK and the far/near flux ratio areshown in Figure C.1. Here, we give explanations of the following subjects:• Shape of the far/near flux ratio,• Possibility of employing near detectors which cover the same geometricalacceptance as SK.

C.1 Shape of the far/near flux ratio
At the near detectors, the geometrical acceptance for low energy neutrinos isdifferent from that for high energy ones. The low energy pions, contributing
145

2

-6

(10 )

0.25

ND

0.2
0.15

SK

Φ /Φ

Φnear (a.u.)

C.1. SHAPE OF THE FAR/NEAR FLUX RATIO

0.1
0.05

1.8
1.6
1.4
1.2

0
0

0.5

1

1.5

2

2.5

3

1

Φfar (a.u.)E ν (GeV)
0.25

0.8

0.2

0.6
0.15

0.4
0.1

0.2
0.05

0
0

0
0.5

1

1.5

2

2.5

3

E ν (GeV)

0

1

2

3

Eν(GeV)

Figure C.1: Neutrino fluxes at the near site and SK (left) and the far/near flux ratio(right) predicted by the beam MC simulation.
to the low energy neutrino flux, decay near the target, while the high energy
pions travel far away from the target before their decays. The decay piont of low
energy pions is far from the near detectors compared with that of high energy
ones. Therefore, the geometrical acceptance of the near detectors for low energy
neutrinos become smaller than that for high energy ones, as shown in Figure C.2.
For examples, the flight length of 0.5 GeV pions is 20 m and that of 2.5 GeV pions
is 100 m. This difference of π flight length results in different 1KT acceptances
for neutrinos by a factor of two, and the flux of low energy neutrinos becomeslow. On the other hand, the difference of π decay point is negligible at SK and thegeometrical acceptance does not depend on the neutrino energy. As a result, thefar/near flux ratio goes down in the low energy region below 0.5 GeV.
In addition, the near detectors are sensitive to neutrinos which travel off thebeam axis (off-axis neutrinos) due to the large detector coverage. Figure C.3 shows
the illustration of off-axis neutrinos. The energy of neutrino (Eν ) from the π decay
is expressed as
m2π − m2µ
,
(C.1)
Eν =
2(Eπ − pπ cos θ)
where mπ , mµ , Eπ , pπ and θ are the pion mass, the muon mass, the pion energy,
the pion momentum and the direction of neutrino with respect to the beam axis.
Figure C.4 shows the neutrino energy as a function of the pion energy for various
146

APPENDIX C. COMMENT ON THE FAR/NEAR FLUX RATIO

1KT

pπ+(high E)

Al
π+(low E)

300m

Figure C.2: Illustration of acceptance for low and high energy neutrinos at thenear site.
off-axis angles. We recognize that the neutrino energy is not very correlated withthe pion energy for off-axis neutrinos, and high energy pions contribute to theneutrino flux around 1 GeV. Therefore, the neutrino energy spectrum has a narrow
peak around 1 GeV at the near detectors and that shows a broad distribution at
SK, as shown in Figure C.1. Consequently, the far/near flux ratio goes up above∼ 1 GeV.
1KT

ν

ν

rad

~20m

targetDecay volume

SK~0.1mrad

ν
300m

250km

Figure C.3: Illustration of off-axis neutrinos.

C.2 Possibility of employing near detectors which
cover the same geometrical acceptance as SK
We consider the case of employing near detectors which cover the very forward
region of ∼ 0.1 mrad (equivalent to the geometrical acceptance of the SK detector).
When we measure the neutrino flux in the very forward region, the contribution of off-axis neutrinos becomes small, but the near detectors are yet sensitive tothem. Due to the spacial spread of pions, the near detectors have a finite geometrical acceptance for off-axis neutrinos produced by pions which have a transverse
147

Eν (GeV)

C.2. POSSIBILITY OF EMPLOYING NEAR DETECTORS WHICH
COVER THE SAME GEOMETRICAL ACCEPTANCE AS SK

5
4
mr

3

θ

2

ad

θ = 10mrad

θ = 20mrad

1
0

.1
<0

0

2

4

6

8
10
Eπ (GeV)Figure C.4: The neutrino energy as a function of the parent pion energy for various
off-axis angles.
momentum or travel far from the beam axis, as shown in Figure C.5. In addition,
the difference of geometrical acceptance between low and high energy neutrinos
still remains, as described above. These make a difference of neutrino energy
spectrum between the near detectors and SK.
Thus, we can not adopt a simple 1/L2 extrapolation to predict the SK event
rate even in that case. We should take into account the energy dependent far/near
flux ratio.

ν

π

0.03m

target300m

Decay volume

Figure C.5: Illustration of off-axis neutrinos contributing to the flux in the very
forward region of the near detectors

148

Appendix D
Decay-electron identification
We identify the decay-electron event to reject the background originated fromνµ -CC interactions.
In SK, the decay-electron events are classified into three categories based on
the time difference ∆t between the parent muon event and the following decayelectron:• primary-event type:
Hits associated with a decay-electron are detected within 1.2 µsec trigger
gate with the primary event of the parent muon.
• sub-event type: A decay-electron is recorded as a separate event from theprimary one.
• splitting-event type:A decay-electron is emitted at the timing around the boarder of the primaryevent time window. Hits of a decay-electron are observed partially in the
primary event and partially in the separate event.
We describe the criteria to select these event categories of decay-electrons.
For the events with the primary-event and splitting-event decays, we observe
another peak in the timing distribution after the primary PMT hits. We identify
the separate events when ∆t is larger than 0.1µsec. We require that the numberof PMT hits associated with a decay-electron should be greater than 40 (20) in
30 nsec time window for SK-I (SK-II).
For the sub-event type decays, the decay-electron ring candidates are selectedby requiring that the goodness of the vertex fitting is more than 0.5 and the total
149

number of photo-electrons is less than 2000. Then, we require that the event
follows the primary event with PMT hits above 60 (30) in 50 nsec time window
for SK-I (SK-II), which corresponds to ∼ 11 MeV decay-electron threshold.
Finally, since we cannot detect the events with ∆t ∼ 1µsec efficiently due to thedead time of the readout electronics, we reject events with 0.8µsec < ∆t < 1.2µsec.

150Appendix E
Comment on the surviving events
before the π0 rejection
We observe five surviving events in the entire data sample before the π0 rejection,
as shown in Figure E.1. Assuming that we observe only νµ -originated background
events, we recognize that all of the observed events lie outside of the most probable region of the Ee range from 150 MeV to 350 MeV and the Minv range from
100 MeV/c2 to 140 MeV/c2 . However, the probability of observing one eventin this region is approximately 40%, and the probability of observing no event
among five trials is estimated to be 7.8% ((1 − 0.4)5 = 0.0778). Ee and Minv also
shows probable values, as shown in Figure E.2.
In addition, we perform statistical tests to make a statement about how well
the observed distribution agree with the MC prediction. We construct a likelihoodof observing five given events. The likelihood (L) is calculated by the product ofprobabilities as
5
Y
(E.1)
L=
P(Eie , Miinv ),i=1

where P(Eie , Miinv ) is the probability of observing an event with Eie and Miinv fori-th event. The probability is estimated by the MC νµ -originated background
events. Figure E.3 shows the likelihood distribution obtained from many virtual
experiments of observing five events. We estimate the probability of obtaining a
result with the same level of discrepancy as the K2K data or higher to be 51.8%.
Further, the two-dimensional Kolmogorov-Smirnov test shows a probability of
47.4%.
151

Minv (MeV/c2)

300
200
100

68%

40%

90%

0

0

500

1000

1500
Ee (MeV)Figure E.1: Distribution of signal candidate events in the Minv -Ee space for K2K-I
and K2K-II. Five surviving events before the π0 rejection in data are shown by
open circles. The MC events originated from νµ are shown by open boxes. The
acceptance region with a 40% (68% or 90%) probability is shown with a contour
line.

0.4
0.4

0.3
0.2

0.2
0.1
0

0

500

1000

1500
2000
Ee (MeV)

0

0

100

200
300
Minv (MeV/c2)

Figure E.2: Distributions of Ee (left) and Minv (right) for the surviving events. The
arrows show the observed events in the data. The histograms show the MC events
originated from νµ .

152

APPENDIX E. COMMENT ON THE SURVIVING EVENTS BEFORE THE
π0 REJECTION
Consequently, we conclude that the observed data stand within the statisticalfluctuation of background events.

0.015

observation

0.01
51.8%

0.005
0
20

25

30

35

40

45
-ln(L)

Figure E.3: Likelihood distribution from many virtual experiments with fiveobservations per experiment. The arrow shows the observed data in K2K. The
probability of obtaining a result with the same level of discrepancy as the observed
data or higher is 51.8%.

153

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161

List of Figures
1.1
1.2

The regions of ∆m2 and mixing angle favored or excluded by various experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Squared-mass spectrum in three-neutrino framework. . . . . . . . .

2.1
2.2
2.3
2.4
2.5
2.6
2.7

Oscillation probability and νµ energy spectrum at SK. . . . . . . . .
Schematic overview of the K2K experiment. . . . . . . . . . . . . . .
Schematic view of the beam-line. . . . . . . . . . . . . . . . . . . . .
Schematic view of aluminum target and magnetic horns. . . . . . .
Neutrino flux at SK with and without horn current. . . . . . . . . .
Schematic view of the pion monitor. . . . . . . . . . . . . . . . . . .
Stability of the center of muon profile measured by the ICH of themuon monitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Schematic view of the near detector complex. . . . . . . . . . . . . .
2.9 Schematic view of the 1kt detector. . . . . . . . . . . . . . . . . . . .
2.10 Schematic overview of the Super-Kamiokande detector . . . . . . .
2.11 Schematic view of a 20-inch PMT. . . . . . . . . . . . . . . . . . . . .
2.12 Schematic view and timing diagram of the GPS system. . . . . . . .
2.13 The integrated number of protons delivered to the target. . . . . . .
3.1
3.2
3.3
3.4
3.5
3.6

6
9
12
14
15
16
17
17
19
19
20
23
24
25
27

Neutrino energy spectra at the near site and SK. . . . . . . . . . . . 31
Neutrino energy spectra at the near site and SK for each neutrino
type with 250 kA horn setting. . . . . . . . . . . . . . . . . . . . . . . 32
Composition of each decay process in νµ and νe . . . . . . . . . . . . 32
Total cross-section of CC interaction as a function of neutrino energy. 34
The cross-section of each neutrino interaction mode with water asa function of incident neutrino energy. . . . . . . . . . . . . . . . . . 34
Cross-sections of π+ -16 O interactions. . . . . . . . . . . . . . . . . . . 35
163

LIST OF FIGURES
3.7

Attenuation coefficients as a function of wavelength in water. . . .

37

4.1

Typical event displays of νe CC-QE interaction and π0 production
background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

5.1
5.2
5.3
5.4
5.5
5.6
5.7

Fiducial volume of the 1KT detector. . . . . . . . . . . . . . . . . . .
Event selection efficiency of 1KT as a function of neutrino energy. .
The event rate per month in the 1KT detector. . . . . . . . . . . . . .
pµ − θµ distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . .
The neutrino energy spectrum measured at near detectors. . . . . .
Schematic view of the HARP detector. . . . . . . . . . . . . . . . . .
The differential cross-section of pions as a function of the pion
momentum integrated over the pion angular range of 30 mrad <θ < 210 mrad, and as a function of θ in the pion momentum range
0.75 GeV/c < p < 6.5 GeV/c. . . . . . . . . . . . . . . . . . . . . . . .
5.8 νµ fluxes at the near site and SK as a function of neutrino energy
predicted by the beam MC simulation with the HARP measurement
and the Cho-CERN model. . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Ratio of νµ flux at SK to the near site predicted by the beam MC
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Expected neutrino energy spectrum at SK. . . . . . . . . . . . . . . .
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

7.1
7.2

Vertex distribution of beam neutrino events in r2 −z space for K2K-I
and K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∆T distribution for each reduction step. . . . . . . . . . . . . . . . .
∆T distribution in a narrow time window. . . . . . . . . . . . . . . .
Neutrino event rate at SK as a function of POT. . . . . . . . . . . . .
Distributions of the ring counting estimator for K2K-I and K2K-II. .
Distribution of single-ring events in the ring pattern and opening
angle parameter space for K2K-I and K2K-II. . . . . . . . . . . . . .
Visible energy distribution of single-ring shower-type events. . . .
Distribution of the number of decay electrons for single-ring showertype events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Illustrations of π0 production background. . . . . . . . . . . . . . .
π0 momentum and Eγ2 − θγγ distribution of NC1π0 background
events in the single-ring shower-type sample. . . . . . . . . . . . . .
164

45
46
47
50
51
53

54

54
55
58

65
67
67
69
70
72
73
74
78
79

LIST OF FIGURES
7.3
7.4
7.5
7.6
7.7
7.8

Energy resolution of gamma-rays for NC1π0 events for K2K-I and
K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

Angular resolution of gamma-rays for NC1π0 events. . . . . . . . .

83

0

0

Reconstructed π invariant mass distribution of NC1π events for
K2K-I and K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

π0 detection efficiency as a function of π0 momentum for K2K-I and
K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

π0 reconstruction efficiency in Eγ2 -θγγ space. . . . . . . . . . . . . .

86

0Invariant mass distribution of π → γγ for single-ring shower-type
events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

Opening angle and energy fraction distributions given by the π0
fitter for single-ring shower-type events. . . . . . . . . . . . . . . . .

88

7.10 Profile histogram of Minv -Ee for νe signal events under the assumption of ∆m2 = 2.8 × 10−3 eV2 . . . . . . . . . . . . . . . . . . . . . . . .

89

7.9

0

7.11 The difference between the shower-type ring energy and the πenergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

7.12 The invariant mass distributions for the atmospheric neutrino eventswith two shower-type rings for SK-I and SK-II. . . . . . . . . . . . .

90

7.13 Comparison of reconstructed gamma-ray energies and opening angle between the standard reconstruction and the π0 fitter for SK-I
and SK-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

7.14 Event distribution of atmospheric neutrinos in Minv -Ee space. . . . .

92

7.15 Invariant mass distribution of single-ring shower-type events foratmospheric neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . . .

92

7.16 Invariant mass distribution of single-ring shower-type events ofatmospheric neutrinos for SK-I and SK-II. . . . . . . . . . . . . . . .

93

7.17 π0 invariant mass distributions of two-ring µ − e sample for atmospheric neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

7.18 Distribution of candidate events in the Minv -Ee space for K2K-I and
K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

7.19 Efficiencies of νµ -originated background rejection and νe signal selection as a function of neutrino energy. . . . . . . . . . . . . . . . .

98

7.20 A candidate event remaining after all selection cut. . . . . . . . . . .

99

8.1

Flux ratio of beam-induced νe to νµ at SK. . . . . . . . . . . . . . . . 105
165

LIST OF FIGURES
8.2

Reconstructed π0 momentum distribution in the 1KT detector andratio of data to the MC expectation. . . . . . . . . . . . . . . . . . . . 107

8.3

Distribution of ring counting estimator for atmospheric neutrino
events with two shower-type rings. . . . . . . . . . . . . . . . . . . . 108

8.4

Detection efficiency of decay-electrons for SK-I and SK-II. . . . . . . 109

8.5

Stability of light attenuation length for SK-I and SK-II. . . . . . . . . 110

9.1

The expected number of events as a function of ∆m2 . . . . . . . . . . 116

9.2

Probability density functions for K2K-I+II. . . . . . . . . . . . . . . 119

9.3

Confidence intervals at 90% and 90% coverage probabilities. . . . . 120

9.4

Upper bounds of νµ → νe oscillation parameters at 90% and 99%
C.L. for K2K-I, K2K-II and K2K-I+II. . . . . . . . . . . . . . . . . . . 121

9.5

Comparison of upper bounds on νµ → νe oscillation parameters
between the Feldman and Cousins method and the classical limit
calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

9.6

Upper bounds of νµ → νe oscillation parameters with (solid line)
and without (dashed line) systematic uncertainties. . . . . . . . . . 123

9.7

Expected sensitivities at 90% and 99% C.L. as a function of POT.
The sensitivities for each C.L. with or without the systematic uncertainties are drawn by solid and dashed lines, respectively. The
numbers of νe signal events are calculated on the assumption of∆m2 = 2.8 × 10−3 eV2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.8

Constraints on ∆m2 -sin2 2θ13 space by various experiments. . . . . . 125

A.1 Cross-section of the CC-QE interaction on a free neutron. . . . . . . 131
A.2 The figuring of CC resonance production in NEUT program library
and, experimental results. . . . . . . . . . . . . . . . . . . . . . . . . 133
A.3 Cross section of the coherent pion production off the 16 O nucleus. . 136
B.1 Schematic views of the SciBar detector and the readout system. . . 138
B.2 A typical event display of CC-QE interaction in the SciBar detector. 139
B.3 Track finding efficiency of the SciBar detector as a function of thenumber of traversed layers for muons, protons and charged pions. 140
B.4 Event display of νe interaction in SciBar. . . . . . . . . . . . . . . . . 140
B.5 Electron energy spectrum for the νe candidate events. . . . . . . . . 142
166

LIST OF FIGURES
C.1 Neutrino fluxes at the near site and SK and the far/near flux ratio
predicted by the beam MC simulation. . . . . . . . . . . . . . . . . . 146
C.2 Illustration of acceptance for low and high energy neutrinos at thenear site. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C.3 Illustration of off-axis neutrinos. . . . . . . . . . . . . . . . . . . . . 147
C.4 The neutrino energy as a function of the parent pion energy forvarious off-axis angles. . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.5 Illustration of off-axis neutrinos contributing to the flux in the very
forward region of the near detectors . . . . . . . . . . . . . . . . . . 148
E.1 Distribution of signal candidate events in the Minv -Ee space for
K2K-I and K2K-II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
E.2 Distributions of Ee and Minv for the surviving events. . . . . . . . . 152
E.3 Likelihood distribution from many virtual experiments with fiveobservations per experiment. . . . . . . . . . . . . . . . . . . . . . . 153

167

List of Tables
2.1

Summary of the experimental configurations. . . . . . . . . . . . . .

26

5.1
5.2
5.3
5.4
5.5

Summary of event rate measurements in the 1KT detector. . . . . .
int
Sources of systematic error on N1KT
. . . . . . . . . . . . . . . . . . .
Results of the spectrum measurement. . . . . . . . . . . . . . . . . .
The error matrix for fiΦ and RnQE . . . . . . . . . . . . . . . . . . . . .
Parameters of the Sanford-Wang differential cross-section formulaobtained by fitting the HARP data. . . . . . . . . . . . . . . . . . . .
Summary of the systematic error sources on the far/near flux ratio
predictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47
48
50
51

6.1

Reduction of fully contained events in the fiducial volume. . . . . .

68

7.1
7.2

Reduction of events for νµ → νe search at SK. . . . . . . . . . . . . . 97
Reduction of νe signal MC events on the assumption of the oscillation parameters of ∆m2µe = 2.8 × 10−3 eV2 and sin2 2θµe = 1.0. . . . . . 97
νµ rejection factors after all the selection cuts for each interaction
mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Breakdown of νµ background events after all the selection cuts. . . 100

5.6

7.3
7.4
8.1
8.2
8.3

53
57

Systematic uncertainties in the expectation of νµ -originated background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Systematic uncertainties in the expectation of beam-νe background. 112
Systematic uncertainties in the expectation of νe signal. . . . . . . . 113

169