Observation of a Small =e Ratio of Atmospheric
Neutrinos in Super-Kamiokande by the Method ofParticle Identi cation
Syunsuke Kasuga

January 1998

Doctor Thesis, University of TokyoAcknowledgements
I would like to express my sincere appreciation to my advisor, Prof.Y.Totsuka, for
introducing me this experiment and encouraging me throughout this work.
I gratefully acknowledge the helpful advice of Prof.T.Kajita, M.Shiozawa, Dr.Y.Itow
and Dr.M.Miura. They are experts in the atmospheric neutrino analysis. Their suggestions and advices were very useful for me.
I owe thanks to my fellow graduate students Y.Hayato, K.Ishihara, K.Okumura,
H.Ishino, M.Eto, J.Kameda and Y.Kanaya. They gave me useful discussions and assistedwith my analysis. Without their supports, I could not accomplish my thesis.
I would like to thank Y.Kitaguchi, K.Fujita, F.Tsushima, E.Ichihara, N.Sakurai and
M.Ota. They gave me useful discussions about experimental details.
I with to express my deeply appreciation to T.Hayakawa and Y.Koshio. They live in
Kamioka and supported me on various occasions.
I would like to thank Prof.Y.Suzuki, Prof.M.Nakahata, Dr.Y.Fukuda, Dr.K.Inoue,
Dr.Y.Takeuchi and Dr.K.Kaneyuki for their advice.
I must thank all the other Super-Kamiokande collaborators for their work, help andwarm hospitality. Especially, Dr.M.Takita, Dr.S.Hatakeyama, Dr.M.Koga, T.Yamaguchi,
H.Okazawa and M.Nemoto gave me many advices.
I must also thank the sta of the KEK. I learned a lot about the experimental
technique there. Prof.K.Nishikawa and Dr.A.Sakai gave me many useful suggestions anddiscussions. I would like to express my appreciation to Dr.Y.Oyama for his advice andsupport. His excellent guidance and suggestions were very useful for me.
I would like to thank C.Mauger for reading and xing this manuscript. I thank thecooperation of Kamioka Mining and Smelting Company and nancial support of theJapan Society for the Promotion of Science.

2

Contents
1 Introduction

11

2 Super-Kamiokande detector

23

3 Calibration

33

1.1 Atmospheric neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Atmospheric neutrino anomaly . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Kamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.2 IMB-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.3 Soudan 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.4 Frejus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.5 NUSEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Possible explanations for the atmospheric neutrino anomaly . . . . . . . . 17
1.3.1 Neutron background . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.2 Proton decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.3 Neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Motivation of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1
2.2
2.3
2.4
2.5

3.1
3.2
3.3
3.4

Water Cherenkov detector . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Water tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
20-inch PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Water puri cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Relative gain calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Single photoelectron distribution . . . . . . . . . . . . . . . . . . . . . . . 35
Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Water transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3

4 Simulations

43

5 Event selection

57

6 Analysis

67

7 Results and discussions

85

8 Conclusion

103

A Absolute energy scale and the stability of the detector

105

4.1 Atmospheric neutrino ux . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Neutrino interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.1 Quasi-elastic interactions . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Single pion production . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.3 Multi-pion production . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.4 Coherent pion production . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Meson nuclear e ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.5 Summary of Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . 54
5.1
5.2
5.3
5.4

First reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Second reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Third reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.1 TDC- t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Ring counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3 Particle Identi cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.1 The Method of Particle Identi cation . . . . . . . . . . . . . . . . 73
6.3.2 PID Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.4 MS- t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.4.1 Fitting method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.4.2 Performance of MS- t . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.5 Momentum determination . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.1
7.2
7.3
7.4

The atmospheric neutrino ux . . . . . . . . . . . . . . . . . . . . . . . . 85
Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Vertex and momentum distributions . . . . . . . . . . . . . . . . . . . . 94
The Zenith angle distribution . . . . . . . . . . . . . . . . . . . . . . . . 95

4

List of Figures
1.1 Atmospheric neutrino uxes at Kamioka . . . . . . . . . . . . . . . . . . 11
1.2 Present atmospheric neutrino experimental status. . . . . . . . . . . . . . 14
1.3 Zenith angle distribution of R for the multi-GeV contained events in
Kamiokande. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4 Constraints to 4m2 and sin2 2. for (a) $ e and (b) $  oscillations. 21
2.1
2.2
2.3
2.4
2.5
2.6

A schematic view of the Super-Kamiokande detector. . . . . . . . . . . .
The structure of the frame for ID and OD PMTs. . . . . . . . . . . . . .
A schematic view of PMT. . . . . . . . . . . . . . . . . . . . . . . . . . .
A typical 1p.e. distribution. . . . . . . . . . . . . . . . . . . . . . . . . .
A ow diagram of the water puri cation system. . . . . . . . . . . . . . .
Inner detector data acquisition system. . . . . . . . . . . . . . . . . . . .

25
25
27
28
29
30

3.1 The relative gain calibration system. . . . . . . . . . . . . . . . . . . . . .
3.2 Relative PMT photo sensitive area as a function of angle and the de nitionof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 The relative gain distribution after the HV adjustment. . . . . . . . . . .
3.4 Schematic view of the Ni-Cf gamma-ray source. . . . . . . . . . . . . . .
3.5 Single photoelectron distribution. . . . . . . . . . . . . . . . . . . . . . .
3.6 A TQ map of a typical PMT. . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Timing resolution of a PMT as function of Q (p.e.). . . . . . . . . . . . .
3.8 Set up of the dye-laser + CCD camera system. . . . . . . . . . . . . . . .
3.9 The light attenuation length at 420nm. . . . . . . . . . . . . . . . . . . .
3.10 The L(),1 plot
as a function of the wave length. . . . . . . . . . . . . .

3.11 The log fQl() plot as a function of l. The solid line shows the result of
tting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Time variation of light attenuation length in water measured by cosmicray muons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

5

34
35
36
36
37
38
38
39
40
41
41

4.1 Observed uxes of primary cosmic ray . . . . . . . . . . . . . . . . . . . 44
4.2 The atmospheric neutrino uxes multiplied by E2 at the Super-Kamiokandesite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 The ux ratio,(+  )/(e + e), at the Super-Kamiokande site. . . . . . 45
4.4 Calculated cross section of  n ! ,p compared with the experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 Calculated cross section of  p ! +n compared with the experimental
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.6 Cross section of  p ! ,p+ compared with the experimental data. . . 48
4.7 Cross section of  n ! ,p0 compared with the experimental data. . . 48
4.8 Cross section of  n ! ,n+ compared with the experimental data. . . . 49
4.9 Cross sections of single pion productions for CC and NC interactions. . . . 50
4.10 Cross sections of multi-pion productions for (a)CC and (b)NC interactions. 51
4.11 Cross-sections for CC and NC coherent pion production. . . . . . . . . . . 52
4.12 Calculated cross sections of the pion in a nucleus compared with the experimental data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.13 Di erential cross section for the pion photo-production. . . . . . . . . . 54
4.14 The quantum eciency as a function of wavelength(nm). . . . . . . . . . 54
5.1
5.2
5.3
5.4
5.5

Algorithm of event selection for FC sample. . . . . . . . . . . . . . . . . . 58
PEMAX /PE300 distributions . . . . . . . . . . . . . . . . . . . . . . . . . 59
The OD-hits distribution for (a)DATA and (b)random trigger events. . . . 59
The OD-hitent=exit distribution for the random trigger events. . . . . . . . 60
A typical through-going muon event rejected by the through-going muoncut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.6 A typical stopping muon event rejected by the stopping muon cut. . . . . 62
5.7 The goodnesslow distribution for muon-decay electron events. . . . . . . . 63
5.8 A typical low-energy event rejected by the low-energy event cut. . . . . . 63
5.9 ID-time distributions for (a)a typical normal event and (b)a ashing PMT
event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.10 A typical ashing PMT event rejected by the ashing PMT cut. . . . . . 64
5.11 OD-time distribution of an accidental hit event rejected by the accidental
hit cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.12 A cable-hole muon event rejected by the cable-hole muon cut. . . . . . . . 66
6.1 The timing residual, ti(nsec.), distribution in a typical event. . . . . . . .
6

68

6.2 (a)A typical PE() distribution for an e-like event and (b) dd2 PE2 distribution
as a function of opening angle. . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Basic concept of the ring counting algorithm. . . . . . . . . . . . . . . . . 72
6.4 The (number of identi ed single-ring q.e. events) / (number of q.e. events)
ratio as a function of momentum. . . . . . . . . . . . . . . . . . . . . . . 73
6.5 The (number of identi ed single-ring q.e. events) / (number of q.e. events)
ratio as a function of dwall. . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.6 Relation between the PMT and Cherenkov photon. . . . . . . . . . . . . 75
6.7 Distribution of the particle PID parameter for single-ring atmospheric
neutrino events for both data and Monte Carlo samples. . . . . . . . . . 78
6.8 PID parameter for cosmic-ray muons (shaded histograms) and muon-decay
electrons (open histograms). . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.9 The pos distribution for (a)e-like and (b)-like sub-GeV single-ring events. 81
6.10 The dir distribution for (a)e-like and (b)-like sub-GeV single-ring events. 81
6.11 The pos== distribution for e-like(left) and -like(right) events. . . . . . . 82
6.12 Relation between Rtot and momentum for the electron and muon. . . . . . 83
6.13 The momentum resolution for (a)elections and for (b)muons. . . . . . . . 84
7.1 Momentum distributions of atmospheric neutrino fully-contained sample. 86
7.2 Distributions of maximum p.e. in a PMT after momentum and DWALL cut. 86
7.3 Distributions of number of OD-cluster hits after momentum, DWALL andmax. p.e. cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.4 The predicted e-like events caused by neutron backgrounds as a functionof DWALL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.5 The sub-GeV single-ring vertex distributions projected to the Z direction. 94
7.6 The (=e)DATA=(=e)M:C: vs Z plot. . . . . . . . . . . . . . . . . . . . . 95
7.7 The sub-GeV single-ring vertex distribution projected to the X and Y plane. 96
7.8 The (=e)DATA=(=e)M:C: vs DWALL plot. DWALL = 0 means the PMT
surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.9 Momentum distribution for (a)e-like and (b)-like events. . . . . . . . . . 98
7.10 The R (=(=e)DATA=(=e)M:C:) vs momentum. . . . . . . . . . . . . . . . 98
7.11 The average angle between reconstructed and parent-neutrino directions
as a function of visible energy of the detected particles, estimated by theMonte Carlo simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7

7.12 The zenith angle distribution for (a)e-like and (b)-like events. The errors
are statistical only. The systematic errors are negligible compared to thestatistical ones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.13 The (cos ) distribution for e-like and -like events divided into two momentum regions, (a)100-400MeV/c and (b)>400MeV/c. . . . . . . . . . . 100
7.14 The R (=(=e)DATA=(=e)M:C:) as a function of cos . . . . . . . . . . . . 100
7.15 The R (=(=e)DATA=(=e)M:C:) as a function of cos  divided into two
momentum regions, (a)<400MeV/c and (b)>400MeV/c. . . . . . . . . . . 101
7.16 The mean of the Rtot for -decay electrons as a function of the zenith
angle (cos .) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
A.1 Momentum spectrum of muon decay electrons in the ducial volume. . . 106
A.2 Momentum spectrum of LINAC electrons. . . . . . . . . . . . . . . . . . 107
A.3 The distribution of the reconstructed invariant mass for the data and theMC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.4 Opening angle vs momentum plots for (a)data and (b)MC stopping muon
events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.5 The hRMC i=hRdata i plots as a function of momentum. . . . . . . . . . . . 109
A.6 The mom./range vs range plot for stopping muon events. Events with arange more than 7m are used for the analysis. . . . . . . . . . . . . . . . 110
A.7 hmom:=rangeidata and hmom:=rangeiMC plots as a function of range. . . . 110
A.8 Summary of the absolute energy scale. . . . . . . . . . . . . . . . . . . . 111
A.9 The time variation of the hmom:=rangei. The x-axis show the day from
Apr. 1,1996. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
A.10 The time variation of the mean energy of the muon-decay electrons. . . . 113

8

List of Tables
1.1 decay mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2 Summary of the sub-GeV atmospheric neutrino data from KamiokandeI,II,III. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 The properties of the 20-inch  PMT . . . . . . . . . . . . . . . . . . . .

27

3.1 Properties of Ni(n, )Ni reactions. There exist many more lines with small
branching ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Summary of the Monte Carlo simulation in sub-GeV energy region. . . . 55
7.1 Summary of the sub-GeV atmospheric neutrino sample compared with
the Monte Carlo estimation. Numbers of the Monte Carlo sample arenormalized by livetime of data. . . . . . . . . . . . . . . . . . . . . . . . . 88
7.2 Fractions of events with -decay in single-ring events. The error of thedata and the rst error of the MC are statistical. The second error of the
MC arises from the detection eciency of muon decay. . . . . . . . . . . 89
7.3 Possible sources of the systematic uncertainties for the sub-GeV =e ratio. 90
7.4 E ects for the number of e-like and -like events and R when the energy
spectrum of the MC atmospheric neutrino is changed. . . . . . . . . . . . 91
7.5 The e ect on the R when we use the result of TDC- t as a nal vertex. . 91
7.6 E ects on the R from the energy-scale uncertainty. . . . . . . . . . . . . . 91
7.7 E ects on R when simulation parameters in the CC quasi-elastic interaction are changed. PF is the Fermi momentum and MA is the axial vector
mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.8 E ects on R when simulation parameters in the CC pion production interaction are changed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.9 E ects on the R when simulation parameters in the CC pion production
interaction are changed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
9

7.10 E ects for the R by changing criteria of maximum p.e. and OD-hit. . . . 93

10

Chapter 1
Introduction
1.1 Atmospheric neutrinos
Atmospheric neutrinos are the decay products of mesons ('s, K 's, and muons) createdin interactions of primary cosmic rays (protons and nuclei) high in the atmosphere.
Fig. 1.1 shows the predicted ux of atmospheric neutrinos. As shown in this gure,

Figure 1.1: Calculated atmospheric neutrino uxes at Kamioka for solar modulation ofmax, mid and min by Honda[1]. The estimated  ( ), e (e) ux at Kamioka site areshown by solid ( , e ) and dashed ( , e) lines. The dotted line is for  ux at IMB
site.
11

the atmospheric neutrino ux depends on the experimental site and solar modulation,
because the geomagnetic latitude and 11-year-period solar activity a ect the ux ofprimary cosmic rays.
When the primary cosmic rays propagate in the atmosphere, they create pions andkaons by interactions with air nuclei. Relevant decay modes of these mesons are shownin Table 1.1. In these decay modes, the following decay chain is dominant.

 !  ( ) ! ee(e) ()K  !  ( )! 0!    + ,! 0( )! 0ee(e)! 00(100%)(100%)(63.5%)(21.2%)(5.6%)(3.2%)(4.8%)(1.73%)

KS0 ! +,

(68.6%)

KL0 ! +,0(12.37%)!    ( ) (27%)! ee(e). (38.6%)
Table 1.1: decay mode !  + ( )# ! e + e(e) +  ( ):The uncertainty in the calculation of atmospheric neutrino ux is mainly due to theuncertainties in the ux of the primary cosmic rays and hadronic interactions and isestimated to be 20%.
In the low energy range (E < 1GeV ), even muons ( mean lifetime = 2.2sec )decay in the atmosphere, thus one expects the ratio of the number of  's to e 's tobe approximately 2:1. At E =1GeV, the  /e ratio is estimated to be 2.1 by several
independent calculations. But at higher energies, muons tend to survive and hit theearth before they decay. This reduces the ux of e and raises the  /e ratio. The
uncertainty in the  /e ratio is estimated to be only 5%, because the uncertainty in12the absolute ux is cancelled out by taking the ratio.

1.2 Atmospheric neutrino anomaly
In the 1980's, massive underground experiments, which could detect atmospheric neutrinos, started at several experimental sites. Originally, these experiments aimed at detecting nucleon decay. Atmospheric neutrinos were only studied to estimate the backgrounds
for nucleon decay searches.
In 1988, however, Kamiokande observed an anomalous atmospheric neutrino avor
ratio through a detailed study of these atmospheric neutrinos. Kamiokande measured
the number of single-ring electron-like (e-like) and muon-like (-like) events, and took
the ratio of these two numbers, -like / e-like. Since the -like (e-like) events are dominated by charged current  (e) interactions, the ratio -like / e-like, approximates theatmospheric ( +)/(e +e) ux ratio. The measured -like / e-like ( /e) ratio wasfound to be only 60% of the expected value.
We usually use the ( +  )=(e + e) ratio to show the atmospheric neutrino results
because the ratio of muon to electron neutrinos has a much smaller uncertainty ( 5%)than the uncertainty of the absolute atmospheric neutrino ux ( 20%). A ratio ofratios, R, is de ned as:)MeasuredR = ((=e
=e)Expected

Results of atmospheric neutrino measurements are shown in Fig. 1.2. The R value
smaller than 1, reported in Kamiokande, is con rmed by IMB and Soudan 2 experiments.
Results of Frejus and NUSEX experiments are consistent with Monte Carlo predictions,but they have larger statistical uncertainty.
In the following sections, I will describe the details of these experiments.

1.2.1 Kamiokande
Kamiokande was an imaging water Cherenkov detector located 1000m underground in
the Kamioka mine. 3000tons of pure water was stored in a cylindrical steel tank. The
water was viewed by 948 20-inch photomultiplier tubes (PMT), covering 20% of thetank inner surface. In Kamiokande-II and also Kamiokande-III, the inner detector was
surrounded by a 4 anticounter layer which contained 1.2-2.0m thick water and viewed
by 123 20-inch PMTs. The operation of Kamiokande started in July 1983 to search fornucleon decay. Kamiokande-II tried to detect low energy, astrophysical neutrinos such13

Kamiokande
IMB
Soudan2Frejus
NUSEX
0

0.2

0.4

0.6

0.8

1
1.2
1.4
R=(µ/e)DATA/(µ/e)MC

Figure 1.2: Present atmospheric neutrino qexperimental status. Inner error bars show
statistical error and outer error bars show (syst:)2 + (stat:)2 .
as solar neutrinos[2]. Successful observation of the neutrino burst from the supernova
SN1987A[3] was especially well known.
In Kamiokande, atmospheric neutrinos were detected by their interactions in water.
The relevant interaction processes were: Charged-current quasi-elastic reaction

l N ! lN 0

 Charged-current single-pion production

l N ! lN 0 +  Charged-current multiple-pion production

l N ! lN 0 + m Neutral-current quasi-elastic reaction

l N ! l N 0

 Neutral-current single-pion production

l N ! l N 0 +  Neutral-current multiple-pion production

l N ! l N 0 + mHere l means e or  and N means nucleon. Kamiokande observed electrons and muons
produced by these reactions.
Table 1.2 is the result on the sub-GeV 1 atmospheric neutrinos observed in Kamiokande
which are compared with the Monte Carlo prediction 2. Though the number of single
ring e-like events is in good agreement with the expected number, a de cit of -likeevents relative to the Monte Carlo prediction is apparent.
0 1 < pe <1.33GeV/c for the e-like events and 0:2 < p < 1:5GeV/c for the -like events.
Monte Carlo prediction is based on 43 kton-years equivalent simulated data which passed throughthe same analysis chain.
1 :

2

14

Data Monte Carlosingle ring 482
584.3
-like234
356.8
e-like248
227.6
multi ring 208
233.8
total ev. 690
818.1(=e)data:06
0:60+0,0:05(=e)M:C:
Table 1.2: Summary of the sub-GeV atmospheric neutrino data from Kamiokande-I,II,III.
The detector exposure is 7.7 kton-years.
The observed (/e)data / (/e)MC was,R = 0:60 00::0605 (stat:)  0:05(syst:):
To verify the Kamiokande result, we constructed a 1000 ton water Cherenkov detector and injected electrons and muons produced by a 12GeV proton synchrotron at KEK
in Japan[4]. By this beam test, we determined the vertex resolution, energy resolution,and especially the performance of the particle identi cation algorithms. The misidenti cation probabilities for e-like and -like events were estimated to be less than 3%
in the momentum range of 250-1000MeV/c except for particles injected at 1.8m fromthe detector wall, which is outside of the ducial volume. Thus, we con rmed that theatmospheric neutrino anomaly was not caused by an experimental aw.

1.2.2 IMB-3
The IMB-3 (Irvine-Michigan-Brookhaven) detector was located in the Morton Salt Minenear Cleveland, Ohio, USA. The detector was an 8 kton water Cherenkov detector which
had 2048 8-inch PMTs with wavelength-shifter plates. The wavelength shifter plate wasinstalled to increase the light collection eciency. The ducial volume was 3.3 kton andwas 2m inside of the PMT surfaces.
Data were taken from May 1986 to March 1991 and the total exposure was 7.7 ktonyears. Single-ring contained events were used for atmospheric neutrino analysis. The
data with momentum, p <1500MeV/c and visible energy, Evis > 100MeV consistedof 325 e-like events and 182 -like events[5]. From Monte Carlo studies, the particle
identi cation capability was estimated to be 92% and 87% for -induced and e-induced
15

events, respectively. In 1992, R was reported as:

R = 0:54  0:05(stat:)  0:12(syst:):1.2.3 Soudan 2
The Soudan 2 experiment was located in an iron mine in northern Minnesota, USA. The
main detector was an iron tracking calorimeter with a total mass of 963 tons, divided
into 224 modules. Each module consisted of 7560 drift tubes in a hexagonal honeycomb
structure. The calorimeter was surrounded by a 1700 m2 active shield of aluminum
proportional tubes to reject background.
The analysis of atmospheric neutrinos was reported in 1997[6] with data from April
1989 to December 1993. The total exposure was 1.52 kton-years. Contained events withenergy more than 200MeV were used for the atmospheric neutrino analysis. A contained
event was de ned as an event in which no primary particle in the event left the ducial
volume of the detector. The ducial volume was de ned by a 20 cm depth cut on all
sides of the detector. The lepton avor of each event was determined by scanners. Using
Monte Carlo simulation to study misidenti cation capabilities, 87% of events assigned
as tracks (-like) had muon avor while 96% of events assigned as showers (e-like) had
electron avor.
They detected 47 track events and 60 shower events, so the R measured in the Soudan
2 experiment was::05
R = 0:72  0:19(stat:)+0,0:07 (syst:):Soudan 2 is still running and the exposure will reach to 5 kton-years in 1999.

1.2.4 Frejus
The Frejus experiment was located in the middle of the Frejus highway tunnel connecting France and Italy. The detector was 912 ton iron calorimeter and measured
6m6m12.3m. It consisted of 912 ash chamber planes and 113 Geiger tube planes
which provided the trigger. A ash chamber plane was made of a sandwich structurewith 3mm thick iron plates and 5mm thick planes of plastic ash tubes.
Data were taken from February 1984 to September 1988. The ducial volume wasde ned such that the interaction vertex had to be located more than 50cm away from thedetector surface. Since this cut reduced the ducial mass to 554 tons, the total exposure
was 1.56 kton-years[7].
16Events were classi ed as contained or non-contained. Non-contained events with
one track were rejected as cosmic-ray muons. They found 142 contained events and
46 non-contained events. These events were also classi ed as charged current  (CC),charged current e(CCe), or neutral current(NC) interactions by visual inspection. The
identi cation eciency for CC and CCe interactions were investigated by simulated
events and the eciency was estimated to be 95% and 85% for muon and electron
neutrino events respectively.
The R from the Frejus analysis of contained and non-contained events, reported in
1989, is:19
R = 1:06+0,0:16 (stat:)  0:15(syst:):In 1995, the data was reanalyzed with an enlarged ducial volume (700 ton). The
new R is,R = 1:00  0:15(stat:)  0:08(syst:):1.2.5 NUSEXThe NUSEX detector was a 150 ton, 3.5m cubical iron tracking calorimeter located in
the Mont Blanc tunnel. The tracking calorimeter was made by 134 horizontal iron platesof 1 cm thickness, interleaved with plastic streamer tubes.
Events with the lepton energy above 200MeV were used in the analysis. The performance of particle type identi cation was tested directly by an accelerator and wasfound to be good. Data were taken from June 1982 to June 1988, corresponding to 0.74
kton-years of total mass exposure. During run time, 32 -like and 18 e-like events weredetected. The R, reported in 1989[8], is:32
R = 0:96+0,0:28 (stat:)

1.3 Possible explanations for the atmospheric neutrino anomaly
In the previous section I presented the status of atmospheric neutrino experiments. The
discrepancy of the ( +  )=(e + e) ratio between the calculations and the resultscannot be explained within the framework of the standard model of particle physics if
the anomaly is not caused by the experimental reasons.
17

In this section, I will describe three possible explanations of the atmospheric neutrino
anomaly.

1.3.1 Neutron background
It was suggested that the small ( +  )=(e + e) ratio could be explained by isolated
neutron interactions in the detector. Neutrons are generated in deep-inelastic scatteringof cosmic-ray muons in the rock around the detector and some of these neutrons go into
the detector and produce 0 's. A from 0 decay could be identi ed as an e-like event
if one of the two 's is not identi ed.
In Kamiokande, the neutron contribution to the atmospheric neutrino measurement
was studied[9]. For the sub-GeV region (Evis <1.33GeV), the vertex-position distribution of 2-ring 0-like events was examined and there was no excess near the detector wall.
Therefore the possible contamination of neutrons in the sub-GeV e-like sample was estimated to be less than 1.2% at the 90% C.L. For the multi-GeV region (Evis >1.33GeV),
the background contamination was estimated using the vertex distribution of the e-likeevents and the possible contamination was estimated to be less than 14% at the 90%
C.L.
In summary, it was veri ed that the neutron background cannot explain the atmospheric neutrino anomaly, especially for the sub-GeV region.

1.3.2 Proton decay
Another explanation proposed to explain the atmospheric neutrino anomaly is proton
decay. This model says that the ux anomaly is caused by an excess of e-like events
which are produced by the proton decay mode, p ! e+ . Since a proton decays into
three particles, the energy spectrum for e+ is broad and its energy is less than 500MeV.
Therefore, if an excess of electrons is found only in the energy region less than 500MeV,
it could be explained by proton decay. The possibility of proton decay will be discussed
in Sec. 7.3.

1.3.3 Neutrino oscillations
Neutrinos are treated as massless in the standard model. However, there is no compelling
reason why neutrinos are massless and why neutrino families should not mix like quarks.
If neutrinos are indeed massive, it is very likely that some mixing occurs among them.
18

Neutrino oscillations are generally predicted to occur for non zero neutrino mass andmixing.
Here, we give a brief explanation of the neutrino oscillations for a simple two neutrino system. The observed neutrinos, e and  , are avor eigenstates. They are notnecessarily identical to mass eigenstates, 1 and 2 . These two eigenstates are combinedby the unitary matrix, U , and described as:

0 1
0 1 0
10 1


cos

sin

e
1
@ A= U@ A= @A @ 1 A2, sin  cos 
2

(1.1)

where  is the mixing angle with 0    4 . Time evolution of mass eigenstates can be
written as:
0
1 0
10
1

(
t
)
exp(
,
iE
t
)
0

(0)
1
1
1
@
A=@
A@
A;
(1.2)
2 (t)
0 exp(,iE2 t)
2(0)where 1 (0) and 2 (0) are the mass eigenstates at T = 0 and and 1 (t) and 2 (t) are themass eigenstates at T = t.
Eq.1.2 is rewritten using Eq.1.1 as:

0
1
0
1 0
1

(
t
)
exp(
,
iE
t
)
0

(0)
1
@ e A=U@A Uy @ 1 A ;(t)0 exp(,iE2 t)
2 (0)(1.3)

Then, the probability that a neutrino born as a e at the source remains as a e is givenby:

P (e ! e) =

0exp(,iE1 t)
1 0 U@
01 0 120
A Uy @ 1 A
exp(,iE2 t)
0= 1 , 21 sin2 2(1 , cos(E2 , E1 )t)(1.4)

Finally, the survival probability can be rewritten as:m L );P (e ! e ) = 1 , sin2 2 sin2 ( 1:274
p
2



(1.5)

where 4m2 = m22 , m21 (eV2 ), and L(km), p (GeV/c) are the path length and momentumof the neutrino, respectively.
Atmospheric neutrinos can be used to study neutrino oscillations by interpretting thesource of the anomaly as muon neutrino oscillations into either electron or tau neutrinos.
Since neutrino oscillations depend on the path length of the neutrinos, L, the zenith
angle distribution of R also provides useful information about neutrino oscillations. The
19

Figure 1.3: Zenith angle distribution of R for themulti-GeV contained events in Kamiokande. The
plots with error bars show the data. Histograms
show the Monte Carlo prediction with neutrino
oscillations. For  $ e oscillation the bestt oscillation parameter sets (sin2 2; 4m2(eV2 ))is (1.0, 1:8  10,2) (dashed line) For  $ 
oscillation the best- t parameter sets is (1.0, 1:610,2) (dotted line).
zenith angle distribution of R for multi-GeV events observed in Kamiokande, as shownin Fig. 1.3, is very suggestive of neutrino oscillations.
Neutrino oscillations searches have been done by many experiments. They have usedsolar, atmospheric, accelerator or reactor neutrinos. Fig. 1.4 shows the present experimental status of neutrino oscillation experiments. Solar neutrino and reactor experiments are sensitive to e $ X oscillations. Solar neutrino experiments indicate threesolutions for neutrino oscillations, small angle, large angle, and justso solutions. Typical (sin2 2, 4m2(eV2 )) of these solutions are (9:1  10,3; 6:3  10,6), (0:7; 2:8  10,5),and (0:8; 7:1  10,11), respectively[10]. Reactor experiments give exclusion regions. Atmospheric neutrino data in Kamiokande indicate neutrino oscillations and the otheratmospheric neutrino experiments and accelerator experiments give exclusion regions.
Gosgen[11], Bugey[12], and CHOOZ[13] are reactor experiments and CDHSW[14] is anaccelerator experiment. Upward-going muons produced by atmospheric neutrinos arealso sensitive to the neutrino oscillations and give an exclusion region for  $ 
oscillations[15].

1.4 Motivation of this thesis
As mentioned in previous sections, the atmospheric neutrino anomaly was reported byseveral experiments, and in order to explain the anomaly, several models were suggested.
We constructed 50 kton water Cherenkov detector, Super-Kamiokande, which enables us to carry a high-statistics atmospheric neutrino measurement for the rst time.
20

1

(b)

2

2

∆m (eV )

(a)

2

2

∆m (eV )1

CDHSW

Gösgen10-110Frejus-1Kamcontained

Kam
contained

Bugey
10

-2

10

-2

Frejus
CHOOZ
10

10

-3

10

-4

0

0.2

0.4

0.6

0.8
1
2
sin 2θ

10

IMB Stop/Through

-3

-4

0

0.2

0.4

0.6

0.8
1
2
sin 2θ

Figure 1.4: Constraints to 4m2 and sin2 2 for (a) $ e and (b) $  oscillations.
The solid lines show excluded region with 90% C.L. and the dashed lines show allowed
region with 90% C.L.
The ducial volume of Super-Kamiokande is more than 20 times as large as that of
Kamiokande. In this thesis, the atmospheric neutrino measurement in the sub-GeV energy range in Super-Kamiokande with 20 kton-years exposure is presented and the  =eratio and the zenith angle distribution will be discussed.

21

Chapter 2
Super-Kamiokande detector
The Super-Kamiokande detector is a ring imaging water Cherenkov detector locatedabout 200m south-west of the Kamiokande detector in the Kamioka mine of Gifu Prefecture, Japan. It is reached by a 2km long access tunnel and lies 1000m under the ground.
The 1000m thickness of the rock is equivalent to 2700m water and it reduces the cosmicray muon rate at the Super-Kamiokande site to 2.2Hz. In the mine, the clean natural
water ows and is used as the primary water for the detector. The water temperature isstable at 9-10C all year long.
In this chapter, the principle of a water Cherenkov detector is explained in Sec. 2.1
and details of the experimental setup are presented in Sec. 2.2-2.5.

2.1 Water Cherenkov detector
A ring-imaging water Cherenkov detector detects Cherenkov photons emitted in waterby charged particles. Based on information of the pulse arrival-time and amplitude fromeach PMT, it is possible to reconstruct the vertex position, direction, momentum andparticle type of the parent charged particle.
A charged particle emits Cherenkov photons 1 if the velocity of the charged particle,, exceeds the speed of light in the medium ;n  1;(2.1)

where n is the index of refraction of the medium (n=1.331.36 in water, depending on
the wavelength of a photon). They are emitted on a cone with a half opening angle, ,1This emission was rst discovered by Cherenkov in 1934.

23

with respect to the particle direction:cos  = n1 :(2.2)

For = 1,  = 42 (in water). The number of photons emitted per unit path length perunit frequency is given by
d2N = 2 (1 , 1 );
(2.3)
dxd
c
n2 2

where is the ne structure constant, x is the path length of the charged particle, and 
is the frequency of the emitted photon. The number of Cherenkov photons emitted in the
wavelength range of 300-600nm, which is the sensitive region of the PMTs, is about 340
per cm in water. The total number of the Cherenkov photons is proportional to the totalenergy deposited by a charged particle, because the track length of a charged particle isalmost proportional to its energy. Cherenkov photons are detected by photomultipliertubes (PMT) which surround the inner water mass. If a charged particle stops insidethe detector, Cherenkov photons image a characteristic ring pattern on the the detector
wall.
Advantages of the ring-imaging water Cherenkov detector are: (1) particle direction
is determined, (2) the detector is very simple and can have a large ducial volume.

2.2 Water tankFig. 2.1 shows a view of Super-Kamiokande. The cavity is coated with 40-50cm thickreinforced concrete on the side wall and the oor and the stainless cylindrical watertank is situated inside of the cavity. The tank is 42m in height, 39m in diameter and50000m3 in volume. Above the tank, there is a space of a hemispherical shape wherefour electronics huts and one central hut are arranged.
The average geo-magnetic eld at the Super-Kamiokande site is 450mG. PMTs do
not work properly in a magnetic eld of more than 100mG. To compensate for the geomagnetic eld, 26 sets of Helmholz coils are arranged in the tank. The geo-magnetic
eld inside the tank is reduced to about 50mG.
The Super-Kamiokande detector has two PMT layers, an inner detector(ID) and anouter detector(OD). The inner detector is completely surrounded by the outer detector.
These two layers are optically separated by a pair of opaque sheets as shown in Fig. 2.2.
The dead region between two sheets is 55cm in thickness. The details of the inner andouter detectors are described in the following subsections.
24

Figure 2.1: A schematic view of the Super-Kamiokande detector.

8 inchPMT

tyvek

black sheet

20 inchPMT

Figure 2.2: The structure of theframe for ID and OD PMTs.

25

Inner Detector
A water Cherenkov detector should have a large photosensitive area in order to collectas many Cherenkov photons as possible. For this purpose, custom 20-inch PMTs areused for the inner detector. On the inner surface of the inner detector, 11146 20-inch
PMTs are placed uniformly and 40% photocathode coverage twice that of Kamiokande
is achieved. The size of the inner detector inside the PMT surface is 33.8m in diameter,
36.2m in height and 32000m3 in volume. The areas between the PMTs are covered withblack PET (polyethylene terephthalate) sheets as shown in Fig. 2.2.

Outer detector
The outer detector is used as a veto-counter which identi es background particles fromthe outside of the detector such as cosmic-ray muons. The outer detector also shields
the inner detector from gamma rays and neutrons from the rock. The outer detector
surrounds the inner detector completely and the thickness of the outer detector is 2.05m
on the side wall and 2.2m on the top and bottom walls. The outer detector is instrumented with 1885 HAMAMATSU R1408 8-inch PMTs. Each 8-inch PMT is attached
by a 60cm square acrylic plate containing a wavelength shifter plate to increase the lightcollection eciency. The surface of the outer detector is covered with a re ective sheet,called Tyvek, to enhance the light collection.

2.3 20-inch PMT
Originally the 20-inch PMT was developed by HAMAMATSU Photonics Company for
the Kamiokande experiment. This PMT has demonstrated excellent performance in the
Kamiokande experiment. For Super-Kamiokande, several improvements in the dynodes
shape and the bleeder chain enable us to obtain even better timing and energy resolutions.
Properties of the PMT are listed in Table 2.1 and a view of 20-inch PMT is shown in Fig.
2.3. A clear single-photoelectron peak can be seen in the pulse height distribution(seeFig. 2.4). In summary, the performance of the 20-inch PMT is good enough to be usedin Super-Kamiokande. More details of the 20-inch PMT are presented in [16].
26

Photo-cathode area
Shape
Window material
Photo-cathode material
Dinodes
Pressure tolerance
Quantum eciency
Gain
Dark current
Dark pulse rate
Cathode non-uniformity
Anode non-uniformity
Transit time
Transit time spread

50cm in diameter
Hemispherical
Pyrex glass(45mm)
Bialkali
11 stage, Venetian blind
6kg/cm2 water proof
22% at  =390nm
107 at 2000 Volt
200nA at gain=107
3kHz at gain=107
less than 10%
less than 40%
100nsec typical, at gain=107
 2.5nsec

Table 2.1: The properties of the 20-inch  PMT

cable length~ 70000

Figure 2.3: A schematic viewof PMT.

φ 116

φ 254 10φ 82 2glass multi-seal

photosensitive area > φ 460< φ 520

cable

water proof structure( 610 20 )

~ 720

(mm)

27

Figure 2.4: A typical 1p.e. distribution.

2.4 Water puri cation
To receive enough Cherenkov photons, we must keep the light attenuation length in thewater a reasonable length and remove radioactive elements in the water to reduce lowenergy backgrounds. For these purposes, water in the tank is circulated and puri ed
continuously. The water puri cation system consists of the following 7 components:
1. 1m Filter to remove dust.
2. Heat exchanger to cool the water temperature to about 13C.
3. Ion exchanger to remove ions.
4. UV sterilizer to kill bacteria.
5. Vacuum degasi er to remove remaining gas such as oxygen and radon.
6. Cartridge polisher to remove ions.
7. Ultra lter to remove small particles( 10nm).
The ow diagram is shown in Fig. 2.5. This system puri es the detector water with aow rate of about 50m3/hour. Ultra lters separate the input water into particle freewater and a small amount of (15%) water containing particles which is sent to a bu ertank. Then it is puri ed by the reverse osmosis and is returned back to the (2)heat
exchanger.
After the water puri cation, the concentration of radon, which is 104Bq/m3 in themine water, is reduced to 5mBq/m3 and the light attenuation length is about 100m at
a wavelength of 420nm. (The attenuation length measurement is presented in Sec. 3.4.)28

m

Figure 2.5: A ow diagram of the water puri cation system.

2.5 Data acquisition system
Electronics for the inner detector
A block diagram of the electronics for the inner detector is shown in Fig. 2.6. Signal
cables from the inner PMTs are fed into the TKO (Tristan-KEK-Online) system. The
TKO system consists of GONG (GO and NoGo trigger distribution module), ATM (Analog Timing Module) and SCH (Super Controller Header, bus-interface module). Mostof signal processing is done by the ATM module, which can measure the charge andtiming of each input PMT signal. The details of the ATM are described in [17]. In the
Super-Kamiokande experiment, 960 ATM cards are used in 48 TKO crates. Each TKO
crate accommodates one SCH and one GONG.
At rst, the inner PMT signals are digitized in the ATM, which provides a 1.2 sfull range with 0:3 ns resolution in time and a 550 pC full range with 0:2 pC resolution( 0:1 p.e.) in charge for each PMT. The ATM has 12 input channels and each channel
has switching two TACs (Time to Analog Converter) and two QACs (Charge to Analog
Converter) to provide deadtime free recording. If a signal exceeds the threshold, a
HITSUM pulse is issued on the front panel and is used to generate the global trigger.
29

20-inch PMT
SCH
ATM
x 20
x 240

ATM
GONG

20-inch PMTSCHATMinterface
SUN classic

x 20
x 240

SMP

ATM

SMP

GONG

online CPU(slave)

SMP
SMP
SMP
SMP

x6

Super Memory Partner

VME
20-inch PMTSCH

SUN classic

ATM

online CPU(slave)

x 20
x 240

SUN classic

ATM
GONG

online CPU(host)

Analog Timing Module

online CPU(slave)
TKO

FDDI

SUN classic

SUN sparc10

online CPU(slave)
SUN classic

online CPU(slave)
SUN classic

FDDI

online CPU(slave)
SUN classic

online CPU(slave)

online CPU(slave)interface
SUN classic
SMP
SMP

SUN classic

online CPU(slave)

SMP
SMP
SMP
SMP

interface

Super Memory Partner

VME
VME

interrupt reg.
TRG

20-inch PMT
SCH
TRIGGERATM

TRIGGER

x 20
x 240

PROCESSORHIT INFORMATION
ATM
GONG

Analog Timing ModuleTKO

PMT x 11200

ATM x ~1000

SMP x 48

online CPU(slave) x 9

Figure 2.6: Inner detector data acquisition system.
30

The pulse height of the HITSUM signal indicates the total number of hit PMTs within
a 200nsec window.
The data in the ATM memory are read out every 16 global triggers and stored in thedata bu er modules called SMP (Super Memory Partner) through the SCH. The SMP
has two 1Mbyte memories and each memory is read out in turn by the front-end work
station(Sun-Classic). In total 8 front-end work stations are arranged in four electronics
hut. The global trigger is controlled by a work station (Sun SPARKstation 10) in thecentral hut.

Electronics for the outer detector
The electronics used in the outer detector are completely di erent from those used in
the inner detector. Signals from 8-inch PMTs are connected to a charge to time converter(QTC) module which generates a rectangular pulse with a width proportional tothe input charge. The pulses, which carry the time and charge information, are digitizedby a LeCroy 1877 multi-hit TDC (Time to Digital Converter). The TDC has 96 input
channels and the minimum time unit of the TDC is 0.5nsec. This TDC can record multihits within a 16sec window. The timing of the trigger in this 16sec window is set to-10 to +6sec relative to the global trigger timing. The TDC is a FASTBUS module andits crate is controlled by a FASTBUS Smart Crate Controller (FSCC). The FSCC sends
the digitized PMT data from TDCs to the dual ported memory(DPM) modules. Finallythese data are read out by the OD data taking work station through a VME bus.

Trigger system
There are two kinds of triggers for the inner detector, LE(low energy) trigger and HE(highenergy) trigger. The di erence between these triggers is only a discriminator threshold for
the HITSUM signal. The discriminator threshold is 29 hits equivalent for the LE trigger
and 31 hits equivalent for the HE trigger. At the time of this writing, the thresholdof the global trigger is identical with the LE trigger, which corresponds to an electronenergy of about 5.7 MeV. For events with the visible energy above 30MeV, the triggereciency is 100%. Once the global trigger is generated, the TRG module distributes
the trigger signal to all ATMs through the GONG modules. The trigger rate for the LE
trigger is 10-12Hz and for the HE trigger is 5-6Hz. It is stable all the year.
For PMTs in the outer detector, the OD-trigger is generated by using the hitsum
signal of the outer PMTs. The discriminator threshold is set to be equivalent to 19 hits31within a 200nsec window. OD-trigger is used to identify cosmic-ray muons. The trigger
rate of the OD-trigger is 3Hz.

Online and Oine system
Each front-end work station reads out the data from electronics independently, converts
the raw data to a simple online format and sorts the data in order of the event number.
All the information from the inner and outer detectors is collected and merged into an
event by the \event builder" program running on the host computer. The data is sent
to the oine computing system every subrun, which has 10-minute of data and is about
100Mbyte in size. On the oine computers the data format is converted to the oine
format(ZBS, Zebra Bank System) and stored in the magnetic tape library.

32

Chapter 3
Calibration
In order to get precise information of an event, it is necessary to calibrate the gain andtiming response of each PMT and to measure the water transparency.
In this chapter the method of relative gain calibration, absolute gain calibration,
timing calibration, and water transparency measurement is presented. The relative gain
calibration adjusts the gain of all the PMTs. The absolute gain calibration is to nd a
relation between a measured photoelectron numbers and the energy of an event. The
timing calibration is to nd a relation between the measured TDC counts and the arrival
time of the input signal.
UV filter ND filter
Xe Flash Lamp

Photo
Diode

SK TANK

Photo
Diode

Optical fiber

ADC

Scintilator Ball
PMT
Scintilator

Monitor20inchPMT

Trigger

Figure 3.1: The relative gain calibration system.
33

3.1 Relative gain calibrationf(θ)

We use a Xe lamp and scintillator ball system in order to calibrate the relative gain of
the PMTs. Fig. 3.1 shows the setup of the relative gain calibration system. Light fromthe Xe ash lamp, which is used as the light source, passes through a UV lter and ND
lter to match the wavelength with the Cherenkov light and to adjust the light intensity,
respectively. Then the light reaches the scintillator ball via an optical ber. To emit
isotropic light, the scintillator ball is made of acrylic resin in which 50ppm BBOT and
500ppm MgO powder are uniformly mixed. The BBOT is used as a wavelength shifterand the MgO is used as a light di user. Typical wave length of the light is 440 nm.
(a)

1

(b)

0.75
direction of

θi

0.5

i th PMT

0.25

0emitted Cerenkov photon

0

20

40

60

80
θ (degree)

Figure 3.2: (a)Relative PMT photo sensitive area as a function of angle,  and (b)thede nition of .
The relative gain of the i-th PMT is expressed by the following equation,
Gi = fQ(i )  ri2  exp( rLi ) = Q0;(3.1)
where f () is the relative photosensitive area of the PMT viewed from an angle  asshown in Fig. 3.2, Qi is the charge in units of pC detected by the i-th PMT, ri is the
distance between the scintillator ball and i-th PMT, L is the light attenuation length in
the detector and Q0 is the normalization factor to adjust the average Gi equal to 1. We
set the high-voltage (HV) value of each PMT so that all PMTs have a common gain.
We took the data for the relative gain calibration 9 times by changing the position of
the scintillator ball from 1 m to 35 m in height from the bottom PMT surface in orderto minimize the ri and f () dependence to each PMT.
After the relative gain correction, we took the data with the same system again tocheck the relative calibration. And the gain spread is estimated to be 7% as shown in34

Fig. 3.3. Since the number of hit PMTs is typically 1300 for atmospheric neutrino
events, ambiguity from the relative gain spread is estimated to be only 0.2%.
Constant
Mean
Sigma

1600

1244.
0.99990.6910E-01

1400
1200

Figure 3.3: The relative gain distribution after the HV adjustment. Solidline shows the tting result.

1000
800
600
400
200
0

0

0.2 0.4 0.6 0.81

1.2 1.4 1.6 1.8June 1996

2

gain value

3.2 Single photoelectron distribution
The absolute gain of the PMT is calibrated by measuring the charge of single photoelectron(p.e.). In order to take the single p.e. data, we use low energy gamma-rays emitted
from thermal neutron capture in nickel, Ni(n, )Ni, because the number of p.e. in a
PMT is at most one. Neutrons are produced by spontaneous ssion of 252 Cf. Fig. 3.4
shows a schematic view of the Ni-Cf source. The 252 Cf source and Ni+water mixture areput into a cylindrical polyethylene case. Energies of emitted gamma-rays are listed inTable 3.1.
Reaction

Energy of
the -ray(MeV)
58 Ni(n, )59 Ni 9.0
60 Ni(n, )61 Ni 7.8
62 Ni(n, )63 Ni 6.8

Natural abundance of
the initial element
(%)
67.88
26.23
3.66

Cross section(barn)
4.4
2.6
15

Table 3.1: Properties of Ni(n, )Ni reactions. There exist many more lines with small
branching ratios.
The single p.e. distribution for a typical PMT is shown in Fig. 3.5. The horizontal
35

Ni wire+waterFigure 3.4: Schematic view of the Ni-Cf
gamma-ray source.

200mm
Cf

190mm

axis shows detected charge in units of pico coulomb(pC). Since the mean value of thischarge distribution above a threshold, which corresponds to about 0.25p.e., is 2.055pC,
the relation between pC and p.e. is
1p:e: = 2:055pC:
We tabulate the mean values for all PMTs and refer to this table everytime we translate
the charge to the number of p.e.
The shape of the single p.e. distribution is also used in the Monte Carlo simulation.
mean

2.055pC

3

Figure 3.5: Single photoelectron
distribution.

2

1

0

0

5

10

pC

36

3.3 Timing Calibration
Timing response di ers for each PMT because of the following two factors:
1. transit-time di erence of the PMT.
2. timing response of the discriminator.
Transit-time di erence depends mainly on high voltage applied to the PMT. And thediscriminator has an e ect that larger pulses tend to cross the threshold earlier thansmaller ones (slewing e ect).
To minimize the systematic error in the timing calibration, the pulse width of calibration light should be narrow. Therefore we used a dye laser pumped by a pulsed N2
laser to measure the timing response of each PMT. The pulse width and wavelength ofthe dye laser is 4 ns (full width) and 384 nm, respectively.
The laser light goes through several optical lters which control light intensity andreaches a di using ball via an optical ber. The di using ball is suspended at the centerof the tank and reemits laser light isotropically. Fig. 3.6 shows timing response of atypical PMT as a function of the observed photoelectrons, Q. This Q-dependence of thetiming is called TQ map1. We obtained TQmaps for all the PMTs. The TQmap corrects
for the relative time di erence of the PMT. The timing resolution can be estimated fromthe TQmap by tting the T distribution with a Gaussian distribution, which is shownin Fig. 3.7. It is used in the Monte Carlo simulation.
T (nsec)

Typical TQ map
980
970
960
950

Figure 3.6: A TQ map of a typical PMT. Circles and error bars show
peak values and resolutions (1 level).

940
930
920
910
900
890
880

Q (p.e.)1

T(timing)-Q(charge) map

37T (nsec.)
4

Figure 3.7: Timing resolution of a
PMT as function of Q (p.e.).

2

0
10

-1

1

10

10

2

Q (p.e.)

3.4 Water transparency
We measure the light attenuation length in water by means of two independent methods.
One method uses a dye laser and CCD camera. By changing the dye of the laser, we
can measure the wavelength dependence of the attenuation length. Another method
uses cosmic-ray muons. This method cannot measure the wavelength dependence, but
it does not need to stop normal data taking and is able to check the stability of watertransparency continuously.
The following subsections present the methods and results of the water transparency
measurement by two independent ways.

Laser and CCD camera method

Figure 3.8: Set up of the dye-laser + CCD camera system.
38

The setup of the dye laser plus CCD camera system is shown in Fig. 3.8. The lightsource is a dye laser pumped by a pulsed N2 laser. The emitted light is divided into
two optical bers, one is connected to a 2-inch PMT to monitor the intensity of thelight (Ilaser ) and the other is connected to the di user ball. The di user ball emits lightin the water isotropically and the CCD camera takes an image of the di user ball andmeasures the intensity of the light which is attenuated in the water (ICCD ). The depthof the di user ball (ld ) is changed from 5m to 30m and at each point Ilaser and ICCD
are measured four times. The attenuation length, L(), is calculated by the following
equation.
!
ICCD = const:  exp , ld ;
(3.2)
I
L()
laser

CCD/PMT

where  is the wave length of the light. Fig. 3.9 shows an example of the IICCD
plot as alaserfunction of ld when the wave length is set to 420nm. The data is tted with a least square
method and the attenuation length at 420nm is determined to be 92.2 m  5.2 m. (Ithas been improved and is 101  6m as of November, 1997.) The results at various wave
lengths are summarized in Fig. 3.10. In this gure, the solid lines show the estimationof Rayleigh scattering, mie scattering and absorption of light, which are considered in
our Monte Carlo simulation. Now, the study of the light attenuation and scattering byusing this system is continuing to understand more details of water characteristics andto tune the Monte Carlo simulation.

10

14-Dec-1996(420nm)
L=92.2±5.2m

4Figure 3.9: The light attenuation length at 420nm.

0

10

20
30
distance from CCD (m)Cosmic-ray muon method
The light attenuation length is also measured by cosmic-ray muons which enter from the
top wall and exit to the bottom wall. The number of p.e. detected by each PMT, Q, is
39attenuation coefficient(1/m)

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

Dec.-14-96
Dec.-27-96
Mar.-6-97-1

10
absorption

total

-2

10
Mie scattering

Figure 3.10: The L(),1 plot as
a function of the wave length.
Solid lines show the attenuation
length used in Monte Carlo simulation.

Rayleigh scattering

-3

10

200

300

400

500

600
700
wavelength (nm)expressed by the following equation:

Q = const:  f (l)  exp(, Ll );(3.3)

where l is the ight length of the Cherenkov photon, and L is the attenuation lengthof the Cherenkov light. Eq.3.4 can be rewritten as





!
Ql
log f () = , L1 l + log(const:)(3.4)

Fig. 3.11 shows log fQl() plot against l in a typical run. The attenuation length isobtained from the tted slope. The attenuation length, L, in run 3106(Nov.15, 1996)
is 105.40.5m (error of the tting). Since the absolute value of L depends strongly on
the method and parameter of the tting, we use the attenuation length measured bythis method only for monitoring possible time variation of the attenuation length, whichcauses a small di erence between MC and data. The attenuation length is calculated
every run. The time variation of the attenuation length is shown in Fig. 3.12. In
this gure, to reduce the statistical uctuation, each plot shows the average attenuation
length of 30 runs. From 200days to 300days, the attenuation length increased. It is due
to installation of the ultra- lter in the water puri cation system. We tabulate these time
variations and use this table to correct for particle momenta.
40

log(Ql/f(θ))

192.0

RUN 3106

500

/ 19
5.987
-0.9487E-04

P1
P2

0.4609E-03
0.4444E-06



400



Figure 3.11: The log fQl() plot
as a function of l. The solid line
shows the result of tting.

300
200
1000

attenuation length (m)

0

2000

3000

4000

5000
l (cm)

120

100

80
May 27,1996

60
0June 25,1997

200

400

elasped days from 1-Apr-1996

Figure 3.12: Time variation of light attenuation length in water measured by cosmic-ray
muons.

41

Chapter 4
Simulations
4.1 Atmospheric neutrino ux
Atmospheric neutrinos are produced by interactions of cosmic-rays and decays of theirsecondary particles in the atmosphere. To calculate the ux of atmospheric neutrinos,
we must know the primary cosmic-ray ux, models for particle interactions and theatmospheric structure. Additionally the e ect of geomagnetic eld must be considered
for low energy cosmic-rays because of the rigidity (=momentum/charge) cuto .
The observed primary cosmic ray uxes are shown in Fig. 4.1. They consist of95% protons, 4.5% helium nuclei, and 0.3% CNO nuclei for the energy above
2GeV/nucleon. Primary cosmic rays have a power spectrum of E ,2:7 above 5GeV.
The spectrum of low energy cosmic rays is a ected by the solar activity as shown in Fig.
4.1, because the solar wind drives the low energy cosmic rays away and the strength of
the solar wind varies with solar activity. The uncertainty in the absolute primary cosmic
ray ux is estimated to be 15%.
The primary and secondary cosmic rays are a ected by the geomagnetic eld. If therigidity of a cosmic ray is lower than the rigidity cuto , the cosmic ray cannot enter theatmosphere. The value of the rigidity cuto depends on the experimental site and arrival
direction of cosmic rays.
The atmospheric neutrino ux has been calculated by a number of theorists. We adopt
Honda's latest calculation[1], because he took into account the e ect of the geomagnetic
eld at the Super-Kamiokande site and covers the neutrino energies from 30MeV to 1TeV.
Fig. 4.2 shows the energy spectra for  +  and e + e at the Super-Kamiokande site,
compared with other calculations. In Fig. 4.3, the ux ratios are shown for various
calculations. It is important that, although the absolute atmospheric neutrino uxes
43

Figure 4.1: Observed uxes of cosmicray hydrogen, helium and CNO nuclei
as a function of kinetic energy per nucleon. The three lines are the uxes
adoopted for calculation at solar max,mid, and min. [1]di er among calculations, the ratio, ( + ) / (e + e), is very similar. The uncertainty
in the absolute neutrino ux is estimated to be 20%, while the uncertainty in the above
ratio is less than 5% because the ambiguity in the absolute ux is cancelled out by taking
the ratio.

3

Honda

-1

BN
10

LK

2

2

-2

νµ + νµ

BGS-1

Flux x E ν ( m sec sr GeV )10

νe + νe

10

1

10

-2

10

-1

10

0

Neutrino Energy (GeV)

10

1

Figure 4.2: The atmospheric neutrino uxes multiplied by E2 at theSuper-Kamiokande site, compared with
Barr,Gaisser and Stanev[18], Bugaev
and Naumov[19], and Lee and Koh[20].
The solid lines show the HONDA ux
at solar mid. The dotted lines are thecalculation without the rigidity cuto
at high energies where the geomagnetic
e ect becomes negligible.

44

2.5

2.5

νµ + νµ

Honda

2.5
BGS

νe + νe

Flux Ratios

νe

2.

2.

1.5

1.5

1.0

10

νe
νe

1.0

10

0

10

1

10

-2

Neutrino Energy (GeV)

10

1.0

νµ

νµ

νµ

νµ

νµ
10

1.5

νe

νµ

νµ

-1

νe

νe

1.0

-2

νe + νe2.

νeνe

νµ + νµLK

νe + νeνe + νe

2.

1.5

2.5

νµ + νµBN

νµ + νµ

-1

10

0

10

1

10

Neutrino Energy (GeV)

-2

10

-1

νµ
10

0

10

Neutrino Energy (GeV)

1

10

-2

10

-1

10

0

10

1

Neutrino Energy (GeV)

Figure 4.3: The ux ratio,(+  )/(e+ e ), at the Super-Kamiokande site calculatedby Honda, BGS, BN, and LK.

4.2 Neutrino interactions
Atmospheric neutrinos interact with nucleons and orbital electrons in water via charged
current(CC) and neutral current(NC) interactions. However, neutrino interaction with
an electron can be safely neglected in the 1GeV energy region. Therefore in our Monte
Carlo the following 8 interactions are taken into account[21]:N ! lN 0

1. CC quasi-elastic scattering
2. NC elastic scatteringN ! N 0

3. CC single-pion production

N ! lN 0 

4. NC single-pion production

N ! N 0 

5. CC multi-pion production

N ! lN 0 m(m  1)

6. NC multi-pion production

N ! N 0 m(m  1)

7. CC coherent pion production

 16 O ! l16 O

8. NC coherent pion production

 16 O ! 16 O

Where N is a nucleon and l is a charged lepton. The details of these interactions aredescribed in the following subsections.
45

4.2.1 Quasi-elastic interactions

σ(10-38cm2)

For the CC quasi-elastic interaction, the energy and momentum of a lepton in the nal
state are determined from the q2 (q = p , pl : 4-momentum transfer)- dependence of thecross section. This cross section is calculated by the standard V , A theory, with MA =1.01 GeV/c2 and MV = 0.84 GeV/c2[22]. Fig. 4.4 and Fig. 4.5 show the calculated total
cross sections of  n ! ,p and  p ! +n, respectively together with experimental
data. From these comparisons systematic uncertainties for the Monte Carlo simulation
are estimated later.
Since the target is H2O, we take into account the Fermi motion of nucleons in a
nucleus and Pauli blocking for the  -16 O scattering. The Fermi momentum distribution
in 16 O is estimated from the e-12C scattering experiment [23]. The Fermi gas model isadopted to consider the Pauli blocking. Momentum of a recoil nucleon must be larger
than the Fermi surface momentum (250MeV/c).
2

Figure 4.4: Calculated cross section of  n ! ,p compared withthe experimental data, ANL[24],
GGM[25], and Serpukhov[26].
Upper and lower dashed lines
show the calculated cross sections
with MA = 1:11 and 0.91, respectively.

ANL
GGM
Serpukhov

1.5

1

0.5

0

1

2

3

4
5
Energy(GeV)

For the NC elastic interaction, we use the following relations according to Ref.[28],[29].

(p ! p) = 0:153  (n ! e,p)( p ! p) = 0:218  ( p ! e+n)
(n ! n) = 1:5  (p ! p)( n ! n) = 1:0  ( p ! p)
NC elastic interactions are visible only if the recoil proton emits Cherenkov light or therecoil nucleon interacts in water and produces pions.
46

σ(10-38cm2)2

1.5

Figure 4.5: Calculated cross section of  p ! +n compared withthe experimental data, GGM[27]and Serpukov. Upper and lower
dashed lines show the calculated
cross sections with MA = 1:11
and 0.91, respectively.

GGM
Serpukhov

1

0.5

0

1

2

3

4
5
Energy(GeV)

4.2.2 Single pion production
We use Rein-Sehgal's method to simulate the single pion production[30] for the hadronic
invariant mass less than 1.4GeV. In this method, the neutrino interaction is separated
into two parts as follows: + N ! l + NN !  + N
N  represents baryon resonances. In this simulation 18 resonances below 2GeV are
used and interferences among resonances are also taken into account. We calculate
the amplitude of each resonance production and multiply the decay probability of eachresonance with the restriction of invariant mass less than 1.4GeV. Fig. 4.6-4.8 show
the calculated total cross sections compared with experimental data. Agreements are
excellent. Fig. 4.9 shows the total cross section for CC and NC single pion production.
The angular distribution of pions from (1232) resonance is also calculated by using
this model. The (1232) resonance is dominant in single pion production, especially forthe low energy region. The angular distribution of pions is assumed to be isotropic forother resonances, because the experimental data do not exhibit any signi cant deviationfrom isotropy.

4.2.3 Multi-pion production
In high energy neutrino-nucleon interactions, the cross section and kinematics are determined under the assumption of Bjorken scaling. The total cross section of multi-pion
47

2

cm )

σ(10

-39

10
8
6

Figure 4.6: Cross section of p ! ,p+ compared withthe experimental data.

4
2
0
0

2

4

6

νµ p → µ p π+

810Energy(GeV)

4

σ(10

-39

2

cm )

-

3

Figure 4.7: Cross section of n ! ,p0 compared withthe experimental data.

2

1

0
0

2

4

6

νµ n → µ p π
-

0

8
10
Energy(GeV)

d2  with an invariant mass above 1.4GeV/c.
production is calculated by integrating dxdy
The mean multiplicity of charged pions, hn i, is estimated from the Fermilab 15-foothydrogen bubble chamber experiment[31], based on the reaction,  p ! ++hadrons,as:hn i = 0:09 + 1:83 ln W 2;
(4.1)

where W is the invariant mass. The forward-backward multiplicity asymmetry is taken
into account using the BEBC data[32], and we set hnF i / hnB i = (0.35+0.41lnW 2) /(0.5+0.09lnW 2).
For the NC cross section, we use the following relations;E  3GeV,

(N ! X ) = 0:26
(N ! ,X )
48

2

cm )

σ(10

-39

4

3

Figure 4.8: Cross section of n ! ,n+ compared withthe experimental data.

2

1

0
0

2

4

6

νµ n → µ n π
-

+

8
10
Energy(GeV)

( N ! X ) = 0:39
( N ! +X )3GeV < E < 6GeV,(N ! X ) = 0:26 + 0:04  ((E , 3:)=3:)

(N ! ,X )( N ! X ) = 0:39 , 0:02  ((E , 3:)=3:)

(nuN ! + X )6GeV < E ,(N ! X ) = 0:30
(N ! ,X )( N ! X ) = 0:37
(nuN
 ! +X )from the Gargamelle experiment[33](E  3GeV) and Ref.[34](3GeV < E ), which measured the ratio of various inclusive total cross sections of NC to CC interactions. Fig.
4.10 shows the calculated cross sections for CC and NC interactions.

4.2.4 Coherent pion production
Pions are also produced by a coherent interaction o the oxygen nucleus. It produces
single pions with very little momentum transfer. Therefore the angular distribution has
a sharp peak in the forward direction.
49

6

2

cm )

νµ p → µ p π-+

4νµ n → µ n π+

νµ n → µ p π

o

-

2

cm )

2

+

-

+

-

+

-

νµ p → µ p π-

νµ p → µ n π
510Energy(GeV)ν CC single π production
o

-

-39

NC ν

σ(10

σ(10

1.5

1

0
0

10
Energy(GeV)ν CC single π production

NC ν

-39

2

cm )

2

2

5

-

νµ n → µ n π

4

2

0
0

-

CC ν

-39

CC ν

-39

8

σ(10

σ(10

6

2

cm )

8

1.5

νµ N → νµ X π

o

1
-

-

νµ N → νµ X πo
0.5

0
0

νµ N → νµ X π±

0.5
νµ N → νµ X π±
-

0
0

5

10
Energy(GeV)ν NC single π production

-

5

10
Energy(GeV)ν NC single π production-

Figure 4.9: Cross sections of single pion productions for CC and NC interactions.
Calculated cross-sections for CC and NC coherent pion production is shown in Fig.
4.11, which is based on the Rein and Sehgal calculation [35].

4.3 Meson nuclear e ects
Pions, produced in a nucleus by a neutrino interaction, sometimes undergo secondaryinteractions before leaving the nucleus. In our Monte Carlo simulation program, thefollowing pion interactions in 16 O are considered: inelastic scattering, charge exchange,
and absorption. We use a cascade model in simulating these pion nuclear e ect. The
actual procedure is as follows. The nucleon density distribution is assumed to be given50

σ(10-38cm2)σ(10-38cm2)8(a) CC
6

ν

4

-

0

5
-

(b) NC
3
2

ν

2

4

ν

1

10

0

Energy(GeV)

5-

ν(ν) N → l (l ) X mπ

-

ν
10

Energy(GeV)-

ν(ν) N → ν(ν) X mπ

- +Figure 4.10: Cross sections of multi-pion productions for (a)CC and (b)NC interactions.
Solid lines show the cross sections for the  and dashed lines show the cross sections forthe :by the Woods-Saxon function,

p(r) = ZA f1 + exp( jrj a, c )g,1;(4.2)

where A is the atomic number,  is the average density of nuclei and a, c are the density
parameter of nucleus. The mean free path is calculated for an incident pion, also taking
into account the Fermi motion of the nucleon in 16 O[36] and the Pauli blocking e ect. Theinteraction point of the pion is then determined. The type of interaction is determined
next. If the inelastic scattering or the charge exchange occurred, the direction andmomentum of the pion are determined by using the result of phase shift analysis obtained
from the  ,N scattering experiments[37]. The Pauli blocking e ect is taken into accounthere by requiring that the nucleon momentum after the interaction must be larger thanthe Fermi surface momentum, PF (r).
PF (r) = ( 23 2p(r)) 31 :(4.3)
These pion interactions are tested in 12 C [38] and 16 O[39] scatterings. Fig. 4.12
shows the simulated cross sections compared with the experimental data. Agreement isquite reasonable.
The pion interaction simulation is also tested in a photo-pion production process. To
simulate the photo-pion production, we use the measured value for the cross section of
51

2

σ(10

-38

σ(10

2

cm )

1.5

-38

2

cm )

2

1.5

1

1

0.5

0.5

0

2

4
-

ν(ν)

16

6

8

10

0

Energy(GeV)2

4-

O → l (l ) X Nπ
- +

ν(ν)

16

6
-

O → ν(ν)

16

8

10

Energy(GeV)O NπFigure 4.11: Cross-sections for CC and NC coherent pion production.
primary interaction ( + n ! , + p)[46]. The results of each simulation compared withthe 12C ! X data[47] as shown in Fig. 4.13. The agreement between the calculationand the expetimental data is good around the peak. Altough the agreement is not goodin lower momentum region, the experimental data has large uncertainty. The systematic
uncertainties for the Monte Carlo simulation are estimated by using these comparisons.

4.4 Detector simulation
Particle tracking
Produced secondary particles are traced by the GEANT program [40], which has beendeveloped at CERN and commonly used in high-energy experiments. And particularly
for hadronic interactions in water, we selected the CALOR program, which had beendeveloped at CERN and was based on the nuclear cascade model[41]. This program
reproduces pion interactions well even at the low energy region (E  1GeV ). However,in a few hundred MeV region, the agreement between the CALOR and experimental
data is not good enough for our experiment[42]. Therefore the total cross section of
the nuclear interaction in water below 500MeV/c is estimated from the results of -12C
scattering[43] and -p scattering[44] experiments. And to determine fraction of eachnuclear interaction mode, we use the result of -Al experiment[45].
52σ(mb)

600
inela+abs+c.exchange
inelastic
absorption

500

charge exchange

400

Figure 4.12: Calculated
cross sections of the pionin a nucleus compared withthe experimental data.

300

200

100

0

0

100

200

300

400

cross section for π + O
+ 16

500

600

Pπ(MeV/c)

Cherenkov photon generation and PMT response
The number of emitted Cherenkov photons, the direction, and the wavelength of Cherenkov
photons are calculated by Eq.2.2 and Eq.2.3. Each Cherenkov photon is traced until ithits a PMT or it is absorbed.
We consider the Rayleigh scattering, Mie scattering, and absorption of Cherenkov
photons in water. Rayleigh scattering is the scattering with water molecules and the crosssection is proportional to ,4 (  : wavelength). The Mie scattering treats scatteringwith a particle in the water and no wavelength dependence is assumed in our simulation.
Fig. 3.10 shows the amount of these scatterings as a function of wavelength. Rayleighscattering is dominant in the short wavelength region and absorption is dominant in thelong wavelength region. In this gure, the total value and the wavelength dependenceof the scattering and the absorption agree with the data measured by the laser system(Sec. 3.4).
When a photon hits a black sheet at the detector wall, its re ection or absorption
is simulated by using the measured data. When a photon hits a PMT, the quantumeciency of the PMT is considered as shown in Fig. 4.14. The response of the PMT issimulated by using measured timing and charge resolutions. And random noises are also
added in each event in order to simulate real circumstances.
53

d2σ/dΩdpπ(µb/sr/(MeV/c))d2σ/dΩdpπ(µb/sr/(MeV/c))

1
0.8
0.6
0.4
0.2
0

1
0.8
0.6
0.4
0.2

0

100
γ+

12

200

300

0

400

Pπ(MeV)C → π + X, Θγπ=44.2 , Eγ=368MeV
-

o

0

100
γ+

12

200

300

400

Pπ(MeV)C → π + X, Θγπ=44.2 , Eγ=468MeV-o

Quantum efficiency

Figure 4.13: Di erential cross section for the pion photo-production, 12 C ( ; ). Plots
show the experimental data and histograms show the calculated cross sections. Hatchedhistograms show the rate of pions which go out of a nucleus without scattering in the
nucleus.

0.2

Figure 4.14: The quantumeciency as a function of
wavelength(nm).

0.1

0

300

400

500

600
700
Wave length (nm)4.5 Summary of Monte Carlo simulation
Number of events predicted by the Super-Kamiokande Monte Carlo for each interaction
mode are given in Table 4.1. They correspond to 10 year observation. About 86% of
sub-GeV events is from CC interactions, (quasi-) elastic interaction amounts to 57%, but
for single-ring events, it increases to 75%. Since the (quasi-) elastic events are dominant
in the sub-GeV sample and cross sections and kinematics of (quasi-) elastic interaction
are much better known than pion productions, the sub-GeV single-ring sample is best
suited for the atmospheric neutrino study.

54total e CC  CC

NC(quasi-) elastic

13810

5204

8480

126

single 

3633

1250

2133

250

single 0

1623

203

440

980

multi 3988

856

1649 1483

coherent 

1031

202

406

total

24085

7715 13108 3262

423

Table 4.1: Summary of the Monte Carlo simulation in sub-GeV energy region.

55

Chapter 5
Event selection
Super-Kamiokande started the observation on April 1, 1996. As shown in Fig. 3.12, thewater attenuation length had been changed signi cantly for the rst two months andbecame stable at the end of May 1996. Therefore we used the data sets from May 27,
1996 to June 25, 1997 in this analysis, which corresponded to 325.8 days of detector
livetime. During this period about 300 million events were recorded.
Fig. 5.1 shows an outline of the event selection. The three software reduction algorithms reject background events so that the reduced data sets are manageable forscanning. After reduction all candidate events are hand-scanned doubly by physicists toreject remaining background events and check the data quality. The nal scan is done
to check the quality of the double scan. The nal data set is xed here and the total live
time is calculated. For the Monte Carlo events, we apply the identical event selection
processes.
In this chapter, the method of event selection is presented.

5.1 First reduction
About 1 million events are triggered and recorded every day. The data size is about
12Gbyte/day. The purpose of the rst reduction is to reduce events quickly and makethe output data easy to handle. Therefore simple criteria are adopted for the rst
reduction, which are:
1. The total number of photoelectrons(p.e.) with a 300nsec time window, PE300 , mustbe larger than 200p.e., which corresponds to 23MeV. This constraint rejects low
energy backgrounds caused by radon or low-energy gamma-rays from the wall.
57

Trigger rate

Raw Data~12Hz

1st. Reduction

cut low E (Evis<23MeV) events
cut Nhit (anti-counter) > 50

2nd. Reduction

cut Nhit (anti-counter) > 25

3rd. Reduction

cut flasher events
cut remaining cosmic ray muon events~3500/day~400 /day~40 /day

Scan1

Scan2

cut remaining flasher events
check the data quality

Final Scan
~15 /dayFinal Sample

Figure 5.1: Algorithm of event selection for FC sample. The left numbers show event
rates for one day.
2. The number of outer detector(OD) hits within an 800nsec time window must be
less than 50. This constraint rejects cosmic-ray muon events(Fig. 5.2).
If an event does not satisfy both criteria, it is rejected. After the rst reduction, theevent rate is about 3500 events/day.

5.2 Second reduction
The data set which has survived the rst reduction is applied to the second reduction.
The criteria of the second reduction are:
1. PEMAX(maximum number of p.e. in a PMT)/PE300 is less than 0.5. This cut
rejects low-energy events with one large accidental hit.
2. OD-hits within an 800nsec time window must be less than 25, or OD-trigger is o .
Fig. 5.2 shows the PEMAX/PE300 distribution. Referring to the right gure, which shows
the Monte Carlo atmospheric neutrino events with vertex larger than 1.5m from thedetector wall, we can see that almost all of PEMAX/PE300 for the atmospheric neutrino
events is less than 0.3. Thus the criterion, PEMAX/PE300 <0.5, is safe for the fullycontained events. The second criterion is essentially the same as the rst reduction. But
58

number of eventa tighter constraint is applied. The OD-hits distribution with an 800nsec time window
is shown in Fig. 5.2. Since the OD-hits of the random trigger events are less than 20
hits, the second criterion is safe for the fully-contained events.
The event rate after the second reduction is about 400 events/day.
5

10
4
10
3
10
2
10
10
1
0

(a)DATA 10

4

10

3

10

2

(b)MC

10
1
0.5
PEMAX / PE300

1

0

0.5
PEMAX / PE300

1

Figure 5.2: PEMAX /PE300 distributions for (a)DATA after the rst reduction and(b)atmospheric neutrino MC events with vertex more than 1.5m from the detector wall.

10(a) after 1st. reduction

2

cut

10

4

10
3
10
2
10
10
1

(b) random trigger
cut

10

20

30

40

50

60

Figure 5.3: The OD-hits
distribution for (a)DATA
and (b)random trigger
events.

70 80 90 100
OD hit (800nsec)

5.3 Third reduction
By the previous two reductions, most of the backgrounds have been removed. Therefore
it is possible to apply a more intelligent reduction algorithm. The third reduction consistsof 6 parts, which are: a through-going muon cut, a stopping muon cut, a low-energy event59cut, a \ ashing"PMT cut, a \cable-hole" muon cut, and an accidental event cut. The
details of these cuts are presented below.

Through-going muon cut
A through-going muon event has two clusters in the OD-layer at the entrance and exit
points. Inner PMTs at the entrance and exit points receive a large number of Cherenkov
photons. If an event satis es the following three criteria, it is identi ed as a through-going
muon event and rejected.
1. The maximum number of p.e. in a PMT is more than 230 p.e.
2. The inner detector(ID)-hits are more than 1000.
3. The number of OD-cluster hits on the entrance or exit point of a particle, ODhitent=exit, is more than 9, where the number of OD-cluster hits is de ned as thenumber of OD-hits within an 800nsec time window within a radius of 8m from theentrance or exit point.

number of event

The entrance and exit points of a through-going muon are determined as the position of
the earliest inner hit-PMT with more than two neighboring inner hit-PMTs and the center position of inner hit-PMTs whose charges are saturated, respectively. Fig. 5.3 shows
the OD-hitent=exit distribution for the random trigger events. There are no events with
OD-hitent=exit larger than 9 hits. Therefore this criterion is safe for the fully-contained
events.
A typical through-going muon event rejected by this cut is shown in Fig. 5.3.
10

5

10

4

10

3

10

2

random trigger
cut

Figure 5.4: The OD-hitent=exit distribution for the random trigger
events.

10
0

2

4
6
8
OD-hitent/exit

10

12

60

NUM
7
RUN
4376
SUBRUN
12
EVENT
544152DATE 97-Jul- 6
TIME
4:17:53
TOT PE: 102657.6
MAX PE:
279.7
NMHIT : 9699
ANT-PE:
110.9
ANT-MX:
22.5
NMHITA:70

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : G
0.00: 0.00: 0.00:0
CANG : RTOT : AMOM : M

Figure 5.5: A typical throughgoing muon event rejected by thethrough-going muon cut. The
small gure on the upper left side
displays OD-hits. The maximum
number of p.e. in a PMT is
RunMODE:NORMALTRG ID :00001111 279.7p.e. and the number of ODT diff.:0.140E+0: 140.
FEVSK :81002003 cluster hits at the entrance is 17.
nOD YK/LW:20/20
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 1
Dec-e: 0( 0/ 0/

Comnt;

VQ:
VT:
VQ:
VT:

0
0
0.
0.

0
0

0.
0.

0
0

0
0

Stopping muon cut
The vertex of remaining events are reconstructed by the \stopping  tter", in which thevertex is determined by looking for the earliest hit PMT and the vertex must be on thedetector wall. The direction of an event is adjusted by maximizing the total number of
p.e. in the Cherenkov cone. An event which satis es one of the following two conditions
is rejected as a stopping muon event.
1. OD-hitent is more than 9.
2. OD-hitent is more than 4 and the goodness of the stopping  tter is more than
0.5. The de nition of the goodness is the same as the TDC- t (see Section 6.1).
By the second criterion, although the number of OD-cluster hits is not more than 9, theevent is de ned as a stopping muon if this event is tted well by the stopping muon tter.
For the fully-contained atmospheric neutrino events we checked that the number of ODcluster hits was at most 2. Since the number of events with OD-hitent=exit larger than 4hits are 38 in 105 events as shown in Fig. 5.3, this criterion safely rejected stopping-muon
events.
A typical stopping muon event is shown in Fig. 5.6.
61

NUM
4
RUN
4376
SUBRUN
11
EVENT
490179DATE 97-Jul- 6
TIME
4: 9:33
TOT PE:
9103.2
MAX PE:
92.2
NMHIT : 2675
ANT-PE:
71.7
ANT-MX:
7.5
NMHITA:56

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : G
0.00: 0.00: 0.00:0
CANG : RTOT : AMOM : M

Comnt;

Figure 5.6: A typical stopping
muon event rejected by the stopping muon cut. The number of
OD-cluster hits at the entrance is
17 and the goodness is 0.71.
RunMODE:NORMALTRG ID :00001111
T diff.:0.183E+0: 18.3FEVSK :81002003
nOD YK/LW:20/19
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 1
Dec-e: 0( 0/ 0/
VQ:
VT:
VQ:
VT:

0
0
0.
0.

0
0

0.
0.

0
0

0
0

low-energy event cut
In order to reject the remaining low-energy events, we apply the low-energy tter for
all candidate events and calculate two parameters, \N50 " and \goodnesslow ". The
low-energy tter uses a grid search method to nd the vertex which maximizes the
goodnesslow . The de nition of the goodnesslow is the same as that of the point- t(SeeSection 6.1).1 N50 is calculated by sliding a 50nsec window through the time residual(time minus the ight time of Cherenkov photon). The maximum number of PMT hits
in the 50nsec window is de ned as N50 . For low-energy events N50 is a good energy
indication, which is proportional to the particle energy. Five hits of N50 correspond toabout 1MeV.
If an event satis es one of the following two conditions, it is rejected as a low-energy
event.
1. The number of ID-hits is less than 500 and N50 is less than 50(10MeV).
2. The number of ID-hits is less than 500 and the goodnesslow is less than 0.5. This
criterion rejects events in which no Cherenkov ring is found.
The goodnesslow distribution for muon-decay electron events is shown in Fig. 5.7. Since
there is only one event with goodnesslow less than 0.5 in 46000 events, this criterion issafe.
A typical low-energy event is shown in Fig. 5.8.
1

For the low-energy tter, the timing resolution, , is 5nsec and the factor is 1.0 in Eq.6.2.

62

number of event

10

5

10

4

10

3

10

2

Figure 5.7: The goodnesslow distribution for muon-decay electron
events.

cut

10
1
0

0.2

0.4 0.6 0.8
goodnesslow

1

NUM
39
RUN
4376
SUBRUN95
EVENT 4670284
DATE 97-Jul- 6
TIME
15: 4:12
TOT PE:
321.9
MAX PE:
100.3
NMHIT :
164
ANT-PE:
30.0
ANT-MX:
5.1
NMHITA:30

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : G
0.00: 0.00: 0.00:0
CANG : RTOT : AMOM : M

Comnt;

RunMODE:NORMALTRG ID :00000111
T diff.:0.307E+0: 307.
FEVSK :81002003
nOD YK/LW: 1/ 0
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 0
Dec-e: 0( 0/ 0/
VQ:
VT:
VQ:
VT:

0
0
0.
0.

0
0

0.
0.

0
0

Figure 5.8: A typical low-energy
event rejected by the low-energy
event cut. The N50 of this event
is 15 and goodnesslow is 0.52.

00Flashing PMT cut
If a PMT has a mechanical problem in the dynode structure, the PMT emit light frominternal corona discharge. These events are categorized as \ ashing PMT" events. A
feature of ashing PMT event is a broad time distribution as shown in Fig. 5.9. To
remove such a ashing PMT event, we calculate the number of hits within a 100nsec
time window. This window is slid from 1200nsec to 1800nsec (outside of the genuine
signal region) and the minimum number of hits, Nmin, is found. If an event satis es oneof the following two conditions, it is rejected as a ashing PMT event.
1. Nmin is more than 14.
2. Nmin is more than 9 and number of ID-hits is less than 800.
63

A typical ashing PMT event is shown in Fig. 5.10.
300

(a)
200

Figure 5.9: ID-time distributions for (a)a typical normal
event and (b)a ashing PMT
event. Nmin of this ashing
event is 21.

100
0
40

(b)

20
0
500

1000

1500

2000

nsec

NUM
44
RUN
4376
SUBRUN115
EVENT 5643687
DATE 97-Jul- 6
TIME
17:35:11
TOT PE:
979.3
MAX PE:
14.8
NMHIT :
717
ANT-PE:
24.2
ANT-MX:
1.9
NMHITA:
35

Figure 5.10: A typical ashing PMT event rejected by
the ashing PMT cut.
90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : G
0.00: 0.00: 0.00:0
CANG : RTOT : AMOM : M

Comnt;

RunMODE:NORMALTRG ID :00000111
T diff.:0.269E+0: 26.9FEVSK :81002003
nOD YK/LW: 3/ 1
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 1
Dec-e: 0( 0/ 0/
VQ:
VT:
VQ:
VT:

0
0
0.
0.

0
0

0.
0.

0
0

0
0

Accidental hit cut
The accidental hit cut rejects an event which has more than two independent particles
in an event accidentally. An event is rejected as accidental if both of the following two
conditions are true.
1. The number of OD-hits with a time window between 1300nsec and 1800nsec ismore than 19.
64

2. The total number of ID-p.e. with a time window between 1300nsec and 1800nsec
is more than 5000p.e.
The OD-time distribution of a typical accidental hit event is shown in Fig. 5.11.
10

3

10

2

10
1
500

1000

1500

2000

nsec

Figure 5.11: OD-time distribution of an accidental hit event rejected by the accidental hit cut.
This event was triggered by alow-energy event and a cosmicray muon about 600nsec later.

Cable-hole muon cut
Cables from ID and OD PMTs are bundled in the upper OD-layer and are taken out of
the tank through the 12 cable-holes. 4 of the 12 cable-holes are located away from thefringe of the tank, and the identi cation eciency of the OD is low for muons passing
near these 4 cable-holes. In order to compensate for the ineciency of OD around thefour cable-holes, we installed 2:0m  2:5m veto-scintillation counters on each of the four
cable-holes in April, 1997. An event, in which one of the veto-scintillation counters is
hit and a vertex is reconstructed within 4m from the cable-hole by the stopping  tter,is identi ed as a cosmic-ray muon and rejected even if there are few OD-hits. A typicalmuon event rejected by this cut is shown in Fig. 5.12.

5.4 Scanning
After the three software reduction steps, the candidate events are reduced to 13451
events, it is about 40 events/day. But there are still remaining cosmic-ray muon eventsand ashing PMT events. Therefore the candidate events are scanned twice by independent scanners to reject these remaining background events. At the same time thescanners check the data quality. When the detector performance is not good, for instance
too many ashing events or some of the PMTs are not active, these runs(subruns) are
regarded as bad-runs(bad-subruns) and are rejected. After the double scan, the nal
65

NUM
55
RUN
4376
SUBRUN132
EVENT 6469507
DATE 97-Jul- 6
TIME
19:43:40
TOT PE:
53673.2
MAX PE:
261.0
NMHIT : 6952
ANT-PE:
51.2
ANT-MX:
12.0
NMHITA:47

90/00/00:NoYet:NoYet
90/00/00:;R= 0:NoYet
R :Z : PHI : G
0.00: 0.00: 0.00:0
CANG : RTOT : AMOM : M

Comnt;

Figure 5.12: A cable-hole muon
event rejected by the cable-holemuon cut. A square mark on the
OD display shows a hit of theveto-scintillation counter.
RunMODE:NORMALTRG ID :00000111
T diff.:0.424E+0: 42.4FEVSK :81002003
nOD YK/LW:12/12
Q thr. :0.0
BAD ch.: masked
SUB EV : 0/ 1
Dec-e: 0( 0/ 0/
VQ:
VT:
VQ:
VT:

0
0
0.
0.

0
0

0.
0.

0 3
0 3
0
0

scan is done to check the consistency of the double scan result and make the nal fullycontained data sample. Finally, 5033 candidate events are selected as the nal data
sample.
We also did the double scan for a part of the event sample just after the second
reduction in order to check performance of the third reduction and about 1000 fullycontained events were collected. Since all of these events were passed the third reduction.
we estimate the probability that the event selection processes reject fully-contained events
to be less than 0.1%. Contamination from ashing PMT and cosmic-ray muon events
are also negligible in the sample of fully-contained events in the ducial volume. Thesee ects are estimated in section 7.2.

Livetime
After removing bad runs by the nal scan, we calculate the total livetime. Livetime isde ned as the time when the electronics are enabled for trigger. It does not include
the pedestal data-taking time and the electronics dead time. From May 27, 1996 toJune 25, 1997, the total data-taking time was 345.5 days. During this period total badrun(subrun) time was 9.9 days and total electronics dead time was 9.8 days (it includes
pedestal data-taking time.) The livetime is calculated to be 325.8 days.

66

Chapter 6
Analysis
After the event selection processes, events were reconstructed by the following four procedures.
TDC- t+Ring counting+

Particle identi cation (PID)

+

MS- t
These procedures are fully automatic. Therefore there is no bias by a scanner orphysicist in the event reconstruction steps.
At rst, the vertex, direction, Cherenkov opening angle and momentum are reconstructed for the most energetic particle in an event using a routine called \TDC- t",which uses timing information of hit PMTs. Once the vertex is determined, \Ringcounting" process tries to nd another Cherenkov ring and judges whether its event issingle-ring or multi-ring. The particle identi cation process classi es a ring as \e-like" or\-like" by the hit-pattern and opening angle of the Cherenkov ring. Using informationof the particle type, \MS- t" further improves the vertex, direction, and momentum forsingle-ring events.

6.1 TDC- t
The TDC- t consists of the following three parts. (1)The \point- t" nds a rough vertex
by using the timing information of the PMTs which caught Cherenkov photons. (2)The
67

100
80

Figure 6.1: The timing residual,ti (nsec.), distribution in a typical event.

60
40
20
0
850

900

950

1000

1050

1100

1150

1200

edge of Cherenkov ring is determined by using the charge information from hit PMTs.
(3)Determine the vertex again. Here, the particle track length and scatter photons aretaken into account to obtain a better vertex resolution.
In following sub-sections, I will describe details of these 3 steps.

Point- t
The principle of the vertex reconstruction is to nd out the position where the timing
residuals, ti , of all hit PMTs are equal. The timing residual, ti, of the i-th hit PMT isde ned as;q(6.1)
ti = t0i , v (q;1 l )  (x , xi)2 + (y , yi)2 + (z , zi )2

where

c

c

t0i : hit time of the i , th PMT
c : light velocity(xi ; yi; zi ) : position of the i , th PMT(x; y; z) : vertex position:vc(q; lc) : light velocity in water:
Since the refractive index of water, n, is a function of wave length, vc depends on the
charge detected by PMT, q, and ight length of Cherenkov photons, lc.
If the point (x; y; z) gives the correct vertex position, the timing residuals should look
like Fig. 6.1. On the other hand, if the point (x; y; z) is not correct, the width of thepeak is broader. The nite width in Fig. 6.1 is due to the timing resolution of PMTs.
A long tail in the histogram is due to scattered Cherenkov photons in water or photons
re ected at the detector wall.
68

We use a goodness, G, to evaluate the accuracy of the vertex reconstruction. The
goodness for the point- t, GP , is de ned as:Xhti)2
exp , 2((ti ,factor
GP = N1
)2
hit i

!

(6.2)

with factor = 1:5,
where Nhit is the number of hit PMTs and  is the typical timing resolution. In the
point- t program,  is taken to be 2.5nsec. The contribution from the scattered light ismade small with an e ective cut-o of  3 represented by the factor = 1:5. In thisway, dark pulses from PMTs and scattered lights are largely removed from the vertex
reconstruction process.
The point, where the GP takes maximum is regarded as the vertex position.

Cherenkov edge search
To nd out the edge of a Cherenkov ring, we de ne three parameters \PE()", \edge"
and \Q". The PE() is the e ective total p.e. as a function of the opening angle which isan angle between particle direction and Cherenkov photon direction. PE() is smoothed
to reduce the statistical uctuation, as shown in Fig. 6.2(a). Next, edge is the opening
angle spanning the Cherenkov edge, which is determined by the following two conditions:(1)edge must be larger than the angle at the peak of PE(), peak , and (2)edge is theangle nearest to peak , where the second derivative, dd2 PE2 , is 0 (See Fig. 6.2(b)).
Under these conditions, edge is obtained by optimizing the following evaluation function, \Q".
!
R edge PE()d(edge , C )20
Q = sin  exp , 2
;
(6.3)
edge
where C and  are the Cherenkov opening angle and its resolution, respectively.
The optimization is carried out by changing the particle direction. The particle
direction and edge where Q takes a maximum value are adopted as the nal ones. Theedge of the Cherenkov ring is then calculated by using these nal direction and edge.

TDC- tAfter the Cherenkov edge has been found, we determine the vertex more precisely byconsidering scattered Cherenkov photons and the particle track length.
69

number of p.e.

150
100
50

second derivarive

0

0

20

40

60

80

0

20

40

60

80

Figure 6.2: (a)A typical PE() distribution for an e-like event and (b) dd2 PE2
distribution as a function of opening
angle.

100-10degree

The goodness is rede ned in the following way.
For the PMTs inside the Cherenkov cone, or the outer PMTs with ti  hti (mean of ti)

!
X1
(
t
i , hti)2
GI = 2 exp , 2(hi  factor)2
i iwith factor = 1:5,

(6.4)

"
!
!#
X1
(
t
(
t
i , hti)2
i , hti)GO = 2 max exp , 2(hi  factor)2 ; 0:8  exp , (20nsec) ;
i i

(6.5)

where i is the timing resolution of the i-th PMT which is a function of its charge, hiis the average of i.
On the other hand, PMTs outside the Cherenkov cone with ti > hti are regarded as
scattered light. For PMTs outside the Cherenkov cone with ti > hti;

where 20nsec is the mean time from direct Cherenkov photons to the scattered photons
estimated from the Monte Carlo simulation.
Finally, G is de ned as;
X(6.6)
G = [GI + GO ]= 12 ;iwhere P 1 normalizes the range of G from 0 to 1.
i i2

i

Next, we consider the nite track length of a particle and the corrected vertex isfound by the following three procedures. (1) Estimate the total track length, Lt , fromthe total number of p.e. within a cone of 70 half opening angle. (2) Re-calculate the70residual time, ti , which takes into account the particle velocity and position along the
track where Cherenkov photon is emitted. (3) Calculate goodness; G, using modi ed
ti. Iterate these procedures and the nal vertex position, direction, and momentum are
adopted where the goodness takes the maximum value. The performance of the TDC- t
will be discussed in Sec. 6.4.

6.2 Ring counting
After the vertex, direction and Cherenkov opening angle of the most energetic Cherenkov
ring have been reconstructed, we try to nd the second Cherenkov ring and judge whether
the event is a single- or multi-ring event. The algorithm, which counts the numberof rings, consists of the following two steps: (1)search for the second Cherenkov ringcandidates, (2)check whether the second Cherenkov ring candidates are true Cherenkov
ring or not.
In the following sections a brief description of the two steps and their performanceare presented. Further discussion is presented in Ref.[48].

Search for the second Cherenkov ring
The direction of the second Cherenkov ring is searched for by using the \charge map".
The charge map is a 2-dimensional array with directions of 72 azimuth angle () and 36
polar angle (), angles being measured from the vertex. Fig. 6.3 shows a basic concept of
the ring counting algorithm. First, the expected number of p.e. from the rst Cherenkov
ring is subtracted from the number of p.e. of each hit PMT. For the i-th bin in thearray (i; i), the total number of p.e. is lled which corresponds to the sum from all the
PMTs that happen to lie on a circle of 42 deg. 1 from the direction (i; i). If the second
Cherenkov ring really exists, the bin corresponding to the true direction of the secondring has the largest number of p.e. all of the other bins. An opening angle between the
direction of the rst and the second Cherenkov ring must be more than 15 degree inorder to keep the ring- nding algorithm e ective.

Number of ring determination
We use the maximum likelihood method to determine whether the second candidate
ring is true or false. The likelihood for the single-ring of double-ring is calculated from1

the angle, 42 deg., is adjusted to get more suitable Cherenkov opening angle in the algorithm.

71

600
400
200
0
150

θ(

PMT HITPOSSIBLE CENTERSde 100
gr
ee 50
s)

300

100
00

)

rees
φ(deg

200

Figure 6.3: Left gure shows PMT hits and possible centers estimated by the direction of
PMT hits. By accumulating all the possible centers for every PMT, we can nd the mostprobable circle center as a focus of these circles. Right gure shows the charge map(; )for a typical two ring event. Two peaks correspond to the respective directions.
the expected number of p.e. from the corresponding number of rings. These likelihood
functions are calculated with weights from the opening angle and overlap area between
the two rings because it becomes incleasingly dicult to identify the second ring if thetwo rings are piled up. If the likelihood for the single ring is larger than the two-ring
likelihood, this event is identi ed as a single ring.
If an event is identi ed as two rings, the third ring is searched for and is examinedby the similar likelihood functions. In the same way, we can count the number of rings
up to 5 rings.

Performance of Ring counting
We check the performance of the ring counting program with Monte Carlo charged
current (CC) quasi-elastic (q.e.) events with visible energies less than 1.33GeV, since CC
quasi-elastic interaction generates only one lepton and should be identi ed as a singlering event. The eciency is de ned as (number of identi ed single-ring q.e. events) /(number of q.e. events). Fig. 6.4 shows the eciency as a function of visible energy.
72

1

0.9

0.8

1

0.9

0.8

0

0

500

10

1000
MeV/c

15
dwall (m)73

Figure 6.4: The (number of identied single-ring q.e. events) / (number of q.e. events) ratio as a functionof momentum, estimated using theMC events generated in the ducial
volume (vertex 2m inside the innerdetector wall).

Figure 6.5: The (number of identied single-ring q.e. events) / (number of q.e. events) ratio as a function of dwall, estimated using theMC events generated in the ducial
volume.

The particle identi cation (PID) algorithm makes use of the pattern and opening angle of
the Cherenkov ring. Electrons produce electromagnetic showers and low-energy electronsin particular exhibit many multiple scatterings and produce rather di use Cherenkov
rings, while muons produce sharp Cherenkov edges. For low momentum particles, infor-

6.3.1 The Method of Particle Identi cation

6.3 Particle Identi cation

595% of q.e. events are correctly identi ed as single-ring event, and there is almost noenergy dependence
Fig. 6.5 shows the eciency as a function of the dwall, which is the distance between
the vertex and the nearest detector wall. The eciency of the single-ring selection does
not have any strong vertex dependence.
single-ring / quasi-elastic
single-ring / quasi-elastic

mation of the opening angle, C , is important because the cos C is proportional to the(n ),1 (see Sec. 2.1).
The PID algorithm starts with expected p.e. calculation.

The Expected Direct p.e. for e-like Events.
Monte Carlo simulation with perfect water transparency is made in order to make a table,
for electrons, of the average number of photoelectrons ,NMC (; pe), received in a circulararea of 50cm diameter (equal to PMT photosensitive area) located on a sphere of 16.9m
in radius.  is an angle between the circular area and the particle direction, and pe isthe electron momentum. Since Cherenkov photons are emitted in a cone, we average thenumber of photoelectrons as a function of the opening angle, , and derive NMC (; pe).
They are tabulated in a two-dimensional form NMC (j ; pej ), where j = 0; 1; 2;    ; 90
and pej =100MeV/c, 300MeV/c, 1000MeV/c. If necessary, interpolation is performed toobtain NMC (; pe) for desired  and pe.
The expected number of p.e. in the i-th PMT produced by an electron is expressedas;Ni:exp(direct) = e  NMC (i; pe)  ( 16:l9m )1:5  exp(, Lli )  f ();(6.7)
iwhere e is the normalization factor, li is the distance from the particle position to thei-th PMT, i is the angle of the i-th PMT from the particle direction, and L is the lightattenuation length. f () is the e ective photo-sensitive area of the PMT as shown in
Fig. 3.2. The third term in the right-hand side of Eq. 6.7 shows the di usion of lightand its power index is estimated by the Monte Carlo simulation.

The Expected Direct p.e. for -like Events
The expected number of p.e. in the i-th PMT produced by a muon is expressed as;
1Ni;exp(direct) = f  sin2 i + Ni;knock (i)g exp(, Lli )  f () (6.8)
dli (sin i + li  ( dx ))where  is the normalization factor. The second term in the right-hand side originatesfrom the ionization energy loss dE
dx in water. As shown in Fig. 6.6, dxsin + ld
takes into account the change in the photon density which is caused by the change in ,
corresponding to the energy loss. sin2 i expresses the intensity variation of Cherenkov
photons (see Eq. 2.3). Ni;knock (i) shows the number of expected photons from knock-on
electrons as a function of i , which is estimated by a Monte Carlo simulation.
74ldθ + dxsinθ

Θ
dθ

l

Figure 6.6:
Relation
between the PMT and
Cherenkov light Cherenkov photon.
θ

muon
dx

Treatment of Scattered Lights
Scattered photons can be separated from the direct Cherenkov photons by checking thearrival time. We rst pick up hit PMTs within a cone having an opening angle of
1:5  C , where C is the reconstructed Cherenkov opening angle. This aims to eliminate
accidental hits which lie mostly outside the Cherenkov cone. Then a histogram of timing
residuals, ti, is made for all the selected PMTs. Scattered photons are selected with thefollowing criterion;

tpeak , 30nsec < ti  tpeak + 2(p:e:i ) + 5nsec ,! direct photons;
tpeak + 2(p:e:i) + 5nsec < ti ,! scattered photons;(6.9)

where tpeak is the peak in the timing histogram and (p:e:i) is the timing resolution of thei-th PMT as a function of the detected number of p.e. The number of p.e. originatingfrom the scattered photons, Ni:exp(scatter) is calculated from Eq.6.9. Thus the expected
number of p.e. for the i-th PMT is given by adding both contributions:

Ni:exp = Ni:exp(direct) + Ni:exp(scatter):(6.10)

Estimator of Particle Identi cation
We now de ne the probability, Prob(Nexp; Nobs), suitable for the particle ID. It is theprobability to observe the number of p.e., Nobs, for an expected mean number of p.e.,
Nexp. The Nobs actually deviates from the ideal Poisson distribution due to uctuationsin ampli cation processes of the PMTs. Therefore, if Nexp is less than 20p.e., the probability function is derived from the composition of single-photoelectron distribution. For
75

Nexp >20 p.e., the probability function is simply given by:
2(6.11)
Prob = p 1 exp(, (Nobs 2,2Nexp) );2
with 2 = 1:22  Nexp + (0:1  Nexp)2;
where the factor 1.2 in  comes from the actual PMT charge resolution and the second
factor in  takes into account the gain uncertainty in the PMT.
The probability function for the i-th PMT Probi is expressed in two di erent ways,
according to whether the PMT is hit by a direct photon or a scattered photon:
For a direct photon,
Probi = Prob(Ni;exp; Ni;data )For a scattered photon,
Probi = Prob(Ni;exp(direct); 0)  Prob(Ni;exp(scatt); Ni;data )Selecting the PMTs inside a cone with an opening angle of 1:5C from the reconstructedparticle direction, the following likelihood function is de ned for e-like or -like events;
Y
Le =Probi(e);i <(1:5C )

L =

Y

i <(1:5C )Probi();(6.12)

where Probi(e) is calculated assuming the event is due to electron, and Probi() due tomuon.
In order to combine the information of the Cherenkov opening angle with the information of the ring pattern, Le and L are transformed into the 2 distributions:2 (e or ) = log1 e  f, log10 Le() g , constant:(6.13)
10
If the degree of freedom ND exceeds 30, which is normally the case, the sigma of the 2
distribution, 2 , is approximated as:q = 2ND :2In this case, the ND is the number of PMTs within the C  1:5. Then the probabilities
by using Cherenkov pattern can be described as:22 (e); 2()] )2g:
Ppattern(e) = expf, 12 (  (e) , min[(6.14)
222(e); 2 ()] )2 g:
Ppattern () = expf, 12 (  () , min[
2


76

Next, the Cherenkov angle will be considered. From the reconstructed momentum wecan calculate the expected Cherenkov opening angle, exp. If the reconstructed Cherenkov
opening angle is given as obs  , the probability is derived as:

Pangle(e) = constant  expf, 12 ( exp(e) , obs )2g(6.15)

Pangle() = constant  expf, 21 ( exp(), obs )2 g

Combining Eq.6.14 with 6.15, the probability P is nally:

P (e) = Ppattern(e)  Pangle(e);(6.16)

P () = Ppattern()  Pangle():A ring is more -like than e-like, if P () > P (e), and vice versa.

6.3.2 PID Performance
The PID performance is checked by (i)Monte Carlo atmospheric neutrino events and(ii)Cosmic-ray stopping muon and muon-decay electron events.

(i)Atmospheric neutrino events
In order to demonstrate the performance of PID, we de ned the PID parameter as:qq

PIDparameter = constant  ( , log P () , , log P (e)):
If the PID parameter is positive(negative), this event is identi ed as e-like(-like) events.
Fig. 6.7 shows the PID parameter distribution for sub-GeV single-ring events for thedata and the Monte Carlo events. e events are clearly separated from  events and theshape of the Monte Carlo PID parameter distribution reproduces the real data well. The
misidenti cation probability for CC e-induced event is 0.50.1% and for  -induced
event is 1.00.1%. Combining these two misidenti cation probabilities, the average
misidenti cation probability for sub-GeV atmospheric neutrino events is estimated to be
0.80.1%.
77

number of events / 20 kton yr

100

DATA

µ-likee-likeM.C.

µ-likee-like

75
50
25
0
100
75
50
25

CC νe

CC νµ
NC

0
-10

-8

-6

-4

-2

0

2

4

6

8

10

PID Parameter

Figure 6.7: Distribution of the particle PID parameter for single-ring atmospheric neutrino events for both data and Monte Carlo samples. If the PID parameter of an event
is positive(negative) the event is classi ed as e-like(-like).

(ii)Cosmic-ray stopping muon and muon-decay electron events
We check the stability of the PID performance by using cosmic-ray muons which stopped
in the detector and also muon-decay electron events. Fig. 6.8 shows the result for these
events together with the corresponding Monte Carlo estimation. The PID parameter
distribution agrees well with the Monte Carlo estimation. The misidenti cation probabilities are 0:4  0:1% and 1:8  0:5% for muons and electrons, respectively. For the:3Monte Carlo events, misidenti cation probability of -like and e-like events are 0.1+0,0:1 %
and 4.41.0%, respectively. Since the energy of muon-decay electrons is lower than electrons produced by the atmospheric neutrinos, the misidenti cation probability is a little
worse. On the other hand, the misidenti cation probability for cosmic-ray muons is better than muons produced by the atmospheric neutrinos, because their energies are higher
than sub-GeV atmospheric neutrino events. The PID performance has been continuously
78checked and indeed found to be stable.
50

Jun. 1996

050

Sep. 1996

050

Dec. 1996

050

Mar. 1997

050

Jun. 1997

0
100

M.C.

0
-10

-5

0

5

10
PID parameter

Figure 6.8: PID parameter for cosmic-ray muons (shaded histograms) and muon-decay
electrons (open histograms). The lowest gure shows the Monte Carlo estimation.

6.4 MS- t
The performance of the TDC- t is good enough for the ring counting and particle identi cation, but the vertex resolution for the longitudinal direction has to be improved. It
is because the TDC- t uses mainly timing information of hit PMTs.
MS- t is a vertex and direction reconstruction algorithm which uses the information of Cherenkov ring pattern like the PID method to improve the longitudinal vertex
resolution.
796.4.1 Fitting method
The MS- t nds the best vertex and direction by adjusting both the vertex position anddirection from initial values given by TDC- t. MS- t uses the xed Cherenkov opening
angle, C , which is calculated under the assumption of particle type. Then the expected
photoelectron numbers for each PMT is estimated.
The algorithm of the MS- t consists of three steps.
1. Iterate the vertex position perpendicular to the particle direction and nd theposition where the goodness takes the maximum value. De nition of the goodness
is the same as used in the TDC- t.
2. Iterate the vertex position parallel to the particle direction and nd the position
where the likelihood (Le or L ) takes the maximum value. This likelihood is thesame as used in the PID except the opening angle, obs . The likelihood in the
MS- t uses C instead of obs .
3. Adjust the direction where the likelihood (Le or L ) takes maximum.
The MS- t iterates the above these three steps several times to get the best t vertex
position and direction.

6.4.2 Performance of MS- t
The performance of the MS- t is estimated by using the Monte Carlo sub-GeV single-ring
events. Fig. 6.9 shows the pos distribution for the e-like and -like events, where thepos is the distance between the tted vertex and original particle position. De ning
the vertex position resolution as the distance where the 68% of events are found withinpos, the resolution for the e-like events is 34cm and the resolution for the -like eventsis 25cm.
For the angular resolution, Fig. 6.10 shows the dir distribution. The dir isthe angle between the tted and true particle directions. The resolution (68% level) is
estimated to be 3:2 for the e-like events and 1:9 for the -like events.
Next, we check the vertex position resolution along the particle direction. Fig. 6.11
shows the pos== distribution for the e-like and the -like events, compared with theresult of the TDC- t. pos== is de ned as the projection of the pos along the particle
direction. It is clear that the resolution of the MS- t is signi cantly improved. Also theMS- t has reduced systematic shift from pos== = 0, though there still remains a small
80

(a) e-like
400(b) mu-like

σ = 34cm

800

300

600

200

400

100

200

0

0

50

100 150 200

0σ = 25cm

050∆pos(cm)∆pos(cm)(a) e-likeoσ = 3.2

150

200

50

100

0

2

4

6

8

∆dir (degree)(b) mu-likeoσ = 1.9

300

100

0

100 150 200

Figure 6.9: The pos distributionfor (a)e-like and (b)-like sub-GeV
single-ring events, estimated fromMC events in the ducial volume.
pos is the distance between thevertex reconstructed by MS- t andtrue vertex. The hatched area corresponds to 68% of the total events.

10

0

0

2

4

6

8

10

Figure 6.10: The dir distributionfor (a)e-like and (b)-like sub-GeV
single-ring events, estimated fromMC events in the ducial volume.
pos is the opening angle between
the reconstructed direction and true
direction. The hatched area corresponds to 68% of the total events.

∆dir (degree)

systematic shift for e-like events. This systematic shift is taken into account when we
estimate the systematic uncertainty (see Sec.7.2).

6.5 Momentum determination
The momentum of a particle is calculated with the information of the vertex, direction
and particle type. We calculate a total number of corrected photoelectron, Rtot , which isrelated to the momentum. To obtain only direct Cherenkov photons, hit PMTs within a
70 opening angle from the particle direction and within a -50 to +250nsec timing window
from the peak of time residual are used. The detected photoelectrons are corrected forby the e ective photo-sensitive area of the PMT, f (), the ight length of photons, andlight attenuation and scattering in water. The relation between Rtot and momentum aredetermined by the Monte Carlo simulation. Fig. 6.12 shows the relation between the Rtot
81

µ-like

TDC-fitMS-fite-like
400

1000

200

500

0

0

300

400

200

200

100
0

-100

0

0

100

∆pos// (cm)

-100

0

100

∆pos// (cm)Figure 6.11: The pos== distribution for e-like(left) and -like(right) events, estimatedfrom MC events in the ducial volume. Upper gures show the result from the MS- t
and lower gures from the TDC- t.

82

Rtot

8000
6000
4000
electron
muon

2000
0
0

500
1000
1500
Momentum (MeV/c)

Figure 6.12: Relation between Rtot and momentum for the electron and muon, estimatedfrom MC events in the ducial volume.
and momentum. The momentum for electron and muon is determined from this gure.
The systematic uncertainty of the absolute momentum scale is checked by using various
sources, such as stopping muons, muon decay electrons, 0 , and so on. It is estimatedto be 2.6%. Details of systematic uncertainty estimation are described in appendix A.
Fig. 6.13 shows the momentum resolution of each particle type as a function of momentum. At this time, the momentum resolution is de ned as 1 width of the Gaussiant. The momentum resolution is estimated to be:
For electrons,
0:6 + q 2:6%:
Pe(GeV=c)
For muons,
1:7 + q 0:7%;
P(GeV=c)
where Pe and P is the momentum of the electron and muon, respectively.

83

resolution(%)108(a) electron

P1
P2
P3

(a) muon

P1
P2
P3

0.7016/ 10
0.556881.83
0.

0.4529

/ 9
1.654
20.23
0.

6
4
2

resolution(%)

0
10
8
6
4
2
0

0

500

1000
1500
Momentum(MeV/c)

Figure 6.13: The momentum resolution for (a)elections and for (b)muons. The solidlines show the tted result, estimated from MC events in the ducial volume.

84

Chapter 7
Results and discussions
7.1 The atmospheric neutrino ux
In this thesis, we use the atmospheric neutrino data with an exposure of 20 kton-years
and Monte Carlo data equivalent to 10 year detector exposure (224.6 kton-years). The
number of Monte Carlo events is normalized to the detector exposure for comparison.
To select the sub-GeV event sample, fully-contained events are further subjected to
the following sub-GeV criteria:
1. Evis < 1.33GeV,
2. DWALL > 200cm,
3. 100MeV/c < Pe for an e-like event, and 200MeV/c < P for a -like event,
4. Maximum p.e. in a PMT < 200p.e.,
5. Number of OD-cluster hits  9,
where DWALL is the distance between the event vertex and the nearest inner detector wall.
The second criterion is a ducial volume cut which removes non-neutrino backgrounds
and the third criterion removes low energy backgrounds such as decay electrons fromlow-energy muons which do not emit Cherenkov light. Fig. 7.1 shows the momentum
distribution for e-like and -like events with Monte Carlo events. Hatched histograms
show the sub-GeV momentum regions. Criteria (4) and (5), shown in Fig. 7.2 and Fig.
7.3, remove remaining partially contained events.
Table 7.1 shows a summary of the sub-GeV atmospheric neutrino sample comparedwith the Monte Carlo estimation. According to the Monte Carlo simulation, 35% of
85

3

10

2

number of events

number of events

10

DATA e-like

10
1
10

3

10

2

MC e-like

2

DATA µ-like

103

MC µ-like

10

2

10
10
1

10
0

1

2

3

0

P (GeV/c)12

3

P (GeV/c)

Figure 7.1: Momentum distributions of atmospheric neutrino fully-contained sample.
Hatched histograms show the sub-GeV momentum regions.

number of events

multi-ring events are produced by neutral current (NC) interactions, which do not remember the avor of the parent neutrinos. On the other hand, the rate of NC events isonly 8% for single-ring events. Therefore we will discuss only the single-ring sample inorder to reduce the NC contamination.
The ( +  )/(e+ e) ratio, R, is calculated to be:)DATA = 0:63  0:03(stat:)  0:05(sys:):R  ((=e=e)M:C:
The systematic error will be discussed later. R is signi cantly lower than 1. This result

102(a)DATA

10

3

10

2

(b)MC

10
10
1

1
0

200

0

200

max p.e.

max p.e.

Figure 7.2: Distributions of maximum p.e. in a PMT for (a)DATA and (b)Monte Carloevents after momentum and DWALL cut.
86

number of events

10

3

10

2

(a)DATA

10
1

10

4

10

3

10

2

(b)MC

10
1
0

10

0

10

OD-cluster

OD-cluster

Figure 7.3: Distributions of number of OD-cluster hits for (a)DATA and (b)Monte Carloevents after momentum, DWALL and max. p.e. cut.
is consistent with those of Kamiokande, IMB-3 and Soudan-2 experiments within theestimated error as shown in Fig. 1.2.
Now, we can independently obtain the information on particle type and hence con rm
the anomalous /e ratio by using the -decay signal. The detection eciency of -decay
electrons was estimated to be 801.2% for + and 631.0% for , by the Monte Carlostudy. These eciencies were also con rmed by real cosmic-ray stopping muons to within
1.5%. Table 7.2 shows the number of events which had -decay electrons. The fractionof events with -decay electrons agrees well with the Monte Carlo estimation. Thus, R
calculated from the particle identi cation algorithm is independently con rmed.
In the next section, I will discuss possible sources of systematic uncertainties andconclude that this small R value is not caused by any detector artifacts.

7.2 Systematic uncertainty
Possible sources which might cause the atmospheric neutrino ux anomaly are summarized in Table 7.3 together with the associated systematic uncertainties.
In the following subsections, each of the possible sources is further discussed. The
theoretical uncertainty in the ( +)/(e +e) ratio is estimated to be 5% as alreadymentioned in Section 4.1.

Primary cosmic-ray ux
As mentioned in Section 4.1, the energy spectrum of primary cosmic-rays is roughly
proportional to E , , where is tted to be 2.710.05. The neutrino energy spectrum
87Monte Carlo

Data

total e CC  CC

NC

single ring 1453

1551.5 539.7

927.8

84.0

e-like718593.8 537.2

8.9

47.7

-like

735

957.7

918.9

36.3

multi ring

533

596.6 148.4

total

1986

2148.1 688.1 1169.1 290.9

2.5241.3 206.9

Table 7.1: Summary of the sub-GeV atmospheric neutrino sample compared with theMonte Carlo estimation. Numbers of the Monte Carlo sample are normalized by livetimeof data.
is proportional to E , f (E ) where f (E ) takes into account the energy dependence of
decay probabilities and meson production cross sections. Therefore, the uncertainty inthe power index of the primary cosmic-ray ux is re ected also in the neutrino energy
spectrum. In order to estimate the systematics, the spectrum has been changed by afactor of (E=2GeV)0:05 at the neutrino energy E . At this time, the absolute ux at
2GeV, which corresponds to the average atmospheric neutrino energy, is xed.
Table 7.4 shows the result when the neutrino spectrum is changed. From this table,
the e ect on R is estimated to be 0.5%.

Particle misidenti cation
As mentioned in Chap.6, the misidenti cation probability was estimated to be 0.80.1%
for the Monte Carlo sample of CC interactions. For CC e ()-induced events, theprobability that an event be identi ed as -like (e-like) was 0.50.1% (1.00.1%). Thus,
the systematic uncertainty for the /e ratio, caused by the particle misidenti cation, isestimated to be 2%.

Single-ring / multi-ring separation
The number of rings in an event is counted automatically by the ring counting programas described in Sec.6.2. Most of the events can be clearly separated into single- or multi88

1 or more muon decay

2 or more muon decay

data

data

MC

30=735 = 4:1  0:7%

4:3  0:1  0:2%MC-like 496=735 = 67:5  1:7% 68:2  0:1  1:0%
e-like67=718 = 9:3  1:1%

8:0  0:3  0:1%

2=718 = 0:3  0:2% 0:5  0:1  0:01%

Table 7.2: Fractions of events with -decay in single-ring events. The error of the data
and the rst error of the MC are statistical. The second error of the MC arises from thedetection eciency of muon decay.
rings. However, low-energy multiple scattering events and high-energy o events aredicult to treat reliably.
The systematic uncertainty of single-ring / multi-ring separation was estimated bycomparing R between automatic ring counting and visual scanning. The di erence between automatic ring counting and visual scanning was found to be 4%, which was taken
as a systematic uncertainty.

Vertex position
In order to check a possible bias in the ducial volume cut, we calculated R based on the
TDC- t, which uses the result of the TDC- t as a nal vertex instead of the MS- t, andcompared with the nal R. The numbers of e-like and -like events changed as shownin Table 7.5. Since R changed by +0.6%, we estimated the uncertainty caused by vertex
reconstruction to be 0.6%.

Energy calibration
The uncertainty caused by the energy determination was estimated by changing theenergy scale in the Monte Carlo sample in the following: -2.1% for e-like events, +2.1%
and -1.5% for high-energy and low-energy -like events, respectively. The details of theenergy scale calibration are described in appendix A. Table 7.6 shows the e ects. From
this result, the systematic uncertainty caused by the energy determination is estimatedto be 1.2%.
89

Sourcedata reduction( + )/(e+e)
E,
Particle Identi cation
single-ring / multi-ring separation
Vertex position
Energy calibration
Non-neutrino backgroundashing PMT
cosmic-ray muon
e-like backgroundCC cross section
NC cross section
Hadron simulator
FC / PC separation
Total

Error(%)
<< 1%
< 5%
0:5%
2%
4%
0:6%
1:3%

< 0:5%< 0:1%< 0:1%
3:6%
2%
0:5%< 0:1%
8:1%

Table 7.3: Possible sources of the systematic uncertainties for the sub-GeV =e ratio.

Non-neutrino backgroundWe considered three sources as possible non-neutrino backgrounds; ashing PMT events,
remaining cosmic-ray muons, and e-like events produced by cosmic-ray neutron interaction in the detector.
For the ashing PMT events, in addition to the ashing PMT cut, we remove themby visual scanning. When we scanned the atmospheric neutrino sample again, the contamination of the ashing PMT events was found to be negligible, thus we estimated thecontamination very conservatively to be <0.5%.
We generated 500 cosmic-ray muons by Monte Carlo and one event was reconstructedin the ducial volume. Since the excess of -like events near the detector wall in theatmospheric neutrino sample is at most 40 events, the contamination from cosmic-ray1 ) events. Thus, the muon background is estimated to be <0.1%.
muons is 0.08 (=40 500
About the neutron background, the contamination of e-like events in the ducial volume is estimated by tting the e-like DWALL distribution with the exponential function,90

E , e-like -likeR= 2.76 +2.0% +1.6% +0.4%= 2.69 -2.03% -1.99% -0.04%
Table 7.4: E ects for the number of e-like and -like events and R when the energy
spectrum of the MC atmospheric neutrino is changed.
TDC- t data Monte Carloe-like +2.8%+3.0%
-like -0.7%
-1.1%
R
+0.6%
Table 7.5: The e ect on the R when we use the result of TDC- t as a nal vertex.
exp(, D44WALLcm ), given by the neutron simulation as shown in Fig. 7.4. The e-like background event was estimated to be only 0.2 events. Since the number of e-like events is718, the contamination of e-like backgrounds is estimated to be <0.1%.

Monte Carlo simulation
Now, we estimate the systematic uncertainties caused by the neutrino cross sections andnuclear e ects. We discuss those in the CC quasi-elastic interaction, CC pion production,
and NC interaction separately.
(i) CC quasi-elastic interaction
The axial vector mass, MA, and the Fermi momentum, PF , in the Fermi gas model werevaried within the allowed ranges. The result is shown in Table 7.7. From this table, weestimated the systematic uncertainty to be 3.6% by assuming that the uncertainty of
MA, PF , and the nuclear potential are independent.
Monte Carloe-like (97.9 < Pe, Evis <1302MeV)-0.3%
-like (197 < P , Evis <1358MeV)
+0.9%
R
-1.2%
Table 7.6: E ects on the R from the energy-scale uncertainty.
91

number of event

neutron MC e-like60

Figure 7.4: The predicted e-like events
caused by neutron backgrounds as afunction of DWALL. The solid line
shows the tted result by a exponential function.

40

20

0
0

100

200

300

400 500
DWALL (cm)CC quasi-elastic
MA :
MA :
PF :
nuclear potential on

e-like -like
R
1.01GeV ! 1.11 +4.6% +5.4% +0.8%
1.01GeV ! 0.91 -4.7% -5.5% -0.9%
250MeV ! 180 +12.3% +8.4% -3.4%(PF is 217MeV)-1.9% -1.4% +0.6%

Table 7.7: E ects on R when simulation parameters in the CC quasi-elastic interaction
are changed. PF is the Fermi momentum and MA is the axial vector mass.
(ii) CC pion production
The uncertainty of the CC pion production cross section is estimated to be 30%. This
comes from the comparison between the calculated value and the experimental data of
the pion scattering and experiment uncertainties as shown in Section 4.2. When wechange the cross section of the CC pion production interaction by 30%, R changes asshown in Table 7.8. The systematic uncertainty is estimated to be 0.2%.
CC pion production e-like -likeRchange  by +30% +6.2% +6.1% -0.2%
change  by -30%
-6.2% -6.1% +0.2%
Table 7.8: E ects on R when simulation parameters in the CC pion production interaction are changed.
(iii) NC interaction
92

The NC cross section was varied by 50% which is very conservative. The result isgiven in Table 7.9. The systematic uncertainty is estimated to be 2.2%. In summary,the systematic uncertainties from CC and NC interactions are estimated to be 3.6% and2.2%, respectively.
NC interaction
e-like -likeRchange  by +50% +4.0% +1.9% -2.0%
change  by -50% -4.0% -1.9% +2.2%
Table 7.9: E ects on the R when simulation parameters in the CC pion production
interaction are changed.
We also changed the hadron simulator from CALOR to FLUKA[49] and checked theirin uence on R. The e ect is estimated to be 0.5%.

FC / PC separation
As mentioned before, partially contained(PC) events were removed by the two criteria,(1)maximum p.e. in a PMT < 200 p.e. and (2)number of OD-cluster hit  9. Wechanged these criteria and checked the e ect on R. Table 7.10 shows the e ects. The
maximum p.e.
maximum p.e.
OD-hitOD-hit! 205 p.e.
! 195 p.e.
!
11
!
7

R
-0.02%+0.02%+0.02%-0.01%

Table 7.10: E ects for the R by changing criteria of maximum p.e. and OD-hit.
criterion of the maximum p.e. is varied by 2.5% which corresponds to the uncertainty
in the absolute energy scale. The number of OD-cluster hits is varied by 2 which isalso conservative. From this table, the uncertainty caused by the FC/PC separation isestimated to be <0.1%.
Adding all of these errors in quadrature, the total systematic error on the =e ratio
for the sub-GeV data is estimated to be 8.1%. In the systematic error of R, we also
add 1.5% from the statistical uncertainty of the Monte Carlo sample.
937.3 Vertex and momentum distributions
Fig. 7.5 shows the vertex distributions projected to the Z direction for (a)e-like and(b)-like single-ring events compared with the Monte Carlo estimation. The excess at
the top detector wall for -like events is due to cosmic-ray muons which entered cableholes without ring the outer detector as mentioned in Sec. 5.5. If the shapes are
assumed to be at with the absolute normalization being free, 2=d:o:f: is 24.6/31 fore-like events and 44.5/31 (5%) for -like events in the ducial volume. R as a functionof Z is shown in Fig. 7.6. The 2=d:o:f: of this distribution is calculated to be 32.0/31.
Thus, the deviation from the at distribution is not signi cant. Fig. 7.7 shows thevertex distributions projected to the X 2 + Y 2 direction for (a)e-like and (b)-like events.
The 2=d:o:f: assuming a at distribution, are 14.6/27 and 29.43/27 for e-like and -likeevents, respectively. Shapes are consistent with the at distribution both for e-like and-like events. Fig. 7.8 shows R (=(=e)DATA=(=e)MC ) as a function of DWALL. The
distribution is consistent with a constant R ratio in the ducial volume. The larger valueof R near the detector wall is again due to cosmic-ray muons that went through the cableholes.

(b) µ-like(a) e-likenumber of event

60
fiducial volume

fiducial volume

40
20
0

-10

0

10

-10

Z (m)

0

10

Z (m)

Figure 7.5: The sub-GeV single-ring vertex distributions projected to the Z direction (+18.1m and -18.1m show the top and bottom PMT surface, respectively ). Error bars
show the statistical error for the real data. Histograms show the Monte Carlo prediction.
The high rate at the highest Z bin is due to cosmic-ray muons that went through thecable holes and hence did not give signals in the outer detector.
94

(µ/e)data / (µ/e)MC2

χ /dof = 1.0
2

fiducial volume

1.5
1
0.5
0

-10

0

10

Figure7.6:The(=e)DATA=(=e)M:C: vs Z
plot. Error bars include both
the real and Monte Carlo statistical errors. Solid line and 2
are the tted results assuming
a at line and free absolutenormalization.

Z (m)The momentum distributions are shown in Fig. 7.9 for (a)e-like and (b)-like events.
It seems that there is a de cit for -like events and there is an excess for e-like events,
but we cannot state a de nite answer because the absolute normalization has a 20%
uncertainty from the neutrino ux calculation and 15% from the neutrino interaction
cross section, resulting in a total of 25%.
Fig. 7.10 shows R as a function of the momentum. It is consistent with a at
distribution within the statistical error (2 =d:o:f: = 1.1/4) in this momentum range.
As mentioned in Section 1.3.2, the proton decay, p ! e+ , predicts an excess of
e-like events, in the momentum range less than 500MeV/c. The data do not support the
proton decay hypothesis to explain the small  =e ratio.

7.4 The Zenith angle distribution
If the atmospheric neutrino anomaly is indeed caused by neutrino oscillations, an updown asymmetry in the zenith angle distribution is expected. The higher the observed
momenta, the better the direction of an observed event follows the original neutrino
direction. Fig. 7.11 shows the Monte Carlo simulation of the angular correlation between
reconstructed and parent-neutrino directions. Events with visible energies less than afew hundred MeV lose directionality, but above 500MeV, the correlation becomes better
than 40o for both e-like and -like events. Therefore even the sub-GeV sample has somedirectional sensitivity.
Fig. 7.12 shows the zenith angle (cos ) distributions for (a)e-like and (b)-likeevents together with the Monte Carlo predictions, where cos  = 1 means down-going.
To check a possible momentum dependence, the cos  distributions are further divided
95

(b) µ-like(a) e-likenumber of event

60
fiducial volume

fiducial volume

40
20
0

0

100

200
2

0

2

100

200
2

R (m )

2

R (m )

Figure 7.7: The sub-GeV single-ring vertex distribution projected to the X and Y plane.
R2 = 0 means the center of the detector. Error bars show the statistical error for thereal data. Histograms show the Monte Carlo prediction.
into two momentum regions as shown in Fig. 7.13. For -like events with momenta above
400MeV/c, the data exhibit a small up-down asymmetry. But for -like events below
400MeV/c, the shape is consistent with at. This is what one expects at low energies.
On the other hand, for e-like events at high energies, the shape is consistent with a at
distribution. We will estimate the systematic up-down uncertainty in the /e ratio in
the next subsection.
R as a function of cos  is shown in Fig. 7.14. The 2 assuming a at R is :2=d:o:f : =18:0=4. The up-down asymmetry is enhanced by an excess in the left most bin (-1< cos  < 0.6) in the lower e-like cos  distribution as seen in Fig. 7.13(a). We believe
the non at e-like distribution was caused by a statistical uctuation, since this e ect
is mostly coming from the momentum region of less than 400MeV/c where we expect
no strong directionality. Again, the cos  distributions are divided into two momentum
regions as shown in Fig. 7.15. The up-down asymmetry of R is seen only in the highmomentum region.

Systematic uncertainty of up-down asymmetry
We have already shown the zenith angle distributions in Figs. 7.12-7.14. In this subsection, we will estimate the systematic uncertainty for the zenith angle distributions.
96

1.5

(µ/e)data/(µ/e)MC

fiducial volume

Figure7.8:The(=e)DATA=(=e)M:C: vs DWALL
plot. DWALL = 0 means the
PMT surface. Error bars include both the real and Monte
Carlo statistical errors.

1

0.5

0

0

5

10

15

DWALL(m)Since the mean neutrino energy for the present sample is about 0.8GeV, and thegeomagnetic eld causes about 30% up-down asymmetry at this energy range, this e ect
could induce some systematic up-down asymmetry in the /e ratio. In order to estimate
this uncertainty, we used two independently calculated uxes[1][50] and compared the(=e)MC ratio using these two calculations, from which we conclude that the possible updown systematic asymmetry is less than 1%. The other source which could produce updown asymmetry is a possible gain asymmetry of the PMTs. We used -decay electrons
to estimate the up-down gain asymmetry. To avoid the muon polarization e ect for
the electron energy spectrum, we selected electrons which direction of with almost rightangles to the directions of the parent muons. Fig. 7.16 shows the average of the corrected
total number of p.e., Rtot , for decay electrons as a function of the zenith angle (cos ).
Note that the Rtot is proportional to the electron momentum as shown in Fig. 6.12.
By this gure, we estimate that the detector gain is uniform within 1:5% between
down-going and up-going particles which may be due to the relative gain variation. This
gain asymmetry could cause only 0.4% up-down asymmetry in R, because it largely
cancels when we take the /e ratio. The contamination of non-neutrino background,less than 0.5%, could have directional correlation and could add a maximum of 1% tothe up-down systematic error. Adding these three in quadrature, the possible systematic
error in the up-down asymmetry of R is 1.5%. This systematic error is negligibly small
compared with the statistical errors in Fig. 7.12.

97

250

number of events(a) e-like(b) mu-like

200
150
100
50
0

0

0.5

1

0

momentum (GeV/c)

0.5

1

1.5

momentum (GeV/c)

Figure 7.9: Momentum distribution for (a)e-like and (b)-like events. Error bars are thestatistical errors of the real data. Histograms show the Monte Carlo prediction.

(µ/e)data / (µ/e)MC

1.5

1Figure 7.10:
The R(=(=e)DATA=(=e)M:C:)vsmomentum. Error bars include
the statistical errors for the data
and Monte Carlo.

0.5

0

0

0.5

1

1.5

momentum (GeV/c)98resolution (degree)

Figure 7.11: The average angle
between reconstructed and parentneutrino directions as a function ofvisible energy of the detected particles, estimated by the Monte Carlosimulation. Filled and open circles
show the resolutions for e-like and like events, respectively.

Monte Carlo

100

75

e-like50

25

0µ-like

0

500

1000
Evis (MeV)

300

number of events(a) e-like(b) mu-like

200

100

0

-1

-0.5

0

0.5

1 -1

cosΘ

-0.5

0

0.5

1

cosΘ

Figure 7.12: The zenith angle distribution for (a)e-like and (b)-like events. The errors
are statistical only. The systematic errors are negligible compared to the statistical ones.
(See the text for details) Hatched histograms show the Monte Carlo prediction and thewidth of these regions represents the statistical uncertainties. Dotted histograms show
the systematic uncertainty on the absolute normalization of the Monte Carlo events.
99µ-like
DATA/MCDATA/MC

e-like(a)100-400MeV/c

2
1.5

1.5

(a)200-400MeV/c

1

1
0.5

0.5

χ /dof = 1.5
2

0

0
1.5

(b)>400MeV/c2

χ2/dof = 0.87

1.5(b)>400MeV/c

1

1
0.5

0.5
0

χ /dof = 1.5
2

-1

-0.5

0
cosΘ

0.5

1

0

χ2/dof = 4.1
-1

-0.5

0
cosΘ

0.5

1

Figure 7.13: The (cos ) distribution for e-like and -like events divided into two momentum regions, (a)200-400MeV/c and (b)>400MeV/c. Solid lines and 2s are the tted
results assuming a at line and free absolute normalization.

(µ/e)data / (µ/e)MC

1.5

1Figure 7.14:
The R(=(=e)DATA=(=e)M:C:)asa function of cos . Error bars
are statistical only.

0.5

0

-1

-0.5

0

0.5

1

cosΘ

100

(µ/e)data / (µ/e)MC(µ/e)data / (µ/e)MC(a) < 400MeV/c

1.5
1
0.5

2

χ /dof = 0.86

01.5(b) > 400MeV/c

1
0.5
2

0

χ /dof = 3.8
-1

-0.5

0
cosΘ

0.5

1

Mean of Rtot

Figure 7.15: The R (=(=e)DATA=(=e)M:C:) as a function of cos  divided into two
momentum regions, (a)<400MeV/c and (b)>400MeV/c. Error bars are statistical only.

210
205
200
195
190
-1

-0.5

0

0.5

1
zen
cos ΘeFigure 7.16: The mean of the Rtot for -decay electrons as a function of the zenith angle(cos .)101

Chapter 8
Conclusion
The atmospheric neutrino ux has been measured using 20.0 kton-years exposure of theSuper-Kamiokande detector. 735 single-ring -like and 718 e-like events were detectedwith momentum pe > 100 MeV/c, p > 200 MeV/c and with visible energy less than
1.33 GeV in the ducial volume (22.5kton). Using the Monte Carlo prediction, basedon the calculations of the atmospheric neutrino uxes provided by Honda et al[1], thedouble ratio R (=(=e)DATA=(=e)M:C:) is;

R = 0:63  0:03(stat:)  0:05(sys:):
R is signi cantly lower than unity and this result con rms the previous results from
Kamiokande, IMB-3, and Soudan-2 experiments. No evidence for the momentum andvertex position dependence of R was observed.
We nd that R depends on the zenith angle. The up-down asymmetry in the zenith
angle distribution may shed light on a possible source of the small value of R.

103

Appendix A
Absolute energy scale and thestability of the detector
In this chapter the ambiguity of the absolute energy scale is estimated using ve calibration sources. Since the systematic uncertainty in the absolute energy scale a ects theatmospheric neutrino ux measurement directly, we must understand how precise theMonte Carlo simulation reproduces the absolute energy scale.

Decay electrons
We have a large number of low energy electrons produced by the decay of cosmic-ray
muons. The absolute energy scale is checked by comparing the the Michel electron
spectrum between the data and the Monte Carlo. Decay electrons are selected with thefollowing criteria:
1. electrons are detected from 1.5sec to 8sec after the trigger of a parent muon.
2. number of ID-hits is less than 1000.
3. goodnesslow is more than 0.5.
4. the vertex position is reconstructed in the ducial volume.
MC events are generated uniformly in the ducial volume and randomly for the direction.
Fig. A.1 shows the momentum spectrum for electrons in ducial volume compared with
MC events. The spectrum of MC takes into account an e ect of the nucleon Coulomb
eld caused by atomic capture of a parent muon[51]. The spectrum of the data agrees
well with the MC. The mean value of the MC is 2.0% lower than that of the data.
105

Mean DATA = 38.64
MC = 37.89
80

Figure A.1: Momentum spectrum ofmuon decay electrons in the ducial
volume. Points with error bars show
the data and histogram shows the MC.

60

40

20

0

0

20

40

60

MeV/c

LINAC
In Super-Kamiokande, an electron linear accelerator(LINAC) is used to understand precisely the performance of the detector for low energy event[52]. The energy of electrons
can be adjusted from 5 to 16MeV and energy spread at the end of beam pipe is less than
0.3%. We use electrons with the energy of 16MeV. The injected position is 6m from the
top PMT surface and the direction is downward. LINAC electron events are selectedaccording to the following criteria:
1. number of ID-hits is between 100 and 210.
2. goodnesslow is more than 0.5.
3. the distance between the injected position and the reconstructed position is lessthan 2m.
Fig. A.2 shows the momentum distribution for LINAC electrons compared with MC
events. The agreement of the momentum distributions between the data and the MC issatisfactory. The mean value of the MC is 2.4% higher than that of the data.

106

Mean

DATA = 16.97
MC = 17.38

100

Figure A.2: Momentum spectrum of
LINAC electrons. Points with error
bars show the data and histogramshows the MC.

50

0

0

10

20

30

MeV/c

0 mass
Single 0 events are produced by the atmospheric neutrino interaction. If the momentumof a 0 is less than about 400MeV/c, in many cases, we can detect two clear Cherenkov
rings produced by two 's from the 0 decay. The 0 mass, m0 , is given by the next
equation:m20 = 2P 1  P 2 (1 , cos );
where P 1 and P 2 are the momentum of two gamma-rays and  is the opening angle between two gamma-rays. The single 0 events are selected from the atmospheric neutrino
fully-contained event sample with the following criteria:
1. total momentum of a event is less than 400MeV/c.
2. 2-rings and both of them are identi ed as e-like.
3. vertex is reconstructed in the ducial volume.
Fig. A.3 shows m0 distribution for the data and the MC events, which are tted by theGaussian distribution. The agreement of tted shapes between the data and the MC issatisfactory. The tted peak of the MC distribution is 2.5% lower than that of the data.
1073.016
Constant
Mean
Sigma

(a) DATA

20

/ 5
15.24
149.9
16.39

2.526
2.265
1.884

10

0

0

50

100

150

200

200
3.828

Constant
Mean
Sigma

(b) MC

150

/ 5
122.6
146.2
19.59

250
6.918
0.9306
0.9529100

Figure A.3: The distribution of
the reconstructed invariant mass
for the data and the MC. The
solid line shows the result of a
Gaussian t.

50

momentum (MeV/c)

0

0

50

100

150

200

250 MeV/c

400(a) DATA(b) MC

350

Figure A.4: Opening angle vs momentum plots for(a)data and (b)MC stopping
muon events.

300
250
200
30

40
30
opening angle (deg.)40

Low energy Stopping muons
Using the opening angle of the Cherenkov ring for low-energy muons, we can estimate
the momentum independently to check the systematic uncertainty of the momentum
reconstruction. The relation between the momentum and the opening angle is given
in Eq.2.2. We used stopping muons which enter from the top wall and have one decay
electron events. Fig. A.4 shows the reconstructed momentum as a function of the opening
angle for the low energy stopping muon events. We calculated a ratio, RdataorMC , which
is de ned as (momentum) / (momentum estimated by the opening angle). To estimate
the momentum dependence, data sets are divided into 5 momentum bins. Fig. A.5
shows the hRMC i=hRdata i plots as a function of momentum. (hRi means the average ofR.) This gure represents the systematic uncertainty of the momentum determination
between the data and the Monte Carlo. The deviation from 1 is less than 2.5%.
108

(MC / DATA)

1.1

Figure A.5: The hRMC i=hRdata i plots
as a function of momentum. Dottedlines show 2.5%.

1

0.9

200

300
400
momentum (MeV/c)High energy Stopping muons
In the high energy region, the range of stopping muons is used to check the absoluteenergy scale. Because a range of stopping muons is proportional to the momentum andit is easy to calculate the end point of the muon by nding the vertex position of themuon-decay electron. The range is de ned as the distance from the vertex position of
the stopping muon to the vertex position of its decay electron. Fig. A.6 shows the ratioof momentum and range, (mom./range) distribution as a function of range. The energy
deposit per 1cm is about 2.5MeV. Since the ambiguity of the vertex determination a ects
the range when the range is short, events with a range larger than 7m are used. Events are
divided into 6 bins by the range. The average of (mom./range) for the data and the MCis calculated and the ratio is taken. The ratio, hmom:=rangeidata and hmom:=rangeiMC
are shown in Fig. A.7. The MC is higher than the data at most 2.6%. In the sub-GeV
range the systematic di erence between the data and the MC is 2.1%.

Summary of the absolute energy scaleFig. A.8 shows the summary of the studies for the absolute energy scale. Events with themomentum from 16MeV to about 10GeV are examined and the energy scale for Monte
Carlo events agree with that for the data within +2.6% and -2.5%.

Stability of the detector
We have been checking the stability of the absolute energy scale using high-energy stopping muons. Fig. A.9 shows the hmom:=rangeidata plots as a function of time. In
109

3

Figure A.6: The mom./range vs range
plot for stopping muon events. Eventswith a range more than 7m are used
for the analysis.

2

1

0

momentum/range (MeV/cm)

momentum/range (MeV/c/cm)

4

1000

2000

3000

4000
range(cm)

4

DATA
M.C.

Figure A.7: hmom:=rangeidata
and hmom:=rangeiMC plots as afunction of range.

3

2

1
0

1000

2000

3000

4000

range (cm)110∆(M.C./DATA) (%)

10

5

0

LINAC
decay-eπ-50low stop µhigh stop µ

-10
10

2

10

3

4

10
10
Momentum(MeV/c)

Figure A.8: Summary of the absolute energy scale.

111

5

Momentum/Range (MeV/cm)

2.6

2.4

May 27,1996

June 25,1997

2.2

0

100

200

300

400

500

elapsed days from 1-Apr-1996

Figure A.9: The time variation of the hmom:=rangei. The x-axis show the day from Apr.
1,1996. Dotted lines show the 1% from the solid line.
calculating the momentum, the attenuation length of the water is corrected. But theenergy scale still correlates with the water attenuation length(see Fig. 3.12). However
the e ect of the water transparency to the momentum is reduced within 1% after end of
May 1996.
We also uses muon-decay electrons to check the detector stability. Fig. A.10 shows
the time variation of the mean electron energy. The reconstructed energies of electrons
are stable within 1% after end of May 1996.

112

mean energy (MeV)

42

40
±1.0%

38

36

May 27,1996

100

200

300

400

500

elapsed day from 1996-1-1

Figure A.10: The time variation of the mean energy of the muon-decay electrons. Dottedlines show the 1% from the solid line.

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