Contents
1 Introduction

12 Physics of n − n̄ Oscillation
4
2.1 Beyond the Standard Model : Grand Unification Theory . . .
4
2.1.1 SU(5) . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2.1.2 SO(10) . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Prediction for n−n̄ Oscillation in L-R Symmetric Gauge Theory 7
2.3 Phenomenology of Neutron Oscillations . . . . . . . . . . . .
8
2.3.1 Free Neutron Oscillations . . . . . . . . . . . . . . . .
92.3.2 Oscillation of Neutrons in an External Field . . . . . . 10
3 Super-Kamiokande
11
3.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.1 Water Tank . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.2 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . 13
3.2.3 PMT Support Structure and Others . . . . . . . . . . 16
3.2.4 Water Purification . . . . . . . . . . . . . . . . . . . . 18
3.2.5 Electronics and Data Acquisition System . . . . . . . 18
3.3 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 Water Transparency Measurement . . . . . . . . . . . 22
3.3.2 Relative Gain Calibration . . . . . . . . . . . . . . . . 26
3.3.3 Relative Timing Calibration . . . . . . . . . . . . . . 27
3.3.4 Other Calibrations . . . . . . . . . . . . . . . . . . . . 27
4 Simulation29
4.1 n − n̄ Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.1 Annihilation and Pionization . . . . . . . . . . . . . . 31
4.1.2 Pion Propagation . . . . . . . . . . . . . . . . . . . . . 31
4.1.3 Fragmentation . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Atmospheric Neutrino . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.2 Neutrino Interactions . . . . . . . . . . . . . . . . . . 38
4.3 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . 42
5 Data Reduction and Reconstruction: Fully-Contained Events 45
5.1 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1.1 1st and 2nd Reduction . . . . . . . . . . . . . . . . . . 46
5.1.2 Third Reduction . . . . . . . . . . . . . . . . . . . . . 46i

5.2

5.1.3 Fourth Reduction . . . . . . . . . . . . . . . . . . . . .
5.1.4 Fifth Reduction . . . . . . . . . . . . . . . . . . . . . .
Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Vertex Fitting . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Ring Counting . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Particle Identification . . . . . . . . . . . . . . . . . .
5.2.4 Precise Vertex Fitting and Momentum Determination

47
47
47
48
48
49
51

6 Search for n − n̄ Oscillation
52
6.1 Event Selection Criteria . . . . . . . . . . . . . . . . . . . . . 52
6.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.3.1 Simple Limit Calculation . . . . . . . . . . . . . . . . 57
6.3.2 Limit for Free Neutrons . . . . . . . . . . . . . . . . . 59
6.4 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.1 Uncertainties in Efficiency and Exposure . . . . . . . . 60
6.4.2 Uncertainties in Background . . . . . . . . . . . . . . 63
6.5 Final Limit Calculation . . . . . . . . . . . . . . . . . . . . . 66
6.5.1 Description of Method . . . . . . . . . . . . . . . . . . 66
6.5.2 Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7 Conclusion

68

ii

List of Figures
1.1

2.1

2.2

Current limits of n − n̄ oscillation time. The horizontal axis
relates limit for free neutron oscillation time measured in reactor experiment and vertical axis for bound neutron oscillation
time in nucleon decay experiments. The bound neutron oscillation time is proportional to the free neutron oscillation timesquared with the constant being theoretically determined, nuclear suppression factor. . . . . . . . . . . . . . . . . . . . . .

3Running coupling constants g, g’ and gs of the electro-weakand strong interactions appear to extrapolate to a single value
at q ∼ 1015 GeV. . . . . . . . . . . . . . . . . . . . . . . . . .
Six quark diagram of n − n̄ oscillation. . . . . . . . . . . . . .

5
8

3.1
3.2
3.3
3.4
3.5

Cherenkov radiation. . . . . . . . . . . . . . . . . . . . . . . .
Neutrino event display in the Super-Kamiokande. . . . . . . .
Schematic view of Super-Kamiokande. . . . . . . . . . . . . .
Schematic view of a 50 cm PMT. . . . . . . . . . . . . . . . .
Quantum efficiency of the photocathode as a function of wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Schematic view of PMT support structure. . . . . . . . . . .
3.7 Schematic view of water purification system. . . . . . . . . .
3.8 A block diagram of ATM board used for inner detector dataacquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 The data acquisition system for the inner detector. . . . . . .
3.10 Outer detector DAQ block diagram and data flow. . . . . . .
3.11 Relative photo-sensitivity. (a) Measurement result, (b) Definition of the incident angle. . . . . . . . . . . . . . . . . . . .
3.12 Effective charge observed as a function of the path length. . .
3.13 Time variation of the water attenuation length measured bythrough-going. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Laser system for water scattering and absorption parametermeasurement and its typical events display. . . . . . . . . . .
3.15 The upper plot is the photon arrival time distribution of the
top PMTs. Dots is data and line is Monte Calro. The lower
plot is the ratio, (MC-DATA)×100/DATA. . . . . . . . . . .
3.16 Time variation measured light attenuation length since November 1999, using the laser system (triangles) and cosmic raymuons (crosses). . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 The relative gain measurement system. . . . . . . . . . . . . .
3.18 The timing calibration system. . . . . . . . . . . . . . . . . .
iii

12
13
14
15
16
17
19
20
20
21
22
23
23
24

25

25
26
28

3.19 A typical plot of timing vs. pulse height. This plot is referred
as ’TQ-map’. . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

4.1

Relative position of annihilation in our simulation, labeled asPartnuc. Consistency is checked with Eftrace used in nucleon
decay study in Super-K and simulation based on peripheral
distribution predicted by Dover is identical to others. . . . . . 32
4.2 Comparison of interpolated data for pion-16 O cross sections
with the predictions of the IMB pion-nucleon interaction modelobtained using deuteron scaling. . . . . . . . . . . . . . . . . 33
4.3 The absorption probability for pions within 3.5 fermi of thecenter of the nucleus. Partnuc, the IMB pion interaction program, is based on πd cross section and Eftrace, the SuperK pion interaction program, is based on π 16 O. Our simulation adopts ”Scaled O16” which Partnuc was developed withscaled absorption probability. . . . . . . . . . . . . . . . . . . 33
4.4 (a) The direction averaged atmospheric neutrino energy spectrum for νµ + ν̄µ calculated by several authors are show bysolid line[44], dashed line[43] and dotted line[45]. (b) The
ratio of the calculated neutrino flux. . . . . . . . . . . . . . . 35
4.5 The flux ratio of νµ + ν¯µ to νe + ν¯e . . . . . . . . . . . . . . . 35
4.6 The flux ratio of νµ to ν¯µ and νe to ν¯e . . . . . . . . . . . . . . 36
4.7 The flux of atmospheric neutrinos v. zenith angle. . . . . . . 37
4.8 The flux of upward-going atmospheric neutrinos vs. zenith
angle for higher energy region. . . . . . . . . . . . . . . . . . 38
4.9 Charged current total cross section divided by Eν for (a) neutrino and (b) anti-neutrino nucleon charged current interactions. Solid line shows the calculated total cross section. The
dashed, dot and dash-dotted lines show the calculated quasielastic, single-meson and deep-inelastic scattering, respectively. 41
4.10 The cross section of π 16 O interactions. The lines show theresults of our calculation based on [64] and the points show
experimental data[66]. . . . . . . . . . . . . . . . . . . . . . . 42
4.11 Wavelength dependence of attenuation coefficient (L−1attenu )obtained by light scattering measurement. Point is measurement in Chapter 3.3.1. . . . . . . . . . . . . . . . . . . . . . . 44
5.1

5.2

5.3
5.4

The number of hits in the largest outer detector cluster, which
is used to separate the fully-contained and partially-contained
event samples. The histogram shows the MC prediction withneutrino oscillation. . . . . . . . . . . . . . . . . . . . . . . .
The distribution of the likelihood difference between a singlering assumption and a multi-ring assumption for sub-GeV(top) and multi-GeV (bottom) FC events. The hatched histograms show the charged current quasi-elastic interactions. .
An event display of a single-ring e-like. . . . . . . . . . . . . .
An event display of a single-ring µ-like. . . . . . . . . . . . .

iv

46

49
50
50

5.5

6.1

6.2

6.3
6.4
6.5

6.6

6.7
6.8
6.9

The distribution of particle identification likelihood for subGeV (top) and multi-GeV (bottom) FC single-ring events,
comparing data (points) and atmospheric neutrino MC. The
MC includes neutrino oscillation. The hatched histograms
show the νµ charged current interactions. . . . . . . . . . . .
Basic plot comparisons : Each plot show Number of rings(Nring), Visible energy (Evis), Total momentum (Ptot) andTotal invariant mass (Mtot). Vertical axes are normalized by
the number of events and oscillation effect was applied in thecase of atmospheric neutrino MC. A peak between 100 and
200M eV /c2 of Mtot distribution is caused by π 0 . . . . . . . .
Visible energy distribution when the number of rings is greaterthan one. The arrows show the selection region of visible energy for this analysis. . . . . . . . . . . . . . . . . . . . . . . .
Total momentum and Invariant mass after passing throughthe selection criterion (a) and (b). . . . . . . . . . . . . . . .
Invariant mass after passing through the selection criterion(a), (b) and (c). . . . . . . . . . . . . . . . . . . . . . . . . . .
Parent neutrino energy of background events. Left figure
shows about 521 background events in total and right figure
shows in each interaction mode. . . . . . . . . . . . . . . . . .
Total invariant mass versus total momentum. The events inside of right lower box in each scatter plot are final sample selected by kinematical cuts for n − n̄ oscillation analysis. With
10.4% detection efficiency in which 521 events are detectedamong 5,000 n − n̄ events, 20 candidates and 21 background
events are observed. . . . . . . . . . . . . . . . . . . . . . . .
Fermi momentum distribution. . . . . . . . . . . . . . . . . .
Likelihood distribution and minimum χ2 . . . . . . . . . . . .
Likelihood distribution and minimum χ2 . From the top, it isfor 2ring/3more ring separation, 3ring/4more ring separationand 4ring/5more ring separation. . . . . . . . . . . . . . . . .

v

51

54

55
55
56

57

58
61
63

64

List of Tables
3.1

Specification of a 50 cm PMT. . . . . . . . . . . . . . . . . .

15

4.1
4.2
4.3

n̄ − n annihilation branching ratio. . . . . . . . . . . . . . . .
n̄ − p annihilation branching ratio. . . . . . . . . . . . . . . .
List of the processes considered in simulator . . . . . . . . . .

30
30
43

5.1

Number of events after each reduction for fully-contained
events during 1489 days of the detector live-time. The Monte
Carlo numbers and efficiencies down to the fifth reduction
are for events whose real vertex is in the fiducial volume, thenumber of outer detector hits fewer than 10 and the visibleenergy larger than 30 MeV. In the last line, the fitted vertex
is used for both data and Monte Calro. . . . . . . . . . . . . .

48

6.1
6.2
6.3

6.4
6.5
7.1

List of background events. . . . . . . . . . . . . . . . . . . . .
Number of events and detection efficiency after each criterion.
Fitted minimum χ2 of likelihood function for ring counting.
We assume these difference from same reason and change thethreshold coherently. . . . . . . . . . . . . . . . . . . . . . . .
Systematic uncertainties in efficiency and exposure. . . . . . .
Systematic uncertainties in background rate. . . . . . . . . .

62
63
65

The lower limits on n − n̄ oscillation time at the 90% CL in
nucleon decay experiments. Oscillation time limit is calculated by T = ² · λ/s. The limits for free neutrons are deduced
from the limits for bound neutrons by the suppression factor,
T = R · τ 2 , and Super-K I limit used a suppression factor of
3.6 × 1023 s−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

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57

Search for Neutron-Antineutron
Oscillation in Super-Kamiokande
Jee-Seung Jang

Department of Physics
Graduate School Chonnam National University(Directed by Professor Jae-Yool Kim)

(Abstract)
A search for Neutron-Antineutron Oscillation, a process of |∆B| = 2
predicted by L-R symmetric gauge theories, was undertaken using the 24.5×1033 neutron-yr exposure of the Super-Kamiokande I, incorporating mostmajor sources of experimental uncertainties. Observing 20 candidates and21.6 background events with 10.4 % signal detection efficiency, the lower
limit on oscillation time for neutrons bound in 16 O has been determined tobe 3.20 × 1032 yr at the 90% CL without inclusion of the effect of systematic
uncertainties. This limit is better than the previous best limit of 7.2×1031 yr
in Soudan 2 by a factor of about 4.5. Taking 15.2% uncertainty in efficiency
and 32.1% uncertainty in background rate into account, the lower limit forneutrons bound in 16 O was estimated to be 1.78 × 1032 yr at the 90% CL
and the corresponding limit for free neutrons was calculated to be 1.25 × 108
s using a theoretical suppression factor of 3.6 × 1023 s−1 .

Chapter 1

Introduction
The Baryon Asymmetry of the Universe (BAU)[1][2] is one of the mostinteresting issues in particle physics and particle astrophysics. Baryon instability [3] in combination with CP violation and non-equilibrium thermodynamics in the early Universe , as first suggested by Sakharov, is the mostpopular explanation of BAU. In the early 1970, attempts at grand unificationof the fundamental interactions[4][5] led to the prediction of baryon number
as well as lepton number violation and even within the Standard Model it
was suggested baryon number was not conserved at the non-perturbative
level[6]. Well established theories such as above have encouraged experimentalists to continue the search for baryon instability, even though direct
experimental evidence supporting baryon number violation has not beenfound yet.
In the 1980’s, people began to be interested in experimental searches ofn − n̄ oscillation (a process that was originally referred to neutron transitions) with |∆B| = 2 rather than usual nucleon decay of |∆B| = 1. It’s interesting to review the motivation behind first experimental search. In 1974,
Georgi and Glashow made first predictions regarding observable nucleon decay modes with |∆B| = 1 such as p → e+ π 0 , p → ν̄K + and p → µ+ K 0
which are favored in minimal SU(5) conserving B − L, which turn out tobe dominant modes in minimal SUSY SU(5). This model yields[7] partial
lifetimes τp /B for p → e+ π 0 and p → ν̄K + are less than about 1035 yr
and 1032 yr respectively but strictly suppresses processes with |∆B| = 2
that violate B − L such as neutron-antineutron transition, the topic of thisdissertation. However, these predictions have been ruled out in recent years
by experimental results. In particular, the lifetime limit for p → ν̄K + , adominant mode of minimal SUSY SU(5), has been shown to be 2.3 × 1033 at
the 90%CL in published result of Super-Kamiokande[8]. As minimal SUSY
SU(5) has been ruled out by stringent limits on |∆B| = 1 processes, it has
become important to study processes that obey different symmetry laws
such as neutron-antineutron oscillation which can occur in large class of suNN
persymmetric SU (2)L SU (2)R SU (4)C [9] (Left-Right symmetric gauge
group).
The n − n̄ oscillation has the additional properties. The n − n̄ oscillation
occurs at energies ∼ 105 GeV[10] compared to the unification scale of SU(5)∼ 1015 − 1016 GeV in which p → e+ π 0 would be observable with a lifetime ofabout 1034 yr. Thus, if n − n̄ oscillation were to be observed experimentally,1new force of nature beyond the standard model would be discovered at
the energy scale above 1 TeV and an explanation of the matter-antimatterasymmetry would be put forward. If it were not to be discovered, it would
provide new limit on the stability of the neutrons.
There are two major experimental methods for an n − n̄ searches: One ofthem is utilizing free neutrons from reactors or neutron spallation sources
such as the ILL at Grenoble[10] and the other method is monitoring neutrons
bound inside the nuclei. In this thesis, neutrons bound in oxygen are studied
in Super-Kamiokande (Super-K). Figure 1.1[11] is showing the relationshipbetween the oscillation time limits of free neutron and bound neutron. Two
methods are related by theoretical ”nuclear suppression factor[12][13][14]”.
Super-Kamiokande is the world’s largest water Cherenkov detector witha net mass 50,000 tons located in Japan for observing neutrinos from various natural sources such as the Sun, the Earth’s atmosphere, supernovae
and other astrophysical sources as well as neutrinos from artificial sources
such as particle beams. Many significant results were published from thefirst phase of Super-Kamiokande (called Super-K I) including the world’s
highest limits on partial lifetimes for nucleon decay in minimal SUSY SU(5)under the condition of |∆B| = 1. n − n̄ oscillation, a process of |∆B| = 2
is studied in this thesis using the 91.7 kton-yr exposure of Super-K I. Even
though searches for this process have been made in various nucleon decay
experiments including IMB[15], Kamiokande[16], Fréjus[17] and Soudan[18],it has not to be observed yet. The current best limit for the n − n̄ oscillation time for bound neutrons is TIron ≥ 7.2 × 1031 by Soudan 2 for ironnuclei. It has been expected that Super-Kamiokande will greatly improve
this limit because it has by far the world’s best neutron exposure, although
the Sudbury Neutrino Observatory[19] (SNO) is also planning on obtaining
a competitive limit for bound neutrons.
In this thesis, n − n̄ oscillation is studied using neutrons bound in oxygen nuclei corresponding to 24.5 × 1033 neutron-yr of Super-Kamiokande
operating from April, 1996 to July, 2001 (the full Super-K I period). Before describing the n − n̄ analysis and result, I’ll outline the physics of n − n̄
search and Super-K detector. MC simulation to estimate detection efficiencyof n − n̄ oscillation and the number of background and detector simulation
are described in Chapter4 and the reduction and reconstruction for Super-K
data are described in Chapter5. In Chapter 6, data analysis methods, procedure and result are described. And the final chapter, Chapter7, contains
the conclusions and suggestions for further research on this topic.

2

Figure 1.1: Current limits of n − n̄ oscillation time. The horizontal axis
relates limit for free neutron oscillation time measured in reactor experiment and vertical axis for bound neutron oscillation time in nucleon decay
experiments. The bound neutron oscillation time is proportional to thefree neutron oscillation time squared with the constant being theoreticallydetermined, nuclear suppression factor.

3Chapter 2

Physics of n − n̄ Oscillationn − n̄ oscillation was first proposed as a possible explanation of BAU by
Kuzmin[2] in 1970 and was developed within the framework of the unification
models by Mohapatra etc.[20][21]. In this chapter, theoretical prediction andphenomenology of the n − n̄ oscillation are described.

2.1

Beyond the Standard Model : Grand Unification Theory

All known particle physics phenomena are well described within standard
model at the low energies. The standard model is a quantum field theory
based on the gauge symmetry SU (3)C × SU (2)L × U (1)Y which includes
the symmetry group of the strong interactions, SU (3)C , and the symmetrygroup of the electroweak interactions, SU (2)L × U (1)Y . In spite of the impressive successes of the standard model, it is a very unsatisfactory model
since it leaves many questions unanswered. For examples, there should be
only one gauge coupling which implies that all interactions should resultsfrom one non-abelian local symmetry. However, standard model has threedifferent group with three different gauge coupling. And Right-handed neutrinos are missed and neutrino masses are assumed to be zero. Moreover
this model can not explain Higgs mass and does not include Gravity.
In this section, physics beyond the standard model is described withGrand Unification Theory (GUT). The most interesting GUT groups are
SU (5), SO(10) and E6 . Since all these groups unify baryon and leptons,
they lead to baryon violating processes such as proton decay, p → e+ π 0
and n − n̄ oscillation. Different models predict different strengths for thesebaryon violating processes and experimental information on these processes
will provide tests of various GUT models. In order to have observable n − n̄
oscillation one needs a low scale (∼ 100 TeV) unification symmetry group
SU (2)L ⊗SU (2)R ⊗SU (4)C which is one intermediate stage to break SO(10)symmetry.

2.1.1

SU(5)

With the success of the unified theory of electro-weak interactions in SM,
it became natural to ask whether the strong interaction could also be united

4with the weak and electromagnetic interactions into a single. The basic ideaof the approach to a universal coupling is illustrated in Figure 2.1.

Figure 2.1: Running coupling constants g, g’ and gs of the electro-weak andstrong interactions appear to extrapolate to a single value at q ∼ 1015 GeV.
The graph indicates the dependence on momentum transfer, or mass scale,of the running coupling constants for the Abelian U (1) field described by
g 0 , for the non-Abelian SU (2) field denoted by g, and for the non-Abelian
SU (3) color field which we denote gs (where αs = gs 2 /4π). As q increases, g 0
increases slightly while g decreased slightly and gs decreased more quickly.
It is a remarkable fact that when all three interactions are extrapolated,
they appear to meet at a single point at the colossal value of q ' 1015 GeV.
(There are numerical constants of order unity multiplying g, g 0 and gs , which
we have omitted from Figure 2.1. Implicit in this enormous extrapolationis the bold assumption that Nature has run out of ideas and has no new
surprises in the range from q ' 30 GeV/c of present accelerator experiments,
all the way to q ' 1015 GeV/c. There may instead be new internal degrees
of freedom, quark or lepton substructure, only just around the corner andto be revealed at the next generation of accelerators. On the basis of pastexperience, one would think that this is rather likely.
There are many ways in which the SU (2), U (1) and SU (3) symmetries
could be incorporated into a more global gauge symmetry. The simplest
grand unifying symmetry is that of the group SU (5)-Georgi and Glashow,
1974. This incorporates the known fermions (leptons and quarks) in multiplets, inside which quarks can transform to leptons, and quarks to antiquarks, via the mediation of very massive (1015 GeV) bosons Y and X, withelectric charges -1/3 and -4/3 respectively. There are a total of 24gaugebosons in the model. These consist of the 8 gluons of SU (3) and the W ± , Z 0and photon of SU (2)×U (1), plus the 12 varieties of X and Y boson (each carrying 3 colors and existing in particle and antiparticle states). The fermions(quarks and leptons) are assigned to different ”generations”, The first gener5

ation consists of 15 states: the u- and d-quarks, each in 3 color and 2 helicity
states; the e− with 2 helicity states; and the νe , with 1 helicity only. By
convention, we write them down as LH states, since, for example, the e− RHstate and the e+ LH state are equivalent (by CP). The 15 states comprise”5̄” and ”10” representations as follows:νe e− 5̄ =  d¯R  ¯  dB 
d¯G LH

}
}

W−
X

}

GBG

(2.1)

The arrows indicate a gluon mediating the color force between quarks,
the W ± mediating the charged weak current, and an X ”leptoquark” bosontransforming a quark to a lepton. The quantum numbers of the ”10” areobtained from the antisymmetric combinations qi qj − qj qi of the members
qi of the ”5” (conjugates of the q̄i of the ”5̄”). Thus,


0
e+
dR
dB
 −e+
0
uR
uB


0
ūG
10 =  −dR −uR −dB −uB −ūG0−dG −uG −ūB −ūR



dG
uG 


ūB 

ūR 
0
LH

(2.2)

These multiplets have the property that the total electric charge ΣQi = 0.
The heavier leptons (µ, νµ , τ, ντ ) and quarks (s, c, b) have to be assigned toseparate quark-lepton generations.
This model make many predictions, some of which are accessible in present
or future experiments. One of them is proton must decay. The favored decay mode is p → e+ π 0 based on SU (5) symmetry (”minimal SU (5)”). Thispredicts partial lifetime of p → e+ π 0 should be less than 1.4 × 1032 yr
assuming[22] ΛM¯S to be less than 400 MeV. However, first generation nucleon decay experiments, KAMIOKANDE[23] and Irvine-Michigan-Brookhaven[24](IMB), motivated by this prediction, observed no evidence and ruled out thismodel. And it turns out that this contradiction to SU (5) can be solved
by incorporating supersymmetry (SUSY). This model[7] shows the constance with experimental non-observation of p → e+ π 0 . However, SuperKamiokande made this model incompatible by non-observation of otherdominant mode, p → ν̄K + over the predicted limit. As the minimal SUSY
SU (5) also was ruled out, other extended models are noticed.

2.1.2

SO(10)The SO(10) symmetry is one of most interesting model to extend theSU (5) GUT since SO(10) has several remarkable advantages.
The SO(10) GUT model which directly breaks to SU (3)C ⊗ SU (2)L ⊗U (1)Y predicts relatively short lifetime of protons and the prediction is notconsistent with experimental result[25]. On the other hand, there are several
ways for SO(10) symmetry to break down to SU (3)C ⊗ SU (2)L ⊗ U (1)Y by

6two steps[26].
SU (5) ⊗ U (1) SU (4) ⊗ SU (2) ⊗ SU (2)



L
R
SO(10) → 
 → SU (3)C ⊗SU (2)L ⊗U (1)Y SU (3) ⊗ SU (2)L ⊗ SU (2)R ⊗ U (1) SU (3) ⊗ SU (2)L ⊗ U (1) ⊗ U (1)(2.3)
One of advantages of SO(10) GUT models is that it can contain the leftright symmetry which is missed in the standard electroweak model. Second
advantage is that SO(10) model has representations of 16 in which there isa room for right handed neutrinos(νR ) missed in the SU (5) model. SO(10)model that implements the seesaw mechanism[27] may explain the neutrino
masses and mixing. Moreover, the fermion unification into a single representation of 16 is a attractive feature of the model.
SO(10) models predict sin2 θW consistent with experimental results andthe running coupling constants can meet at a single unification point[28][29].
Among several intermediate symmetries, SU (4) ⊗ SU (2)L ⊗ SU (2)R which
was suggested by Pati and Salam[4] in 1973 is very interesting because it
contains the left-right symmetry. Within this framework, an immediate implication of (B−L)-symmetry breaking is the existence not only of Majorana
neutrinos (∆L = 2 in the lepton section) but also the new phenomenon ofn → n̄ transition (∆B = 2 in the hadron sector), which we call ”neutron
oscillations”[20].

2.2

Prediction for n − n̄ Oscillation in L-R Symmetric Gauge Theory

There are many models for n − n̄ oscillation. Among them, SU (2)L ×
SU (2)R ×SU (4)C which SU (4) unifies color and B −L symmetry is adopted
in this section. Following prediction for n − n̄ oscillation within this framework is from Mohapatra[10].
Lifetime of n−n̄ oscillation for free neutrons is led with observable strength
depends on the details of the theory such as value of mass scales etc.
τn−n̄ =h2πδmn−n̄(2.4)

where h is Plank’s constant and δmn−n̄ is the transition mass for n → n̄transition. Within the framework of ”partial unification” group SU (2)L ×
SU (2)R ×SU (4)C for electroweak and strong interactions, in order to obtainn − n̄ oscillation process, the gauge symmetry breaking of the model has tobe broken by the Higgs multiplets as in Ref.[21]: A bidoublet, φ(2,2,1),¯ + ∆R (1, 3, 10).
¯
and a pair of triplets, ∆L (3, 1, 10)
The quarks and leptons
are assigned to representations as follows: QL (2, 1, 4) + QR (1, 2, 4). Here
leptons are considered as the fourth color. The allowed Yukawa couplingsin the model are given by:
LY = yq Q̄L φQR + f (QL QL ∆L + QR QR ∆R ) + h.c.

(2.5)

Here all generation indices was omitted and the couplings symbolically omitting charge conjugation matrices, Pauli matrices etc was denoted. The Higgs
7

potential of the model can be easily written down; the term in it which is in0 0 0 0
teresting for the purpose of this study is λεijkl εi j k l ∆L,ii0 ∆L,jj 0 ∆L,kk0 ∆L,ll0 +L → R + h.c..

Figure 2.2: Six quark diagram of n − n̄ oscillation.
In other to proceed towards the goal of estimating the strength of n − n̄
oscillation in this model, we can first note that the original gauge symmetry
here is broken by the < ∆R,44 >= vB−L 6= 0 to the standard model gauge
group. The diagram of Figure 2.2[10] then leads to six quark effective interaction below the scale vB−L of the form uR dR dR uR dR dR . A rough estimateof the strength of neutron oscillations as follows:An−n̄ '

λf 3 < ∆R >
m6∆R

(2.6)

where λ is the scalar self-coupling of the Higgs boson ∆R , f is the strengthof fermion-Yukawa coupling, and m∆R is the mass of the Higgs boson ∆R .
For the scale < ∆R > and m∆R of order 100 TeV and for h ≈ λ ≈ 10−1 thiswill lead to a strength for the six quark amplitude of about 10−29 GeV−5 .
In order to convert it to δmn−n̄ , we need the three quark ”wave function”
of the neutron at the origin. This has been estimated by various people[30]and usually yields a factor of about 10−4 or so. With these values, we
obtain a lifetime for free neutron oscillations in this model, τn−n̄ ' 6 × 108
sec from Eq. (2.4) where h/2π = 6.58 × 10−22 MeV·s. This oscillation
time is related with the nuclear instability life time (This is however only
an order of magnitude estimate since the true value of the parameters that
go into this estimate is unknown. But the main point that this example
makes is that there exist very reasonable theories where n − n̄ oscillation
is observable. Note that this model is a completely realistic extension of
the standard model with many interesting features such as the smallness ofneutrino mass naturally explained etc.

2.3

Phenomenology of Neutron Oscillations

This section describes the basic phenomenology of neutron oscillations.
First we consider free neutron oscillations and the effect of an external field8

on neutron oscillations is treated. In particular the effect of an external magnetic field on the opposite magnetic momentum of n and n̄. This description
is by R. N. Mohapatra and R. E. Marshak[31]2.3.1Free Neutron Oscillations

The starting point is the n − n̄ mass matrix.
Lmass = ψ̄M ψ
where

Ã

ψ=
and

Ã

M=

n
n̄

(2.7)

!

A
δm
δm A

!

(2.8)

In Eq. (1.8), δm is the ∆B = 2 transition mass between n and n̄ states.
The equality of the diagonal elements follows from CPT invariance and thatof the off-diagonal elements from CP invariance. The eigenstates of M canbe written as:
n ± n̄
n1,2 = √2(2.9)

m1,2 = A ± δm

(2.10)

with masses:
Next, the amplitude for finding an n̄ at time t starting with a beam of neutrons at t=0 is:Ã|n(t) >= e−γt2|n1 (0) > e−im1 t + |n2 (0) > e−im2 t√
2!

(2.11)

where we have assumed that the decay widths of n1 and n2 are equal anddenoted by γ. The probability for finding an n̄ at time t, Pn̄ (t) is:Pn̄ (t) =e−γt(1 − cos2δmt)
2(2.12)

If t << 1/γm, then we obtain:Pn̄ (t) ' e−γt (δmt)2(2.13)The upper limit on δm can be estimated from the upper limit on the ∆B = 2”bound” nucleon transition rate, Γ∆B=2 by means of the relation:δm 'pΓ∆B=2 M

(2.14)

Here, M is a typical hadronic mass. This part will be explained again in
Chapter 6.3.2. Anyway, it follows that if a beam of N free neutrons is allowed
to travel for a time T before hitting a target, the number of antineutrons,N̄ , at the target after T should be (assuming γT << 1):N̄ ≤ N (
9

T
τn−n̄

)2

(2.15)

τn−n̄ is n − n̄ oscillation time. With reasonable values of N and T , above
equation would be rather promising for a ”free” neutron oscillation experiment. However, there is a complicating factor resulting from the presenceof the earth’s magnetic field which shifts the energy of n and n̄ by opposite
amounts ±µB ∼ 10−11 eV, which is much larger than δm. We deal withthis situation in the next section.

2.3.2

Oscillation of Neutrons in an External Field

If the neutron oscillation takes place in an external field (such as theearth’s magnetic field or other field) so that the CPT theorem need not be
respected, the picture outlined in previous section changes and we have:
Ã

M=

A1 δm
δm A2

!

(2.16)The neutron mass eigenstates in this case are:|n1 >' |n > +θ|n̄ >|n2 >' −θ|n > +|n̄ >whereθ ' δm/∆M(2.17)

where ∆M ≡ M1 − M2 ≈ A1 − A2 >> δm. And probability is:Pn̄ (t) 'θ2[1 − cos∆M t]
2(2.18)

Above equation is interesting in two limiting cases: (a) ∆M t >> 1 and (b)∆M t << 1. In case (a), the second term oscillates rapidly and the average
probability for finding an n̄, < Pn̄ >av becomes:< Pn̄ >av ' (

δm 2
)
∆M

(2.19)

In case (b), we get:Pn̄ (t) ' (δmt)2
as long as γt << 1.

10(2.20)

Chapter 3

Super-Kamiokande
Super-Kamiokande is the world’s largest water Cherenkov detector witha net mass 50,000 tons located in Muzumi mine, Gifu, Japan. Detector
cavity lies under the peak of Mt. Ikenoyama with 1,000 meters of rockor 2,700 meter-water-equivalent mean overburden. The scientific goal ofthis experiment is observing neutrinos from various natural sources suchas the Sun, the Earth’s atmosphere, supernovae and other astrophysicalsources as well as neutrinos from artificial sources such as particle beams
and includes nucleon decay search. Super-Kamiokande began to take data in
April, 1996. This operating was shut down for maintenance and upgrade in
July, 2001. This running period is referred to as Super-Kamiokande I (SuperK I). During refilling the water to start Super- Kamiokande II, in November,
2001, an apparent cascade of implosions triggered by a single photomultipliertube (PMT) implosion destroyed over half of the PMTs installed in thedetector. In 2002, the detector was reconstructed with 5,000 PMTs (theoriginal number of PMTs used in Super-K is 11,146) encased in acrylic covers
to avoid a similar accident. After partial reconstruction, Super-Kamiokande
II was operated from Dec. 2002 to Oct. 2005 with temporarily reduced PMT
coverage (47% of Super-K I). In June 2006, the third phase experiment,
Super-Kamiokande III, has been started after full reconstruction recovering
PMT coverage as Super-K I. In this thesis, 4.07 years data in Super-K I
period is used for analysis. The configuration and operational characteristicsof the detector in the Super-K I period are described in this chapter basedon [32].

3.1

Cherenkov Radiation

The Super-Kamiokande is water Cherenkov detector which observed relativistic charged particles in water by detecting the Cherenkov light. Cherenkov
photons are radiated when a charged particle in a material medium moves
faster than the speed of light in that same medium. Therefore a particle
emitting Cherenkov radiation must have a velocity
vparticle ≥

c
n

(3.1)

where n is the index of refraction and c is the speed of light in a vacuum[33].
The momentum threshold of Cherenkov radiation is determined by the re11

Figure 3.1: Cherenkov radiation.
fractive index of the medium and the mass of particle. In water, the refractive index is about 1.34, and the momentum threshold for electrons, muonsand pions are 0.57, 118 and 156 MeV/c, respectively.
This radiation creates electromagnetic shock wave. This is illustrated
in Figure 3.1. The coherent wave front formed in conical in shape and isemitted at a well-defined angle
cosθC =

1
nβ

(3.2)

with respect to the trajectory of the particle where β = v/c and this angle
is called as Cherenkov angle. For the particle with β ' 1 in water, theCherenkov angle is about 42o . This angle is dependent on the speed of theparticles and the frequency of the emitted radiation.
The number of photons emitted by Cherenkov radiation is given as afunction of the wave length λ as follows;
d2 N
2πα
1
= 2 (1 − 2 2 )
dxdλ
λ
n β

(3.3)

where x is the path length of the charged particle and α is the fine structure constant. About 340phtons/cm are emitted between the wavelengthof 300nm to 600nm, which is the sensitive wavelength region of photomultiplier tubes. Particle emitting Cherenkov light project ring images on thewall inside of the detector. Figure 3.2 shows display of a typical neutrino
event in the Super-Kamiokande detector.

3.2

Detector

3.2.1

Water Tank

Figure 3.3 shows the schematic view of detector. The outer shell of thedetector is a cylindrical stainless steel tank, 39 m in diameter and 42m inheight. The tank is self-supporting, with concrete backfilled against the12

Figure 3.2: Neutrino event display in the Super-Kamiokande.
rough-hewn stone walls to counteract water pressure when the tank is filledwith water. The capacity of the tank exceeds 50 ktons of water. A cylindrical
PMT support structure divides the tank into two distinct, optically isolated
volumes. The structure has inner dimensions, 33.8 m (diameter) by 36.2m (height), defining the inner detector (ID) which contains 32 ktons ofwater and was viewed by inward-facing 50 cm (20 inch) PMTs (Hamamatsu
R3600). Approximately 2.5 m distance remains on all outside of the support
structure. This outside region defining outer detector (OD), serves as anactive veto counter against incoming particles as well as a passive shield forneutrons and gamma rays from the surrounding rocks. OD was instrumented
with 1,885 outward-facing 20 cm (8 inch) PMTs (Hamamatsu R1408). The
two detector volumes are isolated from each other by two light-proof sheets
on both surfaces of the PMT support structure. The 55 cm thick support
structure comprises dead space from which light in principle cannot escape.
Therefore, any interaction in that space cannot be detected. The OD PMTs
were mounted in water-proof housings which effectively block light from thedead space. However, because the ID PMTs were not fully covered in back,some light generated in this region was still detected by the ID PMTs.

3.2.2

Photomultiplier Tubes

Inner Detector Photomultiplier Tubes
A 50 cm ID PMTs used in this experiment is described in Figure 3.4
and the specifications are summarized in Table 3.1. The bialkali (Sb-K-Cs)
photocathode has peak quantum efficiency of about 21% at 360 nm-400 nm
as shown in Figure 3.5. The collection efficiency for photoelectrons (pe) at
the first dynode is over 70%. The transit time spread for a 1 pe signal is13

Figure 3.3: Schematic view of Super-Kamiokande.
2.2 ns. The average dark noise rate at the 0.25 pe threshold is about 3 kHz
in Super-Kamiokande I. The ID PMTs were operated with gain of 107 at a
supply high voltage ranging from 1700 to 2000 V. The neck of each PMT
was coated with a silver reflector to block external light.
Outer Detector Photomultiplier Tubes
These PMTs were first adopted in the IMB experiment[34] and they arereused in the Super-Kamiokande after finishing that experiment. Light collection efficiency in the OD PMTs is enhanced by wavelength shifting (WS)plates attached to each OD PMT. The WS plates are square acrylic panels,
60 cm on a side and 1.3 cm thick, doped with 50 mg/l of bis-MSB. The WS
plates function by absorbing UV light, and then re-radiating photons in theblue-green, better matching the spectral sensitivity of the PMT’s bialkali
photocathode. The light collection of the PMT plus WS unit is improved
over that of the bare PMT by about a factor of 1.5.

14

Figure 3.4: Schematic view of a 50 cm PMT.

Shape
Photocathode area
Window material
Photocathode material
Quantum efficiency
DynodesGain
Dark current
Dark pulse rate
Cathode non-uniformity
Anodes non-uniformity
Transit time
Transit time spread
WeightPressure tolerance

Hemispherical
50 cm diameter
Pyrex glass (4 ∼ 5 mm)
Bialkali (Sb-K-Cs)
22% at λ=390 nm
11 stage Venetian blind type107 at ∼ 2000 V
200 nA at 107 gain
3kHz at 107 gain
< 10 %< 40 %
90 nsec at 107 gain
2.2 nsec (1 σ) for 1 p.e. equivalent signals
13 kg
6 kg/cm2 water proof

Table 3.1: Specification of a 50 cm PMT.

15

Figure 3.5: Quantum efficiency of the photocathode as a function of wavelength.

3.2.3

PMT Support Structure and Others

Figure 3.6 shows a detail of the PMT support structure. All support
structure components are stainless steel. The basic unit for the ID PMTs
is a supermodule, a frame which supports a 3x4 array of PMTs. Eachsupermodule has two OD PMTs attached on its back side. Opaque black
polyethylene telephthalate sheets cover the gaps among the PMTs in the ID
surface. These sheets improve the optical separation between the ID and
OD and suppress unwanted low-energy events due to residual radioactivity
occurring behind the PMTs.
Light collection efficiency is enhanced by WS as mentioned in previous
section. To further enhance light collection, the OD volume is lined witha reflective layer made from Type 1073B Tyvek manufactured by DuPont.
This inexpensive and very tough paper-like material has excellent reflectivity in the wavelength range in which PMTs are most sensitive, especiallyat short wavelengths. Measured reflectivities are on the order of 90% forwavelengths in excess of 400 nm, falling to 80% at about 340 nm[35]. The
presence of this liner allows multiple reflections of Cherenkov light, which
minimizes the effects of dead PMTs, given their coarse spacing in the OD.
Cherenkov light is spread over many PMTs, reducing pattern resolution but
increasing overall detection efficiency.
To protect against low energy background from radon decay productsin the air, the roof of the cavity and the access tunnels were sealed with acoating called Mineguard produced by Urylon in Canada. In addition,double
doors in the access tunnels restrict air flow from the mine into the detector cavern and ”radon-free” air is supplied and radon-reduced air is also
produced in the mine.
The average geomagnetic field is about 450 mG and is inclined by about

16Figure 3.6: Schematic view of PMT support structure.

17

45o with respect to the horizon at the detector site. The strength anduniform direction of the geomagnetic field could systematically bias photoelectron trajectories and timing in the PMTs. To counteract this, 26 setsof horizontal and vertical Helmholtz coils are arranged around the innersurfaces of the tank. With operation of these coils, the average field in thedetector is reduced to about 50 mG. The magnetic field at various PMT
locations were measured before the tank was filled with water.

3.2.4

Water Purification

Super-Kamiokande should keep the water transparency as high as possible removing small dust, metal ions like Fe, Ni, Co and bacteria in thewater. And radioactive material, mainly Rn, Ra and Th, can be source of
background. Especially, radon is serious background for the solar neutrino
analysis. However, since there is ∼ 60 cm space between the surface of thewater and the top of the water tank, radon gas contaminated in the air in
the gap could dissolve in the water. Therefore, the 50 ktons of purified water in the Super-Kamiokande tank is continuously reprocessed at the rate ofabout 30 tons/hour in this closed cycle system. In the Kamioka mine, thereis clean water flowing near the detector and it can be used freely in large
quantities. This water is circulated through the water purification system
shown in Figure 3.7. The water purification system consists of the following
components;• 1µm Filter• Heat exchanger : The water temperature rises due to the heat generated by pumps and PMTs. The temperature is kept at around 14o C
to suppress bacteria growth.
• Ion exchanger : This removes metal ions in the water.
• Ultra-Violet sterilize : This kills bacteria. The documentation states
the number of bacteria can be reduced to less than 103 ∼ 104 /100ml.
• Vacuum degasifier : This removes gas resolved in the water. It is able
to remove about 99% of the oxygen gas and 96% of the radon gas.
• Cartridge polisher : This is a high performance ion exchanger.
• Ultra filter : This remove small dust even of the order of nanometers.
The typical number of particles larger than 0.2µm is reduced to 6 particle/cc
after purification.

3.2.5

Electronics and Data Acquisition System

Inner Detector Electronics and Data Acquisition
ID PMT signals are processed by custom built TKO modules called AnalogTiming-Modules (ATMs). The TKO (TRISTAN KEK Online) system wasoriginally developed and built by KEK, and is optimized for front-end electronics where a large number of channels are to be handled. The ATM
has the functionality of a combined ADC (Analog-to-Digital Converter) andTDC (Time-to-Digital Converter), and records the integrated charge and18

Figure 3.7: Schematic view of water purification system.
arrival time of each PMT signal. Signals from 12 PMTs are fed to an ATM
board. Figure 3.8 shows a block diagram of the ATM board. The PMT
signal into the current splitter is divided into four signals. One of themis fed to the discriminator with the threshold level for each channel set to-1 mV, which corresponds to 1/4 pe equivalent. When the PMT signal is
above the threshold level, a ”hit” signal with 200 ns width and 15 mV pulse
height is asserted on the ATM front panel. The HITSUM signal, which isused to generate the global trigger signal, is the analog sum of all these
15 mV/Channel pulses. At the same time, either of the split signals, A or
B, is held by a QAC (Charge to Analog Converter), and a TAC (Time to
Analog Converter) starts to integrate constant current. If a global trigger
is received, the information in the TAC/QAC is digitized and stored in internal memory buffers. Since, for each channel, TAC integration is started
by the PMT signal itself, the arrival time of the signal can be inferred fromthe value of the integrated charge. A ”self gate” chip generates start/stop
signals for the TAC, the gate signal for QAC, and clear signals for both.
Output signals from the TAC/QAC are fed to an ADC and digitized. There
are two TACs and QACs for each channel so that events in rapid succession, such as muon followed by its decay electron, can be processed without
dead-time.
Figure 3.9 shows a schematic view of the inner detector data acquisition (ID DAQ) system. There are total 946 ATM modules, located in four”quadrant huts”. ATMs record ADC/TDC data of each PMT above threshold when a global trigger signal is asserted by the VME TRG (TRiGger)

19

Figure 3.8: A block diagram of ATM board used for inner detector dataacquisition.

Figure 3.9: The data acquisition system for the inner detector.

20

Figure 3.10: Outer detector DAQ block diagram and data flow.
module. The global trigger signal and event number information generated
in the TRG module, are distributed to all ATMs via 48 GONG (Go/NoGo)
modules.
Outer Detector Electronics and Data Acquisition
A block diagram of the OD data acquisition (OD-DAQ) system is shown in
Figure 3.10. As with the inner detector, signals from the PMTs are processedand digitized in each of 4 quadrant electronics huts. From there, the signals
are picked off, digitized and stored. As in the ID, local HITSUM pulses
are formed in each quadrant hut and sent to the central hut, where theiranalog sum creates an OD trigger signal when the OD HITSUM thresholdis exceeded. Figure 3.10 illustrates the data flow in a quadrant hut as wellas the overall data flow. When a trigger from any source occurs, the data
are passed out of the quadrant huts to the central hut for further processing.
Once the PMT signals have been picked off, coaxial ribbon cables feed themto the custom charge-to-time conversion modules (QTC). The purpose of
these modules is to measure the hit time and charge of the PMT pulse andconvert it to a form which can be easily read and stored by the time-todigital converters (TDCs). The output of the QTC modules is a logic pulse(ECL level) whose leading edge marks the hit arrival time and whose width
represents the integrated charge Q of the PMT pulse.

21

Figure 3.11: Relative photo-sensitivity. (a) Measurement result, (b) Definition of the incident angle.

3.3

Calibrations

3.3.1

Water Transparency Measurement

Indirect Measurement with Cosmic Rays
The light attenuation length in water can be measured by using throughgoing cosmic ray muons. These muons are energetic enough to deposit almost constant ionization energy per unit path length (about 2 MeV/cm) independent of particle energy. This fact makes it possible to use these muons
as a ”constant” light source. The advantage of this method is that continuous and abundant samples of muons come without cost as we take normal
data. The disadvantage is that we cannot measure the transparency as afunction of wavelength. However, since what we measure is the Cherenkov
spectrum, this disadvantage is not necessarily a problem. Under the assumption that light reaching the PMTs is not scattered, the charge Q observed
by a PMT is expressed by
Q = Q0lf (θ)
exp(− )lL

(3.4)

Where l is the light path length, L the effective attenuation length, Q0 a
constant and f (θ) the relative photo-sensitive area, which depends upon theincidence angle θ of the light on the PMT, as shown in Figure 3.11. Figure
3.12 is as a function of the path length l together with the best fit in the formof the function defined above. The resulting attenuation length is found to
be 105.4±0.5 m.
As the data sample for this measurement is accumulated automaticallywhile we take normal data, it is possible to continuously monitor the attenuation length as a function of time. Figure 3.13 shows the attenuation
length changes with time, which are correlated with water quality. Suchtime variations in the attenuation length are corrected in analysis from thetime series of calibration data.

22

Figure 3.12: Effective charge observed as a function of the path length.

Figure 3.13: Time variation of the water attenuation length measured bythrough-going.

23

Figure 3.14: Laser system for water scattering and absorption parametermeasurement and its typical events display.
Light Scattering Measurement with Laser
To measure the scattering and absorption parameters separately, a combination of dye and N2 lasers of wavelengths 337, 371, 400, 420 nm are used
as light sources. In Super-Kamiokande I, the laser beam is brought into
the top of the detector via optical fibers. Each laser fires every 6 second
during normal data taking. Figure 3.14 shows a schematic view of the laser
calibration setup and a typical event of laser light. A cluster of hits at thebottom of the tank is due to unscattered photons. The remaining hits, inbarrel and top PMTs, are due to photons scattered in the water or reflectedby the bottom PMTs and black sheet. The total charge in the cluster ofbottom hits is used for normalization factor as a reference of light intensity.
Figure 3.15 shows distributions of photon arrival times at the top PMTs.
In the upper plot, the peak near 730 ns is from scattered photons, and thesecond peak represents reflected photons at the bottom of the detector. For
the Monte Carlo, the total number of scattered photons is tuned using thescattering parameters, and the shape of the arrival time distribution is used
to adjust the absorption parameters. The lower plot in Figure 3.15 shows
the time dependence of the ratio between Monte Carlo and data, which agree
within 2%. Using the measured absorption and scattering parameters, thelight attenuation length of water is calculated using the following equation.
Lattenu =1αabs + αscatt(3.5)

Figure 3.16 compares the time variation of the light attenuation length
measured by the 420 nm laser and cosmic ray muon during Super-Kamiokande
I period. The result from cosmic ray muon is with average Cherenkov spectrum so it does not agree with the one from the laser system. However,24

Figure 3.15: The upper plot is the photon arrival time distribution of the
top PMTs. Dots is data and line is Monte Calro. The lower plot is the ratio,(MC-DATA)×100/DATA.

Figure 3.16: Time variation measured light attenuation length since November 1999, using the laser system (triangles) and cosmic ray muons (crosses).

25

Figure 3.17: The relative gain measurement system.
we can see the tendency of time variation is consistent between the two
measurements.

3.3.2

Relative Gain Calibration

The high voltage of each PMT is set to provide approximately equal gain
for all PMTs in the Super-Kamiokande detector. Each PMT came witha nominal high voltage value, which was specified by Hamamatsu Phonics
just after its production, using three calibration light sources : a DC lightsource, a Xe-lamp pulsed light source, and a light source at the single pelevel. However, because of possible long-term drift in the factory calibration
system, which may have caused a systematic difference between tubes manufactured at different times, all PMTs had their gain re-calibrated. Normalized Relative gain was measured by the system shown in Figure 3.17. Light
generated by a Xe lamp is passed through an ultraviolet (UV) filter andinjected into a scintillator ball via an optical fiber. The scintillator ball isan acrylic ball with BBOT (2, 5-bis(5’-tert-butyl-2-benzoxazolyl)thiophene)
wavelength shifter and MgO powder diffuser. BBOT absorbs UV light andemits light with a peak at 440 nm, which is in the sensitive region of the
PMTs used for Super-Kamiokande for Cherenkov light detection. In thismeasurement, each PMT detects a few tens of pe.
The intensity of the primary UV light is monitored by two photodiodes
and one PMT. The output of the monitor PMT is also used for triggering.
The relative gain Gi of the i-th PMT is obtained by
Gi =

Qi
li
· li · exp( )Q0 f (θ)L(3.6)

where Qi is the observed charge by the PMT, Q0 a constant, L the effective
26

light attenuation length, li the distance from the light source to the PMT
and f (θ) the relative photo-sensitivity as a function of the incident angleof light a on the PMT defined in Figure 3.11. The high voltage value foreach PMT is set so that the ”corrected Q” of each PMT is approximately
the same as for all the others. Here, ”corrected Q” is the pulse heightcorrected for light attenuation, acceptance of the PMT, and uniformity ofthe scintillator ball. It is further normalized by the Xe monitor pulse height.
This measurement is done for various positions of the scintillator ball andsettings of the high voltage value. After the initial gain adjustment, longterm stability of PMT gain was monitored using the same system. The
absolute value of PMT gain cannot be measured while the experiment isrunning. The relative gain spread gain is defined as the standard deviation
obtained by fitting the relative gain distribution of all PMTs to a Gaussian.
It was 7.0% at the beginning of Super-Kamiokande I.

3.3.3

Relative Timing Calibration

The relative timing of PMT hits is important for event reconstruction. It
depends on the length of the signal cable between the PMT and the ATM,and also depends on observed charge because of the discriminator slewing
effect. The timing difference in each individual PMT has to be measured
precisely to get better timing resolution. Figure 3.18 shows the system formeasuring the relative timing of hit PMTs. The N2 laser emits intenselight of wavelength 337 nm within a very short time (less than 3 ns). The
wavelength is shifted to 384 nm, which is near the lower edge of sensitivityof a PMT to the Cherenkov light, by a dye laser module. The light intensity
is changed by an optical filter, and the PMT timing is measured at various
pulse heights. After passing through the optical filter, the light goes to the
diffuser ball in the detector through an optical fiber. The schematic viewof the diffuser ball is also shown in Figure 3.18. The diffuser tip located at
the center of the ball is made from TiO2 suspended in optical cement. The
light emitted from the tip is further diffused by LUDOX manufactured byGrace Davison, silica gel made of 20 nm glass fragments. The combination ofdiffuser tip and LUDOX make modestly diffused light without introducing
significant timing spread. A typical scatter plot of the timing and pulse
height is shown in Figure 3.19, which is called a ’TQ-map’. Each PMT has
its own TQ-map, which is applied in data reduction. The timing resolutionof PMTs as a function of pulse height is estimated from the TQ maps.
Typical timing resolution at the single pe level is better than 3 ns.

3.3.4

Other Calibrations

There are other calibrations using stopping muon, neutral pion, LINAC,
etc. The detail of the other calibrations can be found in [32].

27Figure 3.18: The timing calibration system.

Figure 3.19: A typical plot of timing vs. pulse height. This plot is referred
as ’TQ-map’.

28Chapter 4

Simulation
We simulate not only the n − n̄ oscillation but also the background events
since background is pivotal component of a search for a rare process suchas nucleon decay or transition. Atmospheric neutrino interactions with anaverage energy of 1∼3 GeV are most significant source of background forn−n̄ oscillation as well as nucleon decay. We use same 100 years atmospheric
neutrino MC that has been used for neutrino oscillation study in SuperKamiokande I of 4.07 years livetime. In this chapter, I outline the physicalassumptions including those related to kinematics that are used in signal,
background and detector response for n − n̄ search.

4.1

n − n̄ Oscillation

The n − n̄ search focuses on possible oscillation and subsequent annihilation of neutrons bound in 16 O nuclei which are contained in H2 O moleculesin the fiducial volume of Super-K detector. Thus, the kinematics that weshould consider for this search is quite different from that of free neutrons
due to Fermi motion that arises from the Pauli Exclusion Principle and nuclear effect described in terms of secondary particles such as pions. Ourn − n̄ simulation includes four phases.
1. Annihilation phase (∼ 10−22 s): spontaneous oscillation and annihilation of neutron in a 16 O nucleus.
2. Pionization or mesonic phase (∼ 10−18 s): production of the annihilation products.
3. Propagation phase (∼ 10−12 s): propagation and possible decay of theannihilation products through the residual excited nucleus, 14 O or 14 N
for annihilation of the n̄ on a n or p respectively.
4. Fragmentation phase (∼ 10−8 s): decay and fragmentation of residual
nucleus into nuclear fragments that include free neutrons, protons andisotopes of hydrogen and helium.

29

channel
π+π−π0π0π+π−π0π + π − 2π 0
π + π − 3π 0
2π + 2π −2π + 2π − π 0π+π−π0ω
2π + 2π − 2π 0
3π + 3π −3π + 3π − π 0
3π + 3π − mπ 0 (m > 1)

This analysis(%)
2.(±0.4)
1.52(±0.4)6.48(±0.7)
11.(±1.3)
28.(±1.3)
7.(±1.4)
24.(±3.4)
10.(±0.9)
10.(±0.9)
0.
0.
0.

Cresti(1963)(%)
0.33(±0.48)
0.
5.4(±0.7)0.
0.
5.4(±0.3)
22.6(±0.7)
0.
0.
1.7(±0.2)
1.7(±0.2)
0.

Baltay(1966)(%)
0.32(±0.03)
3.2(±0.5)
7.8(±0.90)*
34.5(±1.2)
5.8(±0.3)
18.7(±0.9)*21.3(±1.1)
1.9(±0.2)
1.6(±0.3)
0.3(±0.1)* is the percent in this channel has been added to the percent in the below
and result is reported in the line below.
Table 4.1: n̄ − n annihilation branching ratio.

channelπ+π0
π + 2π 0
π + 3π 0
2π + π −2π + π − π 0
2π + π − 2π 0
2π + π − ω
3π + 2π − π 0
4π + 3π − mπ 0This analysis(%)
1.(±1.0)
8.(±1.2)
10.(±1.2)
0.
22.(±1.8)
36.(±1.8)
16.(±4.0)
7.(±4.0)0.

Bettini(1967)(%)≤ 0.7*
16.4(±0.5)1.57(±0.21)
21.8(±2.2)59.7(±1.2)12.0(±3.0)23.4(±0.7)0.39(±0.07)

Table 4.2: n̄ − p annihilation branching ratio.

30

4.1.1

Annihilation and Pionization

An n̄ that is the product of spontaneous neutron oscillation is assumed toquickly annihilate with one of the remaining n or p in nucleus with probability of 46.7% and 53.3% respectively. These n̄ − n and n̄ − p annihilations are
generated in the oxygen nucleus. Since the literature on n̄ annihilation in
nucleus is meager, p̄p and p̄d data[36][37][38] from hydrogen and deuterium
bubble chambers are used to determine the branching ratios for the annihilation final states, pionic phase. The branching ratios used in our simulation
are summarized in Table 4.1 and are same as those used in the n̄ analysis of
IMB[15]. The kinematics of this pionic phase are determined by relativisticphase-space including Fermi motion[39].
The n̄ annihilations are generated using two methods in n − n̄ searches;
A volume mode in which the nuclear matter density is uniform throughout
the nuclear volume and annihilation vertices are thus uniformly distributed
throughout the nuclear volume, and peripheral mode in which matter density
increased as the nuclear surface is approached and thus annihilation vertices
are more likely to be found near the nuclear surface. Our n − n̄ simulation,
as well as the most resent result in Soudan2, is based on volume mode whichyields more conservative limit[14] although many of n − n̄ searches adopted
the peripheral distribution which were predicted by Dover et al.[40].

4.1.2Pion Propagation

Produced pions from the n̄ annihilation are propagated through the excited residual nucleus before leaving the nucleus with a maximum total
center of mass energy of 1850MeV and 1854MeV, which is the difference
between the mass of an 16 O nucleus (16 AMU) and the mass of an 14 O or
14 N nucleus, for annihilation of an n̄ on a neutron and proton respectively.
This phase is simulated by a set of subroutines called ”partnuc”, which
was written by Tegid W. Jones of IMB collaboration and has been modified for n − n̄ analysis in Super-Kamioande. Figure 4.1 shows the relative
starting position of the annihilation products in n − n̄ simulation. Our simulation result labeled Partnuc is compared with that based on peripheral
distribution predicted by Dover et al.. And consistency was checked withsimulation result by nucleon decay MC in Super-K based on Wood-saxon,
labeled ”Eftrace”. Eftrace is nuclear propagation program for nucleon decay
and neutrino oscillation study in Super-K. The detail kinematics of nuclear
propagation used in Super-K analysis is described in next section, Chapter
4.2.
The kinematics of our n − n̄ simulation are basically same as that of
IMB except for phase space distribution, our n − n̄ simulation uses the routine called ”genbod” from Cern Library for phase space distributions. It is
assumed in this phase that the ∆ resonance dominates, such that inelastic scattering proceeds by a pion interacting with a single bound nucleon
to make a ∆ resonance and that the ∆ subsequently propagates throughthrough nuclear matter. Provided that the ∆ is not absorbed, the final result will be an inelastic or charge-exchange scattering. The cross sections forthese two processes can be reasonably related to the corresponding elastic
and charge-exchange cross sections of pions scattered of free protons that31

Figure 4.1: Relative position of annihilation in our simulation, labeled asPartnuc. Consistency is checked with Eftrace used in nucleon decay study
in Super-K and simulation based on peripheral distribution predicted by
Dover is identical to others.
include the effects of Fermi-motion and Pauli blocking.
We assume pion-nucleon interactions depend linearly on nucleon density
which is determined from electron-nucleon scattering data[41]. Finally thesimulation results of pion-nucleon interactions inside the residual nucleus ischecked using pion-oxygen data. Figure 4.2[15] compares the π 16 O cross sections deduced by IMB in 1983 using deuteron scaling and the π 16 O data interpolated from the pion-nucleus cross sections reported by Ashery at al.[42].
To make above agreement between the model predictions and the data, IMB
made the following approximation. Absorption probability is taken to be
Cσπd ρ2 , where C is an adjustable parameter, σπd is the πd cross section, andρ is the local nuclear matter density. In our pion-nucleon simulation, we attempted to scale the pion absorption cross section by π 16 O instead of πd.
This π 16 O cross section determined from π 16 O interactions used by SuperKamiokande to simulate the interaction of π-mesons produced in nucleon
decay. Our simulation result are plotted in Figure 4.3 and compared.

4.1.3

Fragmentation

The residual nucleus, 14 N∗ after n̄ − p and 14 O∗ after n̄ − n annihilation,
decays and fragments to 2 H, 3 H, 3 He, 4 He, n, p and a remaining large nuclear fragment. The total energy of all of the daughter products from theannihilation and fragmentation must be equal to the mass of the original
16 O nucleus which is 16 AMU (=14,897 MeV). The final state of nuclear
fragments is simulated in the fragmentation phase using an algorithm that
we developed and a subroutine named by ”nucfrag”. Heavy isotopes of hydrogen and all isotopes of helium and larger nuclear fragments are removed
before the Super-K detector simulation since all nuclear fragments otherthan free neutrons and protons give below Cherenkov threshold in detec-

32

Figure 4.2: Comparison of interpolated data for pion-16 O cross sections withthe predictions of the IMB pion-nucleon interaction model obtained using
deuteron scaling.

Figure 4.3: The absorption probability for pions within 3.5 fermi of thecenter of the nucleus. Partnuc, the IMB pion interaction program, is basedon πd cross section and Eftrace, the Super-K pion interaction program, isbased on π 16 O. Our simulation adopts ”Scaled O16” which Partnuc wasdeveloped with scaled absorption probability.

33

tor simulation and Super-K detector simulation do not include these large
nuclear fragments yet.

4.2

Atmospheric Neutrino

Atmospheric neutrino flux and interaction used in MC simulation arepresented in detail in this section.

4.2.1

Neutrino Flux

There are several flux calculations. I outline the methods of the calculation and compare the results from three atmospheric neutrino flux calculations [43][44][45], which cover the energy range relevant to the present analysis, adopted in Super-Kamiokande I analysis. The flux from Honda et al.[44]is mainly used for Super-K analysis. Calculations start with primary cosmic
ray based on measured fluxes, including solar modulation and geomagnetic
field effects. The atmospheric neutrino MC is calculated for 3 years of solar
minimum, 1 year of changing activity and 1 year of solar maximum according to the cosmic ray proton, helium and neutron measurements[46][47].
And the interaction of cosmic ray particles with the air nucleus, the propagation and decay of secondary particles are simulated. A neutrino flux was
calculated specifically for the Kamioka site.
Energy Spectrum
The calculated energy spectra of atmospheric neutrinos at Kamioka areshown in Figure 4.4 (a). Figure 4.4 (b) compares the calculated fluxes asa function of neutrino energy. The agreement among the calculations isabout 10% below 10 GeV. This can be understood because the accuracy
in recent primary cosmic ray flux measurements[48][49] below 100 GeV isabout 5% and because hadronic interaction models in each calculation are
different. However the primary cosmic ray data is much less accurate above
100 GeV. Therefore, for neutrino energies much higher than 10 GeV, theuncertainties in the absolute neutrino flux could be substantially larger thanthe disagreement level among the calculations. Finally, the spectrum of
primary cosmic ray is fitted with different index in the low energy (<100
GeV) and high energy (>100 GeV) region. Taking the flux weighted averageof these spectrum index uncertainties, we assign 0.05 for the uncertainties
in the energy spectrum index in the primary cosmic ray energy spectrum
above 100 GeV.
Flavor Ratio
Figure 4.5 shows the calculated flux ratio of νµ + ν¯µ to νe + ν¯e as a functionof the neutrino energy, integrated over solid angle. This ratio is essentiallyindependent of the primary cosmic ray spectrum. Especially, in the energy
region of less than about 5 GeV neutrino energies, most of the neutrinos
are produced by the decay chain of pions and the uncertainty of this ratio
is about 3%, which is estimated by comparing the three calculation results.
In the higher energy region (10 GeV for νµ + ν¯µ , and 100 GeV for νe + ν¯e ),34

Figure 4.4: (a) The direction averaged atmospheric neutrino energy spectrum for νµ + ν̄µ calculated by several authors are show by solid line[44],dashed line[43] and dotted line[45]. (b) The ratio of the calculated neutrino
flux.

Figure 4.5: The flux ratio of νµ + ν¯µ to νe + ν¯e .

35

Figure 4.6: The flux ratio of νµ to ν¯µ and νe to ν¯e .
the contribution of K decay in the neutrino production is more important.
There, the ratio depends more on the K production cross sections and theuncertainty of the ratio is expected to be larger. A 20% uncertainty in theK/π production ratio cause at least a few % uncertainties in the νµ + ν¯µto νe + ν¯e ratio in the energy range of 10 to 100 GeV. However, as seenfrom Figure 4.5, the difference in the calculated νµ + ν¯µ to νe + ν¯e ratio issubstantially larger than that expected from the K/π uncertainty in the highenergy region. The reason for this difference has not been understood yet.
As a consequence, an energy dependent uncertainty for the νµ + ν¯µ to νe + ν¯eratio above 5 GeV neutrino energy is assumed based on the comparison of
the three flux calculations. It is taken to be 3% at 5 GeV and 10% at 100
GeV.
ν/ν̄ Ratio
Figure 4.6 shows the calculated flux ratios of νµ to ν¯µ and νe to ν¯e . The
calculations agree to about 5% for both of these ratios below 10 GeV. However, the disagreement gets larger above 10 GeV as a function of neutrinoenergies. The systematic errors in the neutrino over anti-neutrino ratio areassumed to be 5% below 10 GeV and linearly increase with logEν to 10%
and 25% at 100 GeV, for the νe to nu¯ e and νµ to ν¯µ ratios, respectively.
Horizontal/Vertical Ratio and Up/Down Ratio
Figure 4.7 shows the zenith angle dependence of the atmospheric neutrino
fluxes for several neutrino energies. At low energies, and at the Kamioka
36

Figure 4.7: The flux of atmospheric neutrinos v. zenith angle.
location, the fluxes of downward-going neutrinos are lower than those of
upward-going neutrinos. This is due to the deflection of primary cosmic
rays by the geomagnetic field, roughly characterized by a minimum rigidity
cutoff. For neutrino energies higher than a few GeV, the calculated fluxes
are essentially up-down symmetric, because the primary particles are moreenergetic than the rigidity cutoff.
One of feature characteristics of full three dimensional flux calculations is
the enhancement of the flux near horizon for low energy neutrinos. However,in Super-Kamiokande, the horizontal enhancement cannot be seen in the lepton zenith angle distribution, due to the relatively poor angular correlation
between neutrinos and leptons below 1 GeV. The uncertainties in the updown and vertical-horizontal ratios of the number of events are estimated bycomparing the predicted ratios of various flux models. These uncertainties
generally depend on the energy and the neutrino flavor. The uncertainty
in the up-down event ratio is about 1 to 2% in the sub-GeV energy region
and is about 1% in the multi-GeV energy region. The main source of theuncertainty in the vertical-horizontal ratio around a GeV is the size of thehorizontal enhancement of the flux due to the three dimensional effect; theuncertainty is estimated to be less than a few percent. In the higher energy region, where upward through-going muons are relevant, the largest
source of the uncertainty in the vertical-horizontal ratio is the K production cross section. We assume that the K/π production ratio uncertainty is
20% in the whole energy region. The uncertainties in the zenith angle andenergy distributions due to the K/π production uncertainty are includedin the systematic errors in the analysis. This error is most important forhigher energy neutrinos. For example, the vertical-horizontal uncertainty
37

Figure 4.8: The flux of upward-going atmospheric neutrinos vs. zenith angle
for higher energy region.
for upward through-going muons due to the K/π production uncertainty is
estimated to be 3%[50]. Figure 4.8 shows the zenith angle dependence of
the atmospheric neutrino fluxes for higher energy region observed as upwardmuons in Super-Kamiokande.
In summary of the atmospheric neutrino flux, we remark that, the νµ + ν¯µto νe + ν¯e ratio is predicted to an accuracy of about 3% in the energy region
relevant to the data analysis discussed in this thesis. The zenith angle
dependence of the flux is well understood, and especially, above a few GeV
neutrino energies, the flux is predicted to be up-down symmetric.

4.2.2

Neutrino Interactions

The simulation of neutrino interactions relies on detailed comparison of
the experimental data with the theoretical expectation. An important element of this is to simulate the interaction of neutrinos from 10 MeV to 100
TeV with the nuclei of water, or in the case of upward going muon, the nucleiof the rock surrounding the detector, assumed to be SiO2 . Two simulation
programs, NEUT and NUANCE, are available for neutrino interaction. In
this section, one of models (NEUT) is described. This program was developed to study atmospheric neutrino and nucleon decay in Kamiokande[51]and has been continuously updated for Super-Kamiokande. In the simulation program, the following interactions were considered.
• quasi elastic scattering νN → lN 0
• single meson production νN → lN 0 m
38• coherent π production ν 16 O → lπ 16 O
• deep inelastic scattering νN → lN 0 hardron
Where, N and N 0 are the nucleons, l is the lepton, and m is the meson,respectively.
Elastic and Quasi-Elastic Scattering
The cross section of quasi-elastic scattering off a free proton, which wasused in the simulation programs, was described by Llewellyn-Smith[52]. For
the ν 16 O scattering, the Fermi motion of the nucleons and Pauli Exclusion
Principle are taken into account. The nucleons are treated as quasi-free particles using the relativistic Fermi gas model of Smith and Moniz[53]. The
momentum distribution of the nucleons were assumed to be flat up to the
fixed Fermi surface momentum of 225 MeV/c. This Fermi momentum distribution was also used for other nuclear interactions. The nuclear potential
was set to 27 MeV/c.
Single Meson Production
To simulate the resonance productions of single π, K and η, Rein and Sehgal’s model[54][55] was adopted. In this model, the interaction is separated
into two parts as follows.
νN → lN ∗N ∗ → mN 0
where m is a meson, N and N 0 are nucleons, and N* is a baryon resonance.
To obtain the cross sections, we calculate the amplitude of each resonanceproduction and then multiply the probability of decay into one pion andnucleon to each resonance. In order to avoid double counting of interaction,
the hadronic invariant mass, W (the mass of the intermediate baryon resonance), is restricted to be less than 2 GeV/c2 . In addition to the dominant
single π production, K and η production is considered. To determine theangular distribution of pions in the final state, Rein and Sehgal’s method for
the P33 (1232) resonance were used. For the other resonances, the directional
distribution of the generated pions is set to be isotropic in the Adler Frame(resonance rest frame). The angular distribution of π + has been measuredfor νp → µ− pπ + mode[56] and the results agree well with the Monte Carloprediction. The Pauli blocking effect in the decay of the baryon resonancewas considered by requiring that the momentum of nucleon should be larger
than the Fermi surface momentum. Pion-less delta decay is also considered,
where 20 % of the events do not have the pion and only the lepton andnucleon are generated[57].
There is a parameter that should be determined by experiment in thequasi-elastic scattering and single meson production. The parameter iscalled axial vector mass, MA . For larger MA values, interactions with higher
Q2 values (and therefore larger scattering angles) are enhanced for thesechannels. The MA value was tuned using the K2K[58] near detector data.
In our atmospheric neutrino interaction Monte Carlo simulation, MA was
39

set to 1.1 GeV for both the quasi-elastic and single meson production channels, but the uncertainty of the value is estimated to be 10%. Coherent
single pion production, the interaction between the neutrino and the entire
oxygen nucleus, was simulated using the formalism developed by Rein and
Sehgal[59].
Deep Inelastic Scattering
The cross sections of deep inelastic scattering was calculated using the
GRV94[60] for the nucleon structure function. In the calculation, the hadronic
invariant mass, W , is required to be greater than 1.3 GeV/c2 . And for actual calculation, we use the probability function of pion multiplicity, which
is a function of W region (W ≤ 2GeV/c2 ). The multiplicity of pions is restricted to be greater than or equal to 2 for 1.3 < W < 2.0GeV /c2 , because
single pion production is separately simulated as previously described. Inorder to generate events with multi-hadron final states, two models wereused. For W between 1.3 and 2.0 GeV/c2 , a custom made program[61] wasused to generate the final state hadrons; only pions are considered in thiscase. For W larger than 2 GeV/c2 , PYTHIA/JETSET[62] was used. Total charged current cross sections including quasi-elastic scattering, single
meson productions and deep inelastic scattering are shown in Figure 4.9.
Nuclear Effect
The interactions of mesons and nucleons, which are generated in 16 O
nucleus, are also important for the atmospheric neutrino interaction andnucleon decay. This process is simulated by a subroutine named ”eftrace”.
In Chapter 6, this program is tested for systematic uncertainty of nuclear
propagation in n − n̄ search. Basically, all of the interactions were treatedby using a cascade model. The interactions of pions are very important because the cross section for pion production is quite large for neutrino energies
above 1 GeV and the interaction cross sections for pions in nuclear matteris also large. In the simulation of pion interactions in 16 O, inelastic scattering, charge exchange and absorption were considered. The procedure tosimulate these interactions is as follows. The initial position of the pion was
generated according to the Woods-Saxon nucleon density distribution[63].
The interaction mode is determined from the calculated mean free path ofeach interaction. To calculate the mean free path, the model described by
Oset et al.[64] was adopted. The calculated mean free path depends not
only on the momentum of pion but also on the position of the pion in the
nucleus. If inelastic scattering or charge exchange occurs, the direction andmomentum of the pion are determined by using the results of a phase shift
analysis obtained from π − N scattering experiments[65]. In calculation of
the pion scattering amplitude, the Pauli blocking effect is also taken into
account by requiring the nucleon momentum after interaction to be larger
than the Fermi surface momentum (PF (r)) at the interaction point defined
as follows.
1
3
PF (r) = [ π 2 ρ(r)]− 3
(4.1)
2

40

Figure 4.9: Charged current total cross section divided by Eν for (a) neutrinoand (b) anti-neutrino nucleon charged current interactions. Solid line shows
the calculated total cross section. The dashed, dot and dash-dotted lines
show the calculated quasi-elastic, single-meson and deep-inelastic scattering,
respectively.

41

Figure 4.10: The cross section of π 16 O interactions. The lines show theresults of our calculation based on [64] and the points show experimental
data[66].
ρ(r) =1Zρ̄
A 1 + exp( |r|−c )

(4.2)

a

where A(=16) is mass number, Z(=8) is atomic number, ρ̄(=0.48 m3π ) isaverage density of nucleus, a(=0.41 fm) and c(=2.69 fm) are density parameters of oxygen nucleus, respectively. The pion interaction simulation
was checked using data for the following three interactions: π 12 C scattering,
π 16 O scattering and pion photo-production(γ +12 C → π − + X)[66]. One ofcomparison is shown in Figure 4.10.

4.3

Detector Simulation

The particles left the oxygen nucleus after anti-neutron annihilation or
neutrino interactions are fed into a detector simulation code. The simulation program includes the tracks of particles, Cherenkov radiation, propagation of Cherenkov photons in water and the response of PMTs and thereadout electronics. The detector simulator program has been developed
based on GEANT package[67]. The program simulates the tracks of particles, Cherenkov radiation, propagation of Cherenkov photons in water, andthe response of PMTs and the readout electronics. And various processes
for each particles are considered in our simulation program as listed in Table
4.3.
When a π 0 escapes from the oxygen nucleus or a π 0 is generated by free
proton interaction, it immediately decays to two gammas (98.8% branchingratio). However, since π ± has relatively long lifetime, the propagation of
π ± in water should be simulated. CALOR package[68] is employed in our
simulation code. This package is known to reproduce the pion interactions
42

γ

e±

µ±

Hadrons(e+ , e− ) pair production
Compton scattering
Photoelectric effectMultiple scattering
Inization and γ-rays production
Bremsstranhlung
Annihilation of position
Generation of Cherenkov radiation
Decay in flightmutiple scattering
Ionization and γ-rays production
Bremsstrahlung
Direct (e+ , e− ) pair production
Nuclear interaction
Generation of Cherenkov radiation
Decay in flight
Multiple scattering
Ionization and γ-rays production
Hadrnoic interactions
Generation of Cherenkov radiation

Table 4.3: List of the processes considered in simulator
well including low energy region ( 1GeV/c). For still lower energy region(pπ ≤ 500 MeV/c), a custom program[69] based on experimental data fromπ − 16 O scattering[70] and π − P scattering[71] is used in our simulation
code.
The Cherenkov photons are generated according the Eq. (3.2) and (3.3).
For the propagation of Cherenkov photons in water, Rayleigh scattering,
Mie scattering and absorption are taken into account. According to thesize of target particles, the interaction types are assigned[72]. Attenuation
coefficients by Eq. (3.5) used in our simulation are show in Figure 4.4, which
are tuned to reproduce the measurement using laser system (Chapter 3.3.1).
Light reflection and absorption on detector material, such as the surface of
PMTs and black sheets, are also simulated using probability functions that
depend on the photon incident angle estimated from direct measurements.
For the simulation of the PMT response, measured quantum efficiency
is used. The total amount of p.e.s detected in each PMT is derived bysumming up individual p.e. with a weight of a single p.e. distribution. The
hit time of each PMT is smeared according to the PMT timing resolution.
Properties of the electronics system, such as the time width of ADC gate
and the signal threshold, are also taken into account.

43

Figure 4.11: Wavelength dependence of attenuation coefficient (L−1attenu ) obtained by light scattering measurement. Point is measurement in Chapter
3.3.1.

44

Chapter 5

Data Reduction andReconstruction:
Fully-Contained Events
The Super-Kamiokande I data was acquired from May, 1996 to July, 2001.
The data are classified into three groups; fully-contained (FC), partiallycontained (PC) and upward-going muons (UPMU). To separate FC and PC
events, a fast spatial clustering algorithm is applied to the outer detector
hits; if the number of hits in the largest OD cluster is less than 10, the eventsis defined as fully-contained. Otherwise, it is defined as partially-contained.
The neutrino energies of partially-contained events are typically 10 times
higher than that of fully-contained. Figure 5.1 shows the separation.
The analyses using these two data sets are based on independent data
reduction and reconstruction. This section outlines the programs for reduction and reconstruction for fully-contained data which is used in atmospheric
neutrino and nucleon decay (including n − n̄ search) analysis. These same
programs are also applied to atmospheric neutrino MC and n − n̄ MC.

5.1

Data Reduction

The Super-Kamiokande has been taking the data with the trigger rateof 10 Hz every day except for 10% down time due to detector calibration,
maintenance of detector and so on. 2.7 Hz are due to cosmic ray muonand 6 Hz are due to relatively low energy (a few MeV) events caused byradioactivity in the detector water or gamma rays from surrounding PMTs
and rocks. Remaining 1 Hz are due to fake triggers caused by reflection of
PMT signals and unwanted PMT signals following highly energetic events(so-called ”after pulsing”). Therefore, we should eliminate these backgroundto find the possible n − n̄ events from the cosmic ray events. Cosmic raymuons are easily discriminated by requiring little or no ring activity in theouter detector. For atmospheric neutrino and nucleon decay analysis, weconsider the events with visible energy above 30 MeV where visible energy(Evis) is defined as the energy of an electromagnetic shower that gives acertain amount of Cherenkov light (for example, a muon of momentum 300
MeV/c yields a visible energy of about 110 MeV). To make the final FC
45

Figure 5.1: The number of hits in the largest outer detector cluster, which isused to separate the fully-contained and partially-contained event samples.
The histogram shows the MC prediction with neutrino oscillation.
data sample, the following five steps of data reduction criteria are used.

5.1.1

1st and 2nd Reduction

Simple and efficient criteria are applied in the first and second reduction
steps:• P E300 > 200 p.e
Where, P E300 is the maximum total photo electrons collected in the
inner detector within a 300 nsec sliding time window.
• P Emax /P E300 < 0.5
Where, P Emax is the maximum p.e. in any single ID PMT.
• N HIT A800 < 25 hits
Where, N HIT A800 is the number of hit OD PMT within 800 nsec
sliding time window.
• T DIF F > 100µ sec
Where T DIF F is the time interval from the preceding event. This is
to reject electrons from stopping muon decays.

5.1.2

Third ReductionMore complex criteria are applied in the third reductions step for further
rejection of cosmic ray muons and low energy events:• N HIT Ain < 10 hits and N HIT Aout < 10 hits
Where, N HIT Ain (N HIT Aout ) is the number of hit OD PMTs within
46

8 m from the entrance (exit) point of muon track fitted using the innerdetector light pattern.
• N HIT50 ≥ 50 hits
Where, N HIT50 is the number of hit ID PMTs in 50 nsec sliding time
window.

5.1.3

Fourth Reduction

Additional selection criteria are used to eliminate spurious events, suchas ”flashing” PMTs that emit light from internal corona discharges. Flasher
events are removed by two different methods.
• Typical flasher events have broader PMT timing distributions than
the neutrino events. Events with broader timing distributions are
eliminated.
• Since flasher events have a tendency to be repeated with similar spatial
hit distribution, the pattern information of observed charge is used on
to eliminate these events. A correlation parameter based on the charge
pattern is calculated with other data events and a ”matched” tag is
assigned for highly correlated events.
A cut is applied based on maximum correlation value and the number of”matched” with other events.

5.1.4

Fifth Reduction

Two further event types are eliminated in the fifth reduction step.
• N HIT Aof f < 10 hits
Where N HIT Aof f is the number of OD hits in 200 nsec sliding time
window preceding the trigger time (-8900 ∼ -100 nsec). This cut eliminates decay electrons from invisible cosmic ray muons that are below
Cherenkov threshold in the inner detector.
• Cosmic ray muons are removed using a more precise fitter and thesame criteria as the first cut of (3).
Finally, the vertex is required to be within a fiducial volume (FV), 2 metersfrom the wall of the inner detector, and the visible energy is required to begreater than 30 MeV. Table 5.1 shows the event rate after each reduction
step.

5.2

Reconstruction

The fully-contained events after passing through the data reduction, undergo reconstruction process.

47

Reduction step
TriggerFirst reduction
Second reduction
Third reduction
Fourth reduction
Fifth reduction
FV and Evis cuts

Data1,889,599,293
4,591,695
301,791
66,81026,93723,984
12,180Monte Carlo
14,013.9 (100.00%)
14,006.3 (99.95%)
14,006.1 (99.94%)
13,993.3 (99.85%)
13,898.1 (99.17%)
13,895.3 (97.15%)
13,676.7 (97.59%)

Table 5.1: Number of events after each reduction for fully-contained events
during 1489 days of the detector live-time. The Monte Carlo numbers andefficiencies down to the fifth reduction are for events whose real vertex is in
the fiducial volume, the number of outer detector hits fewer than 10 and thevisible energy larger than 30 MeV. In the last line, the fitted vertex is used
for both data and Monte Calro.

5.2.1

Vertex Fitting

The reconstruction process starts from vertex fitting. The vertex fitting
consists of following three steps.
1. Point-fit : The point at which the timing residual distribution of hit
PMTs has the sharpest peak is estimated.
2. Ring edge search : The direction and outer edge of the dominant ringis estimated by the Cherenkov opening angle expected from the charge
within the cone.
3. TDC-fit : the track length of the charged particle and scattered Cherenkov
photons are taken into account in the calculation of the time residual.
The vertex resolution is estimated to be 30 cm for single-ring fully-contained
events. The vertex positions are more precisely estimated later by MS-fit
using ring pattern.

5.2.2

Ring Counting

After a ring direction and vertex are roughly found through the previous
vertex fitting algorithm, other possible rings are searched using a Houghtransform[73] based technique. The technique is iterative. A second ring issearched for by choosing possible ring directions based on the Hough map,and a likelihood technique determined if a second ring from the list of thepossible rings is more consistent with the data than just one ring. If a secondring is judged to be more consistent, then this procedure is repeated as
many as necessary until finally no further rings are necessary to fit the data.
Figure 5.2 shows the likelihood difference between the 2 ring assumption
and a 1 ring assumption. In these figures, the oscillation at the best fit
parameters (sin2 2θ = 1.0, ∆m2 = 2.1 × 10−3 eV 2 ) was taken into accountfor the Monte Carlo prediction. A cut was made at likelihood difference48

Figure 5.2: The distribution of the likelihood difference between a single-ringassumption and a multi-ring assumption for sub-GeV (top) and multi-GeV(bottom) FC events. The hatched histograms show the charged current
quasi-elastic interactions.
of 0 to separate single and multi ring events. The efficiency for identifying
charged current (CC) quasi-elastic νe (νµ ) events as single-ring is 93.2 (95.8)% and the track’s angular resolution for these single-ring events is estimatedto be 3.0◦ and 1.8◦ for single-ring e-like and µ-like events, respectively. The
detail description of this process can be found in [74].

5.2.3

Particle Identification

To determine the identity of the final state particles, a particle identification algorithm is applied which exploited systematic differences between
Cherenkov rings produced from different particles. Cherenkov rings from anelectron or gamma-ray exhibit diffuse light distribution because of electromagnetic cascades and multiple scattering and are called e-like events. On
the other hand, Cherenkov rings from muon or charged pion give sharper
ring edge and are called µ-like events. Figures 5.3 and 5.4 show observed
single-ring e-like and µ-like events, respectively.
The opening angle of the Cherenkov cone, which depends on β(≡ v/c),
is also used to separate e-like and µ-like events at low momenta. The validity of the method was confirmed by a beam test experiment at KEK[75].
The misidentification probabilities for single-ring e-like and µ-like events are
estimated to be 0.8% and 0.7% respectively, using simulated charged CC(Charged Current) quasi-elastic neutrino events. The distribution of thelikelihood variable used to discriminate single-ring e-like and µ-like events
are shown for both the data and MC for the sub-GeV and multi-GeV sam49

Figure 5.3: An event display of a single-ring e-like.

Figure 5.4: An event display of a single-ring µ-like.

50

Figure 5.5: The distribution of particle identification likelihood for subGeV (top) and multi-GeV (bottom) FC single-ring events, comparing data
(points) and atmospheric neutrino MC. The MC includes neutrino oscillation. The hatched histograms show the νµ charged current interactions.
ples in Figure 5.5. In both of these cases, the figures show a clear separationof the likelihood variable.
The identification efficiency is checked using cosmic ray muons that stopin the detector and subsequently decay to electrons. These events are easily
selected by their timing signature. The resulting misidentification probabilities for stoping cosmic ray muons and decay electron light patterns are
0.4±0.1% and 1.8±0.5% respectively.

5.2.4

Precise Vertex Fitting and Momentum Determination

To obtain more precise vertex position, the vertex position is estimated by
MS-fit for single-ring events taking into account the expected light pattern
given by the particle identification. In the case of multi-ring events, TDC-fit
is used. After the rings are re-fit, the total photo-electrons are apportioned
to all of the rings. The momentum of a particle is determined from thetotal number of p.e.’s within a 70◦ half-angle of the cone relative to thetrack direction, with corrections for light attenuation and PMT angular
acceptance. And the momentum from each ring is separated based on the
expected p.e. distribution from each ring as a function of the opening angle.
Finally, the number of rings is corrected; Missfitted rings tend to have
low momentum and overlap with the other energetic rings. MC simulationof atmospheric neutrino and the process of reduction and reconstruction are
outlined well in [76].

51Chapter 6

Search for n − n̄ Oscillation
We should extract the candidates of n − n̄ oscillation from the Super-K
I data set of 24.5×1033 neutron-yr. For this work, additional criteria areapplied to the remaining fully-contained (FC) data after passing throughthe reduction algorithm. Studying the FC atmospheric neutrino MC as amost significant source of background, we can estimate the upper limit of
the number of n − n̄ oscillation signal. Finally, the lower limit on neutron
oscillation time is calculated with inclusion of systematic errors. In thisthesis, 5,000 n − n̄ events inside of fiducial volume (FV) and 100 years FC
atmospheric neutrino MC are simulated for Super-K I data set.

6.1

Event Selection Criteria

Candidates of n − n̄ oscillation are extracted based on (a) Number ofrings, (b) Visible energy, (c) Total momentum and (d) Total invariant mass.
The number of rings are understood particles produced by the interaction
and visible energy is defined as the energy of an electromagnetic showerthat gives a certain amount of Cherenkov light. The total momentum isP−→→defined as Ptot = | allringspi | where −pi is reconstructed momentum
vectoriq

2 − P2of i-th ring and the total invariant mass is defined as Mtot = Etot
tot
Pallrings −→where total energy Etot = i|Pi |. Figure 6.1 is comparison of above
4 variables among the n − n̄ MC, atmospheric neutrino MC and data after
reduction and reconstruction processes in same way. To compare the plots,
one addition is taken into account. Strong evidence has been presented thata νµ can oscillate to either a ντ or a sterile ν and this effect is observed onlyin charged current interaction. Therefore in the case of atmospheric neutrinoMC, oscillation effect is applied at the sin2 2θ = 1 and ∆m2 = 0.0021 as Eq.
(6.1) since MC was made without considering the oscillation. As the plotsshow, the number of rings and visible energy are efficient variables to selectthe candidates. So, we can make first criterion to reject dominant background which comes from single ring events. The criterion rejects around
64% background events. Figure 6.2 is the visible energy distribution after
rejecting the single ring events.

P (νµ → νµ ) = 1 − sin2 2θsin2 (1.27

52

∆m2 L
)
Eν

(6.1)

Our goal is to find the n− n̄ oscillation events and calculate the oscillation
time. If we don’t find the events, we set the lower limit of oscillation time.
The lifetime for neutron oscillations is estimated byTn−n̄ =

²×N ×T
.
S(6.2)• ² : signal detection efficiency• N : number of neutrons inside of fiducial volume• T : detector livetime• S : the upper limit on mean of number of signal at 90% CL
and the procedure of calculation is described in Chapter 6.3.
For optimization of selection criteria, signal significance is consideredbased on above calculation as follows ;s²×N ×T ×Γ
√ =
√
b
b

(6.3)

where Γ is event rate and b is number of background candidates. Since
N × T × Γ is consistent,
s
²
√ ∝√
(6.4)
b
b
√
²/ b is used as a factor for criteria optimization. Optimal cut is foundscanning the region which√ is low momentum and high invariant mass basedon maximum value of ²/ b ;(a) Number of rings > 1(b) 700MeV < Visible energy < 1300MeV(c) 0 MeV/c < Total momentum < 450MeV/c(d) 750MeV/c2 < Total invariant mass < 1800MeV/c2
Criterion (a) and (b) rejected the 94% background events and saved 33.5%n−n̄ MC and 6% signal. Figure 6.3 shows the total momentum and invariant
mass distribution after passing through the criterion (a) and (b). Additional
kinematical cuts, (c) and (d) made final sample which is inside of arrows infigure 6.4 for analysis.

6.2

BackgroundAs mentioned above, the most significant source of background in n − n̄
search comes from the atmospheric neutrino interactions as which on anaverage 8 FC events are detected per day during Super-K I full livetime.
Therefore, investigation of the n− n̄ mimic events is performed using the FC
atmospheric neutrino MC. 521 FC atmospheric neutrino simulation events
without inclusion of oscillation effect are alive after passing through theevent selection criteria which was mentioned in previous section. The characteristic is listed up in Table 6.1 in detail. Electron neutrino and muon
neutrino have almost same contribution to background but muon neutrino
will be decreased by neutrino oscillation. And anti neutrino events are much
53

Figure 6.1: Basic plot comparisons : Each plot show Number of rings(Nring), Visible energy (Evis), Total momentum (Ptot) and Total invariant mass (Mtot). Vertical axes are normalized by the number of events andoscillation effect was applied in the case of atmospheric neutrino MC. A
peak between 100 and 200M eV /c2 of Mtot distribution is caused by π 0 .

54Figure 6.2: Visible energy distribution when the number of rings is greaterthan one. The arrows show the selection region of visible energy for thisanalysis.

Figure 6.3: Total momentum and Invariant mass after passing through theselection criterion (a) and (b).

55

Figure 6.4: Invariant mass after passing through the selection criterion (a),(b) and (c).
less than neutrino events. Main contribution is single pion and multi pion
production. The reason can be simply understood, produced pions and particles by neutrino interaction and secondaries make multi rings. Remarkable thing is, topologically even though charged current quasi elastic eventsshould be separated from n − n̄ events since they have lager momentum,
they survived in analysis sample because energetic outgoing nucleon madehadron interactions. The neutral current elastic events are also survived insame way. Figure 6.5 shows the parent neutrino energy distribution for allof background events.

6.3

Results

Final detection efficiency of n − n̄ events and the number of backgroundand candidates after passing through above criteria are summarized in Table

CC quasi elastic
CC single π prod.
CC multi π prod.
CC K or η prod.
NC single π prod.
NC multi π prod.
NC K or η prod.
NC elasticνµ
11 (2.11%)
50 (9.6%)
101 (19.38%)
6 (1.15%)ν̄µνe0
7 (1.34%)
10 (1.92%)
47 (9.02%)
10 (1.92%) 103 (19.77%)
6 (1.15%)8 (1.53%)
17 (3.26%)
125 (23.99%)
2 (0.38%)
1 (0.19%)

Table 6.1: List of background events.

56

ν̄e
0
7 (1.34%)
9 (1.73%)
1 (0.19%)

Figure 6.5: Parent neutrino energy of background events. Left figure shows
about 521 background events in total and right figure shows in each interaction mode.
6.2. For this estimation, atmospheric neutrino MC considered the oscillation
effect and overall normalization[76], a factor of 1.119, and is normalized bylivetime. The detection efficiency is 10.4% and the candidates from SuperK I of 91.7kton-year exposure are 20 events in which 21 background events
are allowed. Figure 6.6 shows final sample for analysis which is selected bykinematical cuts.

6.3.1

Simple Limit Calculation

When we observe N particles for a time T and find a nonzero number of
events, n, with the detection efficiency, ², the event rate, Γ is estimated by;
n
Γ=
(6.5)
NT²
However, when n is zero, a rate can not be accurately calculated and n is nolonger a good estimator of the true mean. So, instead, a limit on the event
rate (oscillation rate in this thesis) at some confidence level is set.
Our result has 20 candidate events but also has background with almost
same level. So, we interpret our result as lower limit of n − n̄ oscillation

Criterion
Inside of F.V.
Nring cut
Evis cutPtot and Mtot cut

n → n̄ MC (%)
5000
4275 (85.5)
1673 (33.5)
521 (10.4)

atm. ν MC (%)
13028.94676.7 (35.8)
909.5 (7.0)
21.6 (0.16)

DATA (%)
12180
3865 (31.7)
731 (6.0)
20 (0.16)

Table 6.2: Number of events and detection efficiency after each criterion.
57

Figure 6.6: Total invariant mass versus total momentum. The events insideof right lower box in each scatter plot are final sample selected by kinematicalcuts for n − n̄ oscillation analysis. With 10.4% detection efficiency in which
521 events are detected among 5,000 n − n̄ events, 20 candidates and 21
background events are observed.

58

time and the limit is calculated by Eq. (6.2) using the quantities in Table
6.2. In simple case, it is common to use the method of Poisson Process with
Background[77]. However since this method does not take any uncertainties
that we may have in the parameters to get the limit, the final limit will be
estimated with other method considering the effect of systematic errors inlast of this Chapter. Firstly, assuming that the systematic uncertainty is
negligible and the number of background(µB ) is known, the lower limit ofoscillation time is calculated simply.
The upper limit on mean of the number of signal S in Eq. (6.2) can be
defined using Poisson distribution[77]:CL = 1 −Pn0(µB +S)nn=0n!
P 0 (µB )ne−µB nn=0n!

e−µB +S(6.6)

where CL is a confidence level and n0 is the number of observed candidates.
Applying n0 = 20 and µB = 21.6, the upper limit S is calculated to be 7.95
at the 90% confidence level. Based on this S, the lower limit on the neutron
oscillation time is calculated as:
Tn−n̄ =×T
² × v × NA × 8neutrons
18g
S

(6.7)

For exposure, v is the fiducial volume of 22.5 kton, NA is Avogadro’s number and T is livetime of 4.07 years. ² is the efficiency to detect neutron
oscillations, 10.4%. Therefore, the neutron oscillation time limit is calculated to be 3.2×1032 yr at the 90% confidence level for 24.5×1033 neutron-yr.

6.3.2

Limit for Free Neutrons

The lifetime of a neutron bound in a nucleus with A nucleons (TA ) is muchlarger than that of a free neutron (τf ree ) due to the suppression of neutron
oscillations by a potential barrier at the edge of the nuclear potential well.
As already mentioned, our search in this thesis is about intranuclear process. Limit can be converted to the limit for free neutron by theoretical
nuclear suppression factor[12][13][14] with following relation.
2
T (intranuclear) = R · τnn̄
(f ree)(6.8)

where R is dimensional ”suppression factor” equal to ∼ 2 · 1023 sec−1 for themost of nuclei. This can be understood from the following considerations
simply.
The neutron bound in nucleus by energy ∆E(∼ 10M eV ) is quasi-free forthe time1∆t ∼∼ 10−22 sec(6.9)∆E
Probability of n − n̄ oscillation during the time ∆t is
P =(

∆t 2
)
τnn̄

59

(6.10)

and above condition occurs per second.
P =∆t 2 1∆t
1=()=
T (intranuclear)τnn̄ ∆t(τnn̄ )2

(6.11)

Intranuclear process are heavily suppressed by R.
T (intranuclear) = R · (τnn̄ (f ree))2(6.12)

1∼ 1022 s−1(6.13)∆t
We call R as nuclear suppression factor. Theoretical progresses on R aredescribed on [12][13][14] and R of 16 O is suggested (0.46 ∼ 1.93) × 10−23
by Dover et al., (1.7 ∼ 2.6) × 10−23 by Alberico and (0.6 ∼ 3.6) × 10−23 byHüfner and Kopeliovich. The most conservative limit is R = 3.6 × 1023 s−1
in most recent theoretical treatment of [14].
Finally, oscillation time limit on bound neutron in previous section canbe translated to 1.67 × 108 s on free neutron by most conservative limit ofnuclear suppression factor.
R∼

6.4

Systematic Errors

We simulated n − n̄ oscillation and background for n − n̄ search and got
the lower limit on neutron oscillation time. However, the limit is affectedby uncertainties in detection efficiency and background due to imperfectionof simulation and measurement. In this section, I estimate the systematic
errors in our n − n̄ analysis.

6.4.1

Uncertainties in Efficiency and Exposure

Incompleteness and model dependence in simulation of n − n̄ oscillation
lead to systematic errors. By estimating the contribution to detection efficiency and exposure from each source of uncertainties, systematic errors inanalysis are obtained. The sources of uncertainties are listed up below;• Detection efficiency– Fermi momentum– Annihilation branching ratio– Nuclear effect– Un-uniformity of detector gain
– Energy scale– Ring counting• Exposure– Detector livetime– Fiducial volume60

Figure 6.7: Fermi momentum distribution.
The uncertainty is caused by imperfect knowledge of n − n̄ oscillation
kinematics. First, I estimated how much fermi momentums of anti-neutronand nucleon, which participate in annihilation process, affect to detection
efficiency. Figure 6.7 shows fermi momentum of anti-neutron which wastransited from neutron. Changing the fermi momentum by 20%, the contribution to detection efficiency is estimated to be 4.2%. And annihilation
branching ratio can be source of uncertainty. Table 4.1 and 4.2 in Chapter
4 show the annihilation branching ratios which are used in this thesis andother experiments. For uncertainty estimation, we generated n − n̄ oscillation MC with other branching ratios, Baltay(1966) for n̄ − n annihilation
and Bettini(1967) for n̄ − p annihilation, and got the change of detection
efficiency by 5.2%. Nuclear effect in pionic phase after annihilation is considered as a main source of uncertainty in efficiency. The errors of crosssection are taken from the figure 4.2. Increasing the probability by 20%of elastic, 30% of charge exchange, 25% of absorption and 30% π production, the uncertainty in efficiency is estimated to be 12.5%. And to checkmodel dependency of nuclear effect, nuclear propagation program ”eftrace”
for nucleon decay study in Super-K analysis is called in n − n̄ simulation
process instead of ”partnuc” which is n − n̄ own nuclear propagation program. Obtaining the small uncertainty of 1.7%, the reasonable consistencyof our simulation is checked with other Model.
And event selection and reconstruction process include possible sourcesof uncertainties. For ”neutrino” oscillation study[76] in Super-K, the difference of energy scale between upward-going and downward-going eventswas measured using decay electrons from cosmic ray stopping muons. The
up/down asymmetry of energy scale was estimated to be 0.6% and this ununiformity of energy scale can affect momentum measurement which is oneof criteria for n − n̄ search. Therefore by changing the momentum cut by±1.2%, we obtained 4% uncertainty in efficiency. In neutrino oscillation
61

study in Super-K, the uncertainty of energy scale for fully-contained eventswas also estimated to be 2%. Based on this report, visible energy cut ischanged by 2.5% and the contribution to efficiency is estimated to be 1.7%.
And for final consideration, we tested the possibility of uncertainty from ringcounting and I’d like to describe procedure of this study in detail below.
Ring candidates are tested by a likelihood method as explained in Chapter
5.2.2. If there is systematic difference of likelihood between data and MC
due to some reason (water transparency, incomplete understanding of thegeometry etc.), it can be source of uncertainty. To investigate the systematicdifference of likelihood, atmospheric neutrino data and MC between 8,000
p.e. and 13,000 p.e. are selected as the sample. Comparing the likelihood
distribution between data and MC with some offset, we find the minimum χ2
defined as (data − αM C)2 /σ 2 . Figure 6.8 shows the likelihood comparisonand χ2 result for 1ring/2more ring separation. The center values of parabola
fitted around the minimum χ2 region are taken as systematic errors of likelihood function. This process is also applied for higher ring separations andFigure 6.9 shows the results. The quantities of the errors estimated above
are summarized in Table 6.3. Finally to estimate the uncertainty causedby ring counting in efficiency of n − n̄ search, ring reconstruction process is
newly applied to n − n̄ MC with new likelihood threshold changed by the error estimated in each ring separation. Changing the threshold of likelihood,the number of n − n̄ events passing through selection criteria is changed by
0.6%.
Separation
1ring/2more ring
2ring/3more ring
3ring/4more ring
4ring/5more ring

minimum χ2 ± 1σ
- 0.733 ±0.137- 0.623 ±0.142- 0.804 ±0.297+ 0.198 ±0.480

Table 6.3: Fitted minimum χ2 of likelihood function for ring counting. We
assume these difference from same reason and change the threshold coherently.
Oscillation time limit is also directly affected by exposure. So, the uncertainties in the exposure are estimated. The livetime is calculated from the
48bit clock counter information recorded in TRG module. The uncertaintyof the observed livetime is estimated by comparing the clock counter withanother clock counter to be < 0.1%. Lastly, uncertainty of fiducial volume isestimated by comparing the number of events inside and outside of fiducial
volume in the case of FC data and MC as follows ;DAT Ain /DAT Aout
= 0.99 ± 0.03
M Cin /M Cout

(6.14)

Above estimation is done using the events of which the number of ring isover two and visible energy is over 30GeV. Uncertainty of fiducial volume isestimated to be 3.2%.
62

Figure 6.8: Likelihood distribution and minimum χ2 .
All of uncertainties in efficiency and exposure are summarized in Table
6.4 and systematic uncertainty in total is estimated to be less than 15.2%.

Detection Efficiency
fermi momentum
annihilation branching ratio
un-uniformity of detector gain
energy scalering counting
nuclear propagation (model dependence)nuclear propagation (cross section)
Exposure
detector livetime
fiducial volume
Total

Uncertainty (%)
14.9
4.2
5.2
4.0
1.7
0.6
1.7
12.5
< 3.2
<0.1
3.2
<15.2

Table 6.4: Systematic uncertainties in efficiency and exposure.

6.4.2

Uncertainties in BackgroundThe uncertainties in background also affect to the lower limit on n − n̄ oscillation time. Neutrino flux and interaction can be sources of uncertainties
since we suppose the fully-contained atmospheric neutrino is main background. And uncertainties related to events selection and reconstruction
are also considered, such as un-uniformity, energy scale and ring counting
in common with the estimation of uncertainty in efficiency.
The detail descriptions of the uncertainties for the atmospheric neutrino
flux and interaction in MC simulation were presented in Chapter 4.2 and 4.3.
63

Figure 6.9: Likelihood distribution and minimum χ2 . From the top, it is for
2ring/3more ring separation, 3ring/4more ring separation and 4ring/5morering separation.
64

By changing the neutrino flux and interaction by the errors, uncertainties inbackground rate are estimated and summarized in Table 6.5. Uncertainties
by un-uniformity, energy scale and ring-counting are estimated in same wayof estimation in efficiency. Changing the boundary values of selection criteria
for visible energy and total momentum changes the number of background
by 9% and 12% respectively. And to estimate uncertainty by ring-counting,ring reconstruction process which has the change of likelihood threshold by
the errors is applied to FC atmospheric neutrino MC and contribution to
background rate is estimated to be 4.3%. The total systematic uncertainty
in background rate is estimated to be 32.1%.

Err.(%)
Neutrino Flux
flux absolute normalization
flavor ratios (Eν < 5GeV, > 5GeV )ν̄e /νe ratio (Eν < 10GeV, > 10GeV )ν̄µ /νµ ratio (Eν < 10GeV, > 10GeV )up/down ratio
horizontal/vertical ratio
K/π ratioenergy spectrum
Neutrino Cross Section
MA in quasi-elastic and single-π
QE scattering (model dependence)
QE scatttering (cross section)
single-π production (cross section)
multi-π production (model dependence)
multi-π production (cross section)
coherent π production (cross section)
NC/CC ratio
nuclear effect in 16 O (mean free path)
Un-uniformity of Detector Gain
Energy Scale
Ring Counting
Total

20
3, 3-10,5, 5-105, 5-25
0.4-2.1
0.3-2.8(3D calc.)
20
0.05 forEp > 100GeV

Uncert.(%)
21.5
20-, 0.1
0.9, 0.8, 5.2
5.8

10
1σ=Fermi-gas
vs. Oset
1010
1σ=w/ vs.
w/o Bodek
5
30
20
30

Table 6.5: Systematic uncertainties in background rate.

65

18
4.4
0.4
2.8
15.5
3.4
0.1
6.2
2.7
9.0
12.0
4.3
32.1

6.5

Final Limit Calculation

In section 6.3, simple limit calculation using Poisson distribution is performed assuming the systematic uncertainties to be negligible. In this section, all of systematic uncertainties are included in the limit calculation by
employing a Bayesian method[78][79].

6.5.1

Description of Method

The expected mean number of candidates, µ, in our data sample isµ = Γλ² + b(6.15)

where Γ is the true event rate (n−n̄ oscillation rate in this analysis), λ = N T
is the true exposure, ² is the true efficiency to detect oscillation events andb is the true mean number of background events. In the counting experiments, the probability to detect n events follows the Poisson distribution
with Poisson parameter µ.
P (n|Γλ²b) =e−(Γλ²+b) (Γλ² + b)nn!

(6.16)

P (A|B) represents the probability of proposition A, given that proposition
B is true.
Applying Bayes’ theorem allows us to write
P (Γλ²b|n)P (n) = P (n|Γλ²b)P (Γλ²b).

(6.17)

Because quantities Γ, λ, ², b are independent, P (Γλ²b) can be disintegrated.
P (Γλ²b) = P (Γ)P (λ)P (²)P (b)(6.18)The quantity in which we are interested, probability density function of Γ
can be obtained by
Z Z Z

P (Γ|n) =P (Γλ²b|n)dλd²db.

(6.19)

By combining above four equations, we obtain
Z Z Z

P (Γ|n) = Ae−(Γλ²+b) (Γλ² + b)n
P (Γ)P (λ)P (²)P (b)dλd²db. (6.20)
n!

Above normalization factor A is resolved by demanding
Z ∞0

P (Γ|n)dΓ = 1.

(6.21)

P (Γ), P (λ), P (²), P (b) in Eq. (6.20) are prior probability density functions(priors) and they enable us to include systematic uncertainties in the limit
calculation. Finally, we can calculate the upper limit of the event rate ΓlimitbyCL =Z Γlimit0

P (Γ|n)dΓ.

(6.22)In this thesis, the limit is calculated at the 90% CL and the lifetime limit(oscillation time limit in this analysis) is the inverse of Γlimit .
66

6.5.2

PriorsThere are two classes of priors in this method. One contains Γ, the othercontains ², λ and b. In the former case, Γ is the parameter we wish to
estimate with the experiment and in the latter, the parameters are notdirectly interesting and are marginalized out of the final result appearing in
calculation process. Each prior is discussed below.
The prior for the event rate P (Γ) is taken to be uniform. This corresponds
to the uniform prior implicitly used in simple Poisson limits[77].
P (Γ) ∝ {1 Γ>00 otherwise(6.23)The priors for the exposure P (λ) and detection efficiency P (²) are taken
as Gaussian distributions, truncated to disallow unphysical regions.
22

P (λ) ∝ {e−(λ−λ0 ) /2σλ0

P (²) ∝ {e−(²−²0 ) /2σ²
0

2

2

λ>0
otherwise(6.24)

0<²<1
otherwise(6.25)

where λ0 and ²0 are estimated exposure and efficiency. The values of σλ andσ² are taken from the Table 6.4 in the previous section.
The background prior P (b) is taken to be a convolution of Poisson andGaussian distributions in order to account for both the statistical uncertainty of a finite background MC sample size and the systematic uncertainty
in the background MC sample.
P (b) ∝

Z ∞ −bM C (bM C )nb − (bC−bM C )2
e
2σ 2
0

e

nb !

b

dbM C

(6.26)

where• nb : MC events passing through n − n̄ oscillation criteria.
• bM C : true mean MC events passing through n − n̄ oscillation criteria.
• C: MC oversampling factor.
• σb : uncertainty due to neutrino fluxed and cross sections etc.

6.5.3

Results

The lower limit on n − n̄ oscillation time is obtained by integrating theparameter in Eq. (6.20) and (6.22). To perform this, GNU Science Librarywhich is available in [80] is used for this thesis. The lower limit on n − n̄
oscillation time of bound neutrons is determined at the 90% CL,
Tn−n̄ > 1.78 × 1032 yr(6.27)

incorporating most major sources of experimental uncertainties. And assuming the suppression factor in 16 O is 3.6 × 1023 s−1 , the corresponding
limit of free neutrons at the 90% CL isτn−n̄ > 1.25 × 108 s.

67(6.28)

Chapter 7

Conclusion
A search for neutron-antineutron oscillation which is a process of |∆B| =2 predicted by L-R symmetric gauge theories was undertaken using the24.5 × 1033 neutron-yr exposure of the full Super-K I data set. In thisthesis, most major sources of experimental uncertainties were incorporated.
The uncertainty in detection efficiency was estimated to be 15.2% from 9
sources of systematic errors and in background was estimated to be 32.1%
from 20 sources of errors.
A lower limit on oscillation time for neutrons bound in 16 O was determined
to be 3.20 × 1032 yr at the 90% CL without inclusion of the effect of thesystematic uncertainties and this limit is better than the previous best limitof 7.2 × 1031 yr in Soudan 2 by a factor of about 4.5. Above lower limit isreduced when the systematic uncertainties are included;Tn−n̄ > 1.78 × 1032 yr
at the 90% CL. And the corresponding limit for free neutrons has been
calculated to beτn−n̄ > 1.25 × 108 s
using a suppression factor of 3.6 × 1023 s−1 which is a relatively large compared to previous theoretical estimation for 16 O.
A Comparison of Super-K I limits with previous neutron oscillation limits
in other nucleon decay experiments is given in Table 7.1. The result inSuper-K I has relatively many candidates with small detection efficiency.
Thus, we hope to have a better limit in near future with improved event
selection criteria that will increase signal detection efficiency and reduce thenumber of background events per unit exposure combining the Super-K II
data set. This means our new selection criteria will improve the ability toidentify the Cherenkov rings from the annihilation products.
The L-R symmetric based models that allow neutron oscillations include
an explanation for the neutrino mass and the origin of masses for quarks aswell as leptons. Therefore, search for neutron oscillations may also give us
indirect informations on those.

68Experiment
Super-K I
Soudan 2
FrejusKamiokande
IMB

Exposure[λ](1032 neutron − yr)
245.5
21.9
5.0
3.0
3.2

Experiment(syst. uncertainties)
Super-K I
Soudan 2
FrejusKamiokande
IMB

Efficiency[²]
(%)
10.4
18.0
30.0
33.0
11.9

Candidate(events)
20
5
0
0
0

Limit for bound neutrons[T ](1032 yr)
w/o
w/
3.20
1.78
0.72
0.47
0.65
0.43
0.24
-

Signal limit[s](events)
8.0
5.5
2.3
2.3
2.3

Limit for free neutrons[τ ](108 s)
w/o
w/
1.67
1.25
1.3
0.61
1.2
1.2
1.1
-

Table 7.1: The lower limits on n−n̄ oscillation time at the 90% CL in nucleon
decay experiments. Oscillation time limit is calculated by T = ² · λ/s. The
limits for free neutrons are deduced from the limits for bound neutrons by
the suppression factor, T = R · τ 2 , and Super-K I limit used a suppression
factor of 3.6 × 1023 s−1 .

69

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73

Acknowledgement
I’d like to express my deep appreciation to people who made many efforts
until this dissertation came out although this writing might not be enoughto express that.
To my advisor, Prof. Jae-Yool Kim, I’d like to thank firstly. He gave me
nice chance and nice environment to keep the High Energy Physics Experiment continuously. And I would also like to give my thanks to Prof. In-Taek
Lim, he cared me like as daughter encouraging me every time. And I thankto every Korean members in Super-Kamiokande beginning with Prof. SooBong Kim. I was happy to work with them.
Until the analysis result came out in this dissertation, several people actually made many efforts. I greatly thank to people in California State
University of Dominguez Hills and Kameda san. Especially, Prof. Ganezer
as a beginner for this study in Super-Kamiokande, introduced and taught
me many things about physics topic in this dissertation and I really thankto him for much kindness so far. Dr. Brandon Hartfiel in CSUDH and
Kameda san in ICRR contributed largely to finalizing this analysis during
last 1 year. Brandon did detail check of our Monte Calro and Kameda san
did uncertainty estimation of ring counting and Background search. Prof.
Ganezer, Brandon and Kameda san helped me even to revise my dissertation. I deeply thank to them. And I thank to Prof. Jim Hill and Dr.
William E. Keig for their constant concern with this analysis.
All of members in analysis group for Atmospheric neutrino and Proton
decay, have given us constant concern and comments. Especially, I’d liketo express great appreciation to Kajita san. We could finalize this analysis
due to his careful concern and detail comments. And I bothered so much
Shiozawa san in ICRR and Kobayashi san in Stony Brook University andlearned many analysis technics.
I’m obliged to all of staff beginning with Suzuki san and Nakahata sanin ICRR and Kamioka Observatory. I could enjoy staying in Japan for along time due to their consideration. While I worked in calibration group,
I was taught many things including electronics by experts beginning with
Moriyama san and the staff were of much help. I really appreciate all ofstaff and students in Kamioka again.
I can not except all of Professors who taught and support me in Department of Physics and Physics Education in Chonnam National University
from this acknowledgement and I’d like to express appreciation to them. I
also thank to students and seniors in Laboratory for High Energy Physics.
Especially I deeply thank to Kyung-Ju Ma who is my senior and was friend
during last 1 year in which we prepared for graduating together.
iI know I can be here due to my parents’ pray. They gave best support
to study, so far. I’d like to give my best thank to my family including him
who is my best friend in my whole life, constant supporter of me and myhusband. I also deeply thank to family in law for their consideration for me.
I close this acknowledgement confessing my faith.

ii