A Study of Particle Identi cation with theSuper-Kamiokande Detector
A Thesis Presented
byKarl Florian Goebelto
The Graduate Schoolin Partial Ful llment of the Requirements
for the Degree ofMaster of ArtsinPhysics
State University of New YorkatStony Brook
December 1996

State University of New Yorkat Stony Brook
The Graduate School
Karl Florian GoebelWe, the thesis committee for the above candidate for the Master of Arts
degree, hereby recommend acceptance of the thesis.

Professor Chiaki Yanagisawa
Department of Physics
Professor Chang Kee Jung
Department of Physics
Professor George Sterman
Department of Physics
This thesis is accepted by the Graduate School.
Graduate Schoolii

Abstract of the Thesis
A Study of Particle Identi cation with theSuper-Kamiokande Detector
byKarl Florian Goebel
Master of ArtsinPhysics
State University of New York at Stony Brook
1996

A particle identi cation algorithm has been developed for the
study of atmospheric neutrinos with the Super-Kamiokande detector. Preliminary results are obtained for identifying electrons
and muons based on a study with a sample of Monte Carlo events.
The identi cation eciency for particles in a visible energy range
100 MeV to 2 GeV is better than 93% for electrons and 91% formuons. A preliminary analysis with a selected data sample shows
results qualitatively consistent with the Monte Carlo study.
iii

iv

Contents
List of Figures : : : : : : : : : : : : : : : : : : : : : : : : : : :ix

List of Tables : : : : : : : : : : : : : : : : : : : : : : : : : : :x

Acknowledgements : : : : : : : : : : : : : : : : : : : : : : : :xi

1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : :1

1.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . 1
1.2 Super-Kamiokande, a Multipurpose Detector . . . . . . . . . . 3
1.3 Historic Overview and Comparison with other Experiments . . 5

2 Neutrino Physics : : : : : : : : : : : : : : : : : : : : : : : : : 11
2.1 General Overview . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Interaction with Matter . . . . . . . . . . . . . . . . . . . . . 21v

3 Detector Description : : : : : : : : : : : : : : : : : : : : : : : 30
3.1 Basic Principle of a Water C erenkov Detector . . . . . . . . . 30
3.2 The Water Tank . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Trigger System and Data Acquisition . . . . . . . . . . . . . . 38

4 Analysis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 44
4.1 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Particle Identi cation . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5 Comparison with Data . . . . . . . . . . . . . . . . . . . . . . 80
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83vi

List of Figures
2.1 Primary Cosmic Ray Flux . . . . . . . . . . . . . . . . . . . . 18
2.2 Atmospheric  - uxes . . . . . . . . . . . . . . . . . . . . . . . 20
2.3  -Flux Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Feynman Diagrams for Elastic e Scattering . . . . . . . . . . 23
2.5 Feynman Diagrams for Quasi-Elastic N Scattering . . . . . . 24
2.6 Feynman Diagrams for Inelastic N Scattering . . . . . . . . . 24
2.7 Cross Section of Charged-Current quasi-elastic interactions . . 25
2.8 Cross Section for CC Single-Pion Production . . . . . . . . . . 26
2.9 Total Cross Section for CC Interactions . . . . . . . . . . . . . 27
2.10 Ratio of e and  Cross Sections . . . . . . . . . . . . . . . . 28
2.11 Comparison of cross section for free and bound nucleons . . . 29
3.1 C erenkov geometry . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Schematic diagram of Super-Kamiokande . . . . . . . . . . . . 33
3.3 The 50 cm Photomultiplier Tube . . . . . . . . . . . . . . . . 35
3.4 Quantum Eciency of a 50 cm PMT . . . . . . . . . . . . . . 36
vii

3.5 Inner PMT circuit and signal decoupling . . . . . . . . . . . . 39
3.6 The analog input circuit of the ATM. . . . . . . . . . . . . . . 41
3.7 Schematic diagram of the Data Acquisition system. . . . . . . 42
4.1 Neutrino ux at Cleveland and Kamioka . . . . . . . . . . . . 47
4.2 Point source and C erenkov light . . . . . . . . . . . . . . . . . 50
4.3 Position resolution of YASTEF . . . . . . . . . . . . . . . . . 54
4.4 Scan of an electron . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Scan of a muon . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.6 Mapping for charge-track-distribution. . . . . . . . . . . . . . 58
4.7 Charge-track-distribution for a \typical" electron. . . . . . . . 59
4.8 Charge-track-distribution for a \typical" muon. . . . . . . . . 60
4.9 Scan of a hard scattered muon in cylindrical perspective. . . . 62
4.10 Charge-track-distribution of the above hard scattered muon. . 62
4.11 The relevant derivatives for Rispid . . . . . . . . . . . . . . . 64
4.12 Rispid for MC electrons and muons . . . . . . . . . . . . . . . 66
4.13 Rispid as function of the distance to the wall . . . . . . . . . . 67
4.14 Rispid as a function of direction . . . . . . . . . . . . . . . . . 69
4.15 Rispid-grid for MC electrons and muons . . . . . . . . . . . . 70
4.16 Rispid and Rispid-grid distributions for di erent energies . . . 71
4.17 Rispid-grid as a function of charge . . . . . . . . . . . . . . . . 73
viii

4.18 Collected charge distribution for MC electrons and muons . . 75
4.19 Rispid-grid separation value as a function of charge . . . . . . 76
4.20 Adpid as a function of charge . . . . . . . . . . . . . . . . . . 77
4.21 Adpid for single ring contained data events . . . . . . . . . . . 81
4.22 Adpid for Monte Carlo single ring contained events . . . . . . 82
4.23 Adpid for MC events followed by a decay electron . . . . . . . 84
4.24 Adpid for data events followed by a decay electron . . . . . . . 85

ix

List of Tables
1.1 Atmospheric neutrino data from 4 experiments . . . . . . . . . 7
1.2 Physical parameters of water C erenkov detectors . . . . . . . . 9
1.3 Performance parameters of water C erenkov detectors . . . . . 10
4.1 Rispid-grid identi cation probability for various energies. . . . 72xAcknowledgements
First, I would like to thank the German-American Fulbright Commission
which made my stay in Stony Brook possible. Here, I had the opportunity towork in an active research group in high energy physics which was a totallynew experience for me.
The Super-Kamiokande experiment is a product of many people and mywork would not have been possible without their contributions. However,some people deserve special mention. First, I thank my advisor Prof. Chiaki
Yanagisawa who guided me during this past academic year and whose support
was not limited to the eld of physics. I also owe many thanks to Prof. Chang
Kee Jung for advise mainly during our weekly meetings.
Much of what I know about computers I learned from my fellow graduate
students Brett Viren and Eric Sharkey. I am thankful to Clark McGrew who
shared his broad knowledge and experience with me and provided me withmany ideas. While writing my thesis I got much support from Jim Hill who
revised my rst drafts. Through many discussions he help me broaden myunderstanding of the physics in Super-Kamiokande. I am grateful to FriedrichKonig for reviewing the initial drafts of my thesis.
Beyond physics, my stay was enriched by many friends here in Stony
Brook. Far from home I received continuous support from my family. Theirregular correspondence, however, never made me feel home was far away.

xii

1

Chapter 1
Introduction
1.1 Theoretical Background
For almost 20 years the \Standard Model" of elementary particle physics
which comprises quantum chromodynamics and the Glashow-Weinberg-Salamtheory of electroweak processes has been accepted as the theory describing
all elementary interactions except gravity. So far there have been no compelling experimental ndings requiring a modi cation of the current Standard
Model. However, there is some reason to believe that there is physics beyond
the Standard Model.
Particle interactions are very successfully described in terms of local
gauge symmetries. In the Standard Model the three fundamental forces
re ect three independent symmetries. It seems natural to develop theories
where these separate symmetries are part of one larger gauge symmetry.

2

From a theoretical point of view these grand uni ed theories (GUTs) aremuch more satisfying than the Standard Model.
Certainly one of the most exciting phenomena predicted by GUTs is
proton decay. In the Standard Model the proton is stable as it is the lightest
baryon. It cannot decay into leptons because baryon number is assumed
to be conserved. However there is no underlying symmetry that requires
baryon and lepton number conservation. In fact most GUTs provide forbaryon-lepton interactions.
In the framework of grand uni ed theories neutrinos are usually put ina large multiplet together with quarks as well as charged leptons [1]. As
neutrinos are treated equally with charged leptons and quarks it is natural
to assume that they are also massive particles. In analogy to quarks, massive
neutrinos can also have avor mixing. This leads to the possibility of the interesting phenomenon of neutrino oscillations where neutrinos change theiravor state. An observation of neutrino oscillations represents an unambiguous evidence for non standard physics. The existence of neutrino mass isalso of importance in Cosmology. Because of the large number of neutrinos
expected in the universe, massive neutrinos might considerably contribute to
the dark mass. This would have a great impact on the cosmological modelof the universe.

3

1.2 Super-Kamiokande, a Multipurpose Detector
Super-Kamiokande is a 50,000 ton Water C erenkov Detector in the
Kamioka mine in Japan. It detects relativistic charged particles by theC erenkov light they emit. The detector is located under 1000 meters ofmountain rock, which can only be penetrated by neutrinos and very energetic cosmic ray muons. Construction has been completed and data taking
started on April 1st, 1996.
Super-Kamiokande is suitable to search for many interesting phenomena
in physics [2]. Solar neutrinos produced by nuclear chain-reactions in the coreof the sun are within the sensitivity range of the detector [4]. Also, in thecase of a nearby supernova explosion the corresponding neutrino burst canbe detected. The particle identi cation program presented in this work is
mainly developed for the analysis of atmospheric neutrinos. However, it isalso relevant to the analysis of proton decay.

Proton Decay
As mentioned in the previous section proton decay is an unambiguous
sign for new physics. If a proton decays inside the detector, charged leptons
or mesons are created either directly or as secondary decay products. These4

decay products can be detected as their kinetic energy is usually enough toradiate C erenkov light.
There are many decay modes predicted by di erent grand uni ed theories. Particle identi cation can be used as a tool to identify these decay
modes. In 5 years of detector lifetime the exposure will be 110 kiloton-years.
This corresponds to a sensitivity to a lifetime of  1033  1034 years for most
predicted decay modes.

Atmospheric Neutrinos
Originally considered as a background to proton decay measurements,
atmospheric neutrinos have attracted much attention because of disagreements between measured and predicted uxes. Studies mainly focused on
the ux ratio ( +  )=(e +  e) which was measured to be smaller than
predicted by Monte Carlo studies [3]. A favored explanation for this de cit
is neutrino oscillation. The study of atmospheric neutrinos might therefore
lead to the discovery of non-standard physics. Improved measurements ofenergy and direction dependence of the  and e ux will help to clarify thissituation.
Atmospheric neutrinos are generated by interactions of cosmic rays withthe atmosphere. Primary cosmic rays create secondary particles which decay
and thereby emit neutrinos. The energy spans from 10's of MeV to over5

10's of TeV. These neutrinos travel 10 km to 10,000 km before reaching thedetector where a small fraction interacts with the water in the tank. Highly
energetic leptons and mesons created in these interactions are detected.
Super-Kamiokande is designed to measure energy, direction and positionof the production vertex of these interaction products. On a statistical basis,
this allows one to infer the original neutrino momentum. Also, at some level, and e interactions can be distinguished. This reconstruction analysis is
the main subject of this thesis.

1.3 Historic Overview and Comparison withother Experiments
The rst detectors for atmospheric neutrinos have been built in the
1960's. Using scintillators and ash tubes they detected events inducedby neutrinos in the surrounding rock. Highly energetic ( )0s (hE i 
100GeV ) create muons that penetrate the detectors. Since the penetration
depth of electrons is much shorter, this technique does not work for e (e)0s.
In the 1980's several massive detectors were designed to search for proton
decay. All of them were deep underground to shield them from cosmic rays.
They were searching for events originating inside of the detector. Since interactions create the same class of events these detectors also began to6study atmospheric neutrinos.
Two di erent detector types were developed. The NUSEX and theFrejus experiments use ne-grained tracking calorimeters [5, 6]. The 150 ton
NUSEX detector, located at a depth of 5000 meter water equivalent (m.w.e.)in the Mont Blanc tunnel, consists of 134 1cm thick iron plates interleavedwith streamer tubes. Frejus (4850 m.w.e.) uses 900 tons iron as the primarysensitive mass. The tracks are detected by ash-chamber and Geiger-tube
planes. Both detectors provide two orthogonal images of an event but nodE=dx information is available.
The two water C erenkov detectors IMB and Kamiokande are similar to
Super-Kamiokande. IMB [7] consisted of an 8 kton water tank (18 m  17 m

 22.5 m) in the Morton Salt mine, Ohio, USA (1570 m.w.e.), and started
taking data in 1982. Only in its nal stage starting in 1986 the detector
had sucient light collection eciency to allow for particle identi cation. In
this stage 2048 20-cm photomultipliers with wavelength shifter plates were
installed on all six surfaces pointing inwards. With a coverage of 4%, it monitored the ring pattern of the C erenkov light emitted by relativistic charged
particles. Operating at a trigger threshold of 15 MeV electrons from muon
decay (maximum 53 MeV) were detected with a probability of about 80%,
which was used to identify the presence of a muon in an event. Particle identication analyzing the di erence between ring patterns produced by electrons

7

Exp.

Data
MC
e-like -like e-like -like

NUSEX 18
Frejus 57
IMB-3 325
Kamiokande 159
Combined

32
108
182
151

20.5
70.6
257.3
164.9

(=e)data(=e)MC:35
36.8 0:99+0,0:25  small:19125.8 1:06+0,0:16  0:15
268.0 0:54  0:05  0:12
:07
260.6 0:60+0,0:06  0:05
0:630  0:04(stat)

Table 1.1: Atmospheric neutrino data from the 4 experiments (from [3]).
and muons was 92% ecient.
Kamiokande [8] is a 4.5-kton cylindrical water C erenkov detector (16 m 19 m) in the Kamioka mine 2700 m.w.e. underground. There are 948
50-cm phototubes installed that provide a 20% photocathode coverage. Up
to 98% eciency of particle identi cation was achieved by this experiment.
A 1.5 m thick anticoincidence detector surrounding the inner detector is used
to veto entering events which are mainly cosmic ray muons.
The total atmospheric neutrino ux measured by the four experiments
described above is lower than the predicted values. However, since the uncertainty in the predicted event rate is approximately 30%, interest has mainly
focused on the ratio ( +  )=(e +  e ). Here, the uncertainties in the total
number of events cancel out. The results obtained by the four experiments
are summarized in Table 1.1. While the ( +   )=(e +  e) ratio obtained

8by Frejus and NUSEX agrees with the predicted values, that measured by
the two water C erenkov experiments, IMB and Kamiokande, is signi cantly
lower. However, as the statistical errors of the results by Frejus and NUSEX
are large, their results do not contradict with those of IMB and Kamiokande.
With a ducial volume 5 times larger than the combined previous atmospheric neutrino detectors, Super-Kamiokande collects contained atmospheric neutrino events at a rate of about 7 per day within the ducial volume
and will soon have accumulated high statistics which allow more detailed
studies. The light collection eciency of 7 photo-electrons/MeV improves
particle identi cation and vertex resolution. Tables 1.2 and 1.3 compare
physical parameters and performance of the two previous water C erenkov
detectors with the Super-Kamiokande detector.

9Table 1.2: Comparison of the physical parameters of the large water C erenkov
detectors.
PARAMETERSTOTAL MASSFIDUCIAL MASS
p-decaysolar
supernova
TOTAL SIZE
DEPTH
# of PMTs
PMT TIMINGRESOLUTIONPHOTOCATHODE
COVERAGE
ANTICOUNTERKAMIOKANDE
III
4500 tons
1040 tons
680 tons
2140 tons
16 m  19 m
2700 mwe
948 @ 50 cm
4 ns @ 1 pe

IMB-3
8,000 tons

SUPER
KAMIOKANDE
50,000 tons

3300 tons
22,000 tons
none
22,000 tons
6800 tons
32,000 tons
22  17  18 m3
41 m  39 m
1570 mwe
2700 mwe
2048 @ 20 cm
11,200 @ 50 cm+ wavelength shifter +2,200 @ 20 cm
11 ns @ 1 pe
2.5 ns @ 1 pe

20%

4%

40%

5 pe/MeV
1.5 m1 pe/MeV7 pe/MeVside only

None

2.5 m
all surfaces

10

Table 1.3: Comparison of the performance parameters of the large waterC erenkov detectors.
KAMIOKANDE
III
5.2 MeV

PARAMETERS
Threshold(trigger)Threshold
7.5 MeV(analysis)
ENERGYRESOLUTION
pe of E(GeV)
3:6%= E( 1GeV )q 4%e( 20MeV )20%= E=(10MeV )POSITIONRESOLUTION
10 MeV e
110 cmp ,! e+0
15 cm
ANGULARRESOLUTION
Cosmic Ray Muons
2:7
10 MeV e28
e= SEPARATION
98%
 DECAY
DETECTION
88%

IMB-3
15 MeVSUPER
KAMIOKANDE
4 - 5 MeV

20 MeV

5 MeV

p

p

|
35 cm

50 cm
 10 cm

5
|
92%

 1

80%

95%

3%= E
2:6%= Ep3%= E
q 2.5%|
16%= E=(10MeV )

28
99%

11

Chapter 2
Neutrino Physics
2.1 General Overview
The neutrino was rst postulated in 1931 by Wolfgang Pauli [9, 10].
The study of beta decay had revealed that energy and momentum were notconserved by the measured decay products.
A X ! A X 0 + e,
Z
Z +1

(2.1)

Whereas in a two body decay like the process above energy and momentumof the outgoing particles are xed, the energy of the electron was foundto vary considerably. To resolve this problem Pauli proposed an electricallyneutral particle with very small or zero mass that does not interact noticeably
with matter. It was known that the spins of the the nuclei involved in beta

12
decay di er by 0 or 1 and that the electron has spin 12 , which violates
angular momentum conservation. Therefore the new particle had to havespin 21 . However, Pauli's ideas were viewed with some skepticism until Fermi
presented his very successful theory of beta decay.
Although the existence of the neutrino was well founded in theory, it was
not proven experimentally until 1953 when Cowan and Reines announced its
observation [11]. Their experiment used the intense neutrino source of a
nuclear reactor. The neutrino was detected by the observation of \inverse"
beta decay reactions

 + p+ ! n + e+:(2.2)

As the equation above already implies the neutrino involved is actuallyan antineutrino. The question whether  and  are really distinct was clari edby an experiment by Davis and Harmer in the late fties. While the reaction

 + n ! p+ + e,

(2.3)

had already been observed, they found that the analogous reaction

 + n ! p+ + e,

(2.4)

did not occur although it should have the same cross section, if  and 

13were identical. To distinguish neutrinos from antineutrinos Konopinski and
Mahmoud introduced a lepton number. Electrons, muons and neutrinos wereassigned the lepton number L = +1 whereas positrons, positive muons andantineutrinos were assigned L = ,1. According to the law of lepton number
conservation L cannot change in any interaction. In addition to their lepton
number,  and  also di er in their helicity: neutrinos are \left-handed"
whereas antineutrinos are \right-handed".
However the concept of lepton numbers was modi ed in the early sixties.
Brookhaven and CERN observed the process + ! + +  followed by

 + n ! , + p(2.5)

 + n ! e, + p(2.6)

but not

The suggested solution was to assign a muon number L = +1 to , and 
and an electron number Le = +1 to e, and e , with a negative number forthe corresponding antiparticles.
The Standard Model nally assumes the existence of neutrinos of three
di erent avors. In addition to  and e, a neutrino associated with the -lepton is universally expected, although no direct observation of it has yet
been made.

14

2.2 Neutrino Oscillations
In the Standard Model all neutrinos are massless. This is mainly basedon experimental ndings. Measurements on the exact shape of the beta-decay
spectrum set limits on the electron neutrino mass M(e)  5.1 eV [12]. Only
one experiment in Moscow claimed to have measured an electron neutrinomass between 17 and 40 eV. This result is very controversial, though.
However, a zero neutrino mass is more an ad hoc statement and is not
required by any theoretical principal. In fact most extensions of the Standard Model predict massive neutrinos. Assuming neutrinos have nite massand their eigenstates are not identical with their weak eigenstates, neutrino
oscillations occur [13].
Similar to the Cabibbo-Kobayashi-Maskawa quark mixing matrix thetransformation from a neutrino avor eigenstate to a mass eigenstate is performed via a unitary matrix U :jj i =

X
2fe;; g

Uj; ji(2.7)

where jj i j 2 f1; 2; 3g denotes mass eigenstates and ji  2 fe; ;  g denotes avor eigenstates. Mass eigenstates propagate in time according tojj (t)i = e,iE t=hjj (0)i:
j

(2.8)

15
The transition amplitude from avor eigenstate  to 0 is3Xh (0)j(t)i = Uy ;j e,iE t=hUj;
0

0

j =1

j

(2.9)

and the transition probability is

P ( ! 0 ) = jh (0)j(t)ij2:0(2.10)In the case that one avor state is not coupled to the other two, the equations
can be decoupled into to a two-state problem and a stationary state. The
transformation matrix can be parametrized as:

0
1
BB
C
BB cos() , sin() CCC
CC
U = B
BB
CC
BB
@ sin() cos() CA(2.11)

if it is further assumed that CP is conserved, which allows to choose a real
unitary matrix. If a  was created at time 0 the probability to observe a e
at time t is:tP ( ! e) = sin (2) sin h (E1 , E2)!
22
2
2 (m1 , m2 ) 3
 sin (2) sin
2ph c t22

16

c2 m2 L= sin (2) sin 2
h
E
2

2

!

(2.12)q
where the Taylor expansion E = (cp)2 + (mc2)2  cp + m22pc3 is used, sincem  E.
The mixing phenomenon described above is known as vacuum oscillation. In the presence of matter this has to be modi ed as rst pointed out by
S. P. Mikheyev and A. Y. Smirnov using ideas developed by Wolfenstein [14].
Due to interactions with the medium, the energy eigenstates are no longer
identical to mass eigenstates in vacuum. This can be described by introducing an e ective mass. The e acquire an extra mass term because they are
the only neutrinos that can undergo charged-current elastic scattering fromelectrons in addition to neutral-current interactions. The e ective mass is afunction of the electron density of the medium. For simplicity a two avor
system is considered. If a e is created in a high density environment, i.e. in
the core of the sun, it primarily is in the upper energy state 2. If the two
eigenstates 1 and 2 never come too close together the adiabatic approximation ensures that the probability for a transition from state 2 to 1 is very
low as the neutrino travels to regions of lower density. In a low density environment the 2, however, corresponds to a . This avor changing process
is known as MSW e ect. Because of the relatively low densities in the earth
and the particular parameter range of interest, this is not expected to have17

a considerable e ect on atmospheric neutrinos.

2.3 Atmospheric Neutrinos
For the analysis of atmospheric neutrinos it is essential to develop reliable
models of their production mechanism. These have to provide quantitative
predictions of ux, spectra and avor composition of atmospheric neutrinos
at the detector site.
Atmospheric neutrinos are produced by cosmic rays that produce secondary particles in the atmosphere, which decay generating neutrinos [15].
The primary cosmic ray ux is relatively well known for energies below 100
GeV. Its composition is H(proton)  90:6%, He  9:0% and CNO nuclei

 0:3% at energies of  100 MeV/nucleon. For higher energies the portionof protons is even higher. The energy spectrum can be seen in Figure 2.1.
The cosmic ray ux reaching the atmosphere is in uenced by solar activity and by the earth's magnetic eld. The solar wind, which depends on
the solar activity, drives back the low energy part of the cosmic rays. The
geomagnetic eld causes a shield e ect, that prevents cosmic rays from arriving at the earth, if their energy is below a certain threshold, which depends
on the entering position on the earth.
Cosmic rays create 's and K 's via interactions with nuclei in the at-

18

10

10

3

2

10

-1

-1

-1

Flux ( m sec sr GeV )

10

4

0

-2

10

1

10

10

10

10

-1

-2

-3

-4

10

-1

0

1

2

10
10
10
10
Kinetic Energy per Nucleon (GeV)

3

Figure 2.1: Observed uxes of cosmic ray protons(upper curve), helium(middle curve) and CNOs(lower curve) as parametrized by Honda [15].
Solid lines are parameterization for solar mid., dash lines for solar min. anddotted lines for solar max.

19
mosphere. The 's account for 90% of the secondaries, thus representing thedominant source of atmospheric neutrinos. The 's decay,

+ ! + +  (BR  99:98%)
, ! , +  (2.13)and their muon secondaries also decay,

+ ! e+ + e +  , ! e, +  e + :(2.14)

Naively one would expect the following ratios by just counting the decay
neutrinos, +    2
e +  e 1(2.15)

1
 1(2.16)

andHowever, these ratios depend on the energy of the neutrinos. For highenergies ( +  )=(e +  e) is larger than 2, because the muons are highly
relativistic and many of them do not decay on their way to the detector

20

3

Honda

-1

BN
10

LK

2

2

-1

νµ + νµ

BGS-1

Flux x E ν ( m sec sr GeV )10

νe + νe

10

1

10

-2

10

-1

10

0

10

1

Neutrino Energy (GeV)

Figure 2.2: Atmospheric  - uxes multiplied by E2 for the Kamiokande site
at solar mid.. Calculations by four di erent authors are shown: Honda [15];Barr, Gaisser and Stanev (BGS)[16]; Bugaev and Naumov (BN)[17]; Lee andKoh (LK)[18]. (from [15])(mainly due to interactions), which means that no e was created. A thoroughstudy includes interactions of 's and 's with matter, a correct 3-dimensional
geometry and the fact that 's created in -decays are fully polarized.
The ux of atmospheric neutrinos at di erent positions on the surfaceof the earth has been calculated by many authors [15, 16, 17, 18] using
di erent techniques. Figure 2.2 shows the results of four calculations for the
Kamioka site. The results in the total ux in the energy range 100 MeV

21

2.5

2.5

νµ + νµ

Honda

2.5
BGS

νe + νe

Flux Ratios

2.

1.0

10

νe
νe

1.0

10

0

Neutrino Energy (GeV)

10

1

10

-2

10

-1

1.0

νµ

νµ

νµ

νµ

νµ
10

1.5

νe

νµ

νµ

-1

νe

1.5

νe

1.0

-2

νe + νe2.

νeνe

νµ + νµ

LK

2.

1.5

νe

νµ + νµνe + νeνe + νe

2.

1.5

2.5
BN

νµ + νµ100

Neutrino Energy (GeV)

10

1

10

-2

10

-1

νµ
10

0

Neutrino Energy (GeV)

10

1

10

-2

10

-1

10

0

10

Neutrino Energy (GeV)

Figure 2.3: The ux ratio of  -species calculated for Kamioka by the sameauthors as in Fig. 2.2. (from [15])
to 10 GeV vary by over 30% due to the use of di erent primary uxes anddi erent interaction models. However, most uncertainties cancel out for theratio ( +  )=(e +  e ) and the predictions disagree by only a few percent
in the energy range of interest. Figure 2.3 shows the energy dependence of( +  )=(e +  e) as predicted by several studies.

2.4 Interaction with Matter
Atmospheric neutrinos are detected through their interaction with matter. To compare the predicted atmospheric neutrino ux with the measured
event rates, the physics of neutrino interactions has to be studied in detail.
In general three di erent classes of interactions of neutrinos with water
can be distinguished: elastic scattering o electrons, quasi-elastic scatteringo nucleons and inelastic interactions with nucleons. They can further be122classi ed as charged-current (CC) or neutral-current (NC) weak interactions.
The tree level Feynman-diagrams for these processes are shown in Fig. 2.4, 2.5
and 2.6. Cross sections for elastic scattering o electrons can be calculatedusing the standard electroweak theory. The total cross section o electrons ishigher for e 's than for 's or  's because they have additional W -exchange
channels available. The inverse muon decay is only possible for very high-energies (E  11 GeV). However the neutrino-electron cross section ismuch lower than the neutrino-nucleon cross section (roughly by the mass
ratio me=mp).
In the energy range E  1 GeV the quasi-elastic neutrino-nucleon
interactions are the dominant mode. Neutral current elastic interactions,however, are practically invisible for water C erenkov detectors, as the recoil nucleon rarely has enough energy (E  1:5 GeV) to generate C erenkov
light. Charged-current quasi-elastic interactions can be described using thestandard V - A theory. The lepton momentum and energy in the nal state
can be determined by the q2 (q = p , plepton ; 4-momentum transfer) dependence of the cross section. Figure 2.7 shows the energy dependence of thecharged-current quasi-elastic cross section.
At higher energies (E > 340 MeV), resonance states heavier than theneutron or proton can be created, which decay into a nucleon and one ormore pions. This interaction is called inelastic scattering. For single pion

23

νe
νe e

e
Z0

νe e

+

νe

νe

e

e

W
νe

e

νe

e
νe
νe e

e

Z0

νe e

+

νe

e

νe

νµ
νµ e

νµ e

e

e

νµ
νµ e

e

Z0
νµ

νµ e

W

Z0
νµ

e

e

Figure 2.4: Tree level Feynman diagrams for elastic e scattering

24

p

l
νl n

W
l p
νl

n

Figure 2.5: Tree level Feynman diagrams for quasi-elastic N scattering

π
l
νl n

π

p

W

l X
νl

n

Figure 2.6: Tree level Feynman diagrams for inelastic N scattering

25

Figure 2.7: Cross section of charged-current quasi-elastic interactions o freenucleons (from [3]).
production satisfactory models have been developed [20, 21]. Cross sections
according to the model of Fogli and Nardulli are shown in Figure 2.8.
For neutrino energies above 1 GeV multiple pion producing inelastic
interactions are frequent. Their theoretical description is not easy becauseof the large number of possible nal states. However, it is expected thatthe cross-section rises linearly with energy. The mean multiplicity of charged
hadrons as determined by high-energy experiments can be parameterized as afunction of the hadronic invariant mass W by hn i = 0:09+1:83ln(W 2). The
total cross-section of charged-current interactions can be seen in Figure 2.9.
The ratio of ( : CC )=(e : CC ) is shown in Figure 2.10. As expected26

Figure 2.8: Cross section for charged-current single-pion production (from
[3]).

27

Figure 2.9: Total cross section for charged-current interactions (from [3]).
the ratio approaches unity for large energies.

E ect of the Nucleus
So far it has been assumed that the neutrinos interact with free nucleons.
The cross sections for low energy neutrino interactions with water have to
be modi ed because 89% of the nucleons are bound in oxygen nuclei. Bound
nucleons are a ected by their Fermi momentum and the energy levels of
the nucleus. This in uences the energy that the nucleon provides to theinteraction. The simplest model to account for bound nucleons is the \Fermi
gas model". It assumes a characteristic momentum distribution for each

28

Figure 2.10: Ratio of the CC total cross section between e and  (from [3]).
bound nucleon. In oxygen the average momentum is about 175 MeV.
For low energy interactions Fermi statistics have to be taken into account. As the energy states below the \Fermi sea" are already occupied,they are not available for outgoing nucleons, by the Pauli exclusion principle.
This so called \Pauli blocking" reduces the overall cross section. Figure 2.11
compares the cross sections o a free nucleon and a bound nucleon.

29

Figure 2.11: Comparison of the calculated cross section of CC quasi-elastic
interactions o a free nucleon and a bound nucleon in 16O (from [3]).

30

Chapter 3
Detector Description
3.1 Basic Principle of a Water C erenkov Detector
Super-Kamiokande is a ring imaging water C erenkov Detector. The basic
detection principle is based on the fact that charged particles with sucientvelocity radiate C erenkov light when passing through a dielectric medium[22, 12]. The threshold velocity depends on the index of refraction of themedium and is given by:

v= 1
c
n

(3.1)

The C erenkov light is emitted at a certain angle called the C erenkov angle
c given by:cosc = n1

(3.2)

31

detector
wall
Cerenkov
ring
PMT

track
θc

Cerenkovcone

Figure 3.1: C erenkov geometry
The geometry of the C erenkov cone can be seen in Figure 3.1. In water theC erenkov angle has a maximum value of 420 for highly relativistic particles( = 1) in the visible light region.
The spectrum of emitted light has a continuous 1=2 dependence. The
number of photons emitted per unit length for a particle of charge z is:d2N = 2 z2 1 , 1
2n2 ()
dxd
2

!

(3.3)

32

or,

d2N = z2 sin2
c
dEdx
h c
 370 sin2c eV ,1cm,1 (z = 1)

(3.4)
(3.5)

The spectrum however is not in nite since the index of refraction in water
approaches unity for higher frequencies, which leads to a cut-o in the spectrum. In the sensitive wavelength range of the photomultipliers (300 nm

   600 nm) a = 1 single-charged particle emits 766 sin2c ( 343 inwater) photons per cm.

3.2 The Water Tank
The Super-Kamiokande detector is situated in the Kamioka mine (thesame mine as Kamiokande) 250 km west of Tokyo. It is shielded by a minimum of 1000 meters rock with an average density of 2:7g=cm3. This determines a minimum energy of about 1.3 TeV, which muons must have at thesurface to reach the detector. It also reduces the cosmic ray muon ux atthe detector by a factor of 105.
The water tank is constructed inside a cylindrical excavation of 39 meters in diameter and 58 meters in height (including 15 meters of dome) (seeFigure 3.2. Its side walls, top and bottom are lined with 40 to 50 cm of

33

Figure 3.2: Schematic diagram of Super-Kamiokande
reinforced concrete. On this uniform structure a layer, consisting of 3 to
4.5 mm of welded stainless steel, is mounted. This provides a water- andairtight barrier. At a height of 41 meters a at roof forms the top of theactual water- lled detector vessel. The tank is lled with a total of 50,000
tons of pure water. The region above the tank is accessible and contains thehigh-voltage supply system, the data acquisition and control computers andother equipment.
The photomultiplier support system consists of a stainless steel structure, 2.5 meters from the walls, bottom and top of the cavity. It optically34

divides the tank into an inner part, 36.20 meters high and 33.80 meters indiameter (32 ktons), and an outer shell of 2 meters thickness. 11,146 50-cm
inner phototubes are mounted on the support system facing inwards. They
provide a total light coverage of 40% of the inner detector surface. 1,857
20-cm outer tubes, facing outwards from the support structure, are used as
an anti-counter to veto events that enter the detector from outside. A layerof black polyethylene sheets, which is set behind the inner phototubes, optically isolates the inner detector. All surfaces of the outer detector are covered
with a white tyvek layer of high re ectivity to increases the light collectioneciency.

A \radon-free" atmosphere is maintained by an air- ltration system anda supply of fresh, low radon air from outside the mine. The backgroundradioactivity of the water is also reduced by the water puri cation system.
In about one month the water in the entire detector is recirculated through altering system. Heavy radioactive particles and small particles are removed.
In addition to that, water from outside the mine is ltered by reverse osmosis.
To prevent bacterial growth the water is sterilized with ultra-violet light. A
water temperature of 110 C helps to suppress biological contamination. With
these combined techniques a water attenuation length of 60 meters has beenachieved.

35

Figure 3.3: The 50 cm Photomultiplier Tube

3.3 Photomultipliers
Two di erent photomutiplier (PMT) types are used for the inner andouter detector. The inner detector is equipped with 11,146 Hamamatsu
R1449 tubes, 50-cm in diameter. 1,857 20-cm Hamamatsu R1408 PMTs
are installed in the outer detector.

Inner Tubes
The inner PMTs are an improved version of the ones used in the Kamiokande
detector [23]. The new tubes (Figure 3.3) are equipped with a quasi-hemisphericalwindow with a bi-alkali (Sb-K-Cs) coating on the inside of the bulb, called

36

Figure 3.4: Quantum Eciency of a 50 cm PMT
the photocathode. When a photon hits this layer an electron can be emitted
by the photo-electric e ect. The probability to knock o an electron (thequantum eciency) is a function of the wavelength of the light, dependingon the photocathode material and the permeability of the window. As can beseen from Figure 3.4, the maximum quantum eciency is 22% at  = 390nm.
Primary photoelectrons from the cathode are accelerated by an electric eld
to a series of plates called \dynodes", which are ordered like layers of venetian blinds in the back of the PMT. When the photoelectron (pe) hits the
rst dynode-layer, it has enough energy to create  5 secondary electron.

37

These are again accelerated to the second dynode, where they create more
electrons. After 11 dynode stages the average gain, which is de ned as theratio of the anode-current to the cathode-current, is 107 at a total applied
voltage of 2000 volts. The collection eciency, which is the probability thata primary pe creates a large enough pulse at the anode, has been determined
to be about 70%.
The improvement of the new PMTs focused on the reduction of the time
jitter and the improvement of the energy resolution, the two most importantcharacteristics for event reconstruction in an imaging C erenkov detector. For
a voltage of 2000 V the transit time (time from the emission of the photoelectron to the appearance of the anode-pulse) is about 100 nsec. A time
jitter (at 1 pe light level) of  3 nsec (1 ) has been measured, which isconsiderably smaller than the value for the older model. The anode-pulse
response to a -function shaped input light has rise- and fall-times of about
10 nsec and a full width half max. of 18 nsec. Energy resolution has also been
improved greatly. The pulse height distribution shows a single-pe peak well
separated from the dark noise peak. This allows the experiment to reduce
the energy threshold to 5 MeV.
PMT performance is sensitive to external magnetic elds, so the earth's
magnetic eld is compensated by 26 coils, attached to the outer walls of thedetector. The eld is kept at a value below 100 mG, as required for the38phototubes.
After 4 months of run time, the average dark noise rate for an individual
PMT, which is mainly due to thermionic emissions of electrons from thephotocathode or the dynodes, has gone down to 3 kHz. Afterpulses, broad
pulses tens of sec after the tube-hit, are found to have amplitudes  0.4%of the primary pulse.

Outer Tubes
For the outer detector the tubes from the IMB experiment are reused.
To increase the photo-sensitive area, each outer PMT is equipped with a
60 cm  60 cm wavelength shifter plate. Photons in the wavelength rangeof 300 nm to 400 nm are absorbed by the wavelength shifter material andisotropically re-emitted with a longer wavelength. Some fraction of thesesecondary photons is internally re ection to the PMT, where they can bedetected.

3.4 Trigger System and Data Acquisition
The electronics in the back of the inner phototube divide the voltage
between the 11 dynodes and the anode as shown in Figure 3.5. The AC
PMT-signal is decoupled from the DC high voltage by a capacitor and then

39

Figure 3.5: Inner PMT circuit and signal decoupling
send to the readout electronics though a coaxial cable.

Front-end Electronic System
ATMs (Analog Timing Modules) are used as \front-end" electronics forthe inner phototubes. Each ATM handles 12 PMT channels. Its main purpose is to record charge and arrival time of the incoming PMT pulses. Eachchannel has an ampli er and a discriminator. When a PMT signal exceeds
the threshold value ( 1/5 pe), the discriminator sends a 400 nsec wide gate
signal to the charge integrator, which integrates a 200 nsec delayed copyof the PMT pulse. The time is measured by integrating a constant current,
which starts with the above signal and lasts until a global trigger arrives. Another output of the discriminator is a 200 nsec wide rectangular signal, which
is summed for all 12 channels giving a HITSUM signal. This is used for the40

global trigger. A diagram of the analog input circuit is shown in Figure 3.6. If
a global trigger signal arrives before 1200 nsec after the discriminator signal,
time and charge information, which are stored in capacitors, are converted to
12-bit digital data and written into a 1Kword FIFO memory together withan event number. It takes about 5 sec to complete the digitizing. To avoid
deadtimes due to the readout time, two identical sets of input circuits areused. Channel B handles any signal if Channel A did not complete digitizing
the previous one. Thus two rapidly successive events, e.g. muon and decay
electron ( = 2:2sec), can be recorded.

Online Data Acquisition
The data acquisition system collects the time and charge data from theATM modules. A schematic diagram can be seen in Figure 3.7. Each of thefour electronic huts contains two Sun SPARClassic (S4/CL) and 240 ATM
modules. A Super Memory Partner (SMP) module with 2 Mbytes internal
memory collects the data output of 20 ATM modules. One S4/CL reads out
the data of 6 SMP modules. The data is then transfered to the central hut.
There, a Sun SPARCstation 10 (S4/10) \builds" the event by concatenating
all signals belonging to one global trigger. Finally the data is sent to theoine site.

41

200 nsec delay
Ch A Gate (400 ns)

200 nsec delay
Ch B Gate (400 ns)

PMT
Input

Current
Splitterstop

Ch A TAC
Start

Discriminator

GlobalTrigger
Input

Output to
HITSUM
circuit

ATM
Logic
PAL

.

stop

Ch B TAC
Start

Current
Integrator"A"

Current
Integrator"B".

Time-toAnalog
Converter"A".

Time-toAnalog
Converter"B".

.
Input fromotherchannels..

.
.

12-bitADC

Output to FIFO
memoryFigure 3.6: The analog input circuit of the ATM.

42

Electronics Hut
PMT

x 12

ATM

x 20

SMP

x 12

x2
S4/CL

x4

Central Hut

S4/10

OfflineFigure 3.7: Schematic diagram of the Data Acquisition system.

Trigger
For the inner detector trigger, the HITSUM outputs of all 240 ATMs ineach electronic hut are put in an analog sum. This signal is then sent to the
TRG module in the central hut. The quasi-analog sum of the signals fromthe 4 electronic huts is compared to a trigger threshold value. Trigger signals
and event counters are then distributed to 48 GONG (GO/NoGo) modules,
which distribute those signals to the ATM modules. Currently the trigger
threshold is set to an equivalent of 29 tube-hits, which corresponds to about 5 6 MeV of visible energy. This means that a global trigger is produced if 29
tubes are hit within a 200 nsec time span. Having a background radioactivity
from Radon decay (222Rn ! 214Bi ! (Emax = 3:26MeV )) of 0.03  0.04
Bq/m3, the trigger rate is 10  12 Hz.

43

Outer Detector
Signals from outer 20-cm PMTs are decoupled in a special HV decoupling card, which is connected to a QTC (Charge to Time Converter) in theelectronic huts. One QTC handles the input of 48 PMTs. For each PMT
there is a logical output, with a short pulse, marking the time, followed bya longer variable width pulse, encoding the charge. The width of the second
pulse is (after subtracting a pedestal) proportional to the PMT charge, integrated over the 200 nsec gate period. The PMT threshold corresponds to 1/4
photo electrons. In addition, the module provides an analog HITSUM output, whose amplitude is proportional to the number of PMTs over threshold
during a coincidence window of 200 nsec. Also, a logical output is provided
when the HITSUM for this module is above a separate adjustable threshold.
80 QTC output channels are fed into a TDC (Time to Digital Converter),where the time and charge information is digitized. If there is a global trigger,
this data is bu ered on an on-board computer. Finally this is read out by
the computer in the central hut.
The analog HITSUMs from the QTCs are used for an outer detector
trigger, to detect events, that do not enter the inner detector. The Trigger threshold is set to an equivalent of 16 coincident PMTs (in a 200 nsec
window).

44

Chapter 4
Analysis
4.1 Monte Carlo
Monte Carlo is the standard technique for physics simulations using random numbers. Like most physics experiments nowadays, Super-Kamiokande
developed simulation programs of the detector's response to high-energy particles. These are useful for several reasons.

 Some calibration techniques are based on comparisons between real andsimulated data.

 Development and testing of analysis software usually requires the useof simulated events.

 In order to compare experimental results to theoretical predictions, theeciency of the detector for di erent types of events is determined45

using Monte Carlo methods.
The Monte Carlo programs currently used by the US collaboration simulate events in reasonably good agreement with data, although some details
and parameters still need to be adjusted. A complete simulation involves
several stages:

 Generation of the initial particles and their physical state (e.g. electron
and recoil proton from a  interaction).

 Propagation of particles in the nucleus (if appropriate).
 Propagation through the detector volume including interactions withwater and other detector material.

 Generation and propagation of C erenkov light from charged particles.
 Detection of C erenkov photons and electronics response.
For many purposes the initial-state particles are selected according tosimple positional, directional or energetic constraints using a program called\kinem". For instance, this can generate a set of monoenergetic electrons
uniformly distributed through the detector. For proton decay and neutrino
events the rst two items require more sophisticated simulations. For thispurpose a program developed by the IMB collaboration is used, in this work
called \Kinematics" [7].

46

The data of initial states is then processed by the detector simulating
program \gtrack". The output are les with simulated data in the sameformat as real data.

Generation of Initial-state Particles with Kinematics
Flux and spectrum of neutrinos at the detector site are important inputs
to the simulation of neutrino induced events. \Kinematics" uses calculations
for the IMB detector location by Lee and Koh [18]. Due to the e ect of thegeomagnetic eld the total ux for the Kamioka mine is considerably di erent. Therefore, \Kinematics" can not be used for any eciency calculations
or to compare measured and predicted event rates. However, the shape ofthe spectrum as well as the  to e ratio are similar for both sites as can beseen from Figure 4.1. For neutrino interactions only the dominant scatteringwith nucleons is used. Elastic, quasi-elastic as well as single and multiple
pion production are simulated using cross sections described in section 2.4.
Hadrons created inside oxygen nuclei are tracked through the nucleus in stepsof 0.1 fm. They may be scattered or absorbed producing secondary outgoingparticles. A Fermi gas model is used and Pauli-blocked states are eliminated.

47

Figure 4.1: Neutrino ux averaged over 4 solid angle at a) Cleveland andb) Kamioka for solar mid.; upper curve: , lower curve: eTracking and Light Simulation
The core of the simulation step that tracks particles through the detector
is \GEANT". This program has been developed at CERN and continuously
been improved since 1974. For hadronic interactions, several software packages are available, where GHEISHA is the one used for the Monte Carloevents in this work.
A light-tracking program has been developed, based on programs written by the IMB collaboration. For each tracking step in GEANT, C erenkov
photons are created according to the angular and energetic distribution discussed in Section 3.1. Photons are then tracked through the tank including
absorption and scattering in the water, re ection and absorption from walls
and phototubes, as well as PMT response. Interactions are performed one

48

photon at a time until it is absorbed or observed. A path length is calculated
for every relevant process of the photon propagation. The physical processthat corresponds to the shortest of these lengths is then simulated.
Once a photon is absorbed by a PMT it may emit a photoelectron. The
simulation of the subsequent electronics response is mainly bookkeeping. An
event is created if the number of hits in a 200 nsec time window exceeds thetrigger threshold.
Many parameters involved in the above processes have already beenmeasured to some precision. Nevertheless, the Monte Carlo has not yet been
tuned by comparison with data.

4.2 Fitting
An essential part of the analysis of the C erenkov ring pattern producedby fast charged particles in the detector is the reconstruction of the event.
Using the timing and geometrical information provided by the PMTs, theoriginal track of the particle has to be determined. Di erent programs havebeen developed, mostly concentrating on tting speci c types of events. Fromthe point of view of physics and analysis the following event classi cation will
be used:49

contained events: The C erenkov light emitting particle is created insidethe ducial volume (e.g. by a  interaction) and slows down belowC erenkov threshold before leaving the inner detector.

partially contained events: The particle is created in the ducial volume,
like in a contained event, but exits the inner detector.

through going events: A highly energetic particle (almost exclusively acosmic ray muon) enters and exits the detector.

stopping events: A particle enters the detector and stops inside the innerdetector.
The ducial volume, in this work, is de ned as the space 2 meters inside theinner detector walls. An additional classi cation of events is based on thenumber of visible C erenkov rings in an event. For the purpose of this work
mainly single-ring and multiple-ring contained events are distinguished.
Fitters for through going and stopping events are important tools forevent selection and analysis of low energy events (mainly solar neutrinos).The
programs described below, however, are mainly developed to reconstruct contained events.

50

short
track

expandingspherical wavefront(point source
approximation)

expanding
Cerenkov wavefront

Figure 4.2: Point source timing approximation of a short, C erenkov lightemitting track

Point Fitters
Point tters are usually the rst step in any tting procedure because
they are fast and give a reliable approximation of the event vertex. They relyon the fact that the timing of a short C erenkov radiating track is similar to
the timing of a point source. The position of the best t is, however, rather
in the middle of the track, which is usually not the vertex of the event. Thiscan be seen in Figure 4.2.
Given a trial point-source at position X~ p and time Tp, the residual ri fora PMT at position ~xi that was hit at time ti is given by:~ri = Tp , ti + jXcp , ~xij
water

(4.1)

This is the di erence between the time the PMT is hit, assuming a point

51

source, and the actually measured time value. The vertex nding programminimizes the 2 of the residuals:

2 =X  ri 2
tubes i i(4.2)

 is mainly determined by the time jitter of the phototube, which decreases
with the amount of collected charge.
The program \Anistrack" minimizes a quantity similar to 2 with slightly
di erent normalization 1. The minimum is found by repeatedly stepping acertain distance in direction of the gradient, until an optimal value is found.
Using only tubes in the residual peak of the previous vertex t, this whole
minimizing procedure is repeated with smaller step-sizes until a step-size of
10 cm is reached.
Once a vertex position is found, a good approximation for the directionof a single track is given by the anisotropy2 vector of the event:P (~x ,X~ ) q
i j~x ,X~ j i
A~ = P
q
i

p

i

p

i i

(4.3)

where ~xi and X~ p are de ned as above and qi is the charge of tube i. The
The actual minimizing function is called pands.
Anisotropy can also be used to determine the net momentum of an event. In
particular it is a measure of how isotopic the event is.
12

52
direction of A~ is the mean direction of the emitted C erenkov light. Becauseof the geometry of C erenkov light this corresponds to the direction of theparticle momentum, in the case of a single track event.

Track Fitters
Track tters are designed to determine the position of the vertex andthe direction of the track as accurately as possible, taking into account thegeometry of the track and the C erenkov cone. A track tting program called
YASTEF, developed by the IMB collaboration, has slightly been modi ed
to be used for the Super-Kamiokande detector. The version used for thiswork, however, is only preliminary. A detailed description of YASTEF canbe found elsewhere [24] and is only summarized here.
The t is found in three phases. In the rst phase, a starting point anddirection is chosen. Isolated PMT hits are vetoed to reject scattered light.
Then the starting values are obtained using a point- tter.
The starting point is usually near the track axis but not necessarilyclose to the actual vertex. Therefore, in the second phase the position ismainly adjusted parallel to the track to get a value that is close to the event
vertex. In a three step cycle the direction, the position along the track andthe position perpendicular to the track are adjusted. The direction is foundby maximizing the charge inside a cone. An angular charge distribution is

53histogramed about the trial direction. The sharpest point of that histogramis identi ed as the edge of the C erenkov ring. Then the vertex position isadjusted along the track to form a cone with the correct C erenkov angle. The
vertex is then moved perpendicular to the track to minimize the residual.
The nal phase improves the t using a similar procedure as the above.
In this case, however, the direction and the position perpendicular to thetrack are adjusted by maximizing the \sharpness" of the ring, which is de ned
as the maximum derivative of the angular charge distribution mentioned
above.
The performance of YASTEF has been analyzed with samples of monoenergetic Monte Carlo events. In Figure 4.3 the di erence between thetrue and the tted position parallel and perpendicular to the track are histogramed. The tted position along the track is systematically shifted backwards for electrons and forwards for muons. This is due to the di erence inangular charge distribution and can only be corrected knowing the identityof the particle.

4.3 Particle Identi cation
As discussed in Section 2.3, the best suited quantity to test our understanding of production and propagation of neutrinos, including new neutrino

54

Figure 4.3: The position resolution of YASTEF parallel to the track (leftcolumn) and perpendicular to the track (right column). Dotted lines are
Monte Carlo electrons, solid lines are MC muons. The energies from top tobottom row are: electrons: 100 MeV, 300 MeV, 600 MeV, 1000 MeV, 1800
MeV; muons: 300 MeV, 500 MeV, 800 MeV, 1200 MeV, 2000 MeV.

55
physics, is the ratio ( +  )=(e +  e). It is therefore necessary to determine
the avor of the observed neutrinos. In charged current interactions a lepton
with the avor of the original neutrino is produced. For quasi-elastic interactions it is therefore possible to infer the presence of a e by observing thecreation of an electron, and a  by identifying a produced muon (here andin the following anti particles are not mentioned explicitly). The situation
is more complicated for inelastic scattering. If the additional pions or theirdecay products (muons and electrons) are above C erenkov threshold, they
may lead to misinterpretations.
The following describes a method developed to distinguish electron-likeC erenkov rings form muon-like ones. Electron-like refers to massless / showering particles (electrons and photons) and muon-like events to massive /non-showering particles (muon, pions etc.). The C erenkov PMT hit patterns
for muon-type events and electron-type events are qualitatively di erent. A
muon-type event creates a ring pattern with a sharp outer edge whereas anelectron creates a ring with a more di use edge. The edges correspond to
the intersection of the 420 C erenkov cone with the detector. As highly energetic electrons develop electromagnetic showers by bremsstrahlung and pair
production, the C erenkov light actually comes from many short tracks ofelectrons in the shower. As they slightly spread in direction, the ring patternis smeared out. Figures 4.4 and 4.5 show hit-patterns of a \typical" electron

56

Figure 4.4: Scan of an electron in cylindrical perspective. This perspective
shows what can be seen, if the observer is at the vertex point and is facing
in direction of the motion of the particle. The grey scale denotes the chargeof the PMTs.
and a \typical" muon respectively.

Charge Track Distribution
Particle identi cation using the hit pattern is in principle a 2-dim pattern recognition problem. A simple mapping, however, can reduce this to a
1-dim problem without losing much information, since the problem is symmetric with respect to rotation around the axis given by the motion of theparticle. First, the vertex and direction of the particle are determined. Theyde ne a straight line called the trajectory. For each hit PMT, the point
where the C erenkov photon was emitted along this trajectory is calculated.
This assumes that all light came from the trajectory and was emitted at a

57

Figure 4.5: Scan of a muon in cylindrical perspective.
420 angle. The charge of the PMT (proportional to the amount of light that
hit the tube) is then histogramed as a function of the position on the trajectory (see Figure 4.6). This histogram is called charge-track-distribution.
Figures 4.7 and 4.8 show the results for the above electron and the muon.
It can be seen that in the case of the muon the rising edge of the peak ismuch steeper. This corresponds to the sharp edge of the muon ring. The
particle identi cation parameter used in this work quanti es the steepness ofthe peak in the charge-track-distribution.

Particle Identi cation with RISPID
In the case of an electron, some fraction of the direct C erenkov light isemitted outside the 420 C erenkov cone. The higher the fraction of photons

58

PMT plane

Cerenkov
cone
track

trajectory

mapping

charge-track-distribution

Figure 4.6: Mapping for charge-track-distribution.

59

Figure 4.7: Charge-track-distribution for a \typical" electron.

60

Figure 4.8: Charge-track-distribution for a \typical" muon.

61

measured outside the cone, the more likely the particle is an electron. To
calculate this fraction, the vertex position or a similar well de ned value has
to be known. The vertex position obtained from YASTEF is not sucientbecause its position along the track is systematically di erent for electrons
and muons. The YASTEF t can, however, be used to histogram a chargetrack-distribution. The steepest point in the charge-track-distribution, X0,
can then be used as the event vertex.
The bins of the histogram have to be small enough (2 cm is chosen) toallow suciently precise measurement of X0. This implies that the histogram
is not smooth. Particularly, the spacing of the PMTs imposes considerable
uctuations. The numeric derivative f 0(xi) at point xi is calculated according
to:

n
X
0
f (xi) = f (xi+j ) , f (xi,j )
j =1

(4.4)

where xi+j , xi = xi , xi,j is called the width of the mask. A wide mask isinsensitive to small scale uctuations but smears out the details. Therefore,
derivatives with two di erent masks are used (120 cm and 250 cm).
The above de nition of X0 as the steepest point of the peak has to bemodi ed to handle hard scattered muons correctly. Figure 4.9 and 4.10 show
the hit pattern and the charge-track-distribution of a hard scattered muon.
The maximum derivative might correspond to the inner ring produced by

62

Figure 4.9: Scan of a hard scattered muon in cylindrical perspective.

Figure 4.10: Charge-track-distribution of the above hard scattered muon.

63

the muon after hard scattering. In this case, the outer ring produced before
hard scattering is falsely interpreted as smeared out light coming from anelectron. Therefore, the outer ring should always be chosen.
Many di erent procedures have been tested and the following 3 step
method has been chosen as the most e ective one. Figure 4.11 shows plotsof the relevant derivatives for the above \typical" electron.
1. An allowed range for X0 is determined using the 2nd derivative withwide mask. The range [x1,x2] is de ned by fwide(x2) = absolute min00

imum and fwide (x1) = maximum with x1 < x2. This is a protection
00

against distant humps. In the following two steps only values withx 2 [x1; x2] are considered.
max, is deter2. The maximum of the 1st derivative with ne mask, ffine
0mined. Then the position x3 of the rst peak (meaning: x3 as small
max is found. This is used because inas possible) with ffine (x3) > 21 ffine00

the case of a hard scattered muon the global maximum might belong
to an inner ring.
3. Finally the zero point ffine(X0 ) = 0, crossing the x-axis from + to 00

and lying closest to x3 is determined. This adjustment is done because
the zero point of the 2nd derivative can be determined more accurately
than the corresponding maximum of the rst derivative.

64

Figure 4.11: The relevant derivatives of the charge-track-distribution of anelectron. The values determined by Rispid are shown65
Once X0 is determined, the ratio of the charge integrated 5 meters before
and 5 meters after X0 is calculated. This ratio is called \Rispid" (RISing edge
Particle IDenti cation). If the distance d between X0 and the intersection of
the trajectory with the detector is shorter than 2 meters, Rispid returns anerror. If d is between 2 meters and 5 meters, the charge on both sides of X0
is only integrated over the range given by d.

R X0
Rispid  R XX00,+ charge
chargeX0

8>< 5m if d  5m
=>
: d if 5m > d  2m

(4.5)

The Rispid value for a sample of 300 MeV MC electrons and 500 MeV
MC muons is shown in Figure 4.12. The vertex point and direction were
determined using YASTEF. In this sample 91:1% of the muons have a Rispid
value smaller than 0.22 and 92.4% of the electrons have a value greater than
0.22. For the samples in Figure 4.12 a ducial cut is applied which requires
the vertex to be at least 2 meters inside the inner walls (this requirement
is more strict than the \2 m along the track" cut mentioned above). Thiscut is motivated by Figure 4.13 which shows the distribution of Rispid as afunction of the distance to the wall of the inner detector.

66

Figure 4.12: Rispid value for 300 MeV MC electrons and 500 MeV MC
muons. The di erence in energy for electrons and muons is chosen so thatthe events in both samples have similar charge (radiated C erenkov light).

67

Figure 4.13: Rispid as function of the distance to the wall of the inner detector. Shaded boxes: 1 GeV electrons; open boxes: 1.2 GeV muons. The
separation is bad for distances smaller than 200 cm.

68

Rispid-Grid
The "raw" Rispid value in many cases is not very useful. There are two
reasons for that. First, the tted vertex might not be very accurate. However,even with an exact (e.g. Monte Carlo) t the charge-track-distribution of amuon might look like that of an electron, if the muon had a hard-scatter.
The shape of the charge-track-distribution is very sensitive to the directionof the track. Figure 4.14 shows the dependence of Rispid on the direction of
the t.
An electron, even using a bad direction, never looks like a muon. Therefore a search for the direction with the most muon-like Rispid value gives
much better results than the raw Rispid function. The program \Rispidgrid" calculates Rispid for many directions in a small region around thetted direction, similar to Figure 4.14. It covers a cone of half opening anglecos = 0.075 and returns the smallest Rispid value.
In Figure 4.15 the Rispid-grid distribution is shown for the same samples
as in Figure 4.12. 97.7% of the electrons have a Rispid value greater than 1.3
and 95.5% of the muons have a value smaller than 1.3. Figure 4.16 displays
the Rispid and Rispid-grid distributions for simulated monoenergetic muonand electron samples at 5 di erent energies. The energy of the muons ischosen to be 200 MeV higher than the energy of the corresponding electrons
to obtain pairs of samples with similar \visible energy". The visible energy

69

Figure 4.14: Rispid of a hard scattered muon as a function of direction. Using
the same vertex position, Rispid is calculated for di erent directions aroundthe original tted direction. X and Y denote the cos with respect to theoriginal direction.

70

Figure 4.15: Rispid-grid value for 300 MeV MC electrons and 500 MeV MC
muons.

71

Figure 4.16: Rispid and Rispid-grid for monoenergetic MC muons and electrons. Dotted lines are electrons, solid lines are muons. The energies from
top to bottom row are: electrons: 100 MeV, 300 MeV, 600 MeV, 1000 MeV,
1800 MeV; muons: 300 MeV, 500 MeV, 800 MeV, 1200 MeV, 2000 MeV.

72

Visible Energy Rispid-grid fraction of correctly identi ed
in MeVcut value
electrons
muons
100
300
600
1000
1800

0.1
0.13
0.17
0.18
0.2

(93.72:2)%(97.71:3)%(99.90:9)%(99.10:9)%(1000:9)%(91.12:6)%(95.52:0)%(94.62:0)%(96.11:9)%(97.61:7)%

Table 4.1: Rispid-grid identi cation probability for various energies.
is proportional to the emitted C erenkov light and for electrons identical tothe physical energy.
For each visible energy range a cut value is determined. The fraction ofcorrectly identi ed muons and electrons are shown in Table 4.1. The errors
quoted in this table are statistical errors from a binomial distribution.
Most muons with very large Rispid-values (> 0.2) have a totally wrong
YASTEF ts as veri ed by scanning. The identi cation eciency for muons
can therefore be improved by hand scanning the tted vertex point anddirection.

Adpid
The energy dependence of Rispid-grid is shown in Figure 4.17. It can be

73

Figure 4.17: The Rispid-grid value of MC samples with di erent energies
are plotted as a function of collected charge. Shaded boxes: electrons; open
boxes: muons

74
seen that the separation value between muons and electrons, Rs , increases
with energy. It is desirable to nd a parameter that allows an energy independent particle identi cation. This is essential when Rispid-grid is histogramed
for non monoenergetic event samples. An ADjusted risPID-grid value is dened by:

Rispid grid , Rs (Q)Adpid  Rispid
grid + R (Q)
s

(4.6)

This function is chosen because it maps muon-like values (Rispid-grid 2[0,RS (Q)]) onto [-1,0] and electron-like values (Rispid-grid 2 [RS (Q),1]) onto
[0,1]. To determine RS (Q) as a function of charge, RS is rst determined asa function of visible energy using the 5 pairs of monoenergetic Monte Carlosamples shown in Figure 4.16. RS is chosen as the cuts in Table 4.1. Visibleenergy then has to be converted into units of charge. In this work the charge
is given in units that convert the original charge unit (pC) into the equivalent
number of photoelectrons (pe). Figure 4.18 shows the charge distribution for
the above samples. This plot allows a charge to energy mapping by determining the mean charge-value for each energy. The RS value for the 5 sample
pairs are nally plotted as a function of charge and tted by straight lines(Figure 4.19). As the resulting function has been determined using Monte
Carlo samples, it might need to be modi ed once an exact energy calibrationof the detector has been achieved.

75

Figure 4.18: The distribution of collected charge for simulated monoenergetic
electrons and muons

76

Figure 4.19: The value of Rispid-grid that separates electrons from muons,Rs as a function of collected charge, Q.
Figure 4.20 shows the Adpid value for the samples from Figure 4.17.
As expected, muons and electrons are separated by an Adpid value of zero,
independent of their energy.

4.4 Event Selection
Before atmospheric neutrino events can be analyzed with the tools described in the previous sections, a sample of candidate events has to be
selected out of the ood of events recorded by Super-Kamiokande. The expected 7 events/day must be ltered out of a data stream with an event rateof about 10 Hz. The eciency to save atmospheric neutrino events should

77

Figure 4.20: The Adpid values of the MC samples from Fig 4.17 are plotted asa function of collected charge. Shaded boxes: electrons; open boxes: muons

78

be close to 100%, while the data size reduction is maximized.
For the purpose of high energy analysis (atmospheric neutrinos and proton decay as opposed to solar and supernova neutrinos) most events can berejected by a simple cut on the total light collected. This removes events originating from radon -decay, nuclear spallations caused by cosmic ray muons,
low energy  -interactions and most kinds of electronic noise.
Entering events like through going and stopping cosmic ray muons are
identi ed by activity in the outer detector. However, to avoid rejection ofpartially contained events (e.g. muons coming from  interactions in the
inner detector), the outer detector activity has to be con rmed by an innerdetector t. Upward going muons are interesting because they originate from interactions in the rocks under the detector.
One type of noise events, so called ashers, is particularly hard to identify. These events originate from defective PMTs that emit light ashes. The
timing and geometrical shape of these events can be very similar to \physics"
events and some of them can only be removed by hand scanning the event.
The nal stage of the US ltering process has not yet been completed.
However, a preliminary event selection process has been developed to test
tting and particle identi cation programs. The following cuts have beenmade:

 The total charge in the inner detector is required to be above 1600 pC.

79This corresponds to a visible energy between 110 MeV and 150 MeV
and removes most noise and low energy events.

 The total number of PMT hit in the outer detector must be less than300. This and the following cut reject entering and exiting events.

 The number of hit outer detector tubes in any 500 nsec window isrequired to be less the 20.

 The charge of any individual inner PMT is required to be below 400
pC.

 Not more than 5 PMTs in the inner detector can have more than 300
pC.

 No inner PMT is allowed to have more charge than 1/10 of the total
inner detector charge. The last three cuts mainly reject ashers andtracks with a very localized exist or entry spot.
In the nal step, contained events are selected by hand scanning. The
events are displayed showing a projection of the PMT plane with color indicating charge or timing information. Trained on Monte Carlo events aphysicist rejects remaining noise events and events that originate close to the
wall.

80

4.5 Comparison with Data
The particle ID parameter Adpid, described in section 4.3 has beendeveloped using Monte Carlo events of electrons and muons with well known
energy and momentum. The crucial test for Adpid is its performance on realdata.
A sample of 102 single ring contained events has been selected using theltering cuts described in Section 4.4. Multi-ring events and events with a\bad" YASTEF t were rejected by hand scanning. Finally a ducial cut
2 m inside the inner detector has been applied.
The Adpid value calculated for this sample is shown in Figure 4.21. Twoclearly separated peaks can be seen. The peak for negative Adpid values canbe identi ed as muons and the one for positive values as electrons.
Atmospheric neutrino events have been simulated using the Monte Carlodescribed in Section 4.1. The same selection criteria as for the data sample
above have been applied to this sample. The Adpid values for the remaining
128 contained single ring MC events are shown in Figure 4.22.
The shape of the histograms for data and Monte Carlo events are similar.
The peaks for data, however, appear to be slightly shifted to negative values.
A cut at -0.05 instead of 0.0 seems to be appropriate. A likely reason forthis di erence is that no energy calibration has been available to tune the81

Figure 4.21: Adpid for single ring contained data events

82

Figure 4.22: Adpid for Monte Carlo single ring contained events

83

Monte Carlo. The conversion of visible energy to total charge discussed in
Section 4.3 probably needs to be corrected.
Muons can also be identi ed if their decay electron is observed. Thiscan be used to check the performance of Adpid. Out of the above MC anddata samples those events are selected that are followed by a decay electron(de ned as any event with more than 100 pe total charge in a 1 - 10 s period
after the primary contained event).
Figures 4.23 and 4.24 show that most events of these samples have Adpid
values corresponding to the muon peak seen in the previous Figures. However, some events are identi ed as electrons ((9:6  4:1)% for MC; (19  7:7)%
for data (statistical error only)). Hand scanning of these events shows thatmost of them actually look like \typical" electrons. Indeed, one expects tond some contained electron events that are followed by a decay electron
event. In inelastic interactions pions below C erenkov threshold can be created in addition to an electron. These pions decay into muons whose decay
electrons can be detected.

4.6 Conclusion
An algorithm for particle identi cation of atmospheric neutrinos with theSuper-Kamiokande detector has been developed. The eciency to correctly

84

Figure 4.23: Adpid for Monte Carlo single ring contained events that are
followed by a decay electron

85

Figure 4.24: Adpid for single ring contained data events that are followed bya decay electron

86
identify Monte Carlo particles with 100 MeV visible energy is (93:7  2:2)%
for electrons and (91:1  2:6)% for muons (the uncertainty represents only
a statistical error). The identi cation eciency increases with the energy ofthe particle ((99:1  0:9)% for electrons and (96:1  1:9)% for muons at 1 GeV
visible energy). A preliminary study on a data sample of -decay candidates
shows that the misidenti cation probability is smaller than 20%.
The work presented in this thesis is preliminary in many ways. The
Monte Carlo simulation program used to develop the particle identi cation
algorithm Adpid has not yet been completely tuned and compared to data.
Particularly, the particle ID program is sensitive to correct energy calibrationand light scattering parameters. A more reliable tter than the one used inthis work is being developed and will most likely improve the performanceof Adpid.

87

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