Abstract
Title of Dissertation: A STUDY OF SOLAR

NEUTRINOS USING THE
SUPER-KAMIOKANDE DETECTOR

Zoa Conner, Doctor of Philosophy, 1997
Dissertation directed by: Professor Jordan Goodman
Dr. Todd Haines
Department of Physics

The rst solar neutrino ux results from the Super-Kamiokande detector are described. This independent analysis is based on a data set from June 1996 throughFebruary 1997. A total neutrino ux of 2.61 0:12 (stat) 0:13 (syst) 106 cm2s is
implied from the data above a 7 MeV energy threshold. When the measurement
is compared with the most recent Standard Solar Model ux prediction (BP95),
the ratio of data/SSM is 0.394  0.018 (stat)  0.019 (syst). The measured uxes
during day and night yield a fractional di erence of +0.019  0.046 (stat). Interpretations are given in the context of vacuum and MSW enhanced neutrino avor
oscillations.

A STUDY OF SOLAR
NEUTRINOS USING THE
SUPER-KAMIOKANDE DETECTOR
by
Zoa Conner
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland at College Park in partial ful llmentof the requirements for the degree ofDoctor of Philosophy
1997

Advisory Committee:
Professor Jordan A. Goodman, Chair
Dr. Todd J. Haines
Professor Elizabeth J. Beise
Professor David Bigio
Professor Rabindra Mohapatra
Professor Greg W. Sullivan

Dedication
To my loving parents,
Laurie and Hal ConneriiAcknowledgements
This dissertation would not have been possible without the members of the SuperKamiokande collaboration. Their hard work went into building, operating, andunderstanding the Super-Kamiokande detector.
Graduate school has been a lot of work, but with my wonderful husband, Walter Roscello, at my side I have had a good time too. His in nite patience with myextra long work hours, support and acceptance of my travel schedule (especiallythose long trips to Japan), and exceptional love enabled me to excel at my research.
Dr. Todd Haines is a practically perfect mentor for me. He is brilliant, creative,
supportive, and caring. Todd has guided me towards becoming the best researcher
possible and has always been there when I needed him. He has been especiallyconcerned with helping me maintain a balance between work and my personal life.
Todd is a patient teacher who has given me an unmeasureable amount of advice.
Dr. Jordan Goodman has been supportive in all the ways an advisor should. He
has prodded me to give a variety of international conference talks and high energy
physics seminars. He enthusiastically supports my work to others in the scienti ccommunity. Jordan pushes me to always put the physics and the scienti c facts
before my desire to always be right. He keeps me in touch with both the scienti cworld and the real world.
I would like to especially thank Dr. Greg Sullivan for becoming an ally so quickly
after joining our group at the University of Maryland and for focussing his e ortiii

on the solar neutrino analysis. John Flanagan and Dr. Clark McGrew have been
worthy opponents and strong supporters when working on detector calibration andsimulations. Our spokesmen, Dr. Yoji Totsuka, Dr. Henry Sobel, and Dr. James
Stone, have provided strong support when the senior graduate student on the experiment, me, wanted to represent the Super-Kamiokande collaboration experiment
at international conferences.
Many other people helped or supported in ways too lengthy to list here: Chris
Agrusti, Betty Alexander, Jesse Anderson, Drew Baden, Tomasz Barszczak, John
Cataldi, Mei-Li Chen, Bob Ellsworth, Sarah Eno, Mark Giddings, Nick Hadley,
Hassan Jawahery, Betty Krusberg, Sam Lo and, Adam Lyon, Sara and Eric Morton, George Parker, Nicholas Phillips, Rob Sanford, Cindy Dion Schwarz, Eric
Sharkey, Andy Stachyra, Juilien Hsu Svoboda, Bob Svoboda, Mark Vagins, BrettViren, Camille Vogts, Russell Wood, the rest of the machine shop crew at Maryland, and the undergrads processing the data at SUNY.
It is nearly impossible to do research of this type without adequate funding support. My stipend and tuition for the last six years have been generously provided
by the the National Physical Science Consortium Graduate Fellowship in conjunction with the National Security Agency and the University of Maryland. My travel
to collaboration meetings, travel to the experiment in Japan, and hardware construction projects have been supported by a subcontract from our collaboration
spokesman, Dr. Henry Sobel. Hank has tried valiantly to make my participationin the Super-Kamiokande experiment possible. This experiment was made possibleby the cooperation and support from the Kamioka Mining and Smelting Company,
the Japanese Ministry of Science, and the U.S. Department of Energy.
iv

Table of Contents
List of Tables

xii

List of Figures

xv

1 Introduction

1

1.1 The Sun and the Standard Solar Model : : : : : : : : : : : : : : : :1.1.1 What is the Standard Solar Model? : : : : : : : : : : : : : :1.1.2 How Does the Sun Shine? : : : : : : : : : : : : : : : : : : :1.1.3 Neutrino Spectra and Flux : : : : : : : : : : : : : : : : : : :1.2 The Homestake Experiment : : : : : : : : : : : : : : : : : : : : : :1.3 Kamiokande : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :1.4 SAGE and GALLEX : : : : : : : : : : : : : : : : : : : : : : : : : :1.5 Current State of the Field : : : : : : : : : : : : : : : : : : : : : : :1.6 Possible Solutions : : : : : : : : : : : : : : : : : : : : : : : : : : : :1.6.1 Reduction of the Central Temperature : : : : : : : : : : : :1.6.2 Smaller Cross Section for 7Be Production : : : : : : : : : : :1.6.3 Low Energy Resonance in 3He + 3He! + 2 p : : : : : : :1.6.4 Smaller  for e Capture on 37Cl and 71Ga : : : : : : : : : :1.6.5 Helium Di usion : : : : : : : : : : : : : : : : : : : : : : : :1.6.6 Neutrino Flavor Oscillations : : : : : : : : : : : : : : : : : :1.6.7 How to Decide Which Solution is Right : : : : : : : : : : : :
v

3
3
7
7
11
15
18
20
22
22
23
23
23
24
24
30

1.7 Sudbury Neutrino Observatory : : : : : : : : : : : : : : : : : : : : 30
1.8 Borexino : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 32

2 Super-Kamiokande Description
2.1
2.2
2.3
2.4
2.5

2.6

2.7
2.8
2.9

34

General : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :Con guration of the Inner Detector : : : : : : : : : : : : : : : : : :Con guration of the Outer Detector : : : : : : : : : : : : : : : : : :Photomultiplier Tubes : : : : : : : : : : : : : : : : : : : : : : : : :Electronics and Data Acquisition Systems : : : : : : : : : : : : : :2.5.1 Inner Detector : : : : : : : : : : : : : : : : : : : : : : : : : :2.5.2 Outer Detector : : : : : : : : : : : : : : : : : : : : : : : : :Triggers : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :2.6.1 Low Energy and High Energy : : : : : : : : : : : : : : : : :2.6.2 Outer Detector : : : : : : : : : : : : : : : : : : : : : : : : :2.6.3 Other Triggers : : : : : : : : : : : : : : : : : : : : : : : : :Oine Data Processing : : : : : : : : : : : : : : : : : : : : : : : : :Water System : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :Clean Air Systems : : : : : : : : : : : : : : : : : : : : : : : : : : :3 Calibration

34
37
38
39
41
42
45
49
50
53
54
55
56
56

59

3.1 Absolute Timing : : : : : : : : : : : : : : : : : : : : : : : : : : : :3.2 Relative Timing : : : : : : : : : : : : : : : : : : : : : : : : : : : : :3.2.1 Light Source : : : : : : : : : : : : : : : : : : : : : : : : : : :3.2.2 Optical Components : : : : : : : : : : : : : : : : : : : : : :3.2.3 Optical Fibers : : : : : : : : : : : : : : : : : : : : : : : : : :3.2.4 Di users : : : : : : : : : : : : : : : : : : : : : : : : : : : : :3.3 Absolute Energy : : : : : : : : : : : : : : : : : : : : : : : : : : : :
vi

59
60
61
62
64
65
67

3.3.1 Muons : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :3.3.2 0 Rest Mass : : : : : : : : : : : : : : : : : : : : : : : : : :3.3.3 Decay Electrons : : : : : : : : : : : : : : : : : : : : : : : : :3.3.4 Radioactive Gamma-Ray Sources : : : : : : : : : : : : : : :3.3.5 LINAC : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :3.3.6 Stopped Muon Capture : : : : : : : : : : : : : : : : : : : : :3.4 Detector Monitoring : : : : : : : : : : : : : : : : : : : : : : : : : :4 Simulations

68
69
69
69
86
88
89

94

4.1 Solar Neutrino Interactions : : : : : : : : : : : : : : : : : : : : : : : 95
4.1.1 Neutrino Energies : : : : : : : : : : : : : : : : : : : : : : : : 95
4.1.2  , e, Scattering : : : : : : : : : : : : : : : : : : : : : : : 96
4.2 Particle Tracking : : : : : : : : : : : : : : : : : : : : : : : : : : : : 97
4.3 C erenkov Light Generation and Tracking : : : : : : : : : : : : : : : 99
4.4 Electronics Simulation : : : : : : : : : : : : : : : : : : : : : : : : : 107
4.5 Trigger Simulation : : : : : : : : : : : : : : : : : : : : : : : : : : : 109

5 Data Reduction - lef1

112

5.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 112
5.2 Goals and Philosophy of lef1 : : : : : : : : : : : : : : : : : : : : : 113
5.3 Event Classi cation Scheme : : : : : : : : : : : : : : : : : : : : : : 115
5.3.1 Null Trigger Events : : : : : : : : : : : : : : : : : : : : : : : 118
5.3.2 Small Events : : : : : : : : : : : : : : : : : : : : : : : : : : 118
5.3.3 Big Events : : : : : : : : : : : : : : : : : : : : : : : : : : : : 122
5.3.4 Minimum Bias Events : : : : : : : : : : : : : : : : : : : : : 125
5.3.5 Record Keeping : : : : : : : : : : : : : : : : : : : : : : : : : 125
5.4 Hayai Vertex Fitter : : : : : : : : : : : : : : : : : : : : : : : : : : : 125
vii

5.5

5.6
5.7
5.8
5.9

5.4.1 Algorithm : : : : : : : : : : : : : : : : : : : : : : : : : : : : 127
5.4.2 Performance : : : : : : : : : : : : : : : : : : : : : : : : : : : 129
5.4.3 E ect of Dwall  1 meter cut : : : : : : : : : : : : : : : : : : 131
Track Fitting : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 134
5.5.1 THR1 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 135
5.5.2 THR2 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 136
5.5.3 FSTMU : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 137
Trashman : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 140
SaveRun : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 144
Livetime : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 147Eciencies : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 148
5.9.1 Muon Identi cation : : : : : : : : : : : : : : : : : : : : : : : 148
5.9.2 Low Energy Events : : : : : : : : : : : : : : : : : : : : : : : 151

6 Data Reduction - lef2

153

6.1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 153
6.2 Good Run/Subrun Selection : : : : : : : : : : : : : : : : : : : : : : 154
6.2.1 lef1 Log Files : : : : : : : : : : : : : : : : : : : : : : : : : 155
6.2.2 Run Log Book : : : : : : : : : : : : : : : : : : : : : : : : : : 160
6.2.3 Run Summary Files : : : : : : : : : : : : : : : : : : : : : : : 161
6.2.4 Decision Making and Record Keeping : : : : : : : : : : : : : 162
6.3 Event Classi cation Scheme : : : : : : : : : : : : : : : : : : : : : : 162
6.3.1 Pedestal Events : : : : : : : : : : : : : : : : : : : : : : : : 166
6.3.2 Minimum Bias Events : : : : : : : : : : : : : : : : : : : : 166
6.3.3 Caterpillar Muons : : : : : : : : : : : : : : : : : : : : : : : : 168
6.3.4 Big Ringing Events : : : : : : : : : : : : : : : : : : : : : : 169
6.3.5 OD Clipping Muons : : : : : : : : : : : : : : : : : : : : : : 169
viii

Fittable Muon Events : : : : : : : : : : : : : : : : : : : : : 170
LE Ringing Events : : : : : : : : : : : : : : : : : : : : : : 170
LE Junk Events : : : : : : : : : : : : : : : : : : : : : : : : 171
Low Energy Events : : : : : : : : : : : : : : : : : : : : : : : 171
ComboFit Precision Vertex Fitter : : : : : : : : : : : : : : : : : : : 172
6.4.1 \Direction Only" Algorithm : : : : : : : : : : : : : : : : : : 174
6.4.2 \Vertex and Direction" Algorithm : : : : : : : : : : : : : : : 175
6.4.3 Performance : : : : : : : : : : : : : : : : : : : : : : : : : : : 176
6.4.4 E ect of Dwall  2 meters Cut : : : : : : : : : : : : : : : : : 180
Muboy Track Fitter : : : : : : : : : : : : : : : : : : : : : : : : : : : 181
6.5.1 Algorithm : : : : : : : : : : : : : : : : : : : : : : : : : : : : 181
6.5.2 Performance : : : : : : : : : : : : : : : : : : : : : : : : : : : 188
Eciencies : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 191
6.6.1 Muon Identi cation : : : : : : : : : : : : : : : : : : : : : : : 191
6.6.2 Low Energy Events : : : : : : : : : : : : : : : : : : : : : : : 192
Level 1 12 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 193
6.3.6
6.3.7
6.3.8
6.3.9

6.4

6.5

6.6

6.7

7 Final Data Reduction

194

7.1 NTUPLE Program - le ntuple : : : : : : : : : : : : : : : : : : : 194
7.2 Sun Location : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 195
7.3 Spallation Events : : : : : : : : : : : : : : : : : : : : : : : : : : : : 199
7.3.1 Characterization : : : : : : : : : : : : : : : : : : : : : : : : 200
7.3.2 Cut Optimization : : : : : : : : : : : : : : : : : : : : : : : : 207
7.3.3 Cubist : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 209
7.3.4 Spall ag : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 213
7.4 Energy Determination : : : : : : : : : : : : : : : : : : : : : : : : : 213
7.4.1 N50 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 214ix

7.4.2 Ne ective : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 216
7.4.3 Performance of Ne ective on Nickel Data : : : : : : : : : : : : 223
7.4.4 Energy from Ne ective : : : : : : : : : : : : : : : : : : : : : : 225
7.4.5 Time Dependence of Ne ective : : : : : : : : : : : : : : : : : : 227
7.4.6 LINAC results : : : : : : : : : : : : : : : : : : : : : : : : : : 229
7.5 Radon : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 234
7.6 \Flashers" : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 236

8 Results

238

Data Set : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 238\Interactive" Cuts : : : : : : : : : : : : : : : : : : : : : : : : : : : 239
Characteristics of Final Event Sample : : : : : : : : : : : : : : : : : 240
Signal Extraction Method : : : : : : : : : : : : : : : : : : : : : : : 241
Measured Solar Neutrino Event Rate : : : : : : : : : : : : : : : : : 246
Eciency : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 250
SSM Expectation : : : : : : : : : : : : : : : : : : : : : : : : : : : : 250
Systematic Errors : : : : : : : : : : : : : : : : : : : : : : : : : : : : 253
8.8.1 Fiducial Volume : : : : : : : : : : : : : : : : : : : : : : : : : 253
8.8.2 Energy Scale : : : : : : : : : : : : : : : : : : : : : : : : : : 253
8.8.3 Time Dependence of Energy Scale : : : : : : : : : : : : : : : 255
8.8.4 Energy Resolution : : : : : : : : : : : : : : : : : : : : : : : 256
8.8.5 Signal Extraction : : : : : : : : : : : : : : : : : : : : : : : : 257
8.8.6 Scattering Cross Section : : : : : : : : : : : : : : : : : : : : 258
8.8.7 Total Systematic Error : : : : : : : : : : : : : : : : : : : : : 258
8.9 Measured Solar Neutrino Flux : : : : : : : : : : : : : : : : : : : : : 259
8.10 Measured Di erential Energy Spectrum : : : : : : : : : : : : : : : : 260
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8

x

9 Interpretation and Conclusions

265

9.1 Comparison with On-Site Group : : : : : : : : : : : : : : : : : : : : 265
9.2 Comparison with Previous Results : : : : : : : : : : : : : : : : : : 267
9.3 Neutrino Oscillation Interpretation : : : : : : : : : : : : : : : : : : 268
9.3.1 Vacuum Oscillations : : : : : : : : : : : : : : : : : : : : : : 269
9.3.2 MSW Enhanced Oscillations : : : : : : : : : : : : : : : : : : 273
9.3.3 Di erential Energy Spectrum : : : : : : : : : : : : : : : : : 275
9.4 Implications : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 279
9.5 Future Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 281

Appendix A Zebra Banks

284

References

291

xi

List of Tables
1.1 SSM solar neutrino ux predictions and uncertainties : : : : : : : : 10
1.2 Initial results for the Homestake chlorine experiment : : : : : : : : 14
1.3 Results from current solar neutrino experiments : : : : : : : : : : : 20
2.1 General properties of Super-Kamiokande and Kamiokande : : : : : 36
2.2 Trigger bit description : : : : : : : : : : : : : : : : : : : : : : : : : 50
3.1 Thermal neutron capture information : : : : : : : : : : : : : : : : : 72
3.2 Additional thermal neutron capture information : : : : : : : : : : : 83
4.1 Trigger conditions for the MC simulation : : : : : : : : : : : : : : : 110
lef1 goals and achievements : : : : : : : : : : : : : : : : : : : : : :

5.1
5.2
5.3
5.4
5.5
5.6

116
Numerical values for the lef1 and lef2 classes : : : : : : : : : : : : 119
1-d and 3-d vertex resolutions of Hayai on MC electrons : : : : : : : 130
Gaussian widths from Hayai t on nickel data and MC : : : : : : : 131
Total vertex errors from Hayai t on LINAC data and MC : : : : : 132
Number of events in each lef1 and hand t class for real muons : : 150

6.1
6.2
6.3
6.4

Criteria to have Good&bad data ags set from the lef1 log les : : 157
lef2's actions on each type of \bad subrun" ag from good&bad data 164
Control parameters for \direction only" version of Combo t : : : : : 175
Control parameters for \vertex and direction" version of Combo t : 176
xii

6.5 1-d and 3-d vertex resolutions of Combo t using MC electrons : : : 177
6.6 Angular resolution of Combo t using Monte Carlo electron events : 178
6.7 Gaussian widths from Combo t on nickel data and MC : : : : : : : 179
6.8 Total vertex errors from Combo t on LINAC data and MC : : : : : 179
6.9 Minimum charge requirements for ID tubes used in Muboy t : : : : 182
6.10 Nearest neighbor requirement for ID tubes used in Muboy t : : : : 182
6.11 Muboy identi cation eciency for muon events taken from the data 189
6.12 Combined lef2 and lef1 eciency for muon events : : : : : : : : : 191
7.1 General event information in the Low Energy NTUPLE : : : : : : : 196
7.2 Spallation variables in the Low Energy NTUPLE : : : : : : : : : : 197
7.3 Sun location information in the Low Energy NTUPLE : : : : : : : 197
7.4 Fit information in the Low Energy NTUPLE : : : : : : : : : : : : : 198
7.5 Previous muon information in the Low Energy NTUPLE : : : : : : 199
7.6 Isotopes with half-lives between 1-100 ms : : : : : : : : : : : : : : : 204
7.7 Isotopes with half-lives between 100-600 ms : : : : : : : : : : : : : 205
7.8 Isotopes with half-lives between 0.6-5 s : : : : : : : : : : : : : : : : 206
7.9 Isotopes with half-lives between 5-70 s : : : : : : : : : : : : : : : : 206
7.10 Measured spallation rates in events per day : : : : : : : : : : : : : : 207
7.11 Spallation cuts used in analysis : : : : : : : : : : : : : : : : : : : : 210
7.12 N50 means and widths for nickel data and MC events : : : : : : : : 215
7.13 Means and widths of Ne ective from nickel data and MC : : : : : : : 224
7.14 Ne ective results from LINAC data and MC : : : : : : : : : : : : : : 233
8.1
8.2
8.3
8.4

Exposure for nal data sample : : : : : : : : : : : : : : : : : : : : : 239
22.5 kton measured signal and background rates : : : : : : : : : : : 248
11.7 kton measured signal and background rates : : : : : : : : : : : 249
SSM predicted solar neutrino event rates : : : : : : : : : : : : : : : 252xiii

8.5 Contributions to energy scale uncertainty : : : : : : : : : : : : : : : 255
8.6 Systematic ux uncertainty due to B.G. slope : : : : : : : : : : : : 258
8.7 Components of the total systematic error on solar neutrino ux : : 259
8.8 Total systematic error on solar neutrino ux : : : : : : : : : : : : : 260
8.9 Ratios of measured  uxes in 22.5 kton to the SSM predictions : : 261
8.10 Ratios of measured  uxes in 11.7 kton to the SSM predictions : : 262
9.1 Comparison of independent solar neutrino ux results : : : : : : : : 266
9.2 Comparison of independent day/night ux di erences : : : : : : : : 267
9.3 Prior experimental solar neutrino results : : : : : : : : : : : : : : : 268
A.1 Names of zebra banks and information contained in each bank : : : 285
A.2 Description of HEAD bank : : : : : : : : : : : : : : : : : : : : : : : 286
A.3 Description of AHEA bank : : : : : : : : : : : : : : : : : : : : : : : 287
A.4 Description of CALI and CALO banks : : : : : : : : : : : : : : : : 288
A.5 Description of lef1 bank : : : : : : : : : : : : : : : : : : : : : : : : 289
A.6 Description of lef2 bank : : : : : : : : : : : : : : : : : : : : : : : : 290xiv

List of Figures
1.1
1.2
1.3
1.4

The PP chain involved in hydrogen burning in the Sun : : : : : : : 8
The Carbon-Nitrogen-Oxygen chain : : : : : : : : : : : : : : : : : : 9
Event correlation with the Sun from Kamiokande-II and III : : : : : 18
Currently allowed regions of MSW oscillation parameters (Hata andLangacker, 1994) : : : : : : : : : : : : : : : : : : : : : : : : : : : : 29

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

Cartoon sketch of the Super-Kamiokande detector : : : : : : : : : :Schematic of a supermodule : : : : : : : : : : : : : : : : : : : : : :Measured transit time jitter of the 50 cm photomultiplier tubes : :Schematic of the inner detector electronics : : : : : : : : : : : : : :Diagram of the outer detector electronics : : : : : : : : : : : : : : :Electronics for the inner detector trigger : : : : : : : : : : : : : : :Layout of the outer detector trigger electronics : : : : : : : : : : : :Outer detector trigger rate as a function of threshold : : : : : : : :

35
37
39
43
46
52
53
54

3.1
3.2
3.3
3.4
3.5
3.6

Layout of light di user locations : : : : : : : : : : : : : : : : : : : :Optical components to the laser calibration system : : : : : : : : :Optical di users for the inner and outer detectors : : : : : : : : : :Energy spectrum of muon decay electrons : : : : : : : : : : : : : :Number of gamma-rays per neutron capture on nickel : : : : : : : :Gamma-ray energies from neutron capture on nickel : : : : : : : : :

62
63
66
70
72
73

xv

3.7 Total energy released in gamma-rays per neutron capture on nickel 73
3.8 Con guration of Cf-Ni gamma-ray calibration source : : : : : : : : 75
3.9 Input card for MCNP : : : : : : : : : : : : : : : : : : : : : : : : : : 77
3.10 Lifetime of neutrons in Cf-Ni source : : : : : : : : : : : : : : : : : : 79
3.11 Diagram of the ionization counter used as a ` ssion trigger' : : : : : 81
3.12 Diagram of the electronics behind a ` ssion trigger' : : : : : : : : : 81
3.13 Example of performing tfission background subtraction : : : : : : 82
3.14 Number of gamma-rays per neutron capture on titanium : : : : : : 83
3.15 Number of gamma-rays per neutron capture on iron : : : : : : : : : 84
3.16 Gamma-ray energies from neutron capture on titanium : : : : : : : 84
3.17 Total energy released in gamma-rays per neutron capture on titanium 85
3.18 Gamma-ray energies from neutron capture on iron : : : : : : : : : : 85
3.19 Total energy released in gamma-rays per neutron capture on iron : 86
4.1 Energy spectrum of 8B solar neutrinos : : : : : : : : : : : : : : : : 95
4.2 Energy spectrum of HEP solar neutrinos : : : : : : : : : : : : : : : 96
4.3 Energy dependence of scattering cross section for several E : : : : 98
4.4 Average multiple Coulomb scattering angle for H2O used by EGS4 : 99
4.5 Absorption length input to the Monte Carlo : : : : : : : : : : : : : 102
4.6 Rayleigh scattering length input to the Monte Carlo : : : : : : : : : 103
4.7 Anomalous scattering length input to the Monte Carlo : : : : : : : 103
4.8 Attenuation length input to the Monte Carlo : : : : : : : : : : : : : 104
4.9 Quantum eciency for both sets of PMTs : : : : : : : : : : : : : : 105
4.10 Time resolution for ID PMTs : : : : : : : : : : : : : : : : : : : : : 106
4.11 Number of ID PMT hits in 200 ns due to dark noise : : : : : : : : : 106
4.12 Re ectivity of the Tyvek material lining the OD : : : : : : : : : : : 107
4.13 Charge distribution for ID PMTs using nickel source : : : : : : : : 108
xvi

4.14 Relative trigger eciencies using nickel data : : : : : : : : : : : : : 111
5.1 Overview of the Low Energy data ltering : : : : : : : : : : : : : : 114
5.2 Sample entry in the lef1 log le : : : : : : : : : : : : : : : : : : : : 126
5.3 1 of Dwall  1 m cut on Hayai vertex calculated using MC electrons 133
5.4 2 of Dwall  1 m cut on Hayai vertex on events in ducial volume : 134
5.5 THR1 angular accuracy and entry point error distributions : : : : : 136
5.6 THR2 angular accuracy distribution : : : : : : : : : : : : : : : : : : 137
5.7 FSTMU angular accuracy and entry point error distributions : : : : 140
5.8 Sample Entry in a Trashman Log File : : : : : : : : : : : : : : : : : 145
5.9 Sample Entry in a SaveRun Log File : : : : : : : : : : : : : : : : : : 146
5.10 Sample Entry in a Livetime Log File : : : : : : : : : : : : : : : : : : 149
5.11 3 of lef1 lter on simulated electrons in 22.5 kton ducial volume 152
6.1 Number of events in each subrun without ID data : : : : : : : : : : 156
6.2 Fraction of events in each subrun without OD data : : : : : : : : : 158
6.3 Rate of thru- events in each subrun : : : : : : : : : : : : : : : : : 158
6.4 Number of saved low energy events in each subrun : : : : : : : : : : 159
6.5 Fraction of noise events in each subrun : : : : : : : : : : : : : : : : 159
6.6 Fraction of saved low energy events in each subrun : : : : : : : : : : 160
6.7 Sample of the CSUDH run list based on the run log book : : : : : : 161
6.8 Sample of a run summary le : : : : : : : : : : : : : : : : : : : : : 163
6.9 Sample of a good&bad data log le : : : : : : : : : : : : : : : : : : 165
6.10 Sample lef2 log le : : : : : : : : : : : : : : : : : : : : : : : : : : : 167
6.11  of Dwall  2 meter cut on Combo t vertex using MC electrons : : 180
6.12 Resolution of Muboy track t on stopping muon events : : : : : : : 189
6.13 Resolution of Muboy track t on through-going muon events : : : : 190
6.14 Resolution of Muboy track t on multiple muon events : : : : : : : 190
xvii

6.15  of lef2 lter on simulated electrons in 22.5 kton ducial volume : 192
7.1 Cylinder cut around a muon track to remove spallation events : : : 200
7.2 Time between muon and Low Energy event : : : : : : : : : : : : : : 202
7.3 Correlation between LE vertex and muon track : : : : : : : : : : : 203
7.4 Total number of ID hits for events correlated with a previous  : : 203
7.5 Time residual distribution for nickel data events : : : : : : : : : : : 215
7.6 E ective area for 50 cm PMT versus incident angle : : : : : : : : : 218
7.7 Geometrical correction factor for Ne ective : : : : : : : : : : : : : : : 219
7.8 Attenuation correction factor for Ne ective : : : : : : : : : : : : : : : 222
7.9 Correlation between Ne ective and total energy using MC events : : : 227
7.10 Ne ective from selected spallation events in August : : : : : : : : : : 230
7.11 Time dependence of t Ne ective from selected spallation events : : : 230
7.12 Time dependent scaling factor for Ne ective : : : : : : : : : : : : : : 231
7.13 Time since the previous trigger from LINAC data : : : : : : : : : : 232
7.14 T0 from Combo t applied to LINAC data : : : : : : : : : : : : : : 233
7.15 Reconstructed energy resolution using MC and LINAC data : : : : 235
7.16 \Flasher" cut using the goodness of Hayai t distributions : : : : : 237
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9

Vertex coordinate distributions from nal sample : : : : : : : : : : 242
Direction cosine distributions from nal sample : : : : : : : : : : : 243
Energy distribution from nal sample (linear and semi-log plots) : : 244
Correlation between the Sun and nal sample event directions : : : 244
Solar peak for the day data with Ereconstruct > 7 MeV : : : : : : : : 245
Solar peak for the night data with Erecontruct > 7 MeV : : : : : : : : 245
cos sun shapes predicted from the Monte Carlo : : : : : : : : : : : : 247
2 minimum for t to background + solar neutrino signal : : : : : : 247
Total eciency versus generated energy : : : : : : : : : : : : : : : : 251
xviii

8.10 Di erential energy spectra from the data and Monte Carlo prediction 263
8.11 Spectral shape of the data relative to the SSM prediction : : : : : : 264
9.1 Vacuum oscillation survival probability : : : : : : : : : : : : : : : : 270
9.2 Radial dependence of the probability to produce a 8B neutrino : : : 271
9.3 Allowed vacuum oscillation parameters using stat only. : : : : : : : 271
2 +  2 +  2 )1=2. : : : 272
9.4 Allowed vacuum osc. parameters using (stat
syst
theo
9.5 Allowed vacuum osc. parameters using (stat + syst + theo). : : : : 272
9.6 Radial dependence of the electron number density : : : : : : : : : : 273
9.7 MSW oscillation survival probability at the Sun's surface : : : : : : 274
9.8 Allowed MSW parameters using stat only. : : : : : : : : : : : : : : 276
2 +  2 +  2 )1=2. : : : : : : 276
9.9 Allowed MSW parameters using (stat
syst
theo
9.10 Allowed MSW parameters using (stat + syst + theo). : : : : : : : : 277
9.11 Allowed MSW parameters using BP92 and stat only. : : : : : : : : 277
2 +  2 +  2 )1=2. 278
9.12 Allowed MSW parameters using BP92 and (stat
syst
theo
9.13 Allowed MSW parameters using BP92 and (stat + syst + theo). : : 278

xixChapter 1

Introduction
Scientists have long studied the Sun. Old questions are: \Why does the Sun shine?"and \How does it do it?". We have measured many important parameters of theSun, such as its mass, radius, and luminosity. Astronomers have a theory aboutstellar evolution that is used to make predictions and interpret observations [1].
This theory has two major successes. The rst is the prediction of the relationshipbetween mass and luminosity of a star (L / M , where ,  3). This relationshiphas been veri ed by many astronomical measurements. The second involves the
explanation of the clustering of observed stars on the Hertzsprung-Russell diagram(luminosity versus a stellar property such as color). The regions in the H-R diagram that stars populate can be explained by the stellar evolution theory. The
implication of this is that the types of stars that may exist can be predicted (faintwhite dwarfs, bright blue stars, etc.). The complete life of a star can be tracked on
the populated regions of the H-R diagram.
There is a collection of models dealing with the mechanisms thought to bepresent inside the Sun. These Standard Solar Models (SSMs) [2] describe the nuclear fusion reactions which we believe provide the Sun's energy. Several of thesereactions produce neutrinos. The \Solar Neutrino Problem" is the disagreement1between the predicted and experimentally measured neutrino uxes. The SSM has
been thoroughly investigated using photons from the Sun and other stars. Everything predicted by the SSM agrees with the experimental measurements. That is,
all except the predictions dealing with solar neutrinos.
Several di erent experiments have observed solar neutrinos and measured theneutrino ux from the Sun. None of these experiments has measured the ux tobe the same as the theoretical ux. The observed uxes are smaller than the predata di ers between the experiments. Several theories
dictions, and the ratio of theory
could explain this apparent lack of observed neutrinos from the Sun (known as the
Solar Neutrino Problem). One of these theories invokes neutrino avor oscillations(new neutrino physics which is currently preferred over other explanations by many
physicists).
This chapter will detail the past experimental and theoretical advances in the
study of neutrinos from the Sun. The current status of the eld will be described.
Several new detectors will be operational within the next few years. Two of them,
SNO, and Borexino, will be brie y described here. Another new detector, SuperKamiokande [3], is the subject of this dissertation and will be described in detailin Chapter 2. An interpretation of the results presented in Chapter 8 will be madein the context of neutrino avor oscillations.

21.1 The Sun and the Standard Solar Model
1.1.1 What is the Standard Solar Model?
The Standard Solar Model is a collection of models that is used iteratively to simulate the Sun over its entire lifetime. There are assumptions, input parameters, andboundary conditions that accompany the SSM. The SSM constantly evolves, hopefully getting closer to reality with decreasing uncertainties. The Sun is modeled on
a computer using some basic initial conditions: it is a main sequence star with inhomogeneous composition (hydrogen, helium, and heavy elements) that burns (fuses)hydrogen in its core (example of hydrogen burning reaction: p + p !2 H + e+ + e).
The hydrogen burning provides radiated light and the thermal pressure needed tocounterbalance the gravitational forces. After every 5 108 or 109 simulated yearsof the Sun's life, the assumptions of the models need to be slightly modi ed toretain their applicability. Changes in composition of the Sun are allowed if due tonuclear reactions. The abundances are computed by detailed numerical integrations
from the currently applicable model of the interior. Details of these calculations
are provided by Bahcall and Ulrich [5]. The entire process quickly sketched above
is iterated in the following manner; accuracies in the total luminosity and radius of
1 part in 105 are usually achieved.

3

1. make initial guesses for parameters
2. run models through to the current age of the Sun(4.6 109 years)
3. compare predicted characteristics of Sun (such as radiusand photon luminosity)
4. modify parameter values and repeat process until good
agreement is achieved between model predictions and observations
Five basic assumptions go into the SSM calculation:
1. the Sun is in hydrostatic equilibrium
2. energy transportation is via photons and convection
3. energy is generated by fusion
4. abundance changes are due to nuclear reactions
5. elemental di usion, convection, and gravitational settlingchange abundances throughout the Sun
Assumption 1 refers to the Sun's outward radiative and particle pressures balancing
the inward gravitational forces. This is known to be an excellent approximation byobservations. If this assumption was not close to the truth, the Sun would collapse
or explode. Assumption 2 has to do with how energy is transported in various
regions of the Sun. Close to the core, photons transport the energy mainly by diffusion. This is the region most important for solar neutrinos, because neutrinos areproduced deep in the interior of the Sun. Assumption 3 assumes that the main energy production is by nuclear fusion, but usually corrections are included for other4sources of energy (such as gravitational expansion and departures from equilibriumcaused by the hydrogen burning). Assumption 4 allows the chemical abundances
to change via nuclear reactions. Assumption 5 explains possible changes in thevolume distribution of various elements in the Sun.
There are many parameters that go into the SSM. The most important to solar
neutrinos are listed and described here.
1. nuclear cross sections
2. total photon luminosity
3. age of Sun
4. equation of state
5. primordial elemental abundances
6. radiative opacity
The nuclear cross sections are needed to compute the reaction rates of each process.
Because few cross section measurements exist in the appropriate low energy regime,
often the cross sections relevant for the solar interior are extrapolations from measurements made at higher energies. The luminosity and age of the Sun are usedas boundary conditions. The luminosity comes from satellite measurements while
the meteoritic measurements determine the age of the Sun. The equation of stateincludes the radiation pressure, gas pressure, and screening and local e ects. The
abundances are needed as initial conditions for the Sun. The radiative opacity tells
how opaque the solar matter is to photons (heavy element abundances are important for the opacity calculation). The opacity is usually computed and tabulated,then incorporated into the SSM. The principal sources of the opacity to photons
are:51. bound-bound transitions (between discrete atomic ormolecular energy levels)
2. bound-free transitions (photoionization and the reverse
process)
3. free-free transitions (Brehmsstrahlung)
4. electron scattering (Thompson and Compton)
5. electron conduction
The opacity ( [m2/g]) can be computed from the density ( [g/m3]), the interaction
cross sections (i [m2/particle]), and the number density for the ith interaction (ni[particle/m3]):Xtot = nii :(1.1)
i

The cross sections for each of the interactions and the number density must be
calculated. This is especially dicult for the bound-bound and bound-free interactions since knowledge of the star's composition and all the appropriate energy levels
is needed. Approximately 55% of the opacity is due to free electron scattering andinverse Brehmsstrahlung on protons and alpha particles. The remaining 45% is due
to transitions involving bound states heavier than helium. Until recently, opacity
computations could only be done by one group (located at Los Alamos National
Laboratory [6]) where there was access to the needed computational power andexperience. Most SSM simulations used the Los Alamos opacity tables as an input
parameter to their model.

61.1.2 How Does the Sun Shine?
It is believed that the Sun `lives' by burning hydrogen. Positrons and neutrinos
are released as protons fuse into helium nuclei. The exact reactions are given in
Figure 1.1 along with the expected neutrino energies. The di erent pathways areusually referred to by path number, indicated in the labels pp-I, pp-II, pp-III, andpp-IV. The pathway is referred to as a termination, since one complete pp-cycle involves the cycle terminating with a particular set of reactions. As time progresses,heavier elements can be produced. The CNO cycle is a series of reactions that
produce energy by fusing protons into alpha particles with the assistance of 12C.
The reactions and the expected neutrino energies are given in Figure 1.2.

1.1.3 Neutrino Spectra and Flux
Neutrinos can only be produced from weak interactions (such as decay). Therefore the shape of the neutrino spectra can be calculated using the weak interaction
theory and nuclear physics. There are no uncertainties in the spectra of the produced neutrinos due to solar parameters. This is not true for the neutrino uxes.
Both the most recent SSM predictions by Bahcall and Pinsonneault [7] and theprevious calculation [4] for the neutrino uxes at the Earth including theoreticaluncertainties are given in Table 1.1. The BP95 SSM improves upon the BP92 SSM
by including the e ects of helium and metal di usion in addition to updated neutrino opacities, heavy element abundances, solar luminosity, age of the Sun, andnuclear cross section factors.
The small uncertainty in the pp ux is due to the well known nuclear cross section. The pp ux is strongly linked to the radiative output of the Sun, which has
7p + p !2H + e+ + e
99.75%
Epp  0.42 MeVAA

p + e, + p !2H + e
0.25%
Epep = 1.442 MeV

A
A



AA
U





2 H + p !3 He +3 He + 3 He !




 PP

PP

PP


PP


PP


PP
)

P
q
?

+2p
pp-I termination

3 He +,,,!7Be +

, @
,
@
,
@

7 Be + e, !7Li + e

3 He + p !

+ e+ + e
EHep < 18.8 MeV
pp-IV termination

@
@
R
@

7 Be + p !8Bi +EBe = 0.861 MeV (90%)
EBe = 0.383 MeV (10%)?

7Li + p !

8 B !8Be + e+ + e?

EB < 15.0 MeV+
pp-II termination

8Be !

?

+
pp-III termination
Figure 1.1: The PP chain involved in hydrogen burning in the Sun8p + 12C !13N +?

13N !13C + e+ + e

EN  1.2 MeV?

p + 13C !14N +?

p + 14N !15O +?

15O !15N + e+ + e

EO  1.7 MeV

XXX
XXX
XXX
XXX
?
z
X

p + 15N !12C +p + 15N !16O +?

p + 16O !17F +?

17F !17 O + e+ + e

EF  1.7 MeV?

p + 17O !14N +Figure 1.2: The Carbon-Nitrogen-Oxygen chain9

Source  Energy
(MeV)
pp
<0.42
pep
1.442
7Be
0.86 (90%)
0.38(10%)
8B
<15.0
Hep
<18.8
13N
1.2
15O
1.7
17F
1.7

BP92 Flux 3 error(cm,2s,1 ) (%)
6.001010
2
1.431084
4.89109
18

BP95 Flux 1 error(cm,2s,1)(%)
5.911010
1
1.401081.5
5.15109
6.5

5.691061.23103
4.92108
4.261085.391066.62106
1.21103
6.181085.45108
6.48106

43
|
51
58
48

15.5
|
18.5
20.5
17

Table 1.1: SSM solar neutrino ux predictions and uncertainties
been measured. There is no uncertainty listed for the Hep neutrinos, but it is large
as the measured cross section for p +3 He ! e+ + e +4 He has an extraordinarily
large assigned error. The 43% uncertainty in the 8B ux is mostly due to errors in
the cross section for 8B production and the heavy element abundances. The CNO
cycle neutrinos have large uncertainties caused by the heavy element abundance
and the production rate of 14N.
The predicted uxes depend on the temperatures in the neutrino production
regions of the Sun. The following form may be used to indicate the temperaturedependence of the neutrino uxes: [1].

(pp)  const:  T,1:2
(Hep)  const:  T,
10

= 3 to 6

(7Be)  const:  T8(8B )  const:  T18
The temperature, however, is not a parameter in the SSM. It is a product of themodel. A change in temperature of the Sun's core must be caused by the evolution
process. To compute the ux of 8B correctly to within a factor of 3 the temperatureof the core must be well known ( TTcc  5-10%).
In order to test any theory, experiments must be performed. The experimental
results are compared to theoretical predictions and an evaluation made about theagreement of the two. Solar neutrino experiments can test the validity of the SSM.

1.2 The Homestake Experiment
In the 1950's a neutrino detector was studied and built at Brookhaven National
Laboratory [8]. The 3900 liter tank lled with C2Cl4 was buried 19 ft undergroundnear Brookhaven. The detector was built to observe:
37Cl +  ! e, +37 Areand

37Cl +  ! e, +37 Ar:
e

(1.2)

The energy threshold for these reactions is 0.814 MeV. This experiment was designed to observe antineutrinos from a nuclear reactor assuming that neutrinos andantineutrinos were identical particles. The rst reaction, 37Cl(e, e,)37Ar, was neverobserved since neutrinos and antineutrinos are di erent particles. At the time, it
was believed that only the pp neutrinos from the Sun would have a high enoughux to be measured, but these were below the threshold for the chlorine reaction.
The neutrinos that could induce the chlorine reaction came from the CNO cycle.
But the ux was expected to be so small that there was not much hope of a good
observation. Some people still thought that a chlorine experiment would be a good11

solar neutrino detector.
Within a few years, the expected rate of solar neutrino captures on chlorinechanged greatly. The cross sections of reactions important to hydrogen burning
were measured; the results were much larger than expected. These experiments
induced much work on the solar models and neutrino ux calculations. The neutrinos from 7Be and 8B were now expected to be observed. New calculations on
the capture cross section on chlorine were also completed, including transitions to
excited states of argon. The capture rate was about 20 times larger than previously thought [9]. Plans for a solar neutrino detector using chlorine quickly followed.
In 1965 a neutrino detector was begun in the Homestake Gold Mine in South
Dakota, USA by R. Davis et. al.[10]. The detector operated using the reaction:
37Cl +  ! e, +37 Ar:
e

(1.3)

The low threshold for this reaction (0.814 MeV) allowed this detector to observethe 8B and 7Be solar neutrinos. The detector contained 615 tons of cleaning uid(C2Cl4) located 4850 ft underground. Approximately 24% of the chlorine atoms
were 37Cl which lead to  2.2  1030 atoms. A neutrino interaction produced 37Ar,
which is a radioactive noble gas. Chemical extraction and radioactive counting
systems were used to determine how many argon atoms were produced during acertain time period. An isotopically pure sample of 36Ar or 38Ar was added to theC2Cl4 as a carrier. Helium gas was bubbled through the detector. The helium
picked up the argon atoms and was collected by a molecular sieve; the argon wasabsorbed in a charcoal trap. This system trapped approximately 95% of the argon.
Argon decays via electron-capture (1=2 = 35 days) producing low energy electrons
and x-rays. The 2.82 keV Auger electron was detected by a small proportional
12

counter. The amount of argon was measured by counting the number of decays.
The number of argon atoms produced was used to compute the measured neutrino
interaction rate. If the cross section for the neutrino interaction in 37Cl is known or
can be accurately calculated, the neutrino ux can also be computed. Additional
errors in the measured ux will be present due to the uncertainties in the crosssection calculation.
There were many sources of background for this experiment:
1. cosmic ray muons and products of their interactions
2. fast neutrons from the rock created by ( ,n) reactions and ssion of 238U
3. 's from uranium and thorium interacting in the C2Cl4
4. cosmic ray neutrinos (produced in cosmic ray air showers)
The contribution from Items 2 and 3 is minimized by requiring the materials usedin the detector to have extremely low emission rates. The majority of the background was initiated by secondaries from high energy cosmic ray muon interactions.
The muons interact with the rock near the detector producing pions, protons, neutrons, etc. These particles ultimately produce argon in the detector via (p, n)reactions. The background was estimated by exposing 600 gallons of C2Cl4 at alevel in the mine closer to the surface and extrapolating to the location of the larger
experiment.
The results from the rst few runs indicate that the majority of the solar energy
does not come from the CNO cycle. Since less than 9% of the energy is produced
via the CNO cycle, it is assumed that the pp cycle generates the other 91% [10].
Some of the rst experimental results [11] are given in Table 1.2, along with thetheoretical prediction (BP92 model [7]) and measured background. A SNU is a
Solar Neutrino Unit equivalent to 10,36 interactions/s/target atom.
13

37Ar production rate

Run 18Run 19Run 20(atoms/day)
0.214
0.490
0.349

(SNU)
1.14
2.62
1.87

expected
1.51  0.20 8.1  1.1
background 0.08  0.003 0.4  0.16
Table 1.2: Initial results for the Homestake chlorine experiment
The Homestake experiment is still taking data. There have been improvements
to the extraction and counting system. Several di erent ways of calibrating thedetector have been tried. The half-life of argon has been measured (and agrees
with expected). The most recent results yield a capture rate of 2.55  0.25 SNU[12]. The SSM prediction (with 1 error) is 8.1  1.1 SNU.
Clearly, the Homestake experiment is not capturing and counting enough solar
neutrino interactions. There are many possible explanations for this discrepancy:14 The theoretical models for processes inside the sun areincorrect, leading to a higher expected neutrino rate.

 Important input parameters to the Standard Solar Modelneed improvement.

 The cross sections for nuclear reactions are smaller thanthought, causing fewer neutrinos to be produced.

 All the anticipated neutrinos are produced, but something
happens to the neutrinos so they are not observed.

 The cross section for neutrino capture on 37Cl is smaller
than calculated.

 The experiment is less ecient than the experimenters
thought/measured.
To help answer some of these questions, more experiments and theoretical work
was needed.

1.3 Kamiokande
Kamiokande is a water-C erenkov detector located in a lead and zinc mine in theJapanese Alps near the town of Kamioka [13]. The Kamiokande experiment is thepredecessor to Super-Kamiokande, the topic of this dissertation. The cylindricaldetector is 15.6 m in diameter and 16.1 m tall. There is a large central region (innerdetector) and an annular region (outer detector) separated by an optical barrier.
The inner detector holding 2140 tons of pure water is viewed by 948 phototubes; thephototubes are 50 cm in diameter. This corresponds to photocathode covering 20%
15

of the surface area of the inner detector. The outer detector is a layer approximately
1.5 m thick (thinner on top) and uses 123 50 cm phototubes. The inner surfaceof the outer detector is covered with re ective material to help collect more light.
Kamiokande observes neutrinos via electron scattering in real time (there is no
waiting for atoms to decay):e + e, ! e + e,

(1.4)

The inner detector observes the scattering event while the outer detector tags incoming cosmic ray muons (large contributor to backgrounds). When this detector
rst became operational, the energy threshold was approximately 10 MeV. Theenergy threshold is de ned as the energy where the trigger eciency is 50%. Since
then much work has been done to reduce the threshold; the current value is 5 MeV
for events in the ducial volume. The energy threshold for the solar neutrino analysis is a bit higher.
A C erenkov detector observes neutrino events in a di erent fashion from theradiochemical experiments (37Cl and 71Ga). The radiochemical experiments use
chemical means to extract the atoms and their radioactive properties to countthem; a C erenkov detector records the pattern of C erenkov light incident on anarray of phototubes. C erenkov light is produced by relativistic charged particles
in a medium (like water) when the particle is traveling faster than light in thatmedium. For electrons in water with ten's of MeV or less, all the energy is lost in
several centimeters. From far away (meters), the C erenkov light appears to comeout in the shape of a cone, with the point of the cone at the location of the particle.
For an ultrarelativistic particle ( = 1) the half opening angle of the cone is 42.
This cone of light hits the wall partially covered with phototubes (PMT), that
detect the light. In a large detector like Kamiokande, all the light appears to come16

from approximately the same point. Using this point approximation and the arrival
times of the photons at each PMT, the location of the electron (vertex position)
can be reconstructed. The direction of the electron can also be reconstructed. The
incident neutrino direction and the direction of the scattered electron are highly
correlated:
1 + MEecos  =
(1.5)
(1 + 2TMee )1=2
where  is the angle between the neutrino direction and the scattered electron
direction, Me is the mass of the electron, Te is the electron kinetic energy, andE is the energy of the neutrino. Kamiokande can determine if the event `points'back towards the Sun. This is one of the great strengths of this type of detector.
Kamiokande was the rst solar neutrino detector to prove that the observed neutrinos were actually originating from the Sun.
After all events in the appropriate energy range are reconstructed, several cuts
are applied to the data to reduce the background. Kamiokande-III (started taking data in December 1990) takes data at 0.5 to 4 Hz [14]. This yields 2105
events/day to analyze. The SSM prediction for a detector that observed  -e scattering depends on the energy threshold. For a threshold energy of 7.0 MeV, theSSM prediction is 0.8 events/day. It is clear that the background must be reduced
by at least ve orders of magnitude. After the cuts are applied, Kamiokande-III isleft with 2023 events for a 314 day period. Not all of these events point towards
the Sun however. The last step in the analysis is to histogram cos sun, the cosineof the angle between the reconstructed electron direction and the vector from thevertex point to the Sun. Figure 1.3 shows the Kamiokande-II and Kamiokande-III
combined results. The solid histogram indicates the SSM expectation above theat background. The dashed histogram shows the best t to the data. The number
17

Number of events / 1036-day:0of events above a at background is counted. They are left with 151.5+21,19:6 events:067(rate of 0.482+0,0:062 events/day). Once again, a de cit of solar neutrinos is observed;#observed = 0:492  0:033(stat)  0:058(sys).
the nal result [15] is #expected
500
400
300
200
100
0
-1

-0.5

0
cosθsun0.5

1Figure 1.3: Event correlation with the Sun from Kamiokande-II and III

1.4 SAGE and GALLEX
Two more underground radiochemical solar neutrino experiments have collectedsolar neutrino data. SAGE is in the Baksan Neutrino Observatory, U.S.S.R.[16];GALLEX is located in the Gran Sasso Laboratory, Italy [17]. These detectors were
designed to observe the pp neutrinos. They are the lowest energy neutrinos, but
the most abundant and well predicted. The detected  reaction is:
71Ga + e!71 Ge + e,

(1.6)

The threshold for this reaction is 0.2332 MeV. Due to the calculated uxes fromdi erent neutrino sources, about half of the expected signal should come from the
pp neutrinos, a quarter from the beryllium neutrinos, and a quarter from the boron
18

and CNO neutrinos. The SSM predicts 132 7 SNU [7], which corresponds to
1.17 atoms/day in a 30 ton gallium detector. The minimum signal that a gallium
detector should see occurs when only the pp neutrinos are detected; the event ratewould then be 71 SNU.
The GALLEX experiment uses 30 tons of gallium in an aqueous solution of HCl
acid. A small amount of germanium carrier is added to the solution. By bubbling
nitrogen gas through the liquid, the GeCl4 can be separated out. The acidity ofthe solution ensures that the germanium will be in a tetrachloride form. After
puri cation, the GeCl4 is put into a proportional counter [18] where the EC decay
from 71Ge (1=2 = 11.4 days) is observed. Pulse shape discrimination allows the71Ge decays to be distinguished from background. Backgrounds for GALLEX are
caused by 71Ge production through non-neutrino mechanisms:
71Ga + p !71 Ge + n(1.7)

with a threshold of 1.02 MeV. These protons may be produced by cosmic muoninteractions, fast neutrons, or residual radioactivity. Radon gas and its daughter
products are also a large cause of background; the radon half-life is 3.8 days. It has
not been possible to totally eliminate the presence of radon, but its series of alphaand beta decays is a recognizable signature. The eciency for cutting out Radonbackground events is 92%. The most recent results from the GALLEX collaboration are 79  10 (stat)  6 (sys) SNU [19].
SAGE consists of 57 tons of liquid metallic gallium. The principles behindthe experiment are almost the same as GALLEX; since SAGE uses liquid gallium
they must have a di erent technique to extract the 71Ge. A small amount of
natural germanium carrier is added to the tanks. A hydrochloric acid solution is19

added in the presence of hydrogen peroxide. This extracts the germanium in the
aqueous phase. Several more steps are completed before the mixture is put into
a proportional counter. The backgrounds are similar to those of GALLEX. The
overall extraction eciency for the natural germanium carrier is 101%  5%. It
is assumed that the eciency is the same for neutrino-produced 71Ge. The most+5
recent results are 74+13,12 (stat),7 (sys) SNU [20].

1.5 Current State of the Field
Table 1.3 summarizes the current experimental results. The measured ux relative
to the prediction is given in as Nmeasured
NSSM . Uncertainties are given for the measurement(expt:) and the SSM expectation (theory). A reminder of which neutrinos eachexperiment is sensitive to is given. All experiments observe a disagreement between
the predicted ux of solar neutrinos and the measured ux, but the experiments
do not show the same de cit.
Experiment

Nmeasured
NSSM

Homestake 37Cl 0.29
Kamiokande 0.49
GALLEX
0.60
SAGE
0.56

expt: theory

sensitivity

0.03
0.07
0.09
0.14

7 Be, 8 B, hep

0.02
0.04
0.05
0.05

8 B, hep

all
all

Table 1.3: Results from current solar neutrino experiments
The SAGE and GALLEX results are constrained by the total solar luminosity
to be above 71 SNU. This minimum neutrino rate is calculated by assuming that
nothing modi es the neutrino energy or avor and that the only reactions which
occur in the Sun are the two that produce the pp and pep neutrinos (pp-I termi20

nation). The rates for these two reactions are constrained such that the total solar
luminosity agrees with the measurements. If the gallium experiments had measured
less than 71 SNU, new neutrino physics would be required to explain the results.
Kamiokande measures only the 8B neutrino ux while Homestake is sensitive
to 8B and 7Be neutrinos. If we assume that Kamiokande correctly reported the 8B
ux and compute the expected 7Be contribution to the Homestake ux, we get asmall or negative value. That is to say RHomestake , 0:49  SSMB  SSMBe whichleaves no room for the existence of 7Be neutrinos that should have been detected by
the Homestake experiment. The suppressions of the 8B and 7Be neutrinos clearly
can not be equal. The combination of these two experiments implies that the 7Be
neutrinos are suppressed more than the 8B neutrinos. This is sometimes referred
to as the \second" solar neutrino problem.
The three results (37Cl, 71Ga, and Kamiokande) together are incompatible withthe standard models (SSM and standard neutrino physics) [21]. The Gallium results
are very close to the minimum neutrino ux that can be observed without drasticchanges to the SSM or new neutrino physics. This implies that the other neutrinos
are suppressed much more than Kamiokande or Homestake show. If the suppressionof the high energy neutrinos is taken from Kamiokande and 37Cl, the 71Ga results
imply fewer pp neutrinos than the luminosity constraint allows. There is also theserious question regarding the relative suppression of 7Be and 8B neutrinos. The
results can not be made to be compatible with each other without increasing theexperimental errors well beyond the reasonable values[21].

211.6 Possible Solutions
There are several possible solutions that are currently being examined. These
include changes to the SSM, overestimations of nuclear cross sections, and changes
to our understanding of neutrinos. Six of the solutions will be brie y described.

1.6.1 Reduction of the Central Temperature
One way to reduce the ux of the higher energy neutrinos is to shift more of thecompleted pp cycles towards the pp-I terminations. One way to accomplish this is
to reduce the temperature of the Sun. This is done in non-standard models by ahomologous transformation; this means that the temperature pro le (dependence
on radius or enclosed mass) remains the same as the SSM, but an overall multiplicative factor (independent of mass) is applied. This reduction in temperature
can be achieved by: reducing the age of the Sun reducing the opacity or the fraction of metallic elements (making the Sun
more transparent)

 increasing the pp cross section to make fusion easier (solar luminosity achieved
with lower temperature)
Due to the assumed homology of the temperature pro le, the temperature dependence can be characterized by the central temperature, Tc. Since the neutrino uxes
depend (sometimes highly) on Tc, the expected signals in the experiments can vary
up to 20% with Tc. However, when the data from the various experiments is
considered together, there are no reasonable modi cations to Tc that will cause theexperiments to agree on the uxes [22].
221.6.2 Smaller Cross Section for 7Be Production
If the cross section for 7Be production were smaller than anticipated, the ux of 7Be
neutrinos could be greatly reduced. The same reduction in the 8B ux would also
occur. The amount of reduction is limited by Kamiokande, which is only sensitive
to 8B and Hep neutrinos. Estimations of the changes in the cross section needed toaccount for the data are very large; this solution is unlikely [23].

1.6.3 Low Energy Resonance in 3He + 3He! + 2 p
It is possible that the cross section for the 3He + 3He reaction is enhanced at theenergies relevant to the Sun. This would imply that fewer pp-cycle terminations
yield the production of 7Be and 8B (and associated neutrinos). The reductions of
the two uxes do not have to be the same. The e ect of the resonance could operate
di erently for di erent kinetic energy of the 3He particles (this creates a temperature dependence). This could cause more suppression for particles created in theouter regions of the Sun (7Be neutrinos). This resonance has not been observed
previously because no experiments have measured this cross section in the relevantenergy range. The value used in SSM computations is an extrapolation from higher
energy data. Examination of the data sets does not yield good agreement [22]. Thispossibility is being investigated by the LUNA experiment located in the Gran Sasso
Lab in Italy [24]. They have a much greater sensitivity to the strength and energyof the possible resonance.

1.6.4 Smaller  for  Capture on 37Cl and 71Gae

A possible argument is that the neutrino capture cross sections of 37Cl and 71Ga
have been overestimated. Up until about 1995, the cross sections used in the
SSM rate prediction had been calculated not measured. A reduction in these cross23

sections would cause the expected rates to decrease. Both SAGE and GALLEX
performed a calibration with a 51Cr neutrino source[25]. The 51Cr source produces aknown intensity of neutrinos with a similar energy distribution to the solar neutrinos
observed by the 71Ga experiments. Both groups measure a neutrino intensity fromthe 51Cr source which is almost equal to the calculated rate prediction. The resultsof this calibration prove that the capture cross section and SSM predictions havebeen accurately calculated.

1.6.5 Helium Di usion
Recent work on non-standard solar models resulted in the reduction of neutrinouxes which agree with the measurements[26]. The focus of this work is the e ect on
the relative reaction rates and the neutrino production caused by the 3He mixing in
the core of the Sun. A phenomenological approach was taken to discover necessarychanges to the SSM which explain the experimental results. Modi cations weremade to the shape of the 3He pro le while meeting the constraint of 3He global
equilibrium in the core. The overall temperature pro le of the Sun was reduced so
the model would satisfy the luminosity constraint. The 3He pro le shapes whichyield neutrino uxes in agreement with the measurements have a general shape:
enhancement at the core by an order of magnitude and reduction at large radii.
The physical plausability of the suggested 3He mixing needs further investigation.

1.6.6 Neutrino Flavor Oscillations
In the particle physics Standard Model theory, neutrinos are massless particles thatinteract with matter via the weak force. The neutrinos that are produced via weakinteractions are called avor eigenstates: electron jei, muon j i, and tau j i. It
is e's that are generated by the hydrogen burning inside the Sun. These avor
24

eigenstates are not necessarily states which have de nite mass (i.e. they may not
diagonalize the time independent Hamiltonian for the weak force). If we assume
that at least one avor neutrino carries a non-zero mass and that the avor eigenstates are not mass eigenstates, neutrino avor oscillations can be induced. If ae changes avor to a  or  , it will be undetectable in most solar neutrino experiments. The Homestake experiment would have diculty observing 37Ar froma  or  interaction with the 37Cl due to the small probability of 37Ar creation.
Kamiokande would detect the  -e scattering from a  , but the cross section for
scattering is smaller by a factor of  6.
The avor eigenstates (e ,  , and  ) are the observable neutrino states. Eachof the observable neutrinos can be considered a mixture of mass eigenstates (1,
2, and 3). To explain neutrino avor oscillations, let us make some simplifying
assumptions. We will consider only two neutrino states. Suppose that j1i and j2i
correspond to the two mass eigenstates of the Hamiltonian. We will express thetwo observable states jei and jxi (x indicates any avor or combination of avors
which does not include e) as a mixture of the mass eigenstates:jei = cos #j1i + sin #j2i
jxi = , sin #j1i + cos #j2i(1.8)

where # is the mixing angle. Because the two mass eigenstates have di erent
masses (m1 and m2), the time dependent eigenstate wavefunctions will oscillatewith di erent phases ( ,iEh 1t and ,iEh 2t ). The energies E1 and E2 correspond to thetotal neutrino energy for a neutrino momentum of p. When the observable states'
time evolution is considered, we get the following equations:je(t)i = cos #e, iEh1 t j1i + sin #e, iEh2 t j2ijx(t)i = , sin #e, iEh1 t j1i + cos #e, iEh2 t j2i
25

(1.9)

We can now compute the probability for a e at time t = 0 to remain a e at timet. This `survival probability' P (e ! e) is computed to be:

P (e ! e) = jhe(0)je(t)ij2 = 1 , sin2 [2#] sin2"

(E1 , E2) t2h#(1.10)For relativistic neutrinos the energy di erence can be written in terms of the massdi erence between the two mass eigenstates: E1 , E2 =  2mE2 (since m2 =
jm22 , m21j is always positive, the appropriate sign is chosen depending on which
eigenstate has the larger mass). The amount of neutrino avor oscillation can becharacterized by the oscillation parameters: m2 and sin2 2#. This simple picture
describes vacuum neutrino oscillations, often called the \just so" solution to thesolar neutrino problem.
In 1978, Wolfenstein described the e ect on avor oscillations of coherent forward scattering of neutrinos travelling through matter[27]. Although the mean
free path of a neutrino is huge, the forward scattering can induce large changes
in the phase of the neutrino wavefunction which is the most relevant quantity for
oscillations. In 1986, Mikheyev and Smirnov discussed the resonant ampli cationof neutrino avor oscillations in dense matter and investigated the impact on solar
neutrinos[28]. If the resonance conditions are met, the oscillation probability will be
maximal. The MSW solution, as it was coined, of matter-enhanced neutrino avor
oscillations predicts a possibly energy dependent decrease in the e ux reaching
Earth.
To gure out the precise e ect of the MSW matter enhanced oscillations, wemust derive the `survival probability' as a function of energy for the solar neutrinos.

26

The wave equation which must be satis ed by the neutrinos is given[29]:,i dtd j i = H j i

where
3
2
3
0 77 y 1 66 A 0 77
5 U + 2p 4
5
2
0 m2
0 0
p
A
=
2
2G N p2
3
2
3 2 F e323
 7
 7 66 cos # sin # 77 66 1 77
6
6
6 e 7
6 1 7
4
5=U4
5=4
54
5
x
2
, sin # cos # 2
2
m21
6
1
6
H = 2p U 4(1.11)

where t is time,  is either of the two avor eigenstates being considered, p is
the neutrino momentum, M 2 is the Hamiltonian, U is the unitary transformation
between the avor eigenstates and the mass basis, A acts like an e ective inducedpmass squared (comes from the e ective potential V = 2GF Ne), GF is the Fermi
coupling constant for the weak force, and Ne is the electron density of the matter.
The right side of the wave equation can be diagonalized by:2
6 M2
Umy HUm = 21p 64 1

3
7
7
5

0
0 M22
n
o
M22;1 = (m21 + m22 + A)  [(A , m2 cos #)2 + (m2 sin #)2]1=2 =2:(1.12)We then write the matter mass eigenstates in terms of the avor eigenstates:2
3 2m 7 66 cos #m
6
6 1 7
4 m 5=4
2
sin #

32
3
, sin #m 77 66 e 77
54
5
cos #
x

(1.13)

where #m is the matter mixing angle as given by

m2 sin 2#)2
sin2 2#m = (A , m2 (cos 2#)2 + (m2 sin 2#)2 :(1.14)

Note that the equation for sin2 2#m displays resonance characteristics. Maximal
mixing can occur between the matter mass eigenstates for particular values of the27induced mass squared: A = m2 cos 2#.
To determine the `survival probability', we must numerically integrate the neutrino wave equation over the time it takes after production for the neutrino to
traverse the Sun. The `survival probability' is the probability that a neutrino generated as a e is observed as a e at time t. This integration is done for a varietyof neutrino energies to achieve the energy dependent probability function.
Each neutrino experiment can probe a particular region in (m2; sin2 2#) space.
When the results are all combined together, there are only two regions in the 2dimensional parameter space still fully allowed, if oscillations are the solution to
the solar neutrino problem. Figure 1.4 shows these allowed regions [30]. These are(m2  10,5 , sin2 2#  10,2 ) (nonadiabatic solution) and (m2  10,5 , sin2 2# 0:5) (large angle solution). These two oscillation solutions can be separated by two
distinct measurements: the energy spectrum and a day/night ux di erence. The
large angle solution hardly changes the spectrum, while the nonadiabatic greatly
distorts the shape of the neutrino spectrum. It is possible for the neutrino ux
reaching a detector to be di erent during the day (when the Sun is above) andduring the night (when the Sun is below the Earth). In the case of the large angle
solution, the fraction of neutrinos exiting the Sun which are e is <50%. Flavor
oscillation would then occur in the Earth's interior, causing  mixing. The net
e ect is that some of the x particles to oscillate back to e. The ux would thenbe higher during the night than the day.

28

-3

10

-4

10

Excluded-52∆m (eV )

10

-6

2

10

-7

10

BahcallPinsonneault SSM-8

10

Combined 95% C.L.
SAGE & GALLEX
KamiokandeHomestake

-9

10

-4

10

-3

-2

10

10

2

-1

10

sin 2θ
Figure 1.4: Currently allowed regions of MSW oscillation parameters (Hata andLangacker, 1994)

29

0

10

1.6.7 How to Decide Which Solution is Right
A measurement of the neutrino spectra would provide a major key to the cause of
the solar neutrino problem. No modi cations to the SSM result in a change to theneutrino spectrum [5]. If the shape of the observed spectrum is di erent than SSM
predictions, then we know some other physics which changes the energy or avorof neutrino is the instigator. In the case of MSW enhanced avor oscillations, forsome values of the mixing parameters there would be resonant oscillations in boththe Sun and the Earth. If oscillations occur in the Earth, neutrinos may oscillateback to look like e . This regeneration of the e s would cause a di erence in theux observed during the day and night (known as the day/night e ect). A moreaccurate measurement of the total neutrino ux would also be helpful. Especially
if this measurement included other types of neutrinos (besides e). Several new
detectors will try to answer some of the open questions regarding the Solar Neutrino
Problem.

1.7 Sudbury Neutrino Observatory
The Sudbury Neutrino Observatory (SNO) [31] should be operational in 1998. SNO
is a C erenkov detector that uses regular and heavy water. It is located in the
Creighton Mine near Sudbury, Ontario. SNO has an inner volume containing 1000
metric tons of D2O encased in an acrylic vessel shaped like a sphere. This vessel sits
inside a cylindrically shaped stainless steel tank. The vessel dimensions are 10 m
in diameter and 14 m tall. Surrounding the heavy water is a 4 m thick layer of
H2O, the stainless steel tank wall, 0.9 m of low radioactivity concrete, and the rockwall. All of the D2O and a 2.5 m layer of H2O is viewed by 8,500 20 cm PMTs.

30

The neutrinos are observed in both types of water via electron scattering:e + e, ! e + e,

(1.15)The scattered electron is observed by the C erenkov light it produces in the water.
Since the value of the refractive index for heavy water and light water are close,
the C erenkov patterns will also be similar. However, because of the presence of
deuterium, SNO has additional mechanisms to observe neutrinos:

e + d ! p + p + e,

(1.16)

x + d ! x + p + n(1.17)

where d stands for the deuteron nucleus and x indicates a neutrino of any avor(e, , or  ). Reaction 1.16 is often referred to as the Charged - Current (CC) interaction (since a charged W boson is exchanged), while reaction 1.17 is called the
Neutral - Current (NC) interaction (since a neutral Z boson is exchanged). Reaction 1.17 has been used in previous neutrino detectors, but SNO is the rst detector
which can detect these reactions to observe solar neutrinos with a reasonable rate.
It is also important for the Solar Neutrino Problem, since all three weak neutrino
avors will interact via the NC reaction. If a sterile neutrino exists, it would not
be detectable via the NC reaction. SNO is sensitive only to 8B neutrinos due tothe few MeV threshold (the actual value depends on the background level). The
analysis of the CC events will be fairly similar to Super-Kamiokande's; SNO will
also have to reconstruct and account for the neutrons.
Due to the large cross section, SNO expects to observe several thousand events
per year from reaction 1.16 (CC). There is an expected angular distribution for theelectrons which has a two-to-one backward to forward asymmetry. Events fromthis reaction could be used to measure the neutrino energy spectrum. To get a31good spectrum measurement, SNO must accumulate a fairly background-free event
sample. The asymmetry is tough to see if a large at background is present. Since
all neutrino avors interact in the heavy water via the NC reaction, this will provide
an absolute measure of the total neutrino ux from the Sun. The ratio of eventsfrom reaction 1.16 to reaction 1.17 provides direct information on the presence ofneutrino avor oscillations. However, to identify events with reaction 1.17, SNO
must be able to detect the neutron resulting from the deuteron disintegration.

1.8 Borexino
Borexino is a scintillation detector1 to be located in the Gran Sasso Lab in Italy[32]. A small prototype version, Counting Test Facility, has been tested already.
The Borexino concept uses high eciency scintillator viewed by low noise photomultiplier tubes. A 8.5 m diameter nylon sphere will hold the liquid scintillator;
the ducial volume is expected to be 100 tons of scintillator[33]. A 2.2 m thickbu er region lled with pseudocumene (the same solvent used in the scintillator)
surrounds the scintillator. The light produced by the scintillator is detected by
2,000 20 cm EMI photomultiplier tubes mounted facing inwards on a stainless steel
sphere of radius 13.7 m. A muon veto is generated by 400 PMTs facing outwards,
also attached to the stainless steel grid. The entire assembly is encased in water toreduce backgrounds further.
Borexino will see elastic scattering events in the scintillator volume: + e, !  + e,

(1.18)

Initially, the design concept for Borexino required the scintillator to be loaded or doped with
Boron to enhance the detection of the B neutrinos. Due to technical diculties, the Boroncomponent of the experiment was dropped.
1

8

32

The e , e elastic scattering event rate for a full SSM neutrino ux would be
50 events/day above threshold in the 100 ton ducial volume. The exact value ofthe energy threshold will be set by the background levels, but 0.25 MeV is believedachievable. The electron energy spectrum should have a \Compton-like" edge atapproximately 665 keV caused by the 7Be neutrino line source at 862 keV. The
observation of this characteristic hard edge from the 7Be neutrinos is one of theprincipal goals of the Borexino experiment.

33

Chapter 2

Super-Kamiokande Description
2.1 General
Super-Kamiokande is a new water-C erenkov detector located in the mountains ofJapan, on the west coast of Honshu. Super-Kamiokande is situated in one of the
Kamioka Mining Company's lead and zinc mines; the same mine as KamiokandeIII. The origin of the Super-Kamiokande coordinate system is the center of thedetector. The average rock overburden due to Super-Kamiokande sitting under amountain has been calculated as 2800 meters water equivalent (mwe). This overburden reduces the atmospheric muon rate at the Super-Kamiokande site to < 3 Hz.
A simple schematic diagram of the Super-Kamiokande detector is shown in Figure 2.1. A cylindrical stainless tank encases the Super-Kamiokande detector. At a
total height of 41 m and diameter of 39 m, Super-Kamiokande is the largest underground water-C erenkov detector built. The tank holds 50,000 m3 of ultra-pure water. Super-Kamiokande is sectioned into two optically separate detectors: inner andouter. The outer detector forms a cylindrical shell of uniform thickness (2.5 m)
which surrounds the inner detector. The separation between the inner and outerdetectors is provided by a stainless steel structural gridwork and Tyvek. Stationed34

on the tank top are ve electronics counting houses. Each quadrant of the detector
requires one counting house; the fth counting house is for detector-wide electronics
such as the triggers. Table 2.1 contains a summary of Super-Kamiokande's speci cations (as relevant to the solar neutrino analysis) in comparison with the previous
water-C erenkov solar neutrino detector, Kamiokande.

6

Vertical Cross Section of Super-Kamiokande Detector

41
meters?b b b b b b b b b b b b b b b b b eb
b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
eee
6
e
b ee
b
e
e
eeeb
b eee
eeeb@I@b eee
eeeb @@
33.8 metersb eeeeeeb Tyvek
b eeeeeeb ,,
b eee
eeeb
b eee
36.2 meters eeb
b eee
eeeb
b eee
eeeb
b eee
eeeb 20 cm
b eee
eeeb PMTs
50 cm PMTsb eeeeeeb 
Ab eeeAeeeb 
Ab eeeAeeeb
A
b eee
A
eeeb
b eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeAUAb b b b b b b b b b b b b ?b b b b e
39 meters

Figure 2.1: Cartoon sketch of the Super-Kamiokande detector

35-Super-Kamiokande Kamiokande-III
Total size
39 m  41 m
16 m  16 m
Total mass
50,000 m3
4,500 m3
Solar  ducial volume22,500 m3
680 m3# PMTs11, 146948
Photocathode coverage
40%
20%Anti counter
2.5 m all surfaces 1.5 m side only
Timing resolution
2.8 ns
4.0 nsTrigger threshold
5.7 MeV
5.2 MeV
Analysis threshold
6.5 MeV
7.5 MeV
pE=17%
pE=20%
Energy resolution
10MeV
10MeV
Position resolution

80 cm

110 cmTable 2.1: General properties of Super-Kamiokande and Kamiokande

36

2.2 Con guration of the Inner Detector
Most of the volume of Super-Kamiokande is contained in the inner detector. C erenkov
light produced in the inner detector is viewed by 11,146 Hamamatsu photomultiplier tubes (PMTs) 50 cm in diameter (model R3600-05). The PMTs are mounted
facing inwards on supermodules attached to the structural gridwork that separates
the inner detector from the outer detector. A diagram of a supermodule is given
in Figure 2.2. The centers of the curved PMT face (center of the \spherical" PMTface) lie on a cylinder of radius 1690 cm and height 3620 cm. Approximately 40%of the inner detector surface area is covered by PMT photocathode. The areas between the PMTs are covered with \black sheet" material so that light which does
not hit the PMTs is absorbed by the black sheeting.
Side Facing Inner Detector

mmmm
mmmm
mmmm

Cross Sectional View


50 cm PMTs
Outer Detector
Side Facing Outer Detector

h

,
,
h
Tyvek

22 cm PMTsInner

Detector





?

Black Sheet

Figure 2.2: Schematic of a supermodule372.3 Con guration of the Outer Detector
The outer detector envelops the inner detector and provides an almost uniformly
thick anti-coincidence shield. Although the inner and outer detectors are opticallyseparated, water can ow between the two detectors. The  2.5 m thick outerdetector is viewed by 1,885 Hamamatsu tubes 20 cm in diameter (these PMTs
were previously used in the IMB detector [35]). The PMTs are supplemented by
60 cm square waveshifter plates, also taken from the IMB detector. The PMTs aremounted on the stainless steel gridwork on the opposite side from the 50 cm tubes.
The 20 cm PMTs face towards the outside tank wall. The center of curvature of
the PMT face lies on a cylinder with radius 1745 cm and height of 3730 cm. The
region between the inner and outer PMTs is often called the `dead space' since inorder to detect light generated in this enclosed region, the light must enter the backof the PMT. Indeed this light can be observed although with an eciency muchsmaller than light which hits the photocathode face on.
All possible surfaces in the outer detector are lined in a re ective material,\Tyvek", to enhance the light collection of the outer detector. Made by DuPont,
Tyvek is formed from woven polyethylene bers and has many common uses such as
mailing envelopes. On the side of the outer wall, the Tyvek fastens at the top cornerof the outer wall, hangs down the length of the wall, and attaches to weights andanchoring wire which counteract the buoyant forces created by being submerged
under water. On the bottom of the tank, large Tyvek strips cover the oor andare weighted down. The roof of the tank has a Tyvek `curtain'. The area between
the 20 cm PMTs and underneath the waveshifter plates is lined with Tyvek that is
attached to the stainless steel gridwork.

38

2.4 Photomultiplier Tubes# of entries

The 50 cm photomultiplier tubes installed in Super-Kamiokande are a much improved version1 of the PMTs used in Kamiokande [36]. The major improvement
to the PMTS that impacts solar neutrino physics is the decreased timing jitter.
The time between a photon hitting the photocathode and a signal traveling outof the PMT on a cable is not always xed; there is some variation. Figure 2.3
shows a measured distribution of the transit times from one of the PMTs at the
beginning of the production run. The distribution is t to an asymmetric Gaussianfunction. The average of the two Gaussian sigmas (P3 and P4) is usually quoted
as the timing resolution. This particular PMT has slightly worse timing resolution
than the average of  = 2:8 ns. Another feature of the PMTs is the distinct single
photoelectron (pe) peak.

PMT Time (nsec)

Figure 2.3: Measured transit time jitter of the 50 cm photomultiplier tubes
The re-design of the PMTs was performed by Super-Kamiokande collaborators A. Suzuki,
M. Mori, K. Kaneyuki, and T. Tanimori.
139

Thermal emission of electrons from the photocathode creates what is known asdark current. This dark current or dark noise needs to be as small as possible in order to keep the trigger threshold low. At room temperature the average dark noise
rate of a 50 cm PMT is 10 kHZ, or 10,000 noise signals every second. These noise
signals are typically at the single photoelectron level. The cooler the photocathode,the lower the noise rate. In the Super-Kamiokande tank, the water is 10C and theaverage PMT noise rate is 3.6 kHz (measured with a 0.25 pe threshold).
The cables attached to the 50 cm PMTs were designed for Super-Kamiokande.
Side by side in a single outer jacket lie a shielded conductor for the signal out of
the PMT and an unshielded HV conductor. The jacket construction was speciallydesigned for use underwater. It was desired to keep the cable lengths for every
PMT the same length for ease in generating the trigger. The cables are almost all
70 meters long (several have had extension cables added). The 50 cm PMTs operate
at a nominal gain of  6:0  106 so that 1 \photoelectron" = 2.055 picoCoulomb.
The quotes around the word \photoelectron" tell you that we do not mean a real
photoelectron. Our units of charge are called \photoelectrons" or \pes" and areclose in magnitude to a real photoelectron. On average, the conversion from ourcharge units to real electrons is given: 1 photoelectron = 1.4 \photoelectrons".
The 20 cm PMTs have a transit time jitter of 5 - 6 ns. With the waveshifter
plate included, the e ective jitter rises to 11 ns. A single photoelectron peak is not
visible from these tubes partly due to their design and partly due to their age. An
RG-59 type of cable is used to supply the high voltage to the tube and to returnthe signal. The cables were constructed to prevent water coming in contact withthe center conductor either by entering a break in the outer jacket or by wicking
40

down the length of the cable. To make the relative timing between the inner andouter detector as close as possible, the cable lengths match those in the innerdetector, 70 meters. There were several PMTs whose cables did not quite reachthe electronics huts and needed extensions. Those small di erences were taken out
in the calibrations. The average dark noise rate of the 20 cm PMTs in the 10 C
water is 3 kHz. The high voltage (HV) on each PMT is set such that the gain of
the PMT is 1:0  108.

2.5 Electronics and Data Acquisition Systems
Due in part to the di erent physics requirements for the inner and outer detectors, the electronics and data acquisition systems (DAQ) for the two detectors were
designed and implemented di erently. The inner detector electronics and data acquisition (DAQ) system was custom designed and built for Super-Kamiokande[34].
One of the main requirements for the inner detector was that the entire detector
should never be `dead'. The DAQ system was thus developed so that individual
channels would be busy handling the output signals from the hit PMTs from one
physics event, but the channels without PMT hits would be able to accept andprocess signals from a di erent physics event. The outer detector dead time requirements are not as strict. Since the outer detector is used as an active vetoshield against entering muons and other particles, it is more important to be able
to record the PMT activity for a long time before a potential neutrino event andfor a short time after the trigger. Hence, the outer detector has a long `look-back'time from every trigger.
Although the speci cs of the DAQ systems di er between the inner and outerdetectors, the systems must work together. The information is collected and com41

bined into a single unit with all the necessary information and data from both theinner and outer PMTs. This intermingling of the data occurs in the event builder,a program whose purpose is to make sure all the available data for each trigger has
been received and assembled to form an \event". The global triggering of SuperKamiokande is controlled by the TRG module. The TRG simultaneously accepts
up to eight input trigger signals, generates a unique global event number, and distributes the trigger signal to the remainder of the DAQ hardware. The PMT datais collected and stored in memory by the inner and outer DAQ systems individually. The event builder then sends out requests for all the information relating
to a certain block of triggers (every trigger has a unique 16 bit number associatedwith it). The event builder waits until it receives the requested information then
combines it all together and sends it to the oine data handling system.

2.5.1 Inner Detector
A simple schematic showing the various parts to the inner detector electronics system is given in Figure 2.4. The mainstay of the electronics for the inner detector
is the Analog Timing Modules (ATM) [37]. Each ATM accommodates 12 PMT
signals and digitizes their charge and leading edge time. The 48 TKO crates eachpower 20 ATMs plus several other TKO modules [38].
For each input signal (PMT) there are two available subchannels (A and B).
Each channel is self-gated; the gating logic sends the PMT signals to the appropriate subchannel by toggling between subchannels A and B. When a PMT `hit'
arrives at the ATM, the signal goes to the discriminator for the `next' subchannel(e.g. A). If the discriminator threshold is passed both subchannels are vetoed for
900 ns (to prevent re ections), the Time to Analog Converter (TAC) for subchannel
42A starts charging, and a 400 ns gate is opened for the Charge to Analog Converter(QAC) associated with subchannel A. The TAC (QAC) charges until a global trigger is received (the gate closes). A 100 ns delay in the PMT pulse arrival at the
QAC implies that the e ective QAC gate width is only 300 ns. If no trigger arrives
within 1.3 s, the channel auto-clears and may process a new hit starting 200 ns
later. Once the 900 ns veto period is over, the remaining available channel (e.g. B)
may accept the new PMT hit.

j\
jJ \\
j@JJ
jZ@
jHZH A
jXX T
j
j M
j,
j,
j
j .
.
.
.

j

.
.
960
ATMs

TKO Crate

JJ

-

S
M
P

.
.
20 ATMs SCH GONG .
.
48 SMPs.
.
48 TKO crates
SS , C



, C

Sun
Z
}
~ Sun
. Z
host
.
.
8
workstations

 -

11146
PMTs
Figure 2.4: Schematic of the inner detector electronics
A hit will be lost if the gating logic points the hit to a busy subchannel (even if
the second subchannel is available). Lost hits rarely happen resulting in the ATM
43system being almost dead time free2. Digitization of the TAC and QAC values
takes approximately 6 s per hit channel (only hit channels are digitized). The
digitized times range from 0 to 1023 ns in increments of 0.25 ns. The digitizedcharges range from 0 to 409.5 pC in 0.1 pC steps. The discriminator threshold for
the ATMs is 1 mV or 1/3 photoelectron.
The triggering for all 20 of the ATMs in one TKO crate is managed by one
GONG (Go/No Go) module [39]. The GONG module receives the global trigger
from the TRG module and provides the trigger to the ATMs via the TKO backplane. The GONG continuously passes the event number signal back to the TKO
backplane, so the ATMs can read the lower 8 bits of the event number. Approximately 500 ns after the trigger signal arrives at the ATMs, the ATMs latch theevent number.
Readout of the ATMs is governed by the Limiter (LIME) module and the Super
Memory Partners (SMPs). The LIME is a NIM module, while the SMPs are VME
modules. The primary function of the LIME module is to limit the number oftriggers between ATM readouts. This limiting will help guarantee that the ATM
8-bit event numbers can be correctly matched to the 16-bit event numbers from the
TRG. A single LIME module counts the number of triggers sent by the TRG. Afterevery 16 triggers a signal is sent to the SMPs which initiate the ATM readout [40].
The data stored in the ATM is passed through the SCH (Super Control Header)to the SMPs. The SMPs hold the data in one of the memory bu ers (2 bu ers
available in each SMP) until 64 ATM readout cycles are completed. After the 64th2

An ATM channel will have both subchannels busy during high rate bursts of triggers. In
this case, the ATM will have a non-zero dead time since it will sometimes be dead when a
hit comes in.

44

time, an interrupt signal is sent from the SMPs to whichever one of the 8 Sun
workstations is in charge of those SMPs. The PMT data and accessory information
for the 64  16 triggers are sent from the SMPs to the Sun. The other bu er in each
SMP is available for storage next time the ATMs require a readout. Each of theeight Sun workstations controls an octant of the inner detector. The event builder
program running on the host computer meshes the data from each workstation (andthe outer detector) into an \event".

2.5.2 Outer Detector
The majority of the electronics for the outer detector was purchased commerciallyfrom LeCroy and other vendors, although key components were custom designed
and built. The overall mode of operation is to use a multi-hit Time to Digital
Converter (TDC) to record each PMT hit to obtain the time and charge of thesignal. The TDCs in each quadrant are usually read out after each of the incoming
triggers. The TDC and other information is bundled together in a package thatthe event builder can accept. Figure 2.5 shows the electronics used for the outerdetector PMTs.
Before the signal can be handled by the electronics, it must rst be separated
from the positive HV supplied to the PMT. HV picko cards accommodate twelve
inputs (PMTs) and output the signals on a single ribbon cable. Now the signal
goes to a custom designed Charge To Time converter (QTC) which tests the signal against a discriminator threshold and generates the pulse which is digitized by
the TDC. The QTC card outputs a pulse whose leading edge is delayed by 200 ns
from the rise of the input PMT pulse and whose pedestal-subtracted width is linearly proportional to the integrated total charge of the PMT signal in a 200 ns
45

self-triggered gate. The discriminator threshold is set to -25 mV or 1/4 photoelectron. The minimum duration of the output pulse is 550 ns; this corresponds
to the charge pedestal. The conversion from pedestal-subtracted pulse width tocharge is: 5 ns = 10 picoCoulomb = 1 photoelectron = 10 TDC counts. The ECL
pulses exit the QTC on ribbon cables that hold 16 signals each and travel to the
TDC.

j\
jJ \\
j@JJHV
jZ@ p
jHZH iQ
jXX c - Tj ko
j f
C
j, f
j,
j
j
.

FASTBUS Crate -C C JJC  C JDC2  .
.
.
4
DC2

5 LatchJ
.
.
J
TDCs
.
.
.
FSCC
.
.
.
40
. 160 QTCs.
.
j cards
4 crates
1885
PMTs

D
P
M

 -

.
.
.
8
DPMs

OD
Sun
6

?

Sun
host

Figure 2.5: Diagram of the outer detector electronics
The pulses carrying the time and charge information are digitized by a LeCroy
1877 multi-hit Time to Digital Converter (TDC). This TDC is a FASTBUS module,chosen for its high channel density (96 channels per module) and other general characteristics. The TDC least count is 0.5 ns. The multi-hit capability is made possible46

by the use of a `pipeline' that records the digitized times of pulses. The length of
this `pipeline' can be adjusted; for the rst six months that Super-Kamiokandecollected data this window size was set to 32 s. The positioning of the trigger inthe 32 s window was set so the trigger occurred at t = 0 and the window extended
from -16 s to +16 s. This con guration enables us to `look back' in the outer detector data for a solar neutrino candidate event and see if a muon or other particle
could have entered the inner detector and produced the candidate via spallation
or muon decay. The ability to `look ahead' was also desirable as we could thensearch for processes like muon decay in the outer detector (assuming there is somereasonable eciency for triggering on the process).
The TDC was con gured to digitize the leading and trailing edges of 8 pulses,
logging the rising and falling edges of each pulse. After 6 months of data taking,
the TDC window size was changed to 16 s to reduce the total data size taken up
by the outer detector. The center of the time window was shifted so it extended
from -10 s to +6 s. This shift reduced the loss of PMT data from tubes withmore than 8 hits. PMT afterpulsing causes extra PMT pulses to be generated after
an initial pulse of intense light is observed. The afterpulsing probability depends onthe charge of the initial pulse, so cosmic-ray muon events which enter the detector
often induce more than 8 hits in a PMT. It is the rst few hits (which contain theentry point information) that will be lost due to the 8 hit limit. The asymmetrictime window reduces the chances that the entry point PMT hits are lost by the
TDCs.
The readout of the modules in each FASTBUS crate is controlled by a single

47

FASTBUS Smart Crate Controller (FSCC)3. When the FSCC receives a trigger
signal, a common stop is issued to the TDCs and the event number is latched by a
Struck FASTBUS Latch module. The latch has the same memory bu ering as the
TDC to make matching TDC data to event numbers simple. All the channels in a`hit' TDC are unavailable for further hits during the digitization. The dead time forthe digitization of a TDC depends on the number of recorded PMT pulses: 750 ns+ 50 ns/edge  (# pulse edges) with a minimum TDC dead time of 1.6 s and amaximum of 78 s [41]. The FSCC sends the digitized PMT data to a DC2-DM115(module which uses VSB bus on a VME crate). The DC2-DM115 latches the TDC
data sent by the FSCC and stores it in memory. The data is then written into
whichever of the two Dual Ported Memory (DPM) modules (Micro Memory 6390)
is available. The DC2-DM115 and DPM communicate via the VSB bus on the
VME crate. The two DPMs operate in ping-pong mode. While the DC2-DM115 iswriting to one DPM over the VSB bus, the other DPM is being read out over the
VME bus by the OD DAQ Sun computer. The OD Sun functions similarly to the
8 Sun workstations collecting inner detector PMT data.
In addition to the PMT data, the OD DAQ collects the GPS time (see Section 3.1). The signals from the GPS antenna are sent into Super-Kamiokande by
an optical ber. The GPS time is decoded and latched every 21 seconds by VME
modules. A 50 MHz \local" VME clock is latched which allows interpolation between the GPS clock latches. Both the GPS clock and the 50 MHz clock are readout for every trigger. The OD data from each quadrant and the central VME crate
is collated by the OD Sun. The data then goes to the event builder running on thehost computer before \events" are assembled.
3

The FSCC has been under development at FermiLab.

48

2.6 Triggers
The Super-Kamiokande detector is always globally triggered. The global trigger isdistributed by a VME module named the TRiGger (TRG) to the inner and outerdetector data acquisition systems. The TRG assigns the unique 16-bit event numbers and distributes or inhibits triggers that are input to the TRG. The actual
decision of whether an event was above a particular trigger threshold is determinedby the various trigger electronics systems. The TRG accepts up to eight input triggers. A trigger signal is sent out by the TRG 30 ns after the input signal arrives.
The TRG records which of the inputs caused the trigger by ipping bits on or o .
Each input has it's own bit. Table 2.2 explains how the bits are assigned. The rst
6 bits correspond to the input triggers; the last two bits are set when triggers startand stop being vetoed by the LIME.
If more than one input trigger arrives within 350 ns, the event counter in the
TRG increments once and a single trigger signal goes out. All appropriate bits are
set to re ect the multiple causes for the global trigger. The timing of the global
trigger issued is not usually set by the input signal created rst. Delays before
the trigger inputs reach the TRG are set so that the Low Energy trigger always
determines the timing of the global trigger. When the LIME counts 16 triggers
since the last ATM readout, the LIME sends a signal to SMPs to begin ATM readout. If the SMPs are still busy from the last ATM read out (which rarely occurs), a
veto signal is sent by the LIME to the TRG so no triggers arrive at the TKO crateduring ATM readout. When this veto signal arrives, the TRG creates an event
header with the `veto start' bit set. The veto signal is asserted until the SMPs areready for ATM read out. The TRG then creates another header, but this time the`veto stop' bit is set. The TRG is read out by the data acquisition system in order49

to obtain the event number and the trigger bit information (the integer containing
the trigger bit information is known as the \trigger id"). Typical data-taking isdone using the Low Energy, High Energy, Outer Detector, and Null triggers.
Bit Number Trigger Description0
Low Energy
1High Energy
2
Calibration I
Outer Detector
3
4Null Trigger
5
Calibration II
Veto Start
6
7
Veto Stop
Table 2.2: Trigger bit description

2.6.1 Low Energy and High Energy
The ability to obtain a high trigger eciency for low energy (5 MeV) solar neutrino
events was of great concern. To accomplish this, we expected to have two di erent triggers: simple and intelligent. The simple trigger would require Ntubes to be
hit within 200 ns of each other. The intelligent trigger would then give us muchhigher eciency for the low energy events (so we could operate with an energy
threshold of 5 MeV). Eciency studies were performed on the proposed intelligent trigger electronics schemes while the Super-Kamiokande detector was being
constructed [42]. The studies concentrated on the e ect of dark noise on the trigger eciency/threshold. It was concluded that none of the schemes were a vast50

improvement over a simple trigger and we would wait until the detector was operating to build an intelligent trigger. This would give us operational experience withthe various backgrounds that are present in the solar neutrino data sample. The
intelligent trigger might then be designed to di erentiate the background eventsfrom the solar neutrino signal. Intelligent triggering schemes to reduce the energy
threshold are being investigated again and should be implemented before SuperKamiokande's rst year of data taking is nished.
The simple trigger that was built (shown in Figure 2.6) uses the `hitsum' signals provided by the ATM. For each hit PMT, a square pulse of height 11 mV
and base-to-base duration 200 ns is generated after the discriminator threshold has
been passed. The `hitsum' signal is the analog sum of these square pulses for the hit
PMTs within one ATM. The hitsums are collected together and summed together
in a custom built analog hitsum adding module (hitsum adder). The hitsum adderalso tries to remove the contribution to the hitsum from dark noise pulses. If one
thinks of the PMT dark noise as a constant background underneath the signals
generated by physics events, it would seem reasonable to subtract o this constantbackground. The hitsum adder attempts to do this by AC coupling the hitsum
signals. The e ective time constant is long compared to 200 ns [43].
The adding of the 960 hitsum signals occurs in three stages. First, the `hitsum'
signals from the 20 ATMs in a TKO crate are summed. Second, `quadrant sums' arecreated from 12 TKO crates per quadrant. The quadrants are then added together
into the overall HITSUM. Both the Low Energy and the High Energy triggers use
this HITSUM signal, albeit with di erent threshold levels. For the rst six monthsof operations, the Low Energy trigger threshold was set to 320 mV and the High
51

Form
Quadrant
Sums

jQ
jHQHQ hitsum
jPPHP signal jPPP
hitsumadderjhhh Aj ( T -11mV/hitj((( M
.
j((
.
j
.
j,,
j, .
48
.
.
960
ATMs

.
.
.

11146
PMTs

-

hitsum
adder
.
.
.
4
adders

- fan

in
fan
out

HITSUM? ? signal
d d
i i
s s
c c
-320 mV-340 mVLE trigger
HE trigger

adders? ?

Global Trigger 

TRG

Figure 2.6: Electronics for the inner detector trigger

52

Energy threshold was 340 mV.

2.6.2 Outer Detector
The major purpose of triggering on the outer detector by itself is to ensure themaximal eciency for correctly identifying entering muon events. This is important for both the solar neutrino and atmospheric neutrino/proton decay analyses
as entering muons can produce background events or are background themselves.
To this end, a simple trigger was built for the outer detector which requires Ntubes
to be hit in a T time window (schematic given in Figure 2.7). In order to ensure
the desired trigger eciency, Monte Carlo studies were done to select the optimum
parameters of the Ntubes trigger (coincidence window and threshold).

Form
QuadrantSumsjQ
hitsumjHQHQ
signaljPPHPHV
jPPP pi Q -64 mV/hit fanjhhh cinj (k -T
j((( oj(( f C.
j f
.
j,,
.
.
j,
4
.
.
.
.

.
40
QTCs

HITSUM- fan signal- disinc-1216 mVOD trigger

FIs

TRG



1885
PMTs

Global Trigger

Figure 2.7: Layout of the outer detector trigger electronics
53?

The outer detector trigger electronics consists of several linear fan-in NIM modules and a discriminator. The QTC cards that deliver the digitized PMT signals
to the TDCs also produce an analog \hitsum" signal which is a square pulse thatrises at a xed time after arrival of the PMT pulse at the QTC. The square pulses
from an individual PMT hit are 200 ns long base-to-base and -64 mV in height.
The 48 \hit" signals from a single QTC card are summed together into a \hitsum" which is output from the QTC card. The 10 \hitsum" signals within each detector quadrant add together, then the 4 quadrants are summed and tested against
a discriminator threshold. The trigger rate was measured as a function of discriminator threshold (Figure 2.8). The discriminator threshold was initially set to beequivalent to a trigger threshold of 19 hit PMTs in a 200 ns coincidence window.
-25 mV QTC Threshold, Normal HV

19 Tube Threshold

Figure 2.8: Outer detector trigger rate as a function of threshold

2.6.3 Other Triggers
A null trigger is a trigger generated by a clock, not a physics event in the detector.
These null triggers have been used among other things to monitor the noise rate of54

the PMTs. A null trigger is generated about every 6 seconds. In addition, there areseveral types of calibration triggers, some of which are used simultaneously. These
are described with the calibration system (Chapter 3).

2.7 Oine Data Processing
As the event builder collects all the information for a given event, it stores the dataon disk in the mine. Every 10 minutes or so, the events kept on disk are packaged
into a \subrun" and sent out of the mine to the oine computer system. This ensures a relatively constant ow of data out of the mine without having to wait for a
run to stop. The data goes rst to a reformatting computer which changes the data
format from a simple binary format to a set of zebra banks [44](see Appendix A).
The reformatting computer then ships the data to another computer for the conversion from digital counts to times in nanoseconds and charges in photoelectrons.
The computer using the calibration constants to convert the time and charge data
(called the `TQ real' process) has a very large ram disk on which the calibration
constants are stored. Once the data is `calibrated' it is placed into memory for
temporary storage. The `uncalibrated' data is also stored on tape in a large magnetic tape library. The computer processes that run `o -line' then read the datafrom memory and go about their job. The on-site analysis groups have their ltering and tting programs running `o -line' and reading data from memory. Theo -site analysis groups have a data copying process that reads data from memory
and writes to a DLT tape (holds 30 Gigabytes) for shipment to the U.S.

55

2.8 Water System
A complex water puri cation system maintains the long light attenuation lengths
and low radon content of the water in the Super-Kamiokande detector. The detailsof the e ect of radon on the solar neutrino measurement will be discussed in Chapter 7. The puri cation system can operate in either ` ll' or `re-circulate' mode.
The ow rate in the ` ll' mode is lower than `re-circulate' mode. The water is puried using lters, ion exchangers, ultra-violet sterilizers, vacuum degasi ers, reverse
osmosis, and ultra- ltration. Each of these components removes materials fromthe water ranging from particulate matter of a certain size to bacteria to radon.
The water to ll Super-Kamiokande is taken initially from sources of running waterin the mine which are not clean enough to go directly into the Super-Kamiokandetank. The full puri cation system was used when lling Super-Kamiokande. Fillingthe entire Super-Kamiokande tank took less than three months. The turnover time
for the Super-Kamiokande tank while in `re-circulate' mode is approximately one
month.

2.9 Clean Air Systems
Because radon can di use from the air into the Super-Kamiokande tank, we needto keep the air above the Super-Kamiokande tank clean. The air in the mine4
has been measured at between 150 Bq/m3 and 2000 Bq/m3. The goal of thecleaning system is a radon content of 4 Bq/m3. (nominal factor of 100 reduction
from the Kamiokande experiment). The chosen method to achieving this goal is acombination of a radon-impenetrable barrier and the introduction of \radon-free"
air. The barrier keeps radon from leaching into the Super-Kamiokande dome from4

In the U.S., OSHA suggests xing your house if it has a radon content above 160 Bq/m .
356

the rock. The imported \radon-free" air replaces the radon- lled mine air near
Super-Kamiokande.
The exposed rock surface in the dome area above the Super-Kamiokande tankis lined with materials designed to retard the di usion of radon from the rock into
the air. The lining consists of three layers: MineguardTM , a vinyl acetate sheet,
and a polypropylene layer. Small pins drilled into the rock anchor the lining to
the rock. MineguardTM is a polyurethane material manufactured by the Canadiancompany Urylon. A 1 mm thick layer of MineguardTM was sprayed onto the vinyl
sheet. A series of pipes attached to the dome drain the water which condenses on
the rock/vinyl surface. The water is guided into the drainage pipes by the vinyl
acetate sheets held on by elastic bands. A soft cloth made of woven polypropylene
bers provides a cover for the anchor needles sticking out from the rock. Tests
comparing various methods for containing Radon show that MineguardTM has apermeability of 2.7  10,9 cms 2 ; other methods yield permeabilities from 10,5 to
10,10 , many of which are not applicable to the Super-Kamiokande site or are prohibitively expensive.
Air cleaned of radon will be piped into the Super-Kamiokande dome by theclean air system. The \radon-free" air system is not yet operational, but is mostly
assembled. Air much cleaner than inside the mine has the radon further removed.
The air intake is located above the \radon hut", which houses the clean air system,
just outside the mine entrance. The starting radon content varies between 10
and 120 Bq/m3 depending on the season. The air will be cooled and dehumidi edthen sent into a carbon lter. The carbon traps radon by adsorbing it and clean
air exits the lter. The air is then warmed, humidi ed, and piped into the Super57

Kamiokande dome. To keep the clean air from escaping, the dome is sealed fromthe rest of the mine by a set of double doors similar to an air-lock. The carbonlters must be re-generated when they ll with radon. This can be accomplishedby either pushing hot air through the lters or by letting the lter sit for several
days until the radon decays away. In the hot air method, the heat breaks the bond
between the radon and carbon and the moving air carries the radon out of thelter. Temperatures and radon levels at various places are measured and much of
the system control and monitoring is performed via a computer inside the mine.

58

Chapter 3

Calibration
Detector calibration is essential for producing data with the Super-Kamiokande
detector [45] which is useful for studying physics problems. Without proper timeand charge calibrations of the photomultiplier tubes (PMTs) and electronics, itwould be dicult at best to use the PMT signals to reconstruct the event. The
PMT timing is calibrated using short bursts of light with varying intensity (systemdescribed in Section 3.1). To calibrate the PMT charge, a variable intensity of lightfrom a xenon ash lamp is sent through a wavelength shifting material then into
the Super-Kamiokande tank.1 Details of the charge calibration system will not begiven [46]. A good absolute energy calibration is necessary if the systematic errors
are to be small for the solar neutrino ux and energy spectrum measurements.

3.1 Absolute Timing
To calibrate the absolute time of the events we use a clock based on the Global
Positioning System (GPS). The GPS system uses satellites to determine the exact
time at and the position of an antenna on the Earth. A GPS antenna receives thesignals from the GPS satellites. The signals are sent down an optical ber from the1

The xenon system was chosen based on its stability over long times.

59

antenna to the central hut on the top of the Super-Kamiokande tank. The timefrom the GPS clock is latched by a VME module. The GPS clock is read out forevery event by the outer detector data acquisition system; the information is stored
in the \anti-header" area of the data (see Appendix A).

3.2 Relative Timing
Due to variations in the length of the cables, transit time across the PMTs, andtransit through the electronics, the time between creating a photoelectron and passing the discriminator threshold will di er from PMT to PMT. The time at which
the discriminator threshold is crossed will vary with the signal pulse height due to`electronic slewing'. (For a given pulse shape, the larger the pulse height the earlier
the discriminator threshold is crossed.) We want to remove these variations so thatthe relative timing of all the PMTs is the same. In order to calibrate the relative
timing between the tubes we need a pulsed source of light which has a variable
intensity and a way to know when the pulse of light was emitted. A laser with avariable attenuation system satis es these requirements.
The basic procedure utilized to calibrate the tubes is to re the laser and record
the time each PMT received a hit. We are interested in the time between the photons hitting the PMT photocathode and the signal being recorded by the ATM.
We need to measure the time between the laser ring (the photons exiting the lightsource) and the photons entering the water in the Super-Kamiokande tank. The
travel time of the photons in the water (from light source to PMT) is calculatedusing the group velocity of the photon wavepacket appropriate for the laser wavelength. Using these two time di erences, we can extract the timing o set between
creating a photoelectron and recording the time with the ATM.
60

3.2.1 Light Source
The laser must meet several criteria. The pulse width of the laser light should benarrow to minimize the systematic error in the time correction at high light levels.
This potential error is due to the ` rst photon e ect'. Photons are emitted fromthe laser uniformly during the pulse window. PMTs trigger upon the arrival of the
rst detected photon. At low light levels where there is only one photon detected,
the PMT trigger will occur randomly in the laser pulse width (t in width). At
high light levels, the rst detected photon occurs on average earlier than at low
light levels. The PMT trigger will occur closer to the leading edge of the laser
pulse by an amount  t/2. The laser wavelength should be close to the peak inthe detectable C erenkov spectrum (approximately 350 nm). Since the laser may
be used for other purposes where a tuneable wavelength was desired, we chose adye laser. The dye laser is pumped by a pulsed nitrogen laser. Our closed system
nitrogen laser (Laser Science Inc. model: VSL-V337ND-S) has an average pulse
energy of 300 J, pulse width of 3-4 ns, and wavelength of 337 nm. The dye module(model: DLMS-220 also from Laser Science Inc.) tunes to wavelengths longer than
337 nm with an accuracy of 0.3 nm. The relative timing calibrations are typically
performed using 384 nm provided by an Exalite 384 dye. A wavelength of 384 nm
is closer to the peak detected wavelength of C erenkov light after travelling througha few meters of water and does not induce uorescence in the optical bers (as337 nm light will do)2.
2

We discovered that the bers inside the optical switch uoresced when 337 nm light wasused. A Germania dopant was used in the core of these short ber sections to change theindex of refraction. Germania has an absorption line at 330 nm which we were exciting.

61

3.2.2 Optical Components
In order to calibrate the PMTs we must bring the light into the tank such that thelight is observable for many of the PMTs and we must know when the laser red.
For the inner detector, a single light source may be placed near the center of thedetector. In the outer detector, the geometry requires that 52 light sources be used
so that all the PMTs can see more than one light source. Optical bers carry thelight from the laser to a light di user which sits in the tank and spreads out the lightfor all PMTs to observe. The positional con guration of the light di users is shownin Figure 3.1. The OD di users are permanently installed in Super-Kamiokande.
The ID di user is inserted in the tank just prior to each calibration run.
Horizontal Cross Sections
At Height A & C
Vertical Cross Section

Height A
Height B
At Height B

Height C

Figure 3.1: Layout of light di user locations
Before the laser light enters the bers it encounters a timing PMT and a seriesof optical splitters and optical switches. Figure 3.2 shows the con guration of these
optical components [47]. The laser is red by an input TTL trigger signal. A photodetector at the back of the laser cavity provides a synch output signal which gives
62the ring time of the laser with a 1 ns accuracy. To improve the timing accuracyof the detector trigger, a PMT with 300 ps timing resolution provides the trigger
signal sent to the TRG. The collimator after the dye laser brings the light into an
optical ber. A continuously-graded logarithmic neutral density lter decreases theintensity of the light. A 1:2 even ber optic splitter sends equal amounts of lightinto two computer-controlled optical switches (custom built by Dicon). The 1:50
switch holds the majority of the outer detector optical bers. The 1:9 switch handles the inner detector, the remainder of the outer detector, and any bers goingto testing stations. This con guration allows us to direct light into the inner andouter detector bers almost independently.

Optics of Laser Calibration System
Collimator
Dye module
A
AU

Laser

Fiber

,
,

,
,
?
,
(
((((





?

A

T

TT

,
,

1:9 switch

JJ
]

A
A
A

....
...

1:2 splitter

A

Filter wheel

Fiber






\O "
Inner
bers

...
....

...
...
1:50 switch .....
.

\O "
Outer
bers
Spares

...
.....

.
....
...

Filter Monitor PMT

Figure 3.2: Optical components to the laser calibration system
A CAMAC-based data acquisition system controls the laser-related hardware
63and collects the auxiliary information during a calibration run. A stepper-motor
controller moves the graduated lter a variable amount to get the desired lightintensity. A TTL trigger signal res the laser. The discriminated monitor PMT
signal is fed into the calibration II input of the TRG. The auxiliary data is passedwith the PMT data to the host computer and is available oine.

3.2.3 Optical Fibers
The optical bers must carry light at ultraviolet and visible wavelengths without
appreciable loss in intensity over the  70 meter ber length. They are continuously
immersed in water and hanging from a single point supporting their own weight.
These conditions greatly a ect the design considerations. To minimize the loss along
the ber length, we chose to use UV/Vis grade bers with both core and cladding
made from fused silica. The ber has a core diameter of 200 m and a cladding
thickness of 10 m. A polyamid coating covers the outside of the cladding; theresultant outer diameter of the coating is 240 m. A polyamid coating was selected
over an acrylite coating because it should reduce the moisture-induced degradationby providing a better moisture barrier around the core and cladding. The bers are
inside a protective jacket. The design and production of the ber/jacket assembly
was orchestrated by C-Technologies Inc. The jacket was designed to be extremely
impenetrable to water and very strong. A double-layer jacket was implemented.
The inner Hytrel jacket ts directly around the ber and has an outer diameterof 0.9 mm. The outer jacket has an inner (outer) diameter of 2.0 mm (3.0 mm)
and was also manufactured out of Hytrel. Hytrel is a special material made by
DuPont which is virtually impenetrable to water but dicult to work with since
few adhesives can bond to it. The space between the two jackets is lled with kevlar
bers which provide the jacket strength in the lengthwise direction. To minimize
64

stress placed on the ber itself, the kevlar bers are attached to the jacket onlyat the end of the ber. We attached the kevlar, the hytrel, and the ber together
using the adhesive Tyrite 7420 from Lord Corporation. When the bers are hunglengthwise in the Super-Kamiokande tank the full weight is held only by the kevlar,
the strongest component. The kevlar also stretches under tension by the smallest
amount of the materials in the ber or jacket.

3.2.4 Di users
The light exiting an optical ber is highly collimated along the ber length. This
light needs to be spread out so that many PMTs can view the laser light without
moving the ber location or orientation. Optical di users uncollimated the lightout of the ber end. So that the timing calibrations could be done using datataken with the di user at only one position, the inner di user should uncollimate
the light such that the intensity is isotropic to better than 20-25%. If the PMTs
see vastly di erent light levels due to anisotropy of the di user, then pulse-height
dependent relative timing calibrations may not be extracted correctly. This could
be avoided by considering the light level on a PMT by PMT basis and taking a large
enough calibration data set to ensure that the full intensity range has been coveredfor each tube, but it was desired to minimize the data set needed to adequately
perform the calibrations. The outer detector (OD) di users only need to spread thelight out enough for many OD PMTs to see. The di users for the inner and outerdetectors have di erent requirements and hence were built with two di erent styles.
The outer detector di users were made from a 10,3 :1 by weight mixture of
Titanium Dioxide (TiO2) powder and a UV transmitting optical cement. The TiO2
powder has a very large re ectivity even in the UV. The powder is uniformly sus65

pended in the optical cement (LensBond F-65 manufactured by Summers OpticalCo.) prior to the cement hardening. Inside of this di user, light undergoes multiple re ections o the TiO2 powder and emerges much more isotropic than the light
exiting an optical ber. A relatively small amount of the TiO2/cement mixture
was dabbed on the ber ends before the cement cured. In addition to providing
a way to di use the light, the optical cement seals the ber end to keep moisturefrom degrading the ber. The nished OD di user shown in Figure 3.3 looks likea hemisphere of radius 1.5 mm stuck on the ber end which is aligned with thecenter of the hemisphere.

Outer Detector

Inner Detector
Diffusers

Diffusers

optical fiber

TiO 2
mirrorsfiber
jacketacrylic
container
10 cm

Ludox liquid

3 mm

Figure 3.3: Optical di users for the inner and outer detectors
The inner detector di user must be constructed di erently due to the isotropy
requirement. The isotropizing technique is the same one which Kamiokande [48]and IMB [49] used since the OD di user material and th other attempted methods absorbed too much of the UV light. Instead of using a TiO2/optical cement
mixture we use small silica (SiO2) spheres suspended in water. Light Rayleighscatters o the silica spheres which are uniformly distributed throughout the water66

volume. Since the intensity of Rayleigh scattered light has a strong wavelength
dependence ( 14 ), this variety of di user will have variable behavior dependent on
the incident wavelength. The silica/water mixture was manufactured by DuPont
Chemical Corporation under the name Ludox TM-50. The silica spheres were givena slightly negative surface charge so that the mutual repulsion of the spheres would
keep them in suspension. By weight, 50% of the mixture was silica spheres witha diameter of 22 nm. The suspension is guaranteed to remain stable and uniform
for approximately one year, after which we may need to replace the Ludox in ourdi user. The nal con guration of the inner detector `laserball'3 is drawn in Figure 3.3. A sealed cylinder made from UV transmitting acrylic contains the Ludox
and the ber end. To improve the isotropy especially in the backwards region, adouble-mirror assembly which has the mirrors bracketing the ber end is inserted
into the Ludox.

3.3 Absolute Energy
Super-Kamiokande has set the goal of knowing the absolute value of the energy
scale to < 1% for the solar neutrino energy range. This goal is based on the ability
to di erentiate between the two possible MSW solutions to the Solar Neutrino
Problem using the shape of the solar neutrino-induced electron energy spectrum.
If the energy scale is shifted due to an unknown systematic error, the ratio of themeasured energy spectrum to the SSM predicted spectrum may not be at. If thestatistical errors in the ratio are small, we may wrongly attribute this to a change
in the neutrino spectrum caused by neutrino oscillations. We want to prevent
making that mistake, and so want to calibrate (and double check) our energy scale.
In the previous versions of Ludox di users, the containers were spherical in shape - hence thename `laserball'.
3

67

Uncertainties in the energy scale contribute a large amount to the systematic error
on the ux measurements (i.e. a 2-3% in the energy scale will cause a 6-9% error
in the ux). We must minimize the uncertainty in the energy scale to keep theux systematic errors small. In order to accomplish this, we use several calibration
sources with well known energies. Some of these sources are external to the SuperKamiokande detector while others are extracted from the data. Multiple sources
allow us to check the linearity of the energy scale. It can be dicult to nd ideal
sources in the energy range desired. Therefore, we must sometimes build our own
calibration sources.

3.3.1 Muons
Several di erent energy calibration sources can be extracted from the data. Single through-going muons provide the highest energy calibration source for SuperKamiokande. Most through-going muons are minimum ionizing particles. For a wellde ned track length (and total muon energy upon entering Super-Kamiokande),the energy deposited via C erenkov light in the inner detector can be computed formuons in the data and muons generated by the simulation program. Sometimes amuon will create a Brehmstrahlung gamma-ray, causing an upward uctuation in
the detected C erenkov light. These events are usually dicult to achieve a goodtrack t. By requiring a good t, the non-minimum ionizing muon events are
excluded from the muon sample used for calibration. This comparison between
detected light from simulated and data muons will set the absolute energy scale forthe highest energy events.

683.3.2 0 Rest Mass
Neutrino interactions can sometimes result in a single 0 particle in the detector. A
0 at rest will decay into two back-to-back gamma-rays. The reconstruction of thedeposited energy for these 0s events should produce a narrow peak at the 0 rest
mass energy. This peak will be used for absolute energy calibration in the several
hundred MeV range, once enough events are collected from the data.

3.3.3 Decay Electrons
The end point of the Michel electron energy spectrum (shown in Figure 3.4) is agood energy calibrator. The end point does not depend on Monte Carlo simulations,correct energy calibration of any additional equipment, or the accuracy of vertex
or track tters. Unfortunately, electronics e ects make the energy calibration withMichel electrons dicult to do accurately. Energetic muons generate many PMT
hits. These hits get digitized and then wait to be read out. PMT hits during thenext events will have to wait longer to get read out if the PMT was already hit by
the muon. This `waiting time' (on the order of s) causes the charge measurementof previously hit PMTs (ATM channels) to become less accurate at the few percent
level (the number of hit tubes is still ne to use). Since Michel electrons naturally
come after a muon event, they are directly a ected by these electronics e ects.

3.3.4 Radioactive Gamma-Ray Sources
Gamma-ray sources have historically been the only way to calibrate a water-C erenkov
detector in the very low energy range [72]. This is mainly because making a sourcewith the desired properties was much easier if the source produced gamma-rays instead of electrons. The use of gamma-rays makes the energy calibration dependent
on the detector simulation. The entire point of an absolute energy calibration is to69

Number of entries per 0.5 MeVMichel Electron Energy (MeV)

Figure 3.4: Energy spectrum of muon decay electrons
be able to say: when Ne ective = Y , the energy deposited in the water = X MeV (seeSection 7.4.2 for the speci c de nition of Ne ective, but it is indicative of the numberof hit PMTs and is directly related to the energy deposited in the water). Since
gamma-rays must convert into electrons via Compton scattering or pair production
before C erenkov light is created, the only way we have to compute the total energy
deposited in the water is to simulate the gamma-ray interactions in the water (using
the Monte Carlo technique - see Chapter 4). The procedure used to perform thecalibration is:
1. Determine what the `energy quantity' (Ne ective) shall be
2. Compute Ne ective for data events from the gamma-ray source and for Monte
Carlo events from the simulated source
3. \Tune" the MC parameters which describe the water quality until the Ne ectivefrom MC and data agree
4. Simulate electron events throughout the ducial volume at many di erent
energies70

5. Compute Ne ective for each electron energy
6. Fit Ne ective versus electron energy ,! this is the actual energy calibration
A good gamma-ray calibration source would produce at least several of the `interesting' gamma-rays every second. The 's should be very close to monoenergetic
with the gamma background from the source neglectable or at least separable. The
most appropriate gamma-ray sources we have found are created by thermal neutron
capture on nuclei:
A Z + n ,!A+1 Z  ,!A+1 Z +(3.1)
Super-Kamiokande plans to utilize sources with several di erent nuclei to provide
several di erent energy s.

Thermal Neutron Capture on Nickel
The primary source uses natural nickel to capture thermal neutrons. Natural nickel
is a mixture of several isotopes all of which must be considered when determining theoutput gamma-ray spectrum after neutron capture. Table 3.1 presents a summaryof the quantities relevant to computing the expected thermal neutron capture rate
and the gamma energy spectrum from natural nickel. For each isotope present innatural nickel, we give the isotopic abundance (in %), the thermal neutron capture
cross section (in barns = 10,24cm2), and the total energy released in gamma-rays
from the nuclear de-excitation. None of these nuclear de-excitations yield a single
gamma-ray. The gamma-ray multiplicity per decay used in the source simulationis shown in Figure 3.5. The simulated individual gamma energies and the totalenergy released in gamma-rays are given in Figures 3.7 and 3.6.

71

Isotope Nat. Abund. [50] Capture  [50] Total Energy [51]1H
0.33 barns
2.2 MeV
58Ni
67.9%
4.4 barns
9.0 MeV60Ni
26.2%
2.6 barns
7.8 MeV61Ni
1.2%
2.0 barns
10.6 MeV
62Ni
3.7%
15 barns
6.8 MeV64Ni
1.0%
1.5 barns
6.1 MeV
Table 3.1: Thermal neutron capture information

Figure 3.5: Number of gamma-rays per neutron capture on nickel

72

Figure 3.6: Gamma-ray energies from neutron capture on nickel

Figure 3.7: Total energy released in gamma-rays per neutron capture on nickel

73

Neutron Source
A traditional source of neutrons is the spontaneous ssion of Californium-252 [52].
Approximately 97% of the time 252Cf decays via an while the remaining 3% of the
decays undergo spontaneous ssion (SF). The half-life of 252Cf is 2.65 years. There
are an average of 3.76 neutrons produced per ssion. The average neutron energyis 2.1 MeV and the spectrum extends up to 14 MeV. This source was chosen since
the maximum allowable source activity that could be used at the Super-Kamiokandesite was 100 Curie and 252Cf yields the most neutrons per Curie of activity. The
neutrons must be thermalized (moderated) before the interaction with the nickel
can proceed. The neutrons loose energy by elastically scattering o the protons inwater. It takes approximately 19 n-p scatters (several cm of travel) and a few s
for a 2 MeV neutron to lose enough energy to be considered thermal [53].

Source Geometry
We need to use the nickel and 252Cf together to provide an isotropic source of
gamma-rays. Since the thermal neutron capture cross section is so small, we want
to minimize the loss due to absorption in the nickel. This is easily done byminimizing the apparent thickness of the nickel. Long strands of nickel wire are
mixed with a light material which can moderate the neutrons (like water) suchthat the average density which the gammas traverse is small. The nal source
con guration uses a cylindrical polyethylene container 20 cm in diameter and 20 cm
tall (see Figure 3.8). Inside the polyethylene container is a 3:3.8 mixture by weightof nickel and water. At the center of the polyethylene container is the 252Cf source.
This con guration yields a nearly isotropic source of gamma-rays.

74

Californium - Nickel Calibration Source
Polyethylene
container

Stainless steel
wire handles

Neutron source and20 cm

Fission Counter

Nickel wire
immersed in water

20 cm

Figure 3.8: Con guration of Cf-Ni gamma-ray calibration source

Simulation of Nickel Source
In order to understand the Cf-Ni source better, a simulation of the neutron capture
and gamma-ray production was done using the MCNP simulation package4 developed by Los Alamos National Laboratory [54]. The Monte Carlo for Neutrons andPhotons (MCNP) simulation package handles detailed particle tracking througha variety of di erent materials and the generation of energy spectra for certain
sources. The user must give details on the desired neutron source, the geometryof the surrounding medium, and the output information needed. Figure 3.9 shows
the input card for our main source con guration.
The material which the neutron traverses must be described to MCNP. Geometrical descriptions are given for each `region'. Regions can have any shape (e.g.
cylindrical, spherical) and are not necessarily enclosed areas. The size of each rePei-Jar Liu and Bob Haight provided a tremendous amount of assistance in learning how to
use MCNP.
475

gion and the chemical makeup of the region are given with the shape. The rst
section in the example input card de nes the 4 `cells' or `regions' using the geometrical objects listed in the second section of the input card. The source area (cell#4) is de ned as the volume inside cylinder #4, below plane #5, and above plane#6. The region with the nickel in it is de ned as being on the `outside' of surfaces#1, 2, and 3 and 'inside' the surfaces #4, 5, and 6. This is really just the volume
between two cylinders of di erent radii and heights. Cell #4 (#3) has a density of
1 g/cm3 (1.4 g/cm3) and is composed of material #1 (#2).
MCNP can simulate many di erent neutron sources, including californium, bylooking up the source properties in a library. By specifying the spatial and time
distribution of each source, any geometrical source con guration can be modeled.
Multi-source combinations can also be accommodated. In our case, MCNP wasgiven a `source input card' (see section 3 of Figure 3.9) which described a point
source of 252Cf at the origin. The neutron energies will be chosen from the Watt
spectrum given the parameters appropriate for californium. Finally, the chemical
makeup of each material is given. Material #1 is simply water (H2O). Material #2
is an equal mixture (by weight) of water and natural nickel.
From the MCNP simulation we extract a lifetime of 83 s for the neutron in
the water/nickel environment. We examined the gamma-ray energy spectrum andidenti ed the peaks due to neutron capture by protons (in the water) and by nickel.
The distributions agreed fairly well with our expectations based on knowledge ofthe nuclear de-excitations. The fact that MCNP veri ed our predictions gives us
con dence in our understanding of the nickel source.

76

Cell Mat Dens Shape/Region

What particles to use?

10

imp:n=0 imp:p=0 !outside world

2

1-1.00 -7 -8 9 (1 : 2 : -3) imp:n=1 imp:p=1 !water barrel

32-1.40 -1 -2 3 (4 : 5 : -6) imp:n=1 imp:p=1 !nickel area

4

1

-1.00 -4 -5 6

7:8:-9

imp:n=1 imp:p=1 !source area

1

cz

10.

! cylinder around z axis with R = 10 cm

2

pz

10.

! plane at z = 10 cm

3

pz

-10.

! plane at z = -10 cm

4

cz

2.

! cylinder around z axis with R = 2 cm

5

pz

5.

! plane at z = 5 cm

6

pz

-5.

! plane at z = -5 cm

7

cz

10.5

! cylinder around z axis with R = 10.5 cm

8

pz

10.5

! plane at z = 10.5 cm

9

pz

-10.5

! plane at z = -10.5 cm

cisotropic point source at (0,0,0) in cell 4

sdef

erg=d1 pos=0 0 0 cel=4

sc1

Californium fission spectrum using Watt spectra

sp1-3 1.025 2.926

m11001 .667 8016 .333

! water

mt1 lwtr
m2! use the light water library

1001 .667 8016 .333 28000.51c 1. ! 50% water, 50% natural nickel

Figure 3.9: Input card for MCNP
77

Fission Trigger
There are several complicated issues related to using the Cf-Ni source for energy
calibration, the rst of which is triggering on the events. When matching the measured energy distribution to that expected for the nickel de-excitations, any energy
dependant e ects can distort the spectrum and add a systematic error in the energy
scale. The trigger eciency as a function of energy can certainly cause spectral distortions. We therefore need a method of triggering on the nickel s in an energy
independent way. This can be done by simply lowering the trigger threshold until
the trigger eciency is at for the entire energy range of the nickel gammas. If
the trigger threshold (50% eciency point) is dropped to 2.5 MeV the detector
trigger rate is then almost 14 kHz. The data acquisition system can not handle
this high rate for an extended period of time. We therefore need another methodof triggering the Super-Kamiokande detector during calibrations.
The second problem is identifying which individual events come from the source
and which events are background for the calibration. Normally this can not be accomplished, which makes average background subtraction a necessity to isolate theenergy spectrum from the nickel source. One possible way to handle this is totake data `on-source' and `o -source' and do a simple subtraction. In our case,`on-source' means Cf-Ni and `o -source' implies Cf only. To do this, the SuperKamiokande tank must be opened and the nickel removed from the container surrounding the Cf. Having the tank open and exposing the PMTs to ambient light
introduces problems with this method of background subtraction.
We have devised a way to solve the trigger and background subtraction problems
simultaneously. We use an ionization counter to detect the Cf ssion products. By
78

Events

amplifying and discriminating the ionization signals, we generate a ` ssion trigger'.
After a ssion trigger, a gate is opened during which we accept Super-Kamiokande
triggers with a very low trigger threshold. The events caused by the nickel source
are more likely to occur soon after a ssion trigger because of the expected 83 slifetime. By correlating the times of the Super-Kamiokande triggers with the timeof the ssion trigger, we can select out the events which are more likely to be fromthe nickel source. Figure 3.10 shows a distribution of the time between the Low
Energy event and the previous ssion trigger. The measured lifetime of the 85.5 sagrees well with the prediction of 83 s from the simplistic MCNP simulation. The
background subtraction is then done by an `on-source' - `o -source' subtraction.
`On-source' events are those which come soon after the ssion trigger; `o -source'
events are late compared to the ssion trigger.

Time Since Fission Trigger (microsec)

Figure 3.10: Lifetime of neutrons in Cf-Ni source
Figure 3.11 contains a sketch of the ionization counter used to generate the ssion trigger. This ssion counter is on loan from Los Alamos National Laboratory
and Oak Ridge National Laboratory. Imbedded inside the gas ionization counter is79

a 252Cf source with an activity of 1.5 Ci. This source emits neutrons at a rate of
1, 700 neutrons/sec. The signal from the gas ionization counter is separated fromthe bias voltage (-200 Volts) and ampli ed (factor of 40) by a pre-ampli er (see Figure 3.12). The pre-ampli er has two output signals: \energy" and \timing". The\energy" output is designed to yield an accurate charge or energy measurement.
This pulse has a rise time of about 200 s and a fall time of 100 s. The \timing"
output is similar to the derivative of the \energy" pulse; it is intended to give afast timing signal so the rise time is quick (10 ns) but the fall time is still fairly
long (100 s). The \timing" signal is ampli ed again, inverted, and discriminatedto produce the ssion trigger signal. The pulses created by the alpha decay of Cf
are clearly visible above the noise. The neutron induced pulses are well separated
from the alpha induced pulses (by a factor of 5 in pulse height). The discriminator
threshold is set at 32 mV to yield a nearly perfect eciency for triggering on theneutrons. The rate of ssion triggers can be pre-scaled down by any factor so thatthe total detector trigger rate is low enough to accommodate the DAQ.
For a xed time after each (pre-scaled) ssion trigger, Super-Kamiokande triggers are accepted with a very low trigger threshold. The trigger threshold must
be low enough in energy so that there is no variation in the trigger eciency forthe nickel events. The chosen threshold for the Super-Low Energy threshold is
150 mV (15 PMT hits during the 200 ns coincidence window) which nominallycorresponds to a 2.5 MeV energy threshold. Since the average time between ssionsis 580 s, the gate width is xed at 500 s. The ssion trigger uses the Calibration I input to the TRG and the Super-Low Energy trigger uses the Calibration II
input. A typical background subtraction assumes the \nickel signal" occurs from10 to 210 s after the ssion trigger while the \background" occurs from 300 to80

Ionization Fission Counter
LEMO cable
SMA connector
Aluminum container
Q
Q
Q

1 inchStructural Components



Q
Q
s
Q
-

'$

v Xy
97% Argon
XXX

XXX

&%
X 3% CO

Sphere covered with Californium

2
gas mixture

Figure 3.11: Diagram of the ionization counter used as a ` ssion trigger'

Fission Trigger
Pre-AmpAmp Disc

HV + signal
 Ionization
Counter

6--\timing"
output

1.7 kHz

HV

HV
Supply-200 V

Coinc

PP
PP
P
q

>




1 kHz
clock

-




Gate
Generator
500 microsec
window-

pre-scaled\ ssion trigger"
11 Hz

Figure 3.12: Diagram of the electronics behind a ` ssion trigger'81

500 s (see Figure 3.10). This will provide a clean \nickel only" sample but obviously does not contain 100% of the events caused by nickel gamma-rays. Example
distributions of Ne ective (see Section 7.4.2) from the \signal" and \background"regions are shown in Figure 3.13 along with the background subtracted histogram.

Figure 3.13: Example of performing tfission background subtraction

Thermal Neutron Capture on Other Materials
In addition to the nickel source, we searched for additional materials which could
be used for gamma-ray calibration. Two other metals in natural form were chosen: titanium and iron. Titanium provides clean 6.8 MeV gamma-rays. Iron yields
many di erent gammas with the most common having 7.6 MeV. Table 3.2 gives thequantities needed to calculate the thermal neutron capture rates and the gamma
energy spectra. These nuclear de-excitations do not yield single gamma-rays. The
gamma-ray multiplicities per decay are shown in Figure 3.14 and 3.15. The individual gamma energies and the total energy released in gamma-rays are given in
Figures 3.16 through 3.19. The rst titanium data was taken recently and the ironsource has not yet been used.
82

Isotope Nat. Abund. [50] Capture  [50] Primary 's in Coinc.[51]
46Ti
8.0%
0.6 barns
7.3 MeV and 1.6 MeV
47Ti
7.4%
1.6 barns
7.2, 2.2, and 1.3 MeV
48Ti
73.8%
7.8 barns
6.8 and 1.4 MeV
49Ti
5.5%
1.8 barns
6.8, 1.5, 1.6, and 1.1 MeV
50Ti
5.3%
0.14 barns
5.2 and 1.2 MeV
54Fe
5.9%
2.2 barns
9.3 MeV in 1 or 2 s
56Fe
91.6%
2.6 barns
7.6 MeV in 1 or 2 s
57Fe
2.2%
2.4 barns
10.0 MeV in 2 or more s
Table 3.2: Additional thermal neutron capture information

Figure 3.14: Number of gamma-rays per neutron capture on titanium
83Figure 3.15: Number of gamma-rays per neutron capture on ironFigure 3.16: Gamma-ray energies from neutron capture on titanium

84

Figure 3.17: Total energy released in gamma-rays per neutron capture on titanium

Figure 3.18: Gamma-ray energies from neutron capture on iron85

Figure 3.19: Total energy released in gamma-rays per neutron capture on iron3.3.5 LINAC
Since the solar neutrino events are really electron events, it is natural to want touse electrons for the energy calibration. That way, the calibration source and thephysics source di er only in the energy spectra. It is, however, dicult to develop
an electron source suitable for a 1% energy calibration in the 5-15 MeV energy
range. A source of electrons is needed which are monoenergetic with an energy
known to < 1%, emitted one at a time, and deposited into the Super-Kamiokandetank. Several years ago, plans were developed to install a linear accelerator near
the Super-Kamiokande site. The LINAC would generate the desired electrons to
be deposited via a beam pipe into Super-Kamiokande.
A medical grade LINAC (Mitsubishi ML15M-III) was purchased from a hospitaland suitably modi ed to produce the desired electrons [55]. The original electron
gun provided a current of several hundred mA. This current was much too high forour purposes, so we built a new electron gun which draws only 50 A. These elec86

trons are accelerated down a 1.7 m tube. The nal electron energy can be adjusted
between 5-20 MeV. The electrons are emitted in \bunches" 1-2 s long. Each bunchcontains  106 electrons. Up to 30 bunches/sec are released. The beam size at theend of the accelerating tube is 6 mm.
The intensity of the beam needed decreased considerably so that we get only one
electron per bunch into the Super-Kamiokande tank. The beam transport systemtakes care of this reduction in intensity. The LINAC itself is placed in a hollowedout section of rock near the edge of the tank but raised above the tank top. The
beamline must bring the electron beam down to the tank top, across the tank to
the desired penetration pipe, and then bend it 90 and shoot it into the tank water.
This is all accomplished using vertical and horizontal collimators, two 15 bending
magnets, horizontal steering magnet and coil, two Q magnets, a 90 bending magnet, two more steering magnets, and a vertical beam pipe with an end cap. All themagnets have -metal magnetic shields. The beam at the end cap is 2 cm andhas a momentum spread of < 0:3%.
The quality of the LINAC data has evolved considerably since the LINAC was
rst turned on. Two di erent con gurations for the end cap have been used. Both
had an exit window for the beam made of 100 m thick Titanium. The trigger used
for the collection of LINAC data is provided by a 1 mm thick plastic scintillator(wrapped in 15 m Aluminum foil). The LINAC trigger is stored in the Calibration II trigger bit (see Section 2.6). The rst end cap (used for the data taken in
December 1996) was as large as the beam pipe (8 cm diameter) all the way down
to the exit window. On the order of 10% of the C erenkov photons emitted by the
low energy electrons were shadowed by this bulky end cap (actual photon loss is87

energy dependent). Upon discovery of this problem, a new end cap was made which
tapers down from a 8 cm top to 4.3 cm at the exit window location. The data taken
in January 1997 5 with this new end cap has much less of this shadowing problem.
Only the January data will be used in this dissertation.
The beam energy is measured to an accuracy of 0.3% using a Germanium detector in the beamline. The energy of the electron as it enters the water must stillbe calculated from the beam energy. The energy lost in the exit window and thetrigger counter must be calculated (or simulated) and subtracted from the beamenergy. Sometimes two electrons will be emitted in one bunch. These two electron events have the potential to disturb the energy calibration accuracy up toa few percent. Ideally, one would `clean up' the LINAC data before using it forenergy calibration. Di erent cleaning techniques will be discussed in Section 7.4.6.
Currently, the LINAC hardware is still being tuned and studied. The long timestability of the beam is as yet unknown. The energy calibrations of the beam arebeing veri ed. The analysis techniques applied to the LINAC data will continue tobe scrutinized before we are completely con dent that we have achieved the desired
absolute energy calibration using the LINAC.

3.3.6 Stopped Muon Capture
There is a myriad of other types of events which can be extracted from the data andused for energy calibration. A convenient low energy source is nuclear de-excitationof 16N. Occasionally, stopping muons with negative charge will get captured by the
Oxygen nucleus before the muon can decay [56]. Approximately 18% of the time
Both the January and the December data were taken with the injection position of X =,12 4 m, Y = ,0 7 m, and Z = +12 1 m.
5

:

:

:

88

[57], the capture of the muon results the interaction 16O + , !16 N +  leaving
16N with an excited nucleus. The remainder of the captures also go to particle
unstable states which usually end up as 14 or 15N and a neutron. Often there are
gamma-rays released as the nucleus goes to the ground state, but these gamma-rays
have not been studied as a potential calibration source.
The excited state of 16N decays to the ground state via a very low energy
gamma (<0.5 MeV). Then it decays back to Oxygen with a half-life of 7.13 s:
16N !16 O + e, +  (Q = 10.419 MeV). There are four di erent nal states forethis reaction which have branching ratios >1% [58]:
16 O nal state
Branching Ratio
Decay Path28%
groundnone
66%
6.13 MeV excitation directly to ground5%
7.12 MeV excitation directly to ground1%
8.87 MeV excitation
2
Nitrogen-16 is a good calibration source because the total rate of events can be welldetermined. The cross section is known fairly accurately from the di erence in lifetimes between , and + [57] and the rate of stopping muons in Super-Kamiokande
is known. Approximately 80 16N events/day occur in the Super-Kamiokande volume. These events could be used to monitor changes in the water quality (amountof light collected in PMTs) and the trigger eciency.

3.4 Detector Monitoring
One of the important things to consider as any experiment starts taking data is
how the behavior of the detector will be monitored. Especially at the beginningof data collection, many things will change. Sometimes the detector performance89will be a ected. A prime example is the transparency of the tank water. As thewater is re-circulated, the impurities in the water will be removed. This may causechanges in the light absorption and scattering lengths in the tank. So for a given
electron energy, the amount of light detected by Super-Kamiokande will be timedependent. The changing water quality will certainly a ect the energy thresholdof the trigger, making it time dependent also. It is therefore important to monitor
the changes in Super-Kamiokande's performance.
Several methods were developed to monitor Super-Kamiokande. Two of them
use portions of the data itself while a third uses an external source. One techniqueuses the through-going muon events to extract an average attenuation length for thewater on a daily basis. Similarly, this analysis uses the spallation events to monitor
the water quality (see Section 7.3 for explanation of spallation and Section 7.4.5 forthe details of the time dependent energy scale study).
The third idea was to install a device which produces short bursts of light whose
intensity is always the same. The rate of bursts will need to be constant over time.
The device would be turned on or o at will. On a weekly basis (or whatever thedesired time scale), this device is turned on and a calibration run is taken for xed
time period. Both the trigger eciency and the number of detected PMT hits canthen be monitored as a function of time. The number of light bursts from thesource during the run can be calculated from the burst rate and duration of thecalibration run. The number of triggers recorded during the calibration run willremain the same with time if the trigger eciency does not change. A drop in thenumber of triggers would indicate a reduction in the trigger eciency. Similarly,
since the burst intensity is constant, the distribution of the number of PMT hits90

should not change if the detector behavior is not time dependent.
To apply this monitoring concept, we need a source of quick bursts of light. The
intensity of the burst should approximately equal the same number of C erenkov
photons that a 5-7 MeV electron in water would produce. The time duration of
the burst should be about the same as the length of time over which C erenkov
photons are emitted from the electron. We decided to use plastic scintillator with aradioactive source imbedded inside. This scheme has the potential to satisfy boththe burst duration and burst intensity requirements, depending on the scintillator
and source chosen. For a charged particle with a given energy, the number of photons emitted by most plastic scintillators will be much higher than the number ofC erenkov photons produced in water. By taking advantage of this increased conversion eciency, we can reduce the required energy from a radioactive source ofmonoenergetic electrons. We could also switch to an alpha source if the total burst
intensity meets our design criteria.
After considering the scintillator and source choices, the best option was chosen
and the sources were manufactured. The radioactive source was 244Cm which decays
via either a 5.81 MeV (77%) or 5.77 MeV (23%): 244Cm ,! +240 Pu. This
source was rated the best choice based on its half-life (17.6 years) and the negligible
background produced by the source. The half-life must be fairly long compared tothe time over which we want to use the source (several years) so that the source
activity does not change appreciably while we use it. Several other isotopes decay
with appropriate half-lives and similar energies, but they emit gamma-rays or
X-rays along with the . Gamma-rays and X-rays can both deposit energy in the
scintillator, creating background photons that will be seen by Super-Kamiokande.
91

The gamma-rays have a large enough radiation length (38 cm) that their energy
deposition in the scintillator can be neglected by using a small enough piece of
scintillator. The energy deposition of the X-rays was much harder to ignore, so wechose the source with the smallest X-ray emission.
Most plastic scintillators emit the photons within a few nanoseconds after theparticle deposits the energy. This is an acceptable time scale for the burst duration
since it is on the order of or smaller than the time resolution of the inner detector
PMTs. Also, most plastic scintillators produce photons with wavelengths in theblue region. The chosen scintillator is Bicron 490, which comes in multi-component
form and is mixed and cast by the user. We considered embedding into the scintillator a small sphere whose surface was covered with the source. A 5.8 MeV willtravel only a few m in the scintillator before it looses all its energy. The scintillator region where the alphas deposit energy would be highly concentrated at thesphere, encouraging saturation of the scintillator near the sphere. Saturation would
cause the scintillation eciency to gradually drop thereby inducing the number of
emitted photons to decrease with time. To eliminate this potential problem, theradioactive source was uniformly dissolved in the scintillator material prior to theplastic scintillator being formed and hardening. This con guration prevents saturation of the scintillator by spreading out where the decay alphas are depositingenergy in the scintillator. Since we needed to cast the scintillator after the sourceis mixed in, our only available scintillator choice was the Bicron 490.
Bicron 490 scintillator generates light with a timing resolution of 2 ns. The
wavelength distribution is peaked at 420 nm and has a full width at half maximumof 25 nm. The number of photons emitted by the standard Bicron 490 scintillator
92

for each 244Cm decay (the intensity of each burst) turned out to be equivalent to
the C erenkov light deposition from a 30 MeV electron. This high intensity could
be useful to have, but a reduction in burst intensity of a factor of 5-6 is required tomonitor the trigger eciency. Discussions with several chemists at Bicron uncovered a way to reduce the scintillation eciency to the desired level with negligible
side e ects. A quencher was added to the scintillator to reduce the eciency by afactor of 5.5 (result called Bicron 490x).
Isotope Products Inc. manufactured the sources, from the 244Cm preparation
to the casting of the scintillator + 244Cm mixture. The nal shape of the source isa solid cylinder 2.5 cm in diameter and 2.5 cm tall. The 244Cm activity is 1.35 nCi
which implies a burst rate of 50 Hz. Two sources with each scintillator type (490 and490x) were made for Super-Kamiokande use. The equivalent electron energies which
produce the same photon deposition from C erenkov light is 6 MeV and 30 MeV.
Information from Isotope Products and Bicron regarding previous sources of thistype indicated that these `scintillator sources' would be stable sources of light for
many years. Unfortunately, the only way to turn the source on and o is to take itin and out of the Super-Kamiokande tank. Because there was no on/o switch andthe collaboration pushed to minimize `down time' from physics data-taking, these
constant light sources are not used very often. They did however considerably help
us understand the detector behavior at the beginning of data taking.

93

Chapter 4

Simulations
A realistic model of the Super-Kamiokande detector allows us to answer designand construction questions, explore calibration options, calculate eciencies, andunderstand the general behavior of the detector. Our simulation program is broken into two main components: the kinematic generation of the physics event andthe detector simulation. Physics events range from solar neutrino interactions withelectrons to proton decay to the gamma-ray emissions of a calibration source. Modelling the Super-Kamiokande detector itself involves tracking particles through thewater, generating and tracking C erenkov light approximating the PMTs and electronics, and simulating the trigger. Each of these topics is described in this chapter.
Our simulation uses the Monte Carlo (MC) technique to model our detector performance. There is no analytic equation which characterizes Super-Kamiokande's
behavior. In the MC technique, every stage that an event goes through is modelled.
Events are simulated by using random numbers to choose which outcomes of thevarious \interactions" the current event/particle will encounter. To learn about
how Super-Kamiokande \sees" certain physics events or how Super-Kamiokande
reacts to particular change in the physical detector, we simulate many of the reactions and look at the average detector behavior. Because the entire data collection94

process is being simulated, only events which generate a detector trigger are written
to the output les.

4.1 Solar Neutrino Interactions
4.1.1 Neutrino Energies

8

Normalized Probability for B solar neutrinos

When we generate solar neutrino events, we want to start with the predicted neutrinos, require neutrino-electron elastic scattering, and choose the nal state properties
for the scattered electron. The electron is then handed to the detector simulation
section for futher processing. Most of our solar neutrino signal somes from the 8B
neutrinos. The incident 8B solar neutrinos will have energies chosen at random fromthe SSM predicted spectrum [59] shown in Figure 4.1. We can also model the HEP
neutrinos, but the ux is so much lower than the 8B neutrinos (see Section 1.1.3)
that we should barely observe the HEP neutrinos. The energy distribution of the
HEP neutrinos is shown in Figure 4.2.

Neutrino Energy (MeV)

Figure 4.1: Energy spectrum of 8B solar neutrinos
95Normalized Probability for HEP solar neutrinos

Neutrino Energy (MeV)

Figure 4.2: Energy spectrum of HEP solar neutrinos

4.1.2  , e, Scattering
Given a neutrino at a particular energy, we need to gure out the electron energy
after the scattering has occurred. The energy dependent cross section provides thisinformation. We use a  , e, cross section which accounts for charged current andneutral current interactions between the neutrino and electron. The equation forthe cross section is given by Okun [60]:d = 2G2F Me
dTe






2

A + B 1 , ETe , gLgREM2 eTefor  scattering: A = gL2 and B = gR2
for  scattering: A = gR2 and B = gL2
gR = sin2 W
for e and e: gL = + 12 + sin2 W
for  ( ) and  ( ): gL = , 12 + sin2 W

96

(4.1)

where : = scattering cross section
Te = kinetic energy of scattered electron
GF = Fermi constant
Me = mass of electronE = neutrino energy
W = Weinberg mixing angle ,! sin2 W = 0:223
We use this di erential scattering cross section to select the kinetic energy for ascattered electron. Figure 4.3 shows the di erential cross section versus electron
kinetic energy for two di erent neutrino energies. We randomly pick from the shapeof the cross section when assigning a kinetic energy to a scattered electron. The
minimum kinetic energy of an electron is zero. The maximum kinetic energy for agiven neutrino energy is:(4.2)
Tmax = EMe
1 + 2EGiven the energy of the scattered electron, the scattering angle is determined. The
scattering angle scat between the neutrino direction and the electron direction is
given by:
1 + MEe(4.3)
cos scat =(1 + 2TMee )1=2

4.2 Particle Tracking
Once the kinematics of the physics (or calibration) event has been determined, eachparticle is followed along its path until it interacts or looses all of its kinetic energy.
The EGS4 [61] package simulates the electromagnetic shower created by electrons(e,), positrons (e+ ), and gamma-rays ( ). The approach taken by EGS4 is to watch
the initial particle take short steps forward along the calculated trajectory. The
97

2

-1

cm MeV )- 44

Differential Scattering Cross Section (10Electron Kinetic Energy (MeV)

Figure 4.3: Energy dependence of scattering cross section for several E
continuous loss in energy along the step length is included. Discrete processes suchas multiple Coulomb scattering (MCS) and point interactions are considered at theend of each step. When additional particles are generated or given kinetic energy,
they are added to the `particle stack'. When EGS4 is nished tracking a particle,
it grabs a new particle o the stack and starts following the new particle.
EGS4 is used basically as a `black box' program. EGS4 is con gured to know
the detector geometry (a big cylinder 41 m  39 m) and materials (water). To ensure that MCS is modelled accurately for energies <20 MeV, the energy-dependent
minimum step size that an electron may take is shortened from the EGS4 default
value [62]. The shortest step size is set so that the largest fractional energy loss
during the step is: 1.0% [63]. MCS changes the direction of travel of electrons in
the water. The average MCS angle [72] is shown in Figure 4.4 as a function ofelectron energy. It is important to simulate accurately the amount of scattering
an electron undergoes in the water so that the angular accuracy of the direction
resonstruction algorithms is reproduced by the Monte Carlo.
98

Mean Scattering Angle (degrees)

Generated Total Electron Energy (MeV)

Figure 4.4: Average multiple Coulomb scattering angle for H2O used by EGS4
Other types of particles are tracked through the water with GEANT [64]. We
use GEANT in a rather unusual mode. GEANT is allowed to follow a particularparticle (by taking short steps) until its rst interaction. The products of theinteraction are returned by GEANT. If any e, , e+, or 's are produced, they are
given to EGS4. Other particles are added to a `particle stack' (separate from theone used by EGS4). We hand particles from this stack to GEANT one at a time.
Interactions are simulated and particles are added to/removed from the stack until
the stack is empty. Once the stack is empty and all the electromagnetic particles
are processed by EGS4, the physics event is nished being simulated.

4.3 C erenkov Light Generation and Tracking
Every time a charged particle takes a step through the water via EGS4 or GEANT,
our C erenkov light package is called. This custom-written simulation code generates the C erenkov light in the detector and follows the photons around the detector
99until they `die' or are detected by a photomultiplier tube.
C erenkov radiation is emitted from charged particles as they travel in a medium
faster than the speed of light in the medium ( nc where n is the index of refraction
of the medium). The threshold velocity ( = vparticlec ) for the emission of Cerenkov
radiation is1(4.4)
threshold =nC erenkov photons are generated uniformly along each segment of charged particle
track. The number of photons generated per unit of tracklength in each wavelengthinterval by a particle with charge ze is:
d2Nphotons = 2 z2 sin2 
(4.5)
c
dld
2
where l is the particle track length,  is the wavelength of the C erenkov photon,1 ), and  is the C erenkov angle. The photons
is the ne structure constant ( 137cdo not all have the same energy (wavelength). The wavelengths are distributed like1
4 . The photons are emitted with directions lying on the surface of a cone withhalf angle (c) such thatcos c = n(1)(4.6)

where n() is the wavelength dependent index of refraction of the medium. TheC erenkov angle is equal to 42 for most of the life of a charged particle. As theparticle slows down, get smaller and the C erenkov cone collapses down to thecentral axis of the cone. The photons are polarized such that the polarization direction ~p = ~vphoton  ~vparticle is normal to the travel directions of both the photon
and the charged particle.

Once C erenkov photons are generated, they must be tracked through the detector. There are many di erent `interactions' which C erenkov photons undergo:100 absorbed by the water scattered in the water re ected o the PMT face transmitted through the face of the PMT create a photoelectron in the photocathode absorbed by the black sheet (ID only) re ected o the black sheet (ID only) re ect o a waveshifter (OD only) absorbed by the waveshifter (OD only) scattered in the waveshifter (OD only) re-emitted by the waveshifter (OD only) re ected o the Tyvek walls (OD only) absorbed by the Tyvek walls (OD only)
The photon simulation package accepts one photon at a time and tracks that photon until it \disappears" or is detected. Before each step begins, distances to thenext interaction of each variety listed (water absorption, water scattering, hitting
a \geometry object" like a PMT) are chosen randomly. This is done by choosing arandom probability for each `interaction' and relating it to the characteristic length
for the `interaction'. The photon trajectory is followed in discrete steps of length
equal to the shortest distance to the next interaction. After the step is taken, theinteraction is executed. If the photon has not `died' during the interaction, anotherstep is chosen and performed. When a photon approaches the outer edge of theinner detector, it will either hit a PMT face or the black sheet which lls the space
between the ID PMTs. If the photon was scheduled to hit the face of a PMT,
certain tests must be performed before the photon can be further tracked.
101Absorption Length (m)Figures 4.5 and 4.7 show the characteristic lengths for water absorption andwater scattering. The shape of the absorption length as a function of wavelength
matches with previous experimental data [65]. The 4 dependence of the scattering length is taken directly from Rayleigh scattering theory [66]. In addition to
the Rayleigh scattering, we need to somehow account for the additional scattering
which is typically observed in water-C erenkov detectors. Particulate matter in thewater is presumed to account for this \extra" scattering (called anomalous scattering). We assume that the wavelength dependence of the anomalous scattering
length is the same as the absorption length. The total attenuation length (not used
as input since absorption and scattering done separately) is displayed in Figure 4.8.
The black sheet re ectivity has been measured to be between 20 and 40%. In theMC, the re ectivity is taken as 30% and at with wavelength. The absolute magnitude of the absorption length and the relative amount of scattering and absorption
are tuned using through-going muons and nickel data1 .

Photon Wavelength (nm)Figure 4.5: Absorption length input to the Monte Carlo1

The tuning of the MC parameters was done in large part by Clark Mc.Grew.

102

Rayleigh Scattering Length (m)Photon Wavelength (nm)

Anomalous Scattering Length (m)Figure 4.6: Rayleigh scattering length input to the Monte Carlo

Photon Wavelength (nm)Figure 4.7: Anomalous scattering length input to the Monte Carlo103

Overall Attenuation Length (m)Photon Wavelength (nm)Figure 4.8: Attenuation length input to the Monte Carlo
When a photon hits a PMT, it can either be re ected, be absorbed, or generatea photoelectron. Which pathway this particular photon will take depends on thevalue of the randomly selected re ection probability and pe eciency. Re ected
photons continue to be tracked through the water. If the chosen pe eciency islarger than the quantum eciency of the PMT (shown in Figure 4.9) at the photon
wavelength, the photon will be absorbed by the photocathode. Absorbed photons
are considered `dead'. Otherwise, another random probability is tested against the`collection eciency'. The collection eciency is our overall scaling factor. It is nota physical quantity. The collection eciency is tuned to force the MC to produce
the same total number of C erenkov photons per MeV of deposited energy as the actual Super-Kamiokande detector. If the probability passes the collection eciency
test, a photoelectron (pe) will be generated.
The arrival time of the hit is selected next. The time each particle or photon
has been incremented from the start of the charged particle tracking, so we know
precisely when the photon was incident on the PMT. There is some fuzziness in the104

Quantum Efficiency (%)

Wavelength (nm)Figure 4.9: Quantum eciency for both sets of PMTs
measured arrival photon times due to the PMT time resolution. We account forthis timing resolution by randomly picking an amount of time by which to `jitter'the pe arrival time. We choose this `jitter time' from the measured time resolution
distribution for 1 pe signals. Figure 4.10 shows this distribution for the inner detector PMTs. The measured time of the pe is the equal to the true arrival time of thephoton plus the `jitter time'. Once the photon `dies' or generates a photoelectron,
the photon tracking package considers itself nished and the next photon from thecurrent physics event is accepted.
The hits created by PMT dark noise are simulated in addition to those generated by C erenkov light. The number of dark noise hits allowed depends on the
average dark noise rate of the PMTs. The times of the dark noise hits are chosenrandomly in a time window much larger than the real TAC/TDC allows. The darknoise hits all have a charge of 1 pe. Any PMT can have a dark noise hit recorded- whether it also has a hit induced by C erenkov light or not. Figure 4.11 compares
the number of dark noise hits in a 200 ns time window from the MC with the same
105

Figure 4.10: Time resolution for ID PMTs#/binfrom the null triggers in the data sample. Note that the MC distribution appears
to be slightly higher than the data.

Number of dark noise induced PMT hits in 200 ns

Figure 4.11: Number of ID PMT hits in 200 ns due to dark noise
Photons in the outer detector have more potential actions than those in the
inner detector. They will bounce o the Tyvek walls quite a few times on their way
106

Tyvek Reflectivity (%)

to the OD PMTs. The re ectivity of the Tyvek is shown in Figure 4.12. The MC
uses the measured re ectivity averaged over incident angles. The OD PMTs also
have the waveshifter plates to model. By absorbing and re-emitting the photons,
the waveshifter plates change the photon wavelengths to a more sensitive region in
the PMT eciency. The overall light collection is enhanced by the waveshifters,
although the timing resolution worsens by almost 50%. The simulation of the outerdetector is not critical for the solar neutrino analysis - so the detailed descriptionof the procedures and input parameters will not be described2.

Wavelength (nm)Figure 4.12: Re ectivity of the Tyvek material lining the OD

4.4 Electronics Simulation
After all the photons for a single physics event have been followed, the electronics
must be modelled. The accuracy of the simulation is sucient for our current use.
Problems apparent only when the trigger rate is very high are not included in ourmodel. Time dependent e ects are not simulated (for example the real electronics
2

This will probably be included in a future disseration discussing the High Energy analysis.

107

e ects which a ect the charge measurement of events just after energetic muons).
All the electronics parameters were matched to the values from the real SuperKamiokande detector (dead times, thresholds, etc.).

#/bin

The electronics simulation is given a list of pes, the hit PMT numbers, andthe measured time of each hit. The photoelectrons must rst be converted into acharge measured by the PMT. The single pe charge distribution and the charge
discriminator threshold must be modelled. The PMT charge is selected randomly
from the shape of the single pe charge distribution (shown for ID PMTs in Figure 4.13). Note that the units of PMT charge are not real photoelectrons (seeSection 2.4). If the resultant charge is below the discriminator threshold, the `hit'
is below threshold and would not have been recorded by the real Super-Kamiokande
detector. Below threshold hits are thrown away in favor of tracking the next photon.

PMT Charge (photoelectron = picoCoulomb/2.055)

Figure 4.13: Charge distribution for ID PMTs using nickel source
Above threshold hits continue through the remainder of the electronics package.
For the inner detector, the QAC gate and the dead time after each hit need to be108

simulated. In the outer detector, the charge integration by the QTC card, edge
recording by the TDC, and digitization dead times need to be included. In bothcases, multiple pes per PMT must be accounted for properly.
If more than one pe hit the same PMT, the total charges and measured time forthe signal must be determined. The earliest pe to hit the tube sets the start time
for the PMT signal and (after the requisite time delay) opens the charge integrationgate. Other pes which later hit the same tube while the integration gate is open
will contribute their charge to the total charge for that hit. After the gate closes,
no more hits are allowed while the signal is digitized. Once the channel becomes`live' again, the next pe (if any) in time to hit the tube will start a second signal
and open the charge gate again.
After the pes are combined together and the electronic components are simulated, a list of hit tubes, times, and charges is created. This list is given to thetrigger simulator.

4.5 Trigger Simulation
The real Super-Kamiokande detector has several di erent triggers which can cause
the detector to be read out. The Monte Carlo simulation can approximate theSuper-Low Energy, Low Energy, High Energy, and Outer Detector triggers. The
trigger algorithm is very simple for these four triggers: search through the list of hit
tubes and times looking for when the trigger condition is met. Multiple triggers canbe generated for each physics event (for example: a muon and its decay electron are
one physics event, but sometimes will produce two triggers). The trigger conditions
are given in Table 4.1. These trigger requirements were chosen to be equivalent to109

the real detector's thresholds. The di erence is that the MC does not attempt thedark noise subtraction which is inherent in the ID trigger electronics. If the trigger
requirements are met at least once, the event is written out in the same format as
the real data. The PMT times are modi ed to be a time relative to the trigger timewith most of the hits causing the trigger occurring between 800 and 1000 ns. Only
the PMT data with times in the `right' regime relative to the trigger are writtenout for each trigger.

Trigger TypeSuper-Low Energy
Low Energy
High Energy
Outer Detector

Condition
24 hit ID PMTs in 200 ns
40 hit ID PMTs in 200 ns
42 hit ID PMTs in 200 ns
24 hit OD PMTs in 200 ns

Table 4.1: Trigger conditions for the MC simulation
The correct behavior of the trigger simulation is critical to understanding theoverall eciency for detecting solar neutrinos. We need a method of comparing theeciency of the MC trigger to the real detector trigger. The nickel calibration data
(see Section 3.3.4) provides this key. The Super-Low Energy trigger and the ssion
trigger are used to collect data from the nickel calibration source. In addition tothese, nickel data is typically taken with the Low Energy trigger bits set. We cansimulate this condition with the MC simply by turning on both the Super-Low
Energy and the Low Energy triggers (see Chapter 3). We can compute a relative
trigger eciency trig and compare the results from data and MC. The eciency is110calculated:# events passing the Low Energy trigger
trig = # events
passing the Super-Low Energy trigger(4.7)

Trigger efficiency

Trigger efficiency

as a function of reconstructed energy. Figure 4.14 show the good trigger eciency
agreement between data and Monte Carlo at two di erent source locations. The
slight disagreement in the rise of the eciency can be attributed to the energy scalefrom the Monte Carlo not perfectly matching the nickel data (see Section 8.8.2).

Reconstructed Energy (MeV)

Reconstructed Energy (MeV)

Figure 4.14: Relative trigger eciencies using nickel data111

Chapter 5

Data Reduction - lef1
5.1 Introduction
Since Super-Kamiokande will see a comparatively large solar neutrino signal every
day, the size of the statistical errors on the ux measurement (among others) willquickly become very small. Because of the small statistical errors, it is importantto get the systematic errors small and to know their magnitude with high con dence. We want to maximize the potential signi cance of any measurements that
may be made by understanding our systematics extremely well. For this reason,
all physics analyses are performed by two completely independent groups of SuperKamiokande collaborators. This dissertation describes the software components ofand results from the `O -Site' Low Energy Analysis Group. A comparison with the`On-Site' LE Group's results will be given in Chapter 9.
Super-Kamiokande collects approximately 1 million events or 30 GigaBytes ofraw data each day. The solar neutrino signal (about 40 events/day) is a small fraction of this data size. We must sift through the data and select out events which
are likely to be generated by solar neutrinos. Since the total amount of raw data
is so formidable, we want to perform this event sorting in a manner that permits
112

future upgrades to the software. We also want to be able to reprocess data without
returning to the raw data. We therefore developed a multi-stage automatic ltering
procedure.
Figure 5.1 shows a simple ow chart which explains the basic steps to our dataprocessing. Starting with the raw data, three separate lters act on the data which
each reduce the size taken up by the data. Each of these lters is automatic,
meaning that a Fortran or C program was written to enact the ltering algorithms
and write out smaller data les. This chapter describes the rst stage lter (lef1).
lef1 was developed such that we would never need to return to the raw data
to reprocess the data, only the lef1 output. lef1.5, lef2, and le ntuple aredescribed in Chapters 6 and 7.

5.2 Goals and Philosophy of lef1
We lter the raw data by executing a custom-written program which reads in theraw data les, runs several algorithms, gures out what information or events canbe removed, and writes out smaller data les with the reduced information andevents. The most critical component of this program are the algorithms to run on
the data and the determination of what information or events we are willing tothrow away. We developed lef1 with certain things understood:
1. We want to save every potential solar neutrino event and throw away the restof the events.
2. Half of the data size (in bytes) is taken up by cosmic ray muons.
3. Muon track ts are needed in order to cut out spallation events, a major
component to the solar neutrino background (see Section 7.3).
113

Raw data - collected at 10 Hz by Super-Kamiokande detector?

`TQ Real' process - applies calibration constants to data?

US copy process - 1 DLT/day (30 GBytes/day)?

lef1

lter - 1 DLT/week?

lef1.5lter - 1 DLT/2 weeks?

lef2

lter - 1 DLT/month?

le ntuple - <2 GBytes of NTUPLEs/lef2 DLT

Figure 5.1: Overview of the Low Energy data ltering

114

4. The majority of the Low Energy triggers have t vertices near the PMTs. It is
presumed that many of our LE triggers are generated by gamma-rays entering
the inner detector. The source of these gamma-rays may be a combinationof the measured gamma-ray background emanating from the rock (produced
by decaying uranium and thorium imbedded in the rock) and the decay ofradioactive impurities in the PMT glass. Since these are background to thesolar neutrino signal, we can save only the LE events which do not have it
vertices close to the edge of the inner detector.
5. Cuts applied to the Low Energy events need to be well understood.
6. Correct identi cation of data with problems is important.
7. Some data has serious problems: no information from part of the inner detector, triggers caused by electronic crosstalk, detector "ringing" after a large
pulse height event, and other electronics glitches.
Based on our knowledge of the make-up of the data, we drafted a set of goals for
the Low Energy Level 1 Filter (lef1). These goals are listed in Table 5.1. Alongside
the goals are comments on the actual performance of lef1. The raw data lls an
average of 1.1 - 1.2 DLTs per day. Approximately 8 raw DLT tapes t onto a single
lef1 DLT, so one lef1 tape holds about 1 week's worth of data.

5.3 Event Classi cation Scheme
The lef1 program attempts to classify each trigger by what type of event caused
the trigger. Based on the event classi cation, lef1 decides if all the information
regarding the event is necessary. Sometimes all information is kept; other times wekeep everything except for the PMT hits. At this stage, an event is never completely removed from the data les. We always keep the header information, the t115

Goals Reduce the data size by a factor of 10

Achievements
 Reduction of 7

 Run at twice the speed of data collection

 Speed = 1.5  data Minimize the # of cuts to the Low Energy(LE) data Maximize the saving eciency for solar neutrino events in the ducial volume

 Cut LE events using well-understood methods which can be reliably studied with thedetector simulation program Produce output sucient for all future data

rate

p
p
p
p

processing (no need to return to raw data)
Table 5.1: lef1 goals and achievements

116

parameters for all attempted ts, and the basic quantities computed or determinedby lef1 (see Appendix A). When an event is `tossed' or `thrown away', its classbecomes negative and everything is written to the output le except the PMT data.
A `saved' event has everything including the PMT data saved to the output le.
Operationally, a `tossed' event and `tossed' PMT data are almost identical. Theyboth end up having no PMT data saved. The di erence is in the sign of the eventclass. Events with negative classes are not processed further by any ltering or
analysis programs.
The lef1 lter can also be run in \tagging" mode when special studies are being
performed on the lef1 lter. There are three di erent ways (controlled by setting
the LE FILTER1 TAG environment variable) to run in tagging mode: tag `tossed'
events (1), tag PMT data (2), or do both (3). Tagging `tossed' events means actually saving them in full (but the events are identi able by the negative class).
Tagging `tossed' PMT data means keeping the PMT data but making the numberof hit tubes negative.
When the O -Site Analysis Groups rst started writing software to lter thedata, it was assumed that a single lter program would be utilized for the Low
Energy and High Energy groups. The pieces necessary to form this combined lter
had already started being assembled1. The Low Energy and High Energy groups
split apart to develop independent lter programs, each starting with the original`Level 1' lter. lef1 is the product of the Low Energy group's development after
this split. Because of the history behind lef1, it uses quite a complicated algorithm
to categorize events. In the remainder of this dissertation, the lef1 classi cations
1

Clark Mc Grew spearheaded this work.

117are given in italics. Table 5.2 shows the event classi cations and the numericalvalues for the event classes. The rst step in the event classi cation algorithm is
to see if the event is a null trigger (see next section). The second step is to lookat the size of the event. If the event has few inner detector tubes (NID tubes < 500)
than the event is small; events with a lot of ID hits (NID tubes > 500) are big.

5.3.1 Null Trigger Events
To assist in monitoring the ambient noise in the ID PMTs, normal data-taking runs
have the `null trigger' turned on. A `null trigger' signal is generated from a clock
approximately every 6 seconds and sent to the TRG module . The PMT data fromthese null triggers should re ect just the PMT noise (no extra hits from C erenkov
light in the inner detector). lef1 nds these events from the data by looking at
the trigger type for each event. If the `trigger id' = 16 (see Section 2.6), the eventis classi ed as a null trigger, certain parameters about this event are added to thenull trigger histograms, and the event is thrown away.

5.3.2 Small Events
From the small events, we want to extract the solar neutrino events. These events
have C erenkov light induced PMT hits only in the inner detector and are completely uncorrelated with any detected light in the outer detector. Knowing this,we need to select out those Low Energy events whose C erenkov light was completely
contained in the inner detector. Small events are further classi ed as those that arecontained and those that may have had a particle in the outer detector. To do this,lef1 does not rely on the OD trigger but looks at the number of OD hits. It must
be careful when doing this, since sometimes the OD tube data is actually a copy
from a previous trigger (such as an entering muon). Looking merely at the total
118

Event Classi cation Class Value
Null Trigger
101
Small
103
Big
104
Small Contained
105
Small Non-contained
106
Noise
108
Low Energy
109
Big Contained110
Null Trigger
111
Thru-
112
Stop-
113
Multi-
114
Exiting
115
Up-
116
Unknown
117

Geiji-
LE Junk
Pedestal
Big Ringing
LE Ringing
OD Clipping
Corner Clipper

119
120
121
122
124
125
126

Table 5.2: Numerical values for the lef1 and lef2 classes
119number of ID hits will then be deceiving. lef1 rst determines if the OD data is acopy. To do this, we look at the `tdc-to-trg' times which are stored for each of the 4huts in the anti-header area of the data. For the 32 s OD window, if the OD data
is not a copy, the average `tdc-to-trg' time will be < -31,500 ns. Events with copied
OD data are automatically called small contained events. After the OD window
size changed from 32 s to 16 s, the `trg-to-tdc' time for non-copy events shouldhave been compared to -15,500 ns. This was not done, so this method of nding
copy events no longer works as expected2. For `new' OD data events, lef1 searches
the times of OD hits with a 200 ns time window looking for the largest number ofhits that occur in the window. If it nds more than 20 OD hits in the window,
it is likely that there was `activity' in the OD and the event is categorized as asmall non-contained event. Small non-contained events are often stopping muons
which had a very short path length in the inner detector. For this reason, small
non-contained events are sent over to the big event section to be tested as a stopping
muon event. If fewer than 20 hits were found, the event is called small contained.
If no OD data exists, lef1 can not tell if the event is contained; it assumes theevent is a small contained one.
All small contained events are then examined for the possibility of havingC erenkov light-induced PMT hits. To do this, we need to determine if the numberof ID hits is consistent with PMT noise. lef1 searches the times of the ID hits tond the maximum number of tubes hit in a 200 ns coincidence window (N200). If
N200  30 the ID appears to not have seen C erenkov light and the event is classi ed
The net e ect of this is that too many events are thought to have copied OD data. These
events typically have no C erenkov induced PMTs in the ID and so are classi ed as noise. If
the OD copies were correctly identi ed, the events in question would have ended up classi ed as
unknown.
2120

as a noise event. Otherwise, the event is called a low energy event and handed overto the Hayai fast vertex tter (Section 5.4).
Hayai returns its best guess at the vertex coordinates of the event (X t, Y t, Z t,

T t) and an estimate of the believability of the t, the goodness of t (GOF). If the
GOF > 0.4, the t is good enough to trust the vertex location. In this case, theevent is cut if the vertex lies within one meter of the inner detector edge or outside
the inner detector. This cut is known as the Dwall  1 meter cut and is applied in
the following way:

RID = 1690 cm (outer radius of inner detector)
ZID = 1810 cm (top edge of inner detector)q
R t = X2 t + Y 2 t
R = RID , R t and Z = ZID , jZ tj
Dwall = MIN(R; Z )Events with Dwall  1 meter are denoted saved low energy events; tossed low energy
events have Dwall < 1 meter. If the Hayai t was not good enough to completely
believe the vertex but still an okay t (0 < GOF < 0:4), the event is tagged as asaved low energy event. Failed Hayai ts are indicated by GOF = 0. Events withfailed ts are identi ed as tossed low energy events.
Tossed low energy events are like any other event which lef1 wants to throw
away - the PMT data is removed. Saved low energy events are not quite saved infull. The data size of these low energy events can be reduced quite a bit if not
all the OD data is retained. lef1 only saves the OD hits which might get studied
later in the data ltering process. Speci cally, those hits are the ones with times
near the trigger time and any clusters of in time hits. The OD PMTs with times
between -5 s and +1 s are near the trigger time and are saved automatically.
121

If more than 6 OD hits occur in a 64 ns window, a time cluster has been found.
The time clusters are actually tagged on-line; the second bit in the `status' word
for each OD hit is a ag indicating if the hit passed the cluster criteria. The codefor the on-line tagging was written by a collaborator (Vladimir Chaloupka), hence
the tagging bit in the data is referred to as the `Vladi' bit. All OD tubes with the`Vladi' bit set are saved with the event. All ID tubes are of course also saved.

5.3.3 Big Events
There are several pathways for big events to take from this point. If there are morethan 1,000 tubes hit in the inner detector, the event is checked to see if it could bea single through-going track. Otherwise, the event is checked to see if it could be a
stopping muon. In either case, the next thing lef1 does is to locate the clusters of
hit OD tubes. A cluster is de ned to have  4 adjacent tubes hit within 50 ns ofeach other. There is also a limit to the spread in PMT charges before a cluster isbroken up into multiple clusters. If there is no OD data for the event, the rest of
the \high energy event" handling of lef1 will not work. No-OD events with a lot of
ID hits are classi ed as big contained events and saved in full for further processing.

Possible Through-going muons
Before spending cpu time attempting to do a precise track t, lef1 does a bit more
to determine whether the event is really likely to be a single through-going track.
A quick check using the OD clusters is performed; for each pair of OD clusters: Compute the distance d and time t between the clusters
 If d > 10 m and t , cd < 66 ns (determined empirically) ,! this event
should continue being tested as a through-going track
122

This criterion was determined empirically from studying the single through-going
muon events in the data. Events that do not pass this test are tested as possible
stopping muon events.
Possible through-going tracks are next passed to the rst track tter, THR1 (seeSection 5.5.1). If the total time residual (,) found by THR1 is small (< 7:0) then theevent is classi ed as a through-going muon (a ectionately known as thru-). When, > 7:0 the event is called a multiple muon (multi-) event, since most times thisis true. Thru-s proceed to have better tters run on them (THR2 and FSTMU).
Most of the time, after FSTMU nishes with the event, the PMT hits are removed
from the output data le. This step alone gives lef1 an output data size reduction
factor of almost 2. If the track directions from THR2 and FSTMU disagree by morethan 25 , the averaged track length is more than 10 meters, and FSTMU's goodnessof t is > 2, the t results are questionable enough that the PMTs for these events
are saved. Multi- events have nothing else done to them until the next lter
program. Consequently, the PMT data is always saved for multi- events. Since6% of the muon events have more than one muon penetrating the inner detector
and since some of the real single through-going muons will accidentally be called
multi- events, on the order of 10% of the muon events will have the PMT data
saved.

Possible Stopping muons
Due to time constraints during the development of lef1, only a moderate attempt
is made to distinguish stopping muons from the other high energy events. lef1
applies exactly the same algorithms to the potential stopping muon events as theinitial `Level 1' lter did. The anis track tter [67] is used to nd the starting vertex
123assuming a single track in the inner detector. If the `goodness' of the anis track t
is > 20 then the t is very poor. In order for the event to get to this point, it
must have had few ID tubes or not satis ed the criteria for a thru-. There isnothing else which lef1 can do with this event, so it is classi ed as unknown. If theanis track goodness was < 20 lef1 continues to investigate the event. The remainderof the algorithm is a remnant from the High Energy analysis group's `Level 1'
requirements. They wanted to separate possible exiting events (the interestingones) from stopping muons. If the anis track vertex is further than 3 m from theinner detector edge, the event is classi ed as exiting. The vertex is projected along
the t direction until it lies on the inner detector wall. If there is no OD cluster
within 6 m of the projected vertex or if the OD cluster time is more than 50 ns
later than the inner detector `entry time', the event is classi ed as exiting. If it
passes all these tests, the event is called a stop-. The disclaimer at the beginningof this section indicates that the eciency for correct tagging of stopping muons
is not very high. The PMT data is always saved for stop-, exiting, and unknown
events.
Up- Events

Since the Muon Analysis Group uses the lef1 output data set, lef1 needs toselect out possible upgoing muon events and save them in full. After the eventclassi cation algorithm is nished, upgoing muon candidates can be selected out.
If the t direction of the track(s) for the event indicates that the track(s) pointed
upward (cos   ,0:1 where cos  = +1 points straight up), the event is classi ed as
an up-going muon (up-). These events have the PMT data saved for the O -Site
Muon Analysis Group.

124

5.3.4 Minimum Bias Events
Since lef1 was designed in a way that would prevent the need to return to the raw
data when future improvements are made to the software, some way was needed
to be able to check the performance of lef1 on the raw data. A `minimum bias'
sample is saved to enable the lef1 monitoring. One event out of every 1, 000 events
processed by lef1 is selected for this minimum bias sample and has all information
saved independent of the event classi cation. These events have a special classassigned them which denotes the event as a minimum bias event but retains theevent type as determined by lef1 (1000 + lef1 class).

5.3.5 Record Keeping
We needed to keep track of the actions taken by lef1 and to monitor the performance of lef1 for any portion of the data as the program was running. Each of thecomponents of lef1 create a log le with a summary of the component's ndings
for every subrun of data processed. An example of the event classi cation log le(named dlt#.lef1. ltlog) is given in Figure 5.2. There is a fair bit of information
computed and stored in a \lef1 zebra bank" saved in the output lef1 data les;more details are given in Appendix A.

5.4 Hayai Vertex Fitter
Since our desire is to reliably t the vertex for every Low Energy event, we developed
a fast vertex tter called Hayai3 . Hayai uses a grid search technique to nd the vertex
which maximizes a \goodness of t" parameter.
3

Hayai (which means fast in Japanese) was developed by Juilien Hsu and Bob Svoboda.

125

New Run : 3138

New Sub Run : 122--> Code Version 1020--> Cuts Version 1020--> Compilation Date 19960920--> Filter Run Started On : 19961214
0 events had no HEAD bank0 events had no CALI bank0 events had no CALO bank
106 null triggers were found and thrown away
5 minimum bias events were saved
1564 LE events were saved
2420 LE events were thrown out
426 LE events thought to be noise and thrown out
967 thru-mus were found and saved
58 stopping-mus were found and saved
34 exiting events were found and saved
83 multi-mus were found and saved
8 upgoing muons were found and saved in full
0 small events (unknown if contained) were found and saved
0 small events (not contained-sneaky mu?) were found and saved
0 big contained events were found and saved
9 events of unknown type were found and saved

Figure 5.2: Sample entry in the lef1 log le126

5.4.1 Algorithm
The rst step for Hayai is the execution of an algorithm named `Mr. Clean'. `Mr. Clean'
selects which PMT hits to use for the t, attempting to keep all the \signal" hits
while reducing the number of \noise" hits. In a typical low energy event, half ormore of the PMT hits are induced by the PMT dark current, not C erenkov light inthe tank. `Mr. Clean' requires that all PMT hits used in the t must be physicallywithin 10 meters of another PMT which was hit within 33.3 ns. After `Mr. Clean',the PMTs are further selected out before the maximization of the goodness of t
begins. PMT hits from low energy events tend to be clustered together in time.
By sliding a 130 ns window through the PMT times, the largest \time cluster" ofhits is found (and contains N0 tubes). The tubes in that large time cluster are theones that are nally used for the remainder of the tting. If N0 < 5, the event can
not be t. Hayai returns failed ts for 0.4% (0.0%) of the 10,000 simulated 5 MeV(10 MeV) electrons spread throughout the ducial volume.
Hayai computes an initial vertex from which to start searching for the maximum

goodness of t. This starting vertex is the center of mass of the PMT hits whichwere selected by `Mr. Clean' and the sliding 130 ns time window. To prevent
starting with a vertex too close to the wall, all vertices are moved 2 meters awayfrom the wall (towards the center of the detector). The goodness of t utilized by
Hayai ranges from 0 (bad) to 1 (good) and is given:
"
#
N0
X
1
(
t
i , te , Toffset)2
GOF = f (a)(5.1)
N0 i=1 exp ,2i2
where f (a) is a function which re ects the shape of the expected C erenkov cone fromthe true vertex (given later in this section), a is the magnitude of the anisotropy
vector ~a, ti is the measured PMT time of the ith hit, te is the expected time of thehit from the ith tube, Toffset is a time o set such that (ti , te , Toffset) is centered127

on zero, and i is the measurement uncertainty in the time recorded by the PMT.
The anisotropy is calculated:
PN0 d~ii=1 qi ~a = j~aj where ~a = PN0 jdij
i=1 qi(5.2)

with d~ as the distance vector from the trial vertex (X0, Y0, Z0) to the hit PMT.
Hayai computes the expected time of the PMT hit to be:q(X0 , xi)2 + (Y0 , yi)2 + (Z0 , zi)2
(5.3)
te = T0 +vgroupwhere T0 is the time when the particle started producing C erenkov light, xi, yi, zi
are the coordinates of the ith PMT, and vgroup is the group velocity in water of thec where c is the speed
photons averaged over the C erenkov spectrum (vgroup = 1:395
of light in vacuum).
Hayai is searching for the vertex (X0 , Y0 , Z0 , T0) which yields the maximum

value for the GOF. From the starting point, Hayai takes steps on a spherical gridto nd a vertex with a higher GOF. The 18 radial spokes of the spherical grid are
centered at the current `best vertex'. Including the center of the grid, there are 19
test vertices per spherical grid. The spokes of the grid lie in the following directions:center of grid andcos  = ,0:75 andcos  = ,0:25 andcos  = +0:25 andcos  = +0:75 andcos  = (+1; ,1) = (0; 2 ; ; 32 ) = ( 4 ; 34 ; 54 ; 74 ) = (0; 2 ; ; 32 ) = ( 4 ; 34 ; 54 ; 74 )The size of the grid starts out large (spokes are 8 m long) and shrinks as Hayai
closes in on the best vertex. As the grid size decreases, the uncertainty in the PMT
timing i changes from 10.2 ns to 2.77 ns (independent of the PMT charge). The
128

anisotropy function f (a) also changes with the grid size. The spoke length follows
the sequence:
Trial number 1 2 3 4 5 6
Spoke Length (m) 8 4 2 1 0.5 0.25
For the rst two trials, f (a) is a Gaussian of mean 0.534 and width 0.134. Thereis no pattern dependence to the GOF during last four trials (f (a) = 1). For eachtrial, whichever of the 19 test vertices produces a larger GOF than the `current
best vertex' becomes the `new best vertex'. As the trials are completed, Hayai
keeps track of which trial point yielded the best GOF. If N0 drops below 5 during
any of the trials, Hayai stops maximizing the GOF and returns the current vertex as
the nal t results. Otherwise, Hayai simply returns the best t vertex coordinates
and the anisotropy from that vertex.

5.4.2 Performance
Hayai can t 30 low energy events per second running on an 233 MHz Alpha

workstation. Since a cut is made based on the Hayai vertex location, we needto understand the resultant ts very well. We studied Hayai using two di erent
yardsticks:
 Gaussian width of t coordinates versus energy and location in tank
 3-dimensional position resolution versus energy and location in tank
We t the coordinate distributions (X, Y, Z) to Gaussian functions. The Gaussian
width (Hayai) is the average of the widths from the t to X, Y, and Z coordinates.
The 3-dimensional position resolution (also called the total vertex error or RHayai )is de ned so that 68% of the events are closer to the true vertex (or source position)
than RHayai . Where it was appropriate, we compared results on the above items
129between calibration data and Monte Carlo simulation.
Table 5.3 contains the Gaussian widths (Hayai) and total vertex errors (RHayai )obtained from running Hayai on 10,000 event samples of Monte Carlo electrons generated at a single location (X = 0, Y = 0, Z given in table). The three di erent
locations in the tank are representative of the detector center, 1 m within the edgeof the 11.7 kton4 ducial volume, and the edge of the 22.5 kton volume.

Hayai (1-Dim)
RHayai (3-dim)
Energy Z = 0 Z = 12 m Z = 16 m Z = 0 Z = 12 m Z = 16 m
(MeV) (cm)
(cm)
(cm)
(cm)
(cm)
(cm)
5
81
65
67
185
140
155
7
62
58
59
125
120
120
10
49
48
49
95
95
105
Table 5.3: 1-d and 3-d vertex resolutions of Hayai on MC electrons
Table 5.4 compares the Hayai between the nickel data and a simulated nickel
source. Source locations with a * are outside the ducial volume. This comparison
shows how accurately the Monte Carlo simulates the detector. Hayai ts the Monte
Carlo nickel events and the nickel data with the same vertex resolution.
Table 5.5 compares the 3-dimensional vertex error (RHayai ) for LINAC data andMC electrons. The LINAC data was taken with the end of the beam pipe at (12.3 m, -0.7 m, 12.3 m). The MC electrons were simulated as a point source located4

In this thesis a ton refers to a metric ton or 1 m .
3130Nickel Source
Source Position Hayai Data Hayai MC
(cm)
(cm)
(cm)
(35, -70, 0)57
57(35, -70, 1200)
56
56(35, -70, 1600)
56
55(35, -1200, -1200)
52
52(35, -1200, 0)56
56(35, -1555, -1200) *51
51(35, -1555, 0) *51
53
Table 5.4: Gaussian widths from Hayai t on nickel data and MC
at the end of the beam pipe with directions pointed straight down. For the LINAC
data and Monte Carlo alike, the X and Y coordinate distributions are symmetricand very well t (small Gaussian widths). The Z coordinate on the other hand ismuch wider and asymmetric. For this reason, we give only RHayai.

5.4.3 E ect of Dwall

 1 meter cut

When we studied the rst Low Energy data collected by Super-Kamiokande, we
discovered that the majority of the Low Energy events t near the edge of theinner detector. By this we mean that Hayai reconstructs the vertices of most LE
events to be within a few meters of the ID PMTs. The Dwall  1 meter cut on the
Hayai vertex was chosen to eliminate these background events. After further studyof the reconstructed LE vertices, it was decided that the largest ducial volume(22.5 kton) that could be used for the solar neutrino analysis corresponded to a131

LINACBeam Energy RHayai Data RHayai MC
(MeV)
(cm)
(cm)
5.866
195
170
6.782
155
145
8.637
140
120
15.92385
75
Table 5.5: Total vertex errors from Hayai t on LINAC data and MC

Dwall  2 meter cut. We therefore need to check the e ect of the Dwall  1 metercut on events which were generated inside of the 22.5 kton ducial volume.
We examined the e ect of the cut on events with vertices closer than 1 meterto the wall (events with Dwall < 1 meter are cut). Monte Carlo electrons were
simulated (including the model of the detector trigger) with locations uniformly
distributed throughout the inner detector with isotropic directions. We then lookedat the eciency for saving events which really had Dwall  1 meter calculated in
the following way:of events which have Dwall[fit]  1 meter1 = # #of events generated with D [MC ]  1 meterwall

The eciency 1 as a function of electron energy is shown in Figure 5.3 for randomly distributed vertex locations. The values given in the graph can be explainedby the Gaussian width of the vertex resolution. Because of the resolution, events
will tend to be t on the order of 30 cm away (in no particular direction) from thetrue vertex. Due to the cylindrical shape of the detector, at any particular point
near the cylindrical edge of the inner detector there is more volume just outside the132

ε1 for Hayai (%)

point than just inside. Events with real vertices inside the ducial volume will get
pushed outside and events really outside will get pulled in. Sometimes the net result is that more events t inside than were generated inside, causing the eciency
to go higher than 100%.

Generated Electron Total Energy (MeV)

Figure 5.3: 1 of Dwall  1 m cut on Hayai vertex calculated using MC electrons
Another item to check is that few of the solar neutrino events located in our
ducial volume will fail the Dwall  1 meter cut. To do this, we need to consider
only those events which were generated with Dwall  2 meter (those inside the22.5 kton ducial volume). A slightly di erent eciency is then calculated:have Dwall [fit]  1 meter and Dwall[MC ]  2 meters2 = # of events#whichof events generated with D [MC ]  2 meters
wall

Figure 5.4 graphs 2 as a function of energy. Note that it is at with energy andnearly 100%. This shows that Hayai has met one of the important goals set for
lef1.

133

ε2 for Hayai (%)

Generated Electron Total Energy (MeV)

Figure 5.4: 2 of Dwall  1 m cut on Hayai vertex on events in ducial volume

5.5 Track Fitting
A simple way to reduce the data size by a factor of two is to throw away the PMT
data on all the cosmic-ray muon events. We need to know the trajectories of themuons to e ectively remove spallation events. We perform track ts and save thet information so the PMT data may be dropped. In order to be con dent enoughabout the track t to drop the PMT hits from the event, we want to have a way tocheck our t results. Several track tters are used by lef1 to enable this doublechecking. They are described in the following subsections in increasing order of
their t accuracy (and decreasing order of their running speed).
The performance of single track tters is examined on actual muon events inthe data. The only `correct' or `true' tracks we can compare with are those t byhand (by eye). Since the human eye excels at observing patterns, we can ` nd'the entry point and exit point for a through-going muon event fairly easily using
a color-enhanced event display program. By comparing the hand t tracks from134

several people, we can estimate the angular accuracy of the hand ts to be 1.

5.5.1 THR1
The rst, most simplistic, track tter uses only the outer detector information.
The basic premise is to look for clusters of tubes in the OD which are separated in
distance and time in a manner consistent with a particle travelling from one cluster
to the other at the speed of light. The algorithm can be described as:
1. Find clusters in the hit OD PMTs
2. For each OD cluster: compute the charge weighted average position and timeof the hit PMTs ,! this is the `cluster' position and time
3. Clean the ID tube hits by requiring that good hits have an immediate neighbor
hit within 4 ns
4. Sparsify the ID data by randomly choosing 10% of the tubes such that the
charge distribution of the hits is preserved (leaving Nreduced tubes to use)
5. For each pair of clusters: use the cleaned, sparsi ed ID data and compute thetotal time residual (,) for the event assuming the clusters are entry and exit
points for a single track:
PNreduced(qii)=1, = PNireduced(qi) 1i=1,: : : where : : : i = ti , Tentry 1 , dvphoton , dparticlecgroupwhere qi is the tube charge, ti is the time of the hit, Tentry 1 is the time ofthe entry cluster, dphoton is the distance the photon went through the waterfrom the emission point along the track to the hit PMT, vgroup is the groupc ), dvelocity for C erenkov light in the water (vgroup = 1:385
particle is the distancealong the track (from the entry point) the particle travelled before emitting
the photon, and c is the speed of light.
135

6. Keep track of which cluster pair yields the smallest ,The THR1 entry and exit points are taken as cluster positions for the pair of clusters
which gave the smallest value for ,. The accuracies of the THR1 entry point andthe direction t are given in Figure 5.5. These distributions compare the THR1
and hand t tracks parameters on a sample of hand-identi ed single through-going
muons from the data.

Figure 5.5: THR1 angular accuracy and entry point error distributions

5.5.2 THR2
Once an event has been tagged as a single through-going muon event, the exit pointis re ned by the THR2 algorithm5. THR2 uses the `hot' inner detector tubes (thosewith a lot of charge) to compute a more accurate exit point. The 10 PMT hits withthe largest charge are selected. The rst iteration computes the charge weighted
position/time of the 10 hottest PMT hits and calls that the exit point. The second
iteration makes a further cut on the hot tubes to require that each tube be within
5

THR2 written by Greg Sullivan.

136

20 ns and 7 m of the rst iteration exit point. The charge weighted position iscomputed again with this smaller set of tubes. For most events, the result of thesecond iteration is returned as the new (better) exit point. Occasionally this second
step will throw out too many tubes (i.e. when you have a cluster of hot tubes andone really hot tube very far away - the charge weighting pulls the average awayfrom the cluster towards the single tube). In this case, both iterations of THR2 are
not to be trusted and the initial OD exit point is returned. The improved angularaccuracy of THR2 is given in Figure 5.6.

Figure 5.6: THR2 angular accuracy distribution

5.5.3 FSTMU
FSTMU6 reliably nds the track for many of the single through-going muon eventsusing the inner detector almost exclusively. FSTMU was designed to run fast enoughto be incorporated into the lef1 program and yet provide accurate enough ts to thetrack parameters to make spallation cuts (see Chapter 7). It is based on FASTMU,
6

Tomasz Barszczak wrote FSTMU.

137

a fast track tter from the IMB experiment.
As is typical with tters designed for Super-Kamiokande, FSTMU rst \cleans"the inner detector PMT data. The objective is to remove the PMT hits which werecaused by dark noise, leaving only the hits induced by the muon's C erenkov light.
Cleaning requires acceptable ID hits to have at least one adjacent PMT which was
hit within 4 ns. Using the cleaned PMTs, FSTMU locates its preferred entry andexit points, assuming that the detected light was produced by a single particle
traveling at the speed of light which enters and exits the inner detector. The basic
idea for the entry point algorithm is to nd a bunch of tubes which are next toeach other and all have early times (compared to most of the PMTs in the event).
These early tubes will de ne the entry point. A bit more care must be taken when
determining the exit point. The exit point will be de ned by a set of neighboring
tubes which have the highest measured charges in the event. It is easy for theexit point to be pulled towards the entry point. This potential bias is removed byneglecting tubes which are closer to the entry point than two PMTs away from thefurthest `hot' PMT (steps 3b and 3c).
The entry point is chosen using the following algorithm:
1. Select the 20 earliest PMTs from the `clean ID PMTs'
2. Locate clusters within the 20 hits
3. Choose largest cluster
4. Calculate unweighted average time of the PMTs in the cluster
5. Select the PMTs which were hit earlier than the average time138

6. Calculate the unweighted average position and time for those early hits,! This yields the entry point and entry time
The exit point is chosen using the procedure:
1. Select 70 hottest (highest charge) PMTs from the `clean PMTs'
2. Find clusters within the hot tubes
3. For each cluster:(a) Select PMTs which are hotter than the average charge of cluster(b) Find PMT which is farthest from the entry point, calculate the distance
between this PMT and the entry point, and subtract twice the PMT
separation distance(c) Reject PMTs closer to the entry point than the distance just calculated(d) Calculate the charge weighted average position and time of the remaining
PMTs ,! This yields an exit point (time) candidate
4. Compute the speed at which a particle would need to travel to go from theentry point to each candidate exit point
5. Calculate the deviation of each `particle speed' from the speed of light
6. If the smallest deviation from the speed of light is > 0:2  c then:Choose the exit point (time) whose speed is closest to c
Otherwise Select the exit point (time) which is farthest from the entry point
The quality of the FSTMU ts can be checked in two di erent ways. The rst is
the deviation from the speed of light of the particle speed necessary to go from theentry point to the exit point in the time computed (exit time - entry time). The
second way is to look at the time residuals. The time residuals are the di erence139between the measured time of each PMT hit and the expected time of the hit given
the particle track location, entry time, and the location of the PMT (assuming thatthe light was emitted at a C erenkov angle of 42 ).
FSTMU ts muons at a rate of 45 Hz as measured on a 333 MHz Alpha (by far

the slowest of the three tters used in lef1). FSTMU's track t accuracy on handt single through-going muons can be seen in several di erent ways in Figure 5.7.
The rst plot shows the distance di erence between the FSTMU entry point andthat from the hand- t. A distribution of the angular deviation between the track
direction found by hand and FSTMU is given in the second graph.

Figure 5.7: FSTMU angular accuracy and entry point error distributions

5.6 Trashman
One of the problems with the low energy data is that about 5% of the triggers areunwanted \junk". Electronics noise and PMT afterpulsing often generate triggers
in which we are not interested. Sometimes an otherwise `good' event will have140

extra PMT hits which are `junk'. Due to the manner in which the O -Site analysis
groups acquire a copy of the data, we sometimes have several (unwanted) copies of
events or runs. Trashman7 has been designed to search out these junk- lled events.
Several categories of \trashy events" exist including: Pedestal
 Crosstalk Ringing `Hut 4 noise' Muon-related junk
 Event number gaps
 Repeated events
 Repeated subrun
A pedestal event is an event which occurred during the pedestal taking period.
Every 1/2 hour or so some of the workstations collecting data from the inner detector switch operating modes from `normal' to 'pedestal' for a few seconds. During
this time the workstation is monitoring the pedestal values of the QACs and TACs
for each ATM the workstation controls. Normal data is taken and assembled into
events using the remaining workstations which are operating in `normal' mode. Effectively, some portion of the inner detector has no data recorded for 1 minuteperiod every half an hour. These events would be very tricky to deal with correctly;
vertex and track tters would perform poorly and the energy of the events can not
be well determined. Trashman identi es these pedestal events so they can be thrownaway (and the livetime adjusted) at a later stage using the following criteria:
1. NID tubes > 1500
7

Trashman was developed by Mark Vagins.

1412. a gap of > 500 sequential wall tubes
Sometimes a workstation drops out of the data ow for di erent reasons (usuallyindicating some problem). These `workstation drop-out' events also will get tagged
as `pedestal' events.
Electronic crosstalk between the outer and inner PMT cables (near the PMTbases) causes hits in inner PMTs within close proximity of a particularly energetic
OD hit. The characteristic pattern of cross-talk is that rectangular patches of ID
tubes near each other are hit. Events with a lot of crosstalk hits have certain
characteristics:
1. NID tubes > 15 which each have q < 0:1 pe
2. NID tubes < NOD3tubes
total < 1:5 pe/tube
3. NQIDID tubes

used by Trashman to tag such events.
After energetic events in the inner detector, we often get triggers generated byelectronic `ringing'. PMT afterpulsing and signal re ections on cables often cause
these triggers. `Ringing' events can be tagged by Trashman using the requirements:
1. NID tubes > 10 which each have q < 0:1 pe
2. NID tubes in Hut 4 < 20 which each have q < 0:25 pe
total < 0:25 pe/tube
3. NQIDID tubes`Hut 4' events are caused by a persistent, localized electronics problem. It is
possible (but not convincingly proven) that insucient grounding of some electron142

ics racks in Hut 4 is the root cause of this electronics problem. Hut 4 events canbe found by:
1. NID tubes in Hut 4 > 20
2. NID tubes in Hut 4 > 10 which each have q < 0:25 pe
4
3. NIDQIDtubesin Hut< 0:45 pe/tube
in Hut 4

There is a Trashman classi cation called `muon-related junk'. Muons sometimes
travel in the dead region between the ID and OD tubes (and are called geiji orcaterpillar muons). The C erenkov light is incident on the backs of the PMTs causing
PMT hits, but the PMT signals are not always useful for tting algorithms. These
caterpillar events almost always have lots of PMTs which have very low charge.
The following criteria were developed to tag these `mu-related junk' events:
1. NID tubes < 1500
2. NID tubes > 15 which each have q < 0:1 pe
total > 1:5 pe/tube
3. NQIDID tubes

The remaining event categories which Trashman searches for are gaps in theevent number within a run and repeated data. For any given run, the event numbers should start at one and constantly increase by one. A gap in the event numbers
would indicate a problem of some sort. Data can occur repeatedly on our data tapes
in two di erent ways, both caused by the calibration process, `TQ real'. Sometimes`TQ real' encounters a problem, sort of gets stuck, and stores the same event to theram disk over and over. Since we copy the data stored on this ram disk without
passing judgement, we copy these repeated events directly to DLT tape. Other`TQ real' problems will cause the calibration process to require re-starting. The
process must be started at the beginning of a run (which has been changed). This143

means that in the middle of a particular run and subrun (e.g. run 1234, subrun56), the data being stored to the ram disk will suddenly start over at the beginningof the run (e.g. run 1234, subrun 1). The subruns 1 through 56 will appear twiceon our data tapes. Trashman watches for these sorts of repeated data by looking
for drops in event number or subrun number within the same run and for multiple
consecutive occurrences of the same event number.
Trashman only tags the junk events it nds using the above described algorithms.

The tag is used further in the next stage of data processing before the uninteresting
events are removed from the data sample. Trashman tags very conservatively so as
to not accidentally toss too many real solar neutrino events; if Trashman calls an
event bad, it is de nitely bad. Consequently even once Trashman-tagged events are
tossed, there is still junk which remains in the data stream. Trashman summarizes
its ndings for each subrun in a log le named dlt#.lef1.trash (example given in
Figure 5.8).

5.7 SaveRun
The SaveRun routine8 collects information from each subrun which will help a later
determination of the quality of that subrun. SaveRun outputs to a log le (naming
convention: dlt#.lef1.saverun) which is used during later data processing. SaveRun
counts the number of events per subrun without outer detector (OD) data and thenumber of events without inner detector (ID) data or OD data. Blocks of no-OD
events are also recorded in the log le. A sample subrun entry in the SaveRun log leis given in Figure 5.9.
8

SaveRun provided by Andy Stachyra.

144

Results of trashman.c
Trashman Revision: 1.10---------------------New Run : 3138 Sub Run : 122
Number of events checked = 5680
O.K. events = 5489
Events with tripped OD high voltage = 0
Events with pedestals in workstation 1 = 0
Events with pedestals in workstation 2 = 0
Events with pedestals in workstation 3 = 0
Events with pedestals in workstation 4 = 1
Events with pedestals in workstation 5 = 0
Events with pedestals in workstation 6 = 0
Events with pedestals in workstation 7 = 33
Events with pedestals in workstation 8 = 52
Events with crosstalk between OD and ID = 64
Events with ringing = 24
Events with hut 4 noise = 1
Events with gap in event number = 0
Events with other muon-related junk = 25
Repeated events = 0
Repeated events due to repeated subruns = 0

Figure 5.8: Sample Entry in a Trashman Log File
145

Start of saverun job

RUN(Revision: 1.4)

3138

SUBRUN

122

First Event Number:

754904

Time:

96/11/23

18:06:50

A series of events without OD data starts at:
Run:

3138

Subrun:Time:

96/11/23

122

Event:

756806

Event:

75681918:10:00

And ends at:
Run:

3138

Time:

96/11/23

It is
Last

Subrun:122

18:10:00

14 events long.

Event Number:This subrun has

760583

Time:

96/11/23

18:16:15

290 ID events missing OD data.

Figure 5.9: Sample Entry in a SaveRun Log File146

5.8 Livetime
The Livetime routine9 computes the length of time over which every subrun extends.
In addition, a lookout is kept for blocks of pedestal events, during which we do notconsider the detector `alive'. The time durations of each pedestal-taking period isrecorded so that the dead time associated with the pedestal events can later be
removed from the total live time of the subrun. All output is saved in a log lenamed dlt#.lef1.live.
Three di erent clocks are used to compute the live time:
1. computer
2. 48 bit
3. GPS
The reading of each clock at the trigger time is stored in the data le for every event.
The computer clock is actually the internal clock of the online host computer. The
time stored in the data le is in Japan Standard Time and is accurate to a second.
The 48 bit clock is the clock inside the TRG module which runs at 50 MHz. The
clock value at the trigger time is readout with the rest of the TRG information.
This is the best clock for measuring the time between events. Rollovers in theclock value must be accounted for. The Global Positioning System (GPS) clock
is our key to the absolute time of the trigger. It is the GPS clock which will be
used to look for coincident time-varying signals between Super-Kamiokande andother experiments. The GPS clock is latched every 21 seconds, but stored in thedata for every event. An accurate GPS time at which every trigger occurred isdesired. A VME scalar running at 50 MHz (the `local clock') is zeroed each time the9Livetime provided by Juilien Hsu.

147

GPS clock is latched and therefore allows interpolation between the GPS latches.
Due to instabilities in the optical ber connection between the GPS antenna andthe VME module which decodes the antenna signals, there are spurts of events
without a reasonable GPS clock time. The quality of each of the clocks is monitored
separately. Sometimes there are problems with the livetime calculation which are of
unknown origin10. Livetime also watches out for pedestal-taking periods by looking
at the event ag in the header of the data and at the output of Trashman's search
for missing workstations from the data. Information about all blocks of pedestal
events are recorded in the Livetime log le (see Figure 5.10).

5.9 Eciencies
5.9.1 Muon Identi cation
We need to know the identi cation eciencies of the lef1 lter for various types ofmuon events. We are most concerned with the mis-identi cation of muons which
result in PMT hits being thrown away, removing the possibility to re- t the event
later. The measurement of these id eciencies requires a sample of muon data withknown event classi cations. A collaborator11 hand scanned and identi ed by eye
10,207 events in order to collect a sample of 2,025 muon events. Using this sample,
the identi cation eciencies were calculated by simply running the lef1 softwareon the data sample and counting the number of events falling into each category.
The number of events with each lef1 classi cation are given in Table 5.6. All themuon events from the hand scan are present in the table. Separate event counts
are given depending on whether the PMTs would have been kept or thrown away.
We think that rollovers in the clock values may not be properly handled.
11Thanks go out to Shige Matsuno for this performing this task.
10148

Livetime Revision: 1.13------------------------***START
run number: 3138

,subrun number: 122

1st event: 754904
GPS(s,us): 848707595 41691760 Scaler: 3227895562
Computer(yr_mth_day,hr_min_sec): 961123,180650
ped_start! evt #: 755011
180657(cmpt) 848707616(gps_sec) 29277987(gps_usec)
ped_end! evt #: 755061
180707(cmpt) 848707616(gps_sec) 36882729(gps_usec)### Ped live time: 7.604740(gps), 50(cmpt) ###ped_start! evt #: 756055
180848(cmpt) 848707702(gps_sec) 46467100(gps_usec)
ped_end! evt #: 756127
180856(cmpt) 848707724(gps_sec) 35105958(gps_usec)### Ped live time: 10.638860(gps), 8(cmpt) ### ... (text removed)
FINISH
last event: 760584
GPS(s,us): 848708153 37014062 Scaler, Rollovers: 1220323765 11Computer(yr_mth_day,hr_min_sec): 961123,181615-------------------------------------Live time: 553.322327(gps), 565(computer), 904.737549(scaler)
Scaler live time is not usable!

Figure 5.10: Sample Entry in a Livetime Log File
149

There are many di erent numbers given in Table 5.6. The most importantones are those for events which have the PMT data thrown away (marked withy ). Once the PMT data is tossed, more ts can not be performed on the eventand the classi cation of the type of muon will not change. Of the 1,747 events
tagged as thru-s, 95.54% of them were really through-going muons which had
their PMT data tossed. This is a fairly high eciency for correctly tagging single
through-going muon events. Forty seven of the thru- events were really multiple
muons which were misidenti ed and had their PMT data thrown out. Six stoppingmuons were called thru-s incorrectly and had their PMT data removed. Thesemisidenti cations (especially the multiple muons) will result in a slightly larger
solar neutrino background rate of spallation products which pass the spallation
cuts (see Chapter 7).

lef1 class# ev.

Thru-

1747
129
132
93
8
514

Stop-
Exiting
Multi-
Up-
Unknown

Hand Fits Results
Thru-
Stopping  Multiple  Other
1846
62
117
Toss Keep Toss Keep Toss Keep All
1669 y
0
0
0
0
0

6y
0
0
0
0
0

16
74
47
20
8
12

1
17
23
7
0
8

47 y
0
0
0
0
0

8
0
0
62
0
0

0
38
62
4
0
494

Table 5.6: Number of events in each lef1 and hand t class for real muons150

5.9.2 Low Energy Events
One of the crucial pieces of knowledge we need about lef1 is its eciency for saving
solar neutrino events generated inside the ducial volume. To study this eciency,
we did several di erent things. First, we examined the behavior of the Hayai vertex tter and the e ect of the cut: Dwall > 1 meter. This work was described in
Section 5.4.2. Second, the eciency of the full lef1 lter program was computedon Monte Carlo solar neutrino events so that the full event identi cation method
could be studied.
We know that due to the vertex resolution, some events with vertices actually
located outside the ducial volume will t inside and vice versa. Therefore, inorder to calculate the eciency correctly using Monte Carlo (MC) event samples,the MC events should have vertices extending all the way up to the edge of theinner detector (de ned as where the `black sheet' lies). The eciency of the lef1
lter for the 22.5 kton ducial volume (Dwall  2 meter) is then:passing lef1 with Dwall[fit]  2 meters3 = ##ofofevents
events generated with D [MC ]  2 meters
wall

(5.4)

Figure 5.11 shows 3 as a function of electron energy. The high eciency which isfairly at with energy is precisely what lef1 was designed to achieve.

151

LEF1 efficiency for F.V. events

Generated Total Energy (MeV)

Figure 5.11: 3 of lef1 lter on simulated electrons in 22.5 kton ducial volume

152

Chapter 6
Data Reduction - lef2

6.1 Introduction
The output of the lef1 lter still contains a lot of events which are not solar
neutrino candidates. The Low Energy Level 2 (lef2) lter was designed to do
everything necessary to meet the following goals:
 Output data set is small enough to distribute to any and all collaborators
 At least keep pace with lef1 lter
 Output contains PMT data only for solar neutrino candidate events
 Nature of output data is unquestionably good
The reduction factor from lef1 output to lef2 output is about a factor of 4.
Whereas 1 week of data ts on 1 lef1 DLT, 1 month of data will t onto 1 lef2
tape. lef2 more than keeps up with the lef1 processing; lef2 (running on a
333 MHz Alpha) can process 7 days of data (one lef1 tape) in 12 day. In orderto accomplish the third and fourth goals, lef2 must complete the following tasks:

 Find multiple muon events and t the tracks
 Find stopping muons and t track153 Decide what should be done with thru- events whose lef1 ts were questionable Handle the big contained events (no OD data events)
 Identify, categorize, and t (if necessary) the unknown events
 Find a more precise vertex for the Low Energy events
 Make the ` nal' cut on vertices of Low Energy events (for largest ducial
volume desired for analysis)

 Remove `junk' and other undesirable events
 Remove subruns or runs with problems
 Create and update a database containing a summary of the processed subruns

6.2 Good Run/Subrun Selection
The very rst thing which lef2 wants to know is \This data which I have, is it
any good?". Information which is used to answer this question is collected by
good&bad data. Several algorithms look for various clues which may point towards\bad" data. Each algorithm sets its own series of ags for every subrun which
are then used to tag the \bad" data. Good&bad data takes the ags from thesealgorithms and combines them into a single ag which is set bit by bit (a particular
bit is set by good&bad data if a particular ag was set by one of the algorithms).
This good&bad data ag is given to lef2 which looks at the bits and decides byitself if the data is really \good" or \bad". The determination of whether a subrun
is \good" or \bad" depends critically on the inherent philosophy behind lef2. The
154

data coming out of lef2 is to be unquestionably good. Any data which is close to
the border between \good" and \bad" is conservatively called \bad".

6.2.1 lef1 Log Files
The main source of information used to tag \bad" data is the log les created by
the lef1 lter program. In order for good&bad data to access this information,
the log les must be read in and parsed for the desired information. There is acomplicated way in which good&bad data gures out which log les to open (there
is one `set' for each raw dlt tape processed by lef1 ) from the number of the tapebeing used as lef2 input. Once the log les are parsed, good&bad data can start
using the information to set ags.
Table 6.1 shows all of the ags set from the lef1 log les and the criteria whichmust be met to have the ag set. A `toga' log le is one created by the main
program which is linked with the lef1 code. It has a single line for every subrun
processed which contains the run #, subrun #, rst and last event # in the subrun,and some other information. This information is gleaned from the data le as thedata is processed by lef1.
Figures 6.1-6.6 show the distributions of the quantities upon which cuts areplaced. The cut values are in some cases closer to the main part of the distribution
than some would generally feel comfortable with. The cuts however re ect the desired conservativeness of the data sample. The number of ID events histogram has
most of the subruns in the rst bin, so an expanded view around the x axis is shown.
The requirement on the fraction of events in a subrun which can have no OD
155

data depends on the width of the the time window. The cut was raised from 2.5%
with the 32 s window to 10% for the 16 s window. The fraction of events without
OD data went up when the window was reduced. Many triggers occur right afteran energetic muon event. When the window size decreased, the hits associated withthe muon event were being digitized when the following triggers were generated.
The OD TDCs were unavailable for these triggers due to the digitization, so thenumber of events without OD data increased.
The cut on the number of saved low energy events is not as stringent as it couldbe, however many of the subruns above the cut and below the peak are eliminatedby the other requirements. The requirement that a run have 3 subruns comesfrom experience controlling the runs. Sometimes an immediate problem will crop
up just after the run starts. Because of the time it takes to observe a problem withthe collected data and to stop the run after nding a problem, these \immediately
aborted" runs are often one or two subruns in length (10 to 20 minutes).

Figure 6.1: Number of events in each subrun without ID data

156

Flag

Criterion

Flags set on subrun basis
Repeated subrun
Listed more than once in the `toga' log leRepeated events
Total number of events processed in subrun is> last event # , rst event # + 1
Too many no-ID events Number of events without
ID data > 108>>
< 2.5% if 32 s OD window#
no-OD
eventsToo many no-OD events># events>>: 10.0% if 16 s OD window# thru- events < 8
Too few thru- events# null triggers
Not enough saved low Fewer than 100 saved low energy events
energy events# noise events
Too many noise events # tossed
low energy events > 0:25
saved low energy events > 1:0
Too many saved low en- ## tossed
low energy events
ergy events
Flags set on run basis
Too few subruns in run < 3 subruns recorded in `toga' log le for the run

Table 6.1: Criteria to have Good&bad data ags set from the lef1 log les157

Figure 6.2: Fraction of events in each subrun without OD data

Figure 6.3: Rate of thru- events in each subrun

158

Figure 6.4: Number of saved low energy events in each subrun

Figure 6.5: Fraction of noise events in each subrun

159

Figure 6.6: Fraction of saved low energy events in each subrun

6.2.2 Run Log Book
There are plenty of ways for a run to contain `non-perfect' or `questionable' datathat are not caught by looking at the lef1 information. As all experimental scientists know, sometimes as the data is collected \things happen" that you would
prefer did not. For example, a calibration run is in progress, but the run operator
told the run control program it was taking a normal run. A note is made in the
run log book that this mistake occurred. Without looking in the log book, there
is no way to nd out about these sorts of instances. We want to prevent these`questionable' data runs from ending up in the solar neutrino nal sample, so we
use the log book to categorize runs as \good" and \bad". A list has been compiled1
which contains the run number, whether the run is \good" or \bad", and a comment which explains the categorization. Unfortunately this list is still somewhat
subjective, so the completed list has been reviewed by several people not associatedwith the list formulation. A short section of the list in shown in Figure 6.7.
1

The CSUDH group has this responsibility; Bill Keig usually makes the list.

160

Run # 3138
Normalgood/* Normal stop because of 24 hour rule */bad/* FIFO busy */good/* Stopped to remove OD PMT 4-1-3-11 */Run # 3139
NormalRun # 3140
NormalFigure 6.7: Sample of the CSUDH run list based on the run log book

6.2.3 Run Summary Files
There is some useful information stored in the `run summary les' created by theon-line run control process. An example of a summary le is given in Figure 6.8.
Speci cally, the summary le can tell us if the right triggers were turned on or
how many records were written. (What good would a run be for the Low Energy
Analysis Group if the Low Energy trigger was turned o ?) A routine was written
to parse the summary les and return certain pieces of information2. The average
event rate for the run is calculated; ags are set if the event rate is out of the`normal' range. A list of all the ags set based on the run summary les is given
below:
2

Andy Stachyra provided the code to read the summary les.

161 Not all triggers (LE, HE, OD) turned on Event rate too high (> 12 Hz)
 Event rate too low (< 8 Hz) Too few events in run (< 6, 000 events)
 Missing summary le (no information)

6.2.4 Decision Making and Record Keeping
lef2 receives from good&bad data aag (set bit-wise) containing all the information found by the \bad data algorithms". lef2 decides for itself which of these\bad data types" are really bad (shown in Table 6.2). Once lef2 decides data
is \bad", the data is not processed any further. All the PMT hits are removed
from the output le, but the rest of the information (header, ts, lef1 and lef2
information) is retained as a record of having processed that data. If lef2 decides
the data is \good", the events continue through the remainder of the lef2 program.
As a record of the ndings of each good&bad data algorithm, a summary of thenumber of events per subrun which have each ag set is written to a log le. The
log le is named tape#.lef2.goodbad and an example is given in Figure 6.9.

6.3 Event Classi cation Scheme
The main task for lef2 is the handling of all remaining events with PMT data.
This includes doing a more precise vertex t for the saved low energy events, tting
the muon events with lots of ID hits, and guring out what kind of particles were
present for the rest of the events. Once an event is deemed by good&bad data andlef2 to be in a good subrun, the event is turned over to the event classi cation
162

Run number: 003138

Status

Shift leader: Kaneyuki,Hsu

Shift member:

Comment: Normal trigger

Run end comment: normalStart time

: Fri Nov 22 20:59:04 1996

Stop time: Sat Nov 23 21:13:40 1996

Number of events: 00867079: stopped

Event rate [Hz]:9.9

Record length [kbyte] : 08768943
ATM threshold: -100Pedestal switch: ON

High rate switch: ON

LowE threshold[mV] : 320

HighE threshold[mV] : 34

sukon1: SERVER

sukon2: SERVER

sukon3: SERVER

sukon4: SERVER

sukon5: SERVER

sukon6: SERVER

sukon7: SERVER

sukon8: SERVER

sukon9: TRIGGER

sukonh: CLIENT

sukant: SERVER

kingfi: MONITOR

Low energy trigger: ON

High energy trigger: ON

Associated trigger: OFF

Anti trigger: ON

Laser trigger: OFF

Xe lump trigger: OFF

Ni trigger: OFF

LINAC trigger: OFF

Random trigger: OFF

Null trigger: ON

Figure 6.8: Sample of a run summary le163

lef2 Action\bad subrun" ag from good&bad data
lef1 requirements on subruns/runs

cut
cut
cut
cut
cut
cut
cut
cut
cut
cut
cut
tag
tag
tag
tag

Repeated subrun
Repeated events in subrun
Not enough saved low energy events in subrun
Too many events with missing ID data in subrun
Fraction of no-OD data events too large in subrun
Too few thru- events in subrun
Too many noise events in subrun
Too many saved low energy events in subrun
Too few subruns in run
Log book requirements on runs
\Bad" runs
Summary le requirements on runs
Not all triggers turned on
Event rate too highEvent rate too low
Too few events
Missing summary leTable 6.2: lef2's actions on each type of \bad subrun" ag from good&bad data164

run 3138

subrun 122

events 5680

0 repeated events

0 events in repeated subruns

123 pedestal events
157 events with no OD but an ID
0 events (too many no OD data events)
0 events (too many no ID data events)
0 events (not enough muons)
0 events (too few LE events to bother)0 events (too many noise events)
0 events (too many LE events saved in lef1)
0 events (# events > (Last ev # - First ev # + 1))
0 events (runs have only 1 or 2 subruns)
0 events did not have all the lef1 info read in
0 events did not have summary file info to read
0 events had too few events in run
0 events in runs with small event rate
0 events in runs with big event rate
0 events in runs with a missing trg bit
0 events in runs with no csudh info

0 events in Nickel cal. runs

5680 events in csudh good runs

0 events in Laser runs

0 events in csudh bad runs

0 events in TEST runs

5680 events in NORMAL runs

0 events in nonexistent runs

0 events in Xenon cal, runs

0 events in OTHER runs

Figure 6.9: Sample of a good&bad data log le165

algorithm.
The algorithm used for event classi cation is basically a series of questions thatare answered by the lef2 program. Once the answer to a question is \yes", thenthe event is nished being classi ed by lef2 and the next event is tested. Events
can be \saved" or \tossed" by lef2, just as with lef1. \Tossed" events havenegative classes and their PMT data removed, but everything else (headers, ts,lter information) is saved. Table 5.2 shows the numerical values for the eventclasses assigned by lef2. A description of the information saved into the data le
by lef2 is given in Appendix A. As with lef1, a log le is kept by lef2 to record thenumber of events in each class found for every subrun processed (tape#.lef2. ltlog).
A portion of a lef2 log le is shown in Figure 6.10. A `tag' mode of operation
exists for lef2 and is controlled by the LE FILTER2 TAG environment variable(similar to lef1, see Section 5.3). lef2 event classi cations are given in bold font.

6.3.1 Pedestal Events
The presence of pedestal-taking periods has already been discussed (Section 5.6).
The beginning and end of each block of pedestal events has been read in from theappropriate log le. If the event number happens to fall within one of the event
blocks listed in the Livetime log le, the event is tagged as a pedestal event.

6.3.2 Minimum Bias Events
The method for tagging a minimum bias event has changed from lef1. A separate
ag is set for every event ( ag = 0 if normal event, ag = 1 if lef1 called event
minimum bias). Minimum bias events are always saved in full regardless of theevent classi cation. Only the events tagged in lef1 are categorized as minimum166--> Code Version 1011--> Cuts Version 1007--> Compilation Date 19961229--> Filter Run Started On : 19970203
Run : 3138 Subrun : 1225680 events in the subrun
2883 events were already thrown out by LEF1
4 events had the same classification as LEF1
123 pedestal events were found and thrown away
612 LE events were saved
586 LE events were thrown out
2 caterpillar (geiji) events were thrown out
52 LE events were considered junk
295 LE events were considered ringing events
2 huge ringing events
0 events are caused by flashers
0 muons that clip OD (dont enter the ID at all)
944 muons had their tubes tossed
82 new through muons found
19 corner clipping muons
45 multiple muons
31 stopping muons

Figure 6.10: Sample lef2 log le167bias (no additional minimum bias samples saved). All minimum bias events willcontinue through the remainder of the lef2 classi cation algorithm.

6.3.3 Caterpillar Muons
An entering muon does not always leave a nice C erenkov ring in the inner detector.
If the muon travels through the `dead space' between the ID and OD, the PMTs
see light entering the back of the PMT. This often causes the PMT hit pattern toresemble a line instead of a C erenkov ring. Only the tubes very near the muontrack are hit, hence the line-like shape of the hits. These muons which speed down
the walls of the detector were nicknamed \caterpillar muons" based on the patternof the hits. In Japanese, these events are \geiji muons". Geiji- events meet oneof the following criteria:
 lef1 class = unknown, stop-, or exiting and Trashman tag = `cross-talk' lef1 class = unknown and Trashman tag = `bad mu-related junk' lef1 class = unknown, stop-, or exiting and NID tubes < 200 lef1 class = stop- or exiting and Muboy called a No Fit lef1 class = unknown, Muboy called a No Fit, and only the OD triggered lef1 class = small non-contained
where NID tubes is the number of hit tubes in the inner detector. The justi cation
for these requirements is simply that the events classi ed as geiji- really looked
like caterpillar muons from the event display. The last requirement is present for
the events which \fell through" lef1 without being classi ed more exactly (signal
was present in the OD, but it did not meet the stop- or exiting event conditions).

168

6.3.4 Big Ringing Events
After energetic muons hit the detector, the inner detector often `rings'. This `ringing' creates triggers; the events look almost like an `echo' of the muon hit pattern.
Sometimes `ringing' events have a lot of ID PMT hits. Events that lef2 classi es
as big ringing events have passed one of the tests:
 lef1 class = multi- and Trashman tag = `ringing' lef1 class = multi- and tprev muon < 20s
 lef1 class = unknown, tprev muon < 20s, and NID tubes > 500
 lef1 class = unknown, Trashman tag = `ringing', and NID tubes > 500
 lef1 class = big contained, Trashman tag = `ringing', and NID tubes > 500
 lef1 class = saved low energy and NID tubes > 200
Note that tprev muon is the time between the current event and the previous muon
event and NID tubes is the number of hit tubes in the inner detector. By looking at
the event display and the classi cation, these criteria are reasonable.

6.3.5 OD Clipping Muons
Sometimes a muon which enters and exits the outer detector will barely touch (ornot touch at all) the inner detector. These OD clipping muons will produce lotsof light in the outer detector while the inner detector will only have PMT noise.
To nd these events, lef2 considers only those events which lef1 classi ed as
unknown. If the event has < 30 ID hits occurring in any 200 ns time window and> 20 OD hits in 200 ns, the event is called an OD clipper. An event can also be
considered an OD clipper if too many of the ID hits in the 200 ns window havenegative charge (Nnegative q in 200 ns > 0:03  NID tubes ) in addition to the > 20 OD
hits in 200 ns.
1696.3.6 Fittable Muon Events
All high energy (NID tubes > 200) events which are not yet classi ed by lef2 andstill have PMT data need to be identi ed and have the track ts performed. Thistask is accomplished by Muboy (see Section 6.5). Muboy will decide if the event has
one track or multiple tracks. When the event is caused by a single track, Muboy
looks to see if the track stopped in the detector or exited. Since Muboy is a full track
tter, the track direction and entry points of each track are returned. When Muboy
has no problem tting and identifying the event, the Muboy event type (in slanttype) is used as the lef2 class (thru-, stop-, multi-, and corner clipper).
Sometimes, Muboy will fail and will call the event a No Fit. In this case, the event
needs to be classi ed as what may have caused the trigger. The categorization ofthese events was already described in the sections about each lef2 `junk' class.

6.3.7 LE Ringing Events
We know from scanning the saved low energy events out of lef1 that many of theevents following a muon are `ringing' events. We also know that in addition to thebogus electronics triggers, we expect sometimes to get a real electron event after amuon. Stopping muons which decay in the inner detector should have `good' low
energy triggers after them corresponding to the decay (Michel) electrons. Although
Michel electrons are a valuable calibration source (see Section 3.3.3), we do not wantthem in the solar neutrino sample. The Michel electrons are therefore classi ed as
LE ringing events along with the junk triggers. The LE ringing events mustmeet one of these requirements:
 lef1 class = unknown, Trashman tag = `ringing', and NID tubes  500
 lef1 class = big contained, Trashman tag = `ringing', and NID tubes  500
 lef1 class = unknown, tprev muon < 20s, and NID tubes  500
170

 lef1 class = saved low energy and tprev muon < 20s
 lef1 class = saved low energy and > 20 hits from the OD

in a 200 ns coincidence window (should not normally happen)

where NID tubes is the number of inner detector hit tubes and tprev muon is the time
di erence between the current event and the previous muon.

6.3.8 LE Junk Events
The LE junk classi cation is intended for `trash' events which lef1 thought weregood low energy events and which are not closely associated with a previous muon.
Most of the `junk' events have been tagged by Trashman, but since Trashman isconservative not all the junk is tagged. If an event meets one of the following
criteria, it is called LE junk.

 lef1 class = saved low energy and Trashman tag = `cross-talk', `ringing', or`bad mu-related junk' lef1 class = saved low energy and Nnegative q in 200 ns > 0:03  NID tubes
The last requirement looks for events with too many \in time" ID hits with negative
charge (negative apparent charge is caused by QAC pedestal shifts). From looking
at the events on the event display, these criteria do indeed identify event which look
like junk. We are not quite sure why the last criteria is needed, but it works.

6.3.9 Low Energy Events
Saved low energy events from lef1 which are not classi ed as LE ringing or
LE junk, are presumed to be \good" events. The next step for these events isthe precision vertex tter. Combo t (described in Section 6.4) is given Hayai's t
results as a starting point. The tter is instructed to use in \direction only" mode171

to nd a good initial track direction. Combo t then runs in \vertex and direction"mode to t the precise vertex and direction for the event. A cut is made using
the new t vertex which corresponds to a 22.5 kton ducial volume. Events with
Dwall  2 meter are denoted saved low energy events while the rest are tossed
low energy events. Tighter ducial volume cuts are made later in the analysis if
desired.

6.4 ComboFit Precision Vertex Fitter
Hayai quickly gured out a reasonably good vertex for the low energy events. A

more accurate determination of the event vertex can still be performed. Combo t
was designed for just that task. Combo t also gures out what direction the particle
was pointed when the C erenkov light was emitted. Since it is an algorithm bent on
precision, Combo t requires a decent starting vertex and a starting direction. Combo t operates in two di erent modes: \direction only" and \vertex and direction".
When in \direction only" mode, the best tting direction vector is found using the
input (starting) vertex. For \vertex and direction" mode, the best tting vertex
and direction are found by adjusting both the vertex and direction away from thestarting values. The typical procedure followed for tting the vertex of low energy
events is to: run Hayai, run Combo t in \direction only" mode, and run Combo t
in \vertex and direction" mode.
The rst thing Combo t does is to pick which tubes will be used for the t basedon the PMT timing. The following requirement must be met in order for the ith
PMT to be used in the t:

jti , Tstart , vdstart j < Tcut
group

172

(6.1)

where ti is the time of the ith PMT, Tstart is the time component of the starting
vertex, dstart is the distance between the ith PMT and the starting vertex (Xstart,
Ystart, Zstart, Tstart), vgroup = 1:c39 is the group velocity in cm/ns, and Tcut = 15 ns
is the value of the cut on the time residuals. This timing cut leaves Nintime tubes
to be used in the t.
Combo t minimizes a 2 function with the AMOEBA routine from Numerical

Recipes [68]. AMOEBA uses the simplex method to \ooze" its way down from thestarting point into the global minimum. For an n parameter t, AMOEBA uses an
n + 1  n-dimensional simplex (a n + 1  n matrix). The simplex can be thought ofas having n arms that stick out in n dimensions from a central point. Each row of
the simplex (center point or an arm) corresponds to a set of the tting parameters.
AMOEBA needs to be given a `characteristic length' for each of the n dimensions,so that it knows the typical range for the parameters. The  vector holds this`characteristic length' of each of the n arms of the simplex. The simplex must be
initialized before it is given to AMOEBA; each arm of the simplex extends from thecomputed starting t parameters into only one dimension a distance equal to the`characteristic length' for that dimension. The global minimum has been reachedwhen the fractional change in 2 across the arms of the simplex is smaller than thetolerance requested. Once the global minimum has been found, it is often a goodidea to feed the minimum back into AMOEBA with a slightly lower tolerance andverify that the global minimum has indeed been reached.
The 2 used by Combo t may be composed of two components: timing andpattern. The precise makeup of 2 depends on the operating mode of Combo t.

173

The timing 2 is given by: 2

2timing = PNi=1intime ii
D j; 2 )jij = MIN(jti , T , vgroupi
i = MIN( p3:q0i ; 0:3) ns(6.2)

where i is the timing residual for the ith tube, (X , Y , Z , T ) is the current vertex, D is the distance from the current vertex to the ith PMT, vgroup is the groupvelocity of the C erenkov light ( 1:c39 ), i is the uncertainty in the measured time forthe ith tube, and qi is the charge for the ith tube. To keep the vertex inside theinner detector, if the vertex is outside the black sheet layer, 2timing = 1020.
The pattern 2 can be described by:2

2pattern = PNi=1intime ii = MIN(i , 42; 2 ),R~ icos i = d~  jRR~~ vertex
vertex,R~ i j(6.3)

with i as the angle between the t direction d~ and the direction from vertex (X ,Y , Z ) to the ith PMT and as the uncertainty in the angle. The remainder of the
Combo t algorithm depends on the operating mode and will be described separately
for each mode of operation.

6.4.1 \Direction Only" Algorithm
Combo t loops through the main body of the algorithm twice. First, AMOEBA isgiven the simplex centered on the given initial direction vector. Then AMOEBA
gets re-started with the simplex centered on the rst iteration's minimum and atolerance smaller by a factor of 10. The basic parameters which control the detailed
behavior of Combo t are given in Table 6.3. The nal direction from the second
loop, (dxbest , dybest , dzbest), is the best direction found and is returned by Combo t.
174

n (# dimensions)3
(0.2, 0.2, 0.2)
Vertex(Xstart, Ystart, Zstart, Tstart)15
2
2pattern
Loop 1Loop 2Tolerance
0.00050.00005
Center of simplex (dxstart, dystart, dzstart)(dx1, dy1, dz1)
Final direction(dx1, dy1, dz1)
(dxbest , dybest , dzbest )Table 6.3: Control parameters for \direction only" version of Combo t

6.4.2 \Vertex and Direction" Algorithm
In this mode, Combo t loops four times through the main algorithm. The behavioral parameters for Combo t are given in Table 6.4. The rst time, AMOEBA isgiven the simplex centered on the given initial vertex (R~ start) and direction vector(d~start). The second and third times, the simplex's center is shifted from the initialvertex. The start time is adjusted accordingly to be the average time residual fromthe shifted vertex. The same direction vector is used as for the rst iteration. For
the fourth iteration, AMOEBA is re-started with the simplex centered on the best
result (denoted by * in the table) from the rst three iterations and a tolerance
smaller by a factor of 10. The nal vertex and direction are: R~ best = (Xbest , Ybest,
Zbest , Tbest) and d~best = (dxbest, dybest , dzbest). The t parameters returned by Combo t are slightly di erent from R~ best and d~best . The vertex is shifted forward 10 cm
along the d~best . This shift removes a systematic bias backwards along the track
direction. Because the tendency of most vertex tters is to be pulled forward along
175

n (# dimensions)7
(0.2, 0.2, 0.2, 15 cm, 15 cm, 15 cm, 0.1 ns)
20
2
2timing + 2pattern
Tolerance
Center of simplex
Final parameters

Loop 10.001
d~start, R~ startd~1, R~ 1

Loop 3Tolerance
0.001
Center of simplex d~start, R~ start , (2 m  d~start)
Final parametersd~3, R~ 3

Loop 20.001
d~start, R~ start , (1 m  d~start)d~2, R~ 2
Loop 40.0001d~start, R~ d~best , R~ best

Table 6.4: Control parameters for \vertex and direction" version of Combo t
the track, we designed Combo t to try several starting points by taking steps backwards. These backwards steps taken by the starting position for the second andthird iterations help to improve the vertex resolution of Combo t, but the resultant
t vertices have a slight backward bias. The 10 cm shift forward removes this bias.

6.4.3 Performance
Combo t runs at 30 events per second running on a 333 MHz Alpha workstation.

Since Combo t's t is our nal attempt at locating the Low Energy vertex andthe track direction, we need to understand the resultant ts very well. We studied
Combo t with the same yardsticks as Hayai (see Section 5.4.2).

176

Table 6.5 contains the Gaussian widths (Combo t) and total vertex errors (RCombo t)
obtained from running Combo t on Monte Carlo events. Samples of 10,000 MC electrons were generated at several locations (X = 0, Y = 0, Z given in table) withrandom directions. The three di erent locations in the tank are representative ofthe detector center, within 1 m of the edge of the 11.7 kton ducial volume, andthe edge of the 22.5 kton volume.

Combo t (1-dim)
RCombo t (3-dim)
Energy Z = 0 Z = 12 m Z = 16 m Z = 0 Z = 12 m Z = 16 m
(MeV) (cm)
(cm)
(cm)
(cm)
(cm)
(cm)
5
67
59
59
140
120
145
7
53
52
52
100
105
115
10
42
43
42
80
80
85
Table 6.5: 1-d and 3-d vertex resolutions of Combo t using MC electrons
Table 6.6 gives the angular resolution () of the Combo t direction for the above
sets of electron events. The angular resolution is de ned such that 68% of theevents have t directions closer to the true direction than the angular resolution:d~fit  d~true = cos # > cos . Note that the position dependence of  is non-negligible
only at the lowest energies, where the vertex is least accurate. The angular resolution of a water C erenkov detector can not get much better than what Combo t
has already achieved. Multiple Coulomb scattering (MCS) of the electrons in water
limits the angular resolution. The average scattering angle for MCS is shown in
Figure 4.4. Direction reconstruction algorithms will not be able to achieve angularaccuracies much better than the average MCS angle.
177Angular Resolution
Energy Z = 0 Z = 12 m Z = 16 m
(MeV) ()
()
()
5
31
35
40
7
40
40
40
10
24
24
27
Table 6.6: Angular resolution of Combo t using Monte Carlo electron events
Table 6.7 compares the Combo t from nickel data and a simulated nickel source.
Points with a * are outside the ducial volume. The Monte Carlo nickel events
systematically yield Combo t coordinate distributions which are 4 cm wider than
the nickel data.
Table 6.8 compares the 3-dimensional resolution RCombo t for LINAC data andMC electrons. The MC electrons were simulated as a point source located at theend of the beam pipe, (-12.3 m, -0.70 m, 12.3 m), with directions straight down.
The MC electrons were simulated as a point source located at the end of the beam
pipe with directions pointed straight down. For the LINAC data and Monte Carloalike, the X and Y coordinate distributions are symmetric and very well t (small
Gaussian widths). The Z coordinate on the other hand is much wider and asymmetric. For this reason, we give only RCombo t.

178

Nickel Source
Source Position Combo t Data Combo t MC
(cm)
(cm)
(cm)
(35, -70, 0)49
52(35, -70, 1200)
46
53(35, -70, 1600)
45
49(35, -1200, -1200)
47
48(35, -1200, 0)46
50(35, -1555, -1200) *45
50(35, -1555, 0) *45
50
Table 6.7: Gaussian widths from Combo t on nickel data and MC

LINAC
Beam Energy RCombo t Data RCombo t MC
(MeV)
(cm)
(cm)
5.866
150
150
6.782
120
125
8.637
100
105
15.92360
70
Table 6.8: Total vertex errors from Combo t on LINAC data and MC179

6.4.4 E ect of Dwall  2 meters Cut
Since lef2 makes a ducial volume cut based on the Combo t vertex, the eciency
for saving the solar neutrino events inside the ducial volume should be studied.
We do this by studying the energy dependence of the the eciency 1:of events which have Dwall[fit]  2 meter1 = # #of events generated with D [MC ]  2 meterwall

ε1 for Combofit (%)

This eciency is shown in Figure 6.11. The Monte Carlo events were generated all
the way up to the inner detector wall. Events with generated vertices outside the
ducial volume may t inside the ducial volume, thereby increasing the observed
eciency for saving events. There is some slight energy dependence which is dueto the tter resolution as a function of electron energy.

Generated Electron Total Energy (MeV)

Figure 6.11:  of Dwall  2 meter cut on Combo t vertex using MC electrons1806.5 Muboy Track Fitter
lef2 needs routines which can perform track ts for multiple muon, stopping muon,and through-going muon events which may not have OD data. Muboy3 is all theserolled into one neat package. Muboy determines if an event was produced by asingle track or multiple (parallel) tracks in the inner detector. If it is a single
track event, Muboy looks to see if it stopped in the ID (the OD is used also if itexists). An event classi cation is returned with the tted track parameters; thedi erent classi cations are: No Fit, Thru Mu, Stop Mu, Multi Mu1, Multi Mu2,
or Corner Clipper. The Multi Mu1 and Multi Mu2 classes both indicate multiple
muon events, just identi ed with di erent algorithms. Corner Clipper events areusually through-going muons which just clip a corner of the ID. They are tagged
di erently from the rest of the Thru Mus since the t direction is not very reliable.

6.5.1 Algorithm
Before Muboy starts trying to t the event, it selects out the PMT hits which will
be used for the t. All used inner detector PMT hits must pass a charge cut (given
in Table 6.9) which depends on the number of hit ID tubes in the event (NID tubes).
Tubes which pass the charge cut are subjected to the nearest neighbor cut. Each
used ID tube is required to have at least Nnn adjacent PMTs hit within 10 ns. Table 6.10 shows the values for Nnn as a function of the total number of hit ID tubes.
The nal number of \good" ID tubes is Nclean. If at any point in the algorithm
Nclean < 10 hits then the event is called a No Fit and Muboy stops working withthat event. The only cleaning applied to the OD hits is that the tubes used musthave a positive charge.
3

Muboy was developed by Bob Svoboda.

181

NID tubes
Minimum charge in ID tube
>10,000
3.0 pe8,000 - 10,000
2.5 pe<8,0002.0 peTable 6.9: Minimum charge requirements for ID tubes used in Muboy t

NID tubes Minimum value of Nnn>7,500
5 tubes
5,000 - 7,500
4 tubes
2,500 - 5,000
3 tubes
500 - 2,500
2 tubes<500
1 tubeTable 6.10: Nearest neighbor requirement for ID tubes used in Muboy t

182

Muboy gures out moderately reasonable guesses for an entry point and track

direction before it can nd the `best' track. The starting entry point is found by
selecting the earliest PMT which has 3 nearest neighbors. If no tube meets thiscriterion, the required number of nearest neighbors is reduced one at a time until
an entry point candidate tube is located. The entry position is the coordinates ofthe early tube; the entry time is the time of the tube hit. The rst guess at anexit point is the center of the `mini-patch' of 9 tubes (1 tube and its 8 surrounding
neighbors) which contains the most charge. A line drawn between the entry andexit yields a starting direction for the track.
To reduce the noise much further around the entry point, a `causality' cut ismade to the tubes. We know that if a muon enters the ID at the entry point/time,then PMT hits which are produced by \direct" light from the muon (light which
is not scattered) can not be hit earlier than the travel time of the muon: Tentry +dentry pmt where dentry pmt is the distance from the entry point to the hit tube andv1
v1 is the muon speed. If there are multiple particles in the detector simultaneously,
there maybe some of these `early' PMT hits. The hits can not be hit later than
the travel time of light in the water: Tentry + dentryv2 pmt where v2 is the speed oflight in water. Light which scattered in the detector will occur late. Light fromother tracks in a multi-track event can be early or late. Muboy allows the maximum and minimum speeds to be a bit farther apart so the `causality' cut is not
too stringent: v1 = 34:0 cm/ns and v2 = 18:0 cm/ns. Multiple muon events can berecognized because they often have a lot of hits which occur `earlier' than causality
allows. For this reason, Muboy counts the number of tubes Nearly which appear
to be hit at speeds faster then 33 cm/ns. If Nearly > 45, the event is called a
Multi Mu1 event. For these events, the causality cut is tightened to remove even183

more of the hits induced by the other tracks: v1 = 32:0 cm/ns and v2 = 19:5 cm/ns.
Muboy maximizes a `goodness of t' (GOF) parameter. The GOF is de ned as:

GOF = F (fcone )

NX
clean

i=1

g(ti)(6.4)

where F is a function of the fraction of hits in the C erenkov cone (fcone ), g is afunction of the the time residual ti = Texpected , ti, ti is the measured time of tubei, and Texpected is the calculated time at which the tube should have been hit.
Tubes are considered `in the C erenkov cone' if either of these conditions aremet:R~ pmt ,R~ entry  d~track > 0:74
jR~ pmt,R~ entry j(6.5)
ORjR~ pmt , R~ entry j < 2 m
Once it is known which of the PMT hits are `in the cone', the fraction of hits inthe cone (fcone ) can be computed. F , the pattern component to the GOF, takes
the following form::9 f
if fcone < 0:75
then
F (fcone) = C0cut
cone:9,Ccut
if fcone > 0:75
then
F (fcone ) = 0:1fcone1,+0
Ccut
where
Ccut = 0:74

(6.6)

The below two forms for g(ti) were determined by looking at timing distributions
from the data.
hi(qi ))2
if ti < 0 or qi > 30 pe g(ti) = exp , (ti,2tmean(qi )2hi
if ti > 0g(ti) = exp , t(qii)hii [ns]
where
(qi) = 1:690 + 2:514 exp , 2:q453hii [ns]
(qi) = 1:254 + 14:863 exp , 2:q316

184

(6.7)

The GOF is maximized by allowing the track direction to move around on a grid andkeeping the entry point and time xed. Once the best t track direction is found, asecond iteration is performed for all events not classi ed as a Multi Mu1. This time
when the track direction changes, the entry time is also allowed to change; it iscalculated from the hits which occur within a 26.7 ns time residual window aroundthe track. A third step is to compute the GOF with a slightly di erent patterncomponent from previous calculations: Ccut = 0:65. After this second maximization, Muboy counts the number of early hits Nearly2. If Nearly2 > 35 and the event
has not been classi ed yet, it is called a Multi Mu2. If the event still does not havea class, it is called a Thru Mu. Direction tting is nished for the Thru Mu events,
but not for the Multi Mu1s or Multi Mu2s.
All Thru Mu events with Ntubes < 2,000 are examined for the possibility of beinga through-going track which clips the corner of the ID. It is very hard to t the
track direction well for these events due to the small lever arm of the track in the
ID. Corner clipping muons can be identi ed by their tracks entering and exiting
the ID near the edges. If a track starts near the top corner and is heading `out'
entry dx+Yentry dy > 0:05), the event is tagged as a Corner Clipper. If the track( Xp
2 +Y 2
Xentryentry
comes in the bottom corner, and the distance between the entry point and the exit
point (as de ned by the `mini-patch') is < 3 m, the event is classi ed as a Corner
Clipper.
The remaining Thru Mu events are checked to see if they are stopping muons.
To recognize a stopping muon, Muboy looks at the charge generated by the endof the track (and if present the OD data near the exit point). The total charge
QID exit is counted for the tubes whose positions lie within 2 m of the exit point for185the tted track. The OD tubes within 4 m of the exit point (projected to the OD
PMT plane) have their charge totaled into QOD exit. An event can get classi ed asa Stop Mu by meeting any of the following requirements:

 QID exit < 200 pe
 QID exit < 400 pe and 0 < QOD exit < 30 pe
 QOD exit > 30 pe and QID exit < 150 pe no OD data and QID exit < 300 pe
Muboy is nished with events which are still classi ed as Thru Mu. Events called
Stop Mu

have the stopping point calculation as the nal Muboy step.

To calculate the stopping point, Muboy looks at the observed energy loss via
C erenkov light production per unit track length, dEdxlight . This is done by looking at
the amount of detected light per unit track length. By assuming that most of the
PMT hits were induced by unscattered light from the muon track, the time of the
PMT hit is used to determine the photon emission point on the muon track. By
examining the amount of charge detected from each section of muon track, dQdxdet , weshould be able to see the drop o which corresponds to the end of the muon track.
The dQdxdet of the track is histogrammed in 50 cm dx bins. The nominal dQdxdet value
for the minimum ionizing portion of the track is calculated by averaging together
the rst 3 bins in the dQdxdet histogram. The second consecutive bin which has dQdxdet

fall below dQdxdet cut is the bin which contains the stopping point. The value for




dQdet
dQdet
=
0
:
4
dx cutdx nominal is not allowed to go below 1 pe/cm.
Multiple muon events go through a second round of the above described iterations. Before Muboy runs o to do this last set of GOF maximizations, more hits
from the `other' tracks must be removed so the accuracy of the rst track t can
186be improved. All hits outside a 13.3 ns timing residual window around the current
track are cut. The rst iteration ( xed entry time) is repeated with the new set ofcleaned tubes. The second iteration is repeated using only the tubes inside a 10 ns
time residual window. Multi Mu1 and Multi Mu2 events are now nished with thedirection tting.
At this point in the tting, Muboy has a direction and entry point for one of the
tracks in a multi-track event. It is assumed that the multiple muons have parallel
track directions. Entry points are needed for the rest of the tracks, once the numberof tracks is determined. To do this, Muboy wants to reverse some of the cleaning
done to the PMTs; the Nclean PMTs passing the initial charge and nearest neighborcuts are used. To this sample of PMT hits, a cut is applied which saves only thehits near the beginning of the track:~ntube  d~track > 0(6.8)

where ~ntube is the normal to the PMT and d~track is the track direction. The tubes
are further selected to try and collect the tubes which are near the muon tracks.
This is done by computing the `plane wave time' tplane at which the PMT would
have been hit if the light was a plane wave traveling at speed c:~~ )  d~track jtplane = Tentry + j(Rpmt , Rentry(6.9)
cwhere R~ pmt is the PMT position vector and R~ entry is the vector to the entry point.
If ,33:3 ns < tplane , ti < 16:6 ns, the tube is kept. An event which has fewer
than 4 tubes left is said to only have 1 track (but classi cation is still Multi Mu1
or Multi Mu2). Since the goal now is to nd entry points for the `other' tracks,
Muboy removes the hits closely associated with the rst track. This is done byrejecting PMTs which have 0 < Texpected , ti < 10 ns and are within 12 m of the187track. Muboy iterates the following procedure until the number of remaining tubes
is <6 or until 9 tracks have been found.
1. Locate earliest hit ,! this tube gives entry point and time
2. Cut tubes closer than 12 m to the track with 0 < Texpected , ti < 10 ns
3. Count number of tubes just cut ,! if > 5, the track is valid
4. Count number of tubes left after cut ,! if  6 tubes, go back to (1)Once Muboy nished the above steps, it has calculated the track direction andentry points for all the tracks in the Multi Mu events and is completely nishedwith multi-track events.

6.5.2 Performance
Several things about Muboy have been studied: the track resolution for each typeof event and the event identi cation eciency. To compute the identi cation eciency, the hand scanned data sample of 10, 207 events was used. No ltering wasdone to the data prior to giving all events with >200 ID PMT hits to Muboy. Table 6.11 contains the Muboy event identi cation results. Overall, Muboy correctly
identi es a very large fraction of the events, including the dicult multiple muons.
The resolution of the Muboy track t must be studied for each type of muon separately. The entry point error (entry ) and the angular error (dir ) in the direction
t will be given for each event type. Figure 6.12 shows the distributions of entry
and dir for the events which both the hand scan and Muboy called stopping muons.
Figures 6.13 and 6.14 give the same type of distributions for single through-going
muons and multiple muon events. The through-going muons were classi ed as suchby the hand scan and Muboy. On the multiple muon events, entry and dir are
calculated for each track assuming that there were less than 3 tracks.
188

Hand Fits Results
Muboy class # ev. Thru- Stopping  Multiple 
Thru-



C.C.


Multi-Stop-

No Fit

1728
77
113
129
0

1717
74
28
17
0

3
1
57
0
0

6
0
0
112
0

Table 6.11: Muboy identi cation eciency for muon events taken from the data

Figure 6.12: Resolution of Muboy track t on stopping muon events

189

Figure 6.13: Resolution of Muboy track t on through-going muon events

Figure 6.14: Resolution of Muboy track t on multiple muon events

190

6.6 Eciencies
6.6.1 Muon Identi cation
As with lef1, the eciency for lef2 recognition of muon events was studied. Because lef2 is run after lef1, the eciency that we will compute is a combinedeciency of both lters together. Table 6.12 gives the number of events of eachtype found by lef2 in the hand scanned sample of 10, 207 events. Each column
has two numbers listed; Toss is the number of events with the PMT data thrownout while Keep is the number of events with PMT data saved. The C.C. classcorresponds to corner clipper muons. All but 11 events from the hand t sample are present in the table; the missing 11 events (10 through-going muons and 1
stopping muon) were classi ed as geiji-. The key piece of information containedin the table is: the misidenti cation probability for muon events is low.
Hand Fits Results
Thru-
Stopping  Multiple  Other
lef2 class # ev.
1836
61
117
Toss Keep Toss Keep Toss Keep All

Thru- 1827 1690
C.C.
51
41
Stop- 74
10
Multi- 81
6

78
7
2
2

10
1
50
0

0
0
0
0

48
0
0
69

0
0
0
0

1
2
12
4

Table 6.12: Combined lef2 and lef1 eciency for muon events

191

6.6.2 Low Energy Events
We have already seen the eciency of the Dwall  2 m cut on the Combo t vertex.
The eciency of the lef2 lter as a whole to save ducial volume solar neutrino
events needs to be examined. The intention is to check the identi cation eciency,
but some aspects simply can not be checked with the Monte Carlo simulated events.
For example, solar neutrinos are generated by themselves (i.e. without any muon
events thrown in), so the cuts on tprev muon will not be mimicked. However, mostof the cuts which the Monte Carlo does not model can be accounted for by a loss inthe total live time instead of contributing to an energy-dependent eciency. Having
said all that, the eciency is calculated to be:# of events passing lef2
1 = # of events generated
with D [MC ]  2 meterswall(6.10)

LEF2 efficiency for F.V. events

Figure 6.15 shows 1 as a function of electron energy. The high at eciency is
precisely what lef2 was designed to achieve.

Generated Total Energy (MeV)

Figure 6.15:  of lef2 lter on simulated electrons in 22.5 kton ducial volume192

6.7 Level 1 21
While the good run criteria was being fully developed, lef2 could not be processing
data. We wanted to use the available CPU without waiting for lef2 to be fully
ready. The two CPU-hungry processes inside lef2 are Muboy and Combo t. lef1.5
was born to run Muboy on the relevant events, save the t information, and throw
away PMT data for the events which Muboy could identify and t. lef2 then reads
the output data tapes from lef1.5. It was believed that this was a safe method ofutilizing available CPU in a way which would not be `wasted' in the future. lef2
only needed minor modi cations to accommodate lef1.5. The rst modi cation
was to add another lookup table for good&bad data so it could gure out which
lef1 log les to open based on the lef1.5 tape number. Also, lef2 checks for
the Muboy t information in the data le before calling Muboy. The identi cation
algorithm for events did not change at all with the addition of lef1.5. Three lef1
tapes t onto a single lef1.5 output tape. One output tape from lef2 holds two
lef1.5 tapes. lef1.5 is now a standard component to the Low Energy data ltering.

193

Chapter 7
Final Data Reduction

The output of the lef2 lter yields approximately 1 DLT tape (30 GBytes) per
month of low energy events. Still, a very small fraction of these events are real solar
neutrinos. In order to further extract the neutrino signal, we must apply physicsbased cuts to the lef2 data sample. There are several ways in which these cuts canbe made. One way is to run a `level 3' lter program which writes out a data lewith the events which pass the nal cuts. The method we utilize creates NTUPLE
les [70] with a summary of the event information. Using PAW [69], the cuts areapplied to the NTUPLE when making plots, etc. The bene t of using NTUPLEs
and making the nal cuts \interactively" is that the cuts can be changed at any
time without having to re-process data.

7.1 NTUPLE Program - le ntuple
A special program (called le ntuple) collects the needed information and creates
the NTUPLE les [69]. le ntuple performs several functions: compute Ne ective for every LE event call Cubist to tag spallation events194 create a log le containing the run #, subrun #, Cubist exposure, and a \keep
or toss" ag for every subrun

 create lists of good and bad subruns
The Ne ective calculation and Cubist are described in this Chapter. The log le ispart of our bookkeeping system to keep track of the processed subruns.
The structure of the NTUPLE was designed to have enough information sothat most cuts could be studied and optimized. Tables 7.1 through 7.5 list all theinformation contained in the NTUPLE. Some of the information is accumulated
from zebra banks (see Appendix A) such as the header bank (HEAD), the lef1
and lef2 banks, and tter banks (COMB and HAYA). A few things (spallationags, energy) are the results of routines called by le ntuple which are describedin the next sections.

7.2 Sun Location
An electron undergoing neutrino-electron elastic scattering preserves the incident
neutrino direction. The directions of the solar neutrino induced events in SuperKamiokande therefore will correlate with the location of the Sun. In order to see
the events pointing back to the Sun, we must know where the Sun is at all times ofthe day. Determining the Sun location is a fairly straightforward process, once thecoordinates of the Super-Kamiokande site and the time of day are known. SuperKamiokande is situated at a latitude and longitude of 36.426 degrees and 137.313
degrees respectively. The ,y^ axis of the Super-Kamiokande coordinate system
points 49.85 degrees West of magnetic North. The GPS clock is usually used forthe time of day. Sometimes the ber link connection from the GPS antenna to
195

FieldDescription

run
run #
subrun subrun #eventnum event #trg id `trigger id'
yrmthday date event triggered (computer clock)
hrminsec time event triggered (computer clock)
Ntotal total # of ID hits
Nq<0 # of ID hits with negative charge
trash Trashman event tag
minbias minimum bias event tag
goodbad good&bad data subrun tag
tped time (in s) since last pedestal period
ttime (in s) since previous trigger
Qtotal total charge in ID
Table 7.1: General event information in the Low Energy NTUPLE

196

FieldDescription

cubistspall agtnofitQnofitclassno ttgeijitodclip

Cubist tag

tag for spallation cuts similar to Cubist
time (in s) since last Muboy No Fit event
total ID charge for the last Muboy No Fit event
lef2 class for the last Muboy No Fit event
time (in s) since last geiji- event
time (in s) since last OD clipper event

Table 7.2: Spallation variables in the Low Energy NTUPLE

Field

Description(dxsun , dysun , dzsun ) direction vector pointing to the Suncos suncosine of angle between Combo t track directionand (dxsun , dysun , dzsun )clock
ag for which clock was used to locate the Sun(GPS or computer)
Table 7.3: Sun location information in the Low Energy NTUPLE

197

FieldDescription
Combo t information(Xc, Yc, Zc, Tc) vertex(dxc, dyc, dzc) track direction
2cchi-squared
Hayai information(Xh, Yh, Zh, Th) vertex
GOFh
Hayai goodness of t(dxh, dyh, dzh) anisotropy vector
Energy information
N50c
N50 computed from Combo t vertex
N50h
N50 computed from Hayai vertex
Neff
Ne ective computed from Combo t vertex
Eenergy of event computed from Neff
Table 7.4: Fit information in the Low Energy NTUPLE

198

FieldDescription

Information on each of the (10) previous
muons within 10 s and 5 m of this eventclass of ith  lef2 classi cationNi
total # of ID hits in  eventtitime di erence (in s) since muon
Qitotal ID charge in  eventd
distance of closest approach between  track and LE vertex
Ltracktrack length of muon
Table 7.5: Previous muon information in the Low Energy NTUPLE
Super-Kamiokande goes down. When this happens, the GPS time recorded in thedata corresponds to a date which is before the Super-Kamiokande detector was
operational. The GPS time is checked to see if it is later than April 1, 1996. If it
is not, we use the clock time from the online host computer which is stored in theheader.

7.3 Spallation Events
When energetic muons travel through water, they will sometimes cause oxygen
nuclei to break up. This general process, called `spallation', occurs with lots ofdi erent nuclei. The remnant pieces of the oxygen nucleus are often unstable elements like 12B and 12N. These radioactive spallation products will decay and appear
to look like contained low energy events. However, they are de nitely not solar
neutrino-induced events. Spallation products form a signi cant contribution to thesolar neutrino background.
199

To remove the spallation events from the solar neutrino sample, we want tomake cuts based on the positional correlation between the low energy vertex andthe muon track and time correlation between the muon and low energy events.
Historically, spallation events are removed by cutting the low energy events withina certain time of the muon which have vertices inside of a cylindrical volume aroundthe muon track. Figure 7.1 shows pictorially a typical spallation cut around a muontrack.
To Remove Spallation Events

Muon Track

Cylinder cut aroundmuon track for a time ∆ T

R cut

Figure 7.1: Cylinder cut around a muon track to remove spallation events

7.3.1 Characterization
The spallation-induced events in our lef1 data sample have been studied in great
detail1. The goals of this investigation were to characterize the time scales, explain the possible source isotopes, and calculate the event rates of the spallation
events. The results of this characterization study will be given. The optimization of1

This spallation study was completed by Bob Svoboda.

200the speci c `spallation' cuts made to the nal data sample will then be summarized.
In order to see correlations between the muon and low energy events, a runninghistory of the muon events in the past minute is kept. The track t parameters
come from FSTMU and MUBOY while Hayai gives the low energy vertex position(The tuning of Combo t was not nished when this work was done.). The importantparameters for the characterization of spallation events are:
TTime between the LE event and the previous muon event
D
Distance of closest approach by the muon track to the LE vertex
NID tubes Total number of ID tubes (to check the approximate energy)

1 ms Time Scale
An exponential decay with a half-life of 100 s (dicult to t well) is seen in thetime di erence between low energy (LE) events and muon events (see Figure 7.2).
The correlation distance (D) between the LE event vertex and the muon trackis shown in Figure 7.3. The two horizontal scales are D and its square. The
non-spallation events should yield a at (D)2 distribution. The sharp peak inthe (D)2 distribution is the spallation events. The D distribution may be alittle more intuitive, but the spallation peak is harder to identify because of the low
statistics and the shape of the background. The distribution of the number of ID
PMT hits shows a clear bump for the events with vertices within 3 m of the muontrack and time di erences <1 ms (Figure 7.4). The NID tubes bump falls o above10 MeV (very coarse estimate). The number of hits does not appear correlatedwith the charge deposition of the muon, which is expected of `ringing' events. No
candidate decay sources were found in the Table of Isotopes [71] with this end
point energy and half-life. All listed isotopes that could be created from oxygen201

have half-lives of a few milliseconds and larger. However, the Table of Isotopes is
not a complete listing of the resultant isotopes from the breakup of oxygen.

Figure 7.2: Time between muon and Low Energy event

1-100 ms Time Scale
It was known apriori that many isotopes could contribute to spallation events on
the 100 ms time scale. These are listed in Table 7.6. By looking at the T
distribution for events within 3 m of a single through-going muon, an e ective
half-life of 18 ms is t. The NID hits distribution has an end point at about
15 MeV. A graph of the spallation probability as a function of Qtotal depositedin the ID shows that the muons should be separated into three distinct categories:
Class A:Class B:Class C:

Qtotal < 5:0  105 pe
5:0  105 < Qtotal < 1:0  106 pe
1:0  106 < Qtotal pe

Many events are found on this time scale which are correlated with single throughgoing muons and multiple muons. No signi cant signal was seen after stopping202

Figure 7.3: Correlation between LE vertex and muon track

Figure 7.4: Total number of ID hits for events correlated with a previous 203muons. Also, a fairly high rate of events was found for Muboy No Fit events which
had >500 pe in the inner detector. For these No Fit events a global veto must be
done - since there is no muon track to correlate with the LE vertex.
Isotope Half-Life
11Li
8.5 ms
13O
15B
12N
14B
13B
12B
12Be

8.6 ms10.5 ms
11.0 ms
13.8 ms
17.4 ms
20.2 ms
23.6 ms

EnergyBranching Ratio
E =20.6 MeV
39%
E =11-19 MeV
60%
E =16.7 MeV
89%
E =18.0 MeV
100%
E =17.3 MeV
95%
E =14.5 MeV E =6.1 MeV
82%
E =13.4 MeV
92%
E =13.4 MeV
97%
E =11.7 MeV
100%

Table 7.6: Isotopes with half-lives between 1-100 ms

100-600 ms Time Scale
In this time regime, the T distribution for events within 2 m of a through-going
muon track ts well to an exponential decay with an e ective half-life of 0.11 s indicating that spallation events are de nitely being observed. The T distribution
for events between 2 and 3 m of the track is at. No spallation is discernible fromstopping muons. After multiple muons events with more than 6 tracks, the T
distribution also ts well to a 0.11 s half-life. Table 7.7 shows the few isotopes
listed in the Table of Isotopes which can contribute to spallation on this time scale.

204

Isotope Half-Life
8He
0.119 s9C
0.127 s9Li
0.178 sEnergyBranching Ratio
E =10.7 MeV
84%
E =4.4-16.5 MeV
E =13.6 MeV
50%
E =11.2 MeV E =2.4 MeV
34%

Table 7.7: Isotopes with half-lives between 100-600 ms

0.6-5 s Time Scale
With this time scale, the \natural" time scale due to the trigger rate comes intoplay. Even though the average time between triggers is 0.1 s, the average time
between events which are within a few meters of a muon event is much longer.
The \natural" fall-o must be removed from the T distribution before tting forthe e ective half-life of 0.9 s. The rate from multiple muon events with 4 tracks
and the rate after Muboy No Fit events are dicult to see due to a limitation in
the analysis program used for this study. Previous time scales showed that thespallation rates from two categories of multiple muon events were comparable; it isassumed that the same is true for this time scale also. No track-related events areapparent after stopping muons. Isotopes that may cause the observed events are
given in Table 7.8.

5-70 s Time Scale
The isotopes with half-lives between 5 and 70 s are listed in Table 7.9. Productionof 16N occurs when a stopped , is captured by the oxygen nucleus, which is notstrictly speaking spallation. To remove 16N events (and any other event which iscorrelated with a muon stopping point), a spherical volume centered on the stopping
205

Isotope Half-Life
EnergyBranching Ratio
16 C !15 N 0.747 s E =5 MeV E =3 MeV
84%
Eneutron =3.35 MeV
8B
0.770 sE =18 MeV
100%
8Li
0.838 sE =16 MeV
100%
15 C
2.45 s
E =9.8 MeV
37%
E =4.5 MeV E =5.3
63%
Table 7.8: Isotopes with half-lives between 0.6-5 spoint is cut. Because of the low end point energy, the 14O decay will become
more important as Super-Kamiokande continues to take data and lower the energy
threshold. With this long time scale, it is dicult to separate the spallation T
decay from the \natural" fall-o with the present analysis. The optimization of acut on this time scale will need to be performed using di erent analysis tools.
Isotope Half-Life
EnergyBranching Ratio
16N
7.13 s E =6.13 MeV E =4.3 MeV
66%
11Be
13.8 s
E =11.5 MeV
55%
E =9.4 MeV, E =2.1 MeV
31%
10 C
19.3 s
E =2.9 MeV
99%
14O
70.6 s E =2.6 MeV E =2.3 MeV
Table 7.9: Isotopes with half-lives between 5-70 s

206

Spallation Rate
All these time scales, muon categories, and track correlation distances can becomea bit confusing. It is dicult to gure out which muon type and time scale generates the most spallation events. Obviously, the modes which produce the mostbackground events deserve to have the most attention when the cuts are tuned.
Table 7.10 gives the rate estimates from this study for each spallation mode. These
rates were calculated from the D distributions using the t half-life time to theT distribution. Using all time scales and all muon events, the total spallation
rate is 600 events/day.

Time

Thru 

1 ms
8-14
100 ms153
600 ms
34
5s
96
70 s
64
ev
TOTAL 355-361 day

Event TypeMultiple Stopping  Muboy No Fit<4 tracks 4 tracks
3-5
16-27
18
19
105
6
4
10
14
14
none ?
8
8
none ?
none ?
ev
ev
94-96 day131-142 day

Table 7.10: Measured spallation rates in events per day

7.3.2 Cut Optimization
We need to remove as many of the possible spallation events as we can from thesolar neutrino data sample. This can obviously be done most simply by cutting out
the entire detector for a certain amount of time after a muon event. This simplis207

tic cut however can result in a very large dead time. The reduction of spallation
events must be done in a way that does not greatly reduce the overall live time.
The spallation cuts must be optimized to keep the solar neutrino signal and throw
away the spallation signal. The cuts for each time scale and each muon class must
be optimized separately.
The probability of making a spallation event on the 1 ms time scale was checked
for the various types of muons. The total dead time from cutting the entire detector
for 1 ms is only 0.2 %. It was felt that this small loss of live time was acceptable;
there was no need to optimize a cut on only a part of the detector on this time scale.
The optimization of the `cylinder' spallation cuts shown in Figure 7.1 was amulti-step process2. The goal of the optimization was to maximize the signi cance( pSB ) of the signal which remains after a track-correlated cut. The signal (S ) andbackground (B ) are given as:
2 Ltrack )R Tcut ]
S = LR [V0 , (Dcut
2 Ltrack )R Tcut ]
B = N0Pspall + Ndc [V0 , (Dcut
 2RTcut L 2
 = 1 , Dcut Ltrack
V0 L
hi
Pspall = 1 , (1 , exp ( ,Dcut )2)(1 , exp ( ,Tcut ))where:
L = live time [s]h iR = solar neutrino rate m13 s
V0 = e ective volume [m3]Dcut = radius of cylinder which forms the cut volume [m]Ltrack = mean track length of these muons [m]2This work was performed by Rob Sanford.

208

(7.1)

R = muon rate for this class of muon [1/s]Tcut = length of time to hold the cylinder cut of radius Dcut [s] = non-overlap fractionh i
N0 = spallation rate m13
Pspall = probability of being spallation = characteristic distance from track [m] = characteristic time scale [s]h i
Ndc = dc background level m13
When overall constants are ignored, the equation for pSB ends up being independentof R and L. The values for R , Ltrack , ,  , and NNdc0 are all taken from the data.
Using this equation for pSB , the values of Dcut and Tcut are optimized for eachmuon class (with a track t) and time scale. This optimization is done successively,
meaning that the best cut values for longer time scales will depend on the resultsfrom the shorter times. The nal cuts used in this analysis are given in Table 7.11.

7.3.3 Cubist
The loss in detector exposure (volume  live time) from making these `cylinder
cuts' must be accounted. One can think of the total exposure after spallation cuts
as an e ective (smaller) livetime times the full ducial volume. An e ective livetime
for the 22.5 kton ducial volume (corresponding to Dwall  2 m) can be computedwith varying degrees of accuracy. One of the diculties in getting an accurate
measure of the e ective livetime is overlapping muon tracks. For a particular setof cuts, the exposure lost by the `cylinder' cut (cut ) would be:cut = R2cutLtrack Tcut

209

(7.2)

Event Typeany muon
any muon

Time Cut Distance Cut Spall ag
p
1 ms
globalp
120 msR=3 mcylinderMuboy No Fit Qtotal < 500 pe

100 ms1 ms

globalglobalstopping 
stopping 

10 s
30 s

Rcylinder = 1:5 m
Rsphere = 1:5 m

0.5 s
4.0 s
10 s
0.8 s
7.5 s
50 s
0.6 s
6.5 s
25 s

Rcylinder = 2:2 m
Rcylinder = 1:2 m
Rcylinder = 0:6 m
Rcylinder = 3:0 m
Rcylinder = 3:0 m
Rcylinder = 0:8 m
Rcylinder = 3:0 m
Rcylinder = 2:8 m
Rcylinder = 1:6 m

Muboy No Fit

thru 
thru 
thru 
thru 
thru 
thru 
thru 
thru 
thru 

Class AClass AClass AClass BClass BClass BClass CClass CClass C

multiple multiple multiple multiple <6 tracks
100 msglobal6 tracks
3s
global<3 tracks
10 s
Rcylinder = 2:5 m<3 tracks
30 s
Rcylinder = 1:5 m
Total dead time =12%
Table 7.11: Spallation cuts used in analysis

210

-

p
p
p
p
p
p
p
p
p
p
p
p
-

p
p

where Rcut is the maximum perpendicular distance from the track for a `cut' low
energy vertex, Ltrack is the track length of the muon, Tcut is the length of time
time after the muon for which events are cut. This equation assumes the most
simplistic type of track - one which is perpendicular to the tank walls on entry andexit. This con guration does not happen often. Usually the tracks are not normal
to the walls and the cut exposure becomes more complicated. The equation for cut
becomes more complicated still if the muon track scrapes a wall such that the full
cylindrical volume does not lie in the inner detector. If two muon tracks are closeenough that the `cut' regions overlap, the loss in exposure is not cut1 + cut2 . It is
actually smaller by an amount which depends on the volume of the overlap region.
It is dicult to accurately account for these overlaps analytically. A method oftagging the spallation events and accurately computing the total exposure of thedetector was needed.
Cubist 3 solves the problem of determining the detector exposure after spallation

cuts. Inside Cubist, the volume of the inner detector is broken up into 22803 \cubes"
which each take up 1 m3. Each cube has an \alarm clock" which is \set" whena muon passes near the cube (or when a global veto is on). The timers on thealarm clocks run down as the event times progress forward. While the timer ona particular cube's alarm clock is non-zero, any low energy event with a vertex in
the cube is tagged as a spallation event. A cube is considered \active" if the alarm
clock is not set. The detector exposure for a subrun is calculated:total =X
eventsNactive  T

(7.3)

where Nactive is the number of active cubes during each event and t is the time
di erence between successive events. The key to computing the exposure is simply
3

Mark Vagins conceived of and developed Cubist.

211

the ability to count the number of active cubes correctly.
So when do cubes become inactive? Usually, Cubist looks for muons tracks as t
by FSTMU or Muboy and makes `cylinder cuts' around each track for certain periodsof time. The speci cs of these cuts were given in Section 7.3.2. The entire detector
is vetoed for several di erent reasons as described in Table 7.11. In addition to themuon related spallation cuts, Cubist also vetoes the entire detector during pedestal
taking and for 30 s after the period ends (2.5% dead time), for 30 s after the startof a new run in the data, and for 30 s after Cubist starts executing. Finally, Cubist
does its own bookkeeping and creates an output log le with a summary for every
subrun.
There are two things about Cubist which detract from its desirability. One
is its running speed. The sheer number of computations Cubist does per event
keeps the speed fairly slow. When Cubist is used in le ntuple (which does only
minor computations itself), we can process a single lef2 tape in several days on a
333 MHz Alpha (which is actually not so bad given that this corresponds to about
1 month of data). The second reason has to do with Cubist's ability to implement
the speci c distance-to-track cuts from the cut optimization. Cubist uses 1 m3
cubes. How well can it apply a D > 1:6 m cut? Cubist will still give the correct
exposure for the cuts which it actually applied, but we may not be getting thesame background reduction from the spallation cut as the cut optimization would
indicate. A simple way to resolve this is to reduce the cube size. The number ofcubes and the computation time will then rise. We could not accept the increasein computation time for this analysis, so the 1 m3 cube size was not changed.

212

7.3.4 Spall ag
Cubist is very CPU intensive and takes a relatively long time to run on the data.

We wanted a quick way to get `close' to the same spallation cuts as Cubist, without
actually taking the time to run Cubist. We use a more traditional way to tag
spallation events that does not compute the exposure or account for overlapping
tracks. A routine was created which cycles through the muons previous to a solar
neutrino candidate event and computes the time and spatial correlation between
the LE event and the muon. A ag (spall ag) is set if the LE event did not pass thedialed in spallation cuts. The subset of Cubist's cuts used is indicated by the checkmarks in the spall ag column of Table 7.11. The spall ag routine also provides asanity check on Cubist for the entire data set.

7.4 Energy Determination
The vertex and direction of every event have already been found in the processof ltering out the good low energy events. The energy of the event is still an
unknown. We need a way to reconstruct the event energy using the PMT data.
Until the charged particle slows down appreciably, the number of C erenkov photons
produced during each centimeter of the particle's track is a constant. If we know
the total number of C erenkov photons emitted, we can calculate the total initialenergy of the particles in the event. We will make Ereconstruct equal to the totalenergy held by an electron that creates the same number of C erenkov-induced
PMT hits as the real Super-Kamiokande detector observed. Since the amountof C erenkov light produced by an electron does not depend on how the light isobserved, the reconstructed energy Ereconstruct must be uniform over the ducial
volume and independent of the track direction. We need to ascertain the best way
213to calculate Ereconstruct.

7.4.1 N50
The simplest idea was to count the number of `in time' PMT hits, N50. The reconstructed energy would then be: Ereconstruct = A + B  N50. More speci cally, thetime residuals (time minus the light transit time to the PMT) for all the PMTs arecalculated. A sample distribution of the time residuals from the Combo t vertex
using the nickel source is shown in Figure 7.5. A 50 ns window slides through thetime residuals. The maximum number of PMTs in the 50 ns window is de ned as
N50.
How does N50 perform as an energy scale? Table 7.12 shows the mean value of
N50 and the width of the distribution (from a Gaussian t) as a function of locationin the detector. The results from the nickel gamma-ray source and Monte Carlosimulation are given; the nickel source was modeled as a point source of gamma-rays
with the same energy distribution as the real source. The table shows that the N50
from Monte Carlo simulation and the data are not quite the same. The MC does
not vary as much over the volume as the data. The mean N50 for the data varies
on the order of 15% across the ducial volume (points denoted by * are outside the
ducial volume). This variation is completely unacceptable behavior for a quantity
which should relate directly to Ereconstruct. Although we initially used N50 to indicate
approximate energies and to compare with the On-Site Group, a di erent approach
must be taken in order to achieve a reasonable energy reconstruction.

214

Figure 7.5: Time residual distribution for nickel data events

N50 for Nickel Source
Source Position
Mean
Gaussian Width
Data MC DataMC(cm)(hits) (hits) (hits) (hits)(35, -70, 0)37.27 37.31 9.75
8.54
(35, -70, 1200)
40.26 39.08 10.86 8.88
(35, -70, 1600)
42.74 40.76 11.36 8.92
(35, -1200, -1200) 42.23 41.72 10.74 9.10
(35, -1200, 0)40.78 40.41 11.12 9.19
(35, -1555, -1200) * 41.73 40.97 12.49 9.80
(35, -1555, 0) *41.46 40.86 12.32 9.46
* denotes the source as outside the ducial volume
Table 7.12: N50 means and widths for nickel data and MC events
215

7.4.2 Ne ective
Reality is the main reason that just counting the number of PMT hits in a time
window does not yield a good energy scale. The water, although highly puri ed, attenuates C erenkov light. Attenuation causes the number of hit PMTs to depend on
the event location and direction. The non- at shape of the 50 cm PMTs introducessome directional variation in the number of PMTs hit. Events at the center of thedetector generate almost exclusively 1 pe PMT hits. As the event vertex approaches
the walls, the probability for a tube's charge to be > 1 pe goes up. Simply counting
PMT hits will not be sucient for events with vertices near the walls. All these effects (and possibly more) need to be accounted for in the computation of Ereconstruct.
The calculation of Ne ective uses the \in time" PMT hits, each with a di erent
weight. The tube weights account for the attenuation, geometry, and charge corrections which need to be made. The dark noise contribution to Ne ective is removed
by subtracting away a term proportional to the number of dark noise hits in the\in time" window and proportional to the corrections (which should not have been
applied to the dark noise hits). The expression for Ne ective is:
Ne ective = (1 , NNout time )in timeX
in timeAi Gi Ci

(7.4)

where Nin time is the number of \in time" hits, Nout time is the number of \out oftime" hits, the sum is over the \in time" tubes, Ai is the attenuation correction for
the ith PMT, Gi is a geometrical correction, and Ci is the charge correction. The
attenuation and geometry correction factors depend on the location and directionof the event. The charge weighting varies with the PMT charge. Each of theseweights is described in the following sections.

216

\In Time" Window
The width of the window used for the computation of N50 was chosen because it was
reasonable. The width was not optimized at all. For Ne ective, we want the optimal
Signalwindow size. Using simulated electron events, we studied the pBackgroundof thehits in the time residual window as a function of window width. The PMT hits
generated by the Monte Carlo simulation come with a ag indicating if the PMT
was hit by C erenkov light or simulated dark noise. This ag was used to separate
the `signal' hits from the `noise' (background) hits. This study was performed before
the Super-Kamiokande detector was operational, so the PMT dark noise rate was
unknown. We therefore optimized the window width using several di erent noise
rates. Because of the asymmetric shape of the timing jitter distribution (more hits
arrive late than early), the time residual (t) distribution is also asymmetric (shownin Figure 7.5). In order to include the largest number of hits from the time residual
distribution, the \in time" window is not centered at zero. \Late" hits are more
likely than \early" hits, which is re ected in the direction of the window center
shift. The optimum window width found from this study is 30 ns. The Nin time \intime" hits used for the Ne ective are those within this time residual window from
-10 ns to +20 ns.

Geometry Correction
We need to consider the variations in the apparent area of the PMTs on the wall. If
the PMT face was at, the fractional area taken up by the PMT on the wall would
2 cos pmt
pmt = rpmt
not change with incident angle (pmt): AAwall
d2 cos pmt = constant. The faceof a 50 cm PMT is not at; its shape is like a \squished hemisphere". The fractionof the wall area covered by the 50 cm PMT de nitely depends on the incident
angle to the wall. The e ective area of the 50 cm PMTs has been measured in situ
217Normalized Effective Area

using the Nitrogen laser system. Two di erent measurements were made: one with
only air inside the tank and one just after lling the tank with water. There isclearly a di erence in the e ective area as a function of incident angle on the PMT.
The air/water di erence was shown to be mostly due to re ections o the glass
face of the PMT. The measured e ective area was t to the function f (cos pmt)(polynomial of cos pmt) shown in Figure 7.6. The correction factor Gi is given ascos pmt . Figure 7.7 shows G as a function
the inverse of the PMT fractional area: f (cosipmt )of cos pmt.

Incident angle to PMT (degrees)

Figure 7.6: E ective area for 50 cm PMT versus incident angle

Attenuation Correction
We must be cautious to use the right kind of correction factor for the water attenuation. Often times, when people talk about \attenuation" they really mean
\absorption". In the Super-Kamiokande water, we have absorption and scattering.
Absorption removes the light entirely from the water before it can be detected.
Scattering sends the light in a direction di erent from the initial case. Scattered
light usually arrives \late" to the PMT since it took a longer path then the direct218

Geometrical Correction Factor G

Incident angle to PMT (degrees)

Figure 7.7: Geometrical correction factor for Ne ective
way from the production point to the PMT. Often times `di use attenuation" ismeasured using cosmic-ray muons. For these through-going muons, the charge (after some geometrical corrections) in each PMT is plotted versus the photon travel
distance in the water. A `di use attenuation length' of 78 m is extracted by tting
an exponential to this distribution. This is not the same measure of attenuation asis needed for Ne ective. The total PMT charge in a muon event will include somelight that was scattered and arrived late. If the PMT gets hit by `direct' light, theQAC gate will already be open and the scattered light will contribute to the total
charge for that hit. This will not happen for low energy events. There are so few
tubes hit in a low energy event, that the chances of light scattering to a PMT which
was already hit is very unlikely. That means scattered light is detected by a `new'
PMT. Scattered light can not arrive very late and still have the hit count as an\in time" tube. Ai needs to correct for absorption and the small angle scattering
which still arrives \in time".
To ensure the applicability in Ne ective, the attenuation correction factor Ai
219

should be extracted from the calibration data. We chose to use data from thenickel gamma-ray calibration source to nd Ai. We looked at the probability ofgetting an \in time signal" PMT hit as a function of distance (P (r)) the light musttravel to the PMT. To get this distribution correctly, two di erent backgroundsubtractions must be done. We made several distributions which are used forbackground subtraction to get the nal `probability versus distance'. To remove
any geometrical e ects (see next section), we require the incident angle on the wall
to be nearly normal (cos pmt > 0:9) for a tube to go into any histogram. Usingnickel source data at many di erent locations, we made several versions of the \#hits versus travel distance" distributions (listed below). \In time" (\out of time")
tubes have -10 < ti < +20 ns (+300 < ti < +330 ns).

 Dist. # 1 : 10 < tfission < 110s using \in time" tubes(nickel events, signal PMT hits) Dist. # 2 : 10 < tfission < 110s using \out of time" tubes(nickel events, noise PMT hits) Dist. # 3 : 400 < tfission < 500s using \in time" tubes(background events, signal PMT hits) Dist. # 4 : 400 < tfission < 500s using \out of time" tubes(background events, noise PMT hits) Dist. # 5 : \# PMTs versus travel distance" histogram using all tubes (thisis just the apparent geometry of the detector from the vertex; an entry ismade once for every ID PMT)
where tfission is the time since the ssion trigger (see Section 3.3.4). To remove
the histogram contribution from PMT dark noise, we take (Dist. # 1(3) - Dist.
220

# 2(4)) to yield distributions for `in time signal hits only'. As was discussed in
Section 3.3.4, the non-nickel events are removed by background subtraction. The
background is identi ed as the events very late compared to the ssion trigger while
the signal comes soon after the ssion trigger. We need to account for the densityof PMTs not being uniform. The PMT density is contained in Dist. #5. The net
e ect of all these steps is:, [Dist: #3 , Dist: #4]
P (r) = [Dist: #1 , Dist: #2]
Dist: #5

(7.5)

This probability function P (r) is the `raw' probability of getting a PMT hit as afunction of distance. The r12 drop o in light intensity has not yet been removed
from P (r). The amount of attenuation (A) as a function of distance is equal to
P (r)  r2. The nickel data told us that A ts well to the functional form:

A(r) = A1 exp , Lr + A2 exp , Lr
1

2



(7.6)

where L1 and L2 are attenuation lengths and A1 and A2 are the weights of eachcomponent. The attenuation correction would then be:

Ai = A(1r )
i

(7.7)

where ri is the distance from the vertex to the ith PMT. We could not, however,obtain reliable t parameters from the data. Because of the low PMT density at
small distances, the error bars on A(r) were large. At longer distances where thestatistics are higher, the higher PMT density at the corners caused some problems
with the shape of A(r). Instead of ddling around with excluding certain regions
from the t to A(r), we decided to take a more straightforward approach.
We empirically determined the values of L1, L2, A1, and A2 by changing thevalues and studying the uniformity of Ne ective from the nickel source across the221ducial volume. Starting values for the parameters came from our initial t to thenickel data. The parameters were varied until Ne ective was most uniform acrossmost of the ducial volume (a slight drop in Ne ective at the edge was allowed since
the charge correction would bring the value back up). Before this optimization, it
was decided that no attenuation correction should be applied for distances shorter
than 5 meters. We then need to ensure that the correction function is normalized
at a distance of 5 meters. The best t function is (shown in Figure 7.8):
exp( 200r m )+0:1exp( 22rm )ri > 5 m Ai = A(ri) = exp( 5 m )+0:1exp( 5 m )200 m

ri  5 m(7.8)

Attenuation Corrections

Ai = 1:

22 m

Distance (m)Figure 7.8: Attenuation correction factor for Ne ective

Charge Correction
The attenuation and geometry corrections yield an Ne ective which is fairly uniform
across the detector's ducial volume. However, there is still a drop in Ne ective overthe last few meters near the ducial edge. We know that the probability of getting
a multi-pe hit increases as the production point of the C erenkov light approaches
222the wall. This e ect can be included in Ne ective by a larger weighting factor for thehigh charge tubes.
To determine what this weighting factor should be, the PMT charge distribution
for nickel events was studied. We plotted the di erence between the distribution ofqi for nickel events at the center and at the ducial volume edge. There was a clear
di erence in the number of PMT hits with qi > 1:7 pe. These tubes are the ones
with real 2 pe signals (or occasionally larger). Clearly these hits need to count morethan the ones with smaller charge, but we do not want to overcompensate. We also
don't want to overweight a tube that may have extraordinarily high charge. Of themethods tested, the simplest weighting scheme seemed to work the best:
if qi  2:0 pe Ci = 1:0
if qi > 2:0 pe Ci = 2:0(7.9)

7.4.3 Performance of Ne ective on Nickel Data
The entire point of making the corrections which make up Ne ective is to remove
the detector e ects. We need to verify that the Ne ective energy scale is indeed
uniform across the ducial volume. We do this using the nickel gamma-ray source.
Table 7.13 shows the t mean and Gaussian width from the Ne ective distribution
from the nickel data as a function of source position. The Ne ective distributions
from the nickel source are background subtracted. Also given is the same quantities extracted from the MC simulation of the nickel source. The mean value of thedata Ne ective is constant across the ducial volume to <2% (the two points with a* in Table 7.13 are outside the ducial volume). Therefore, Ne ective meets the mostimportant requirement for the energy scale parameter. The Ne ective distribution
from the nickel data is about 5% wider than that from nickel Monte Carlo. Thismay be due to the water absorption and scattering models or the nickel gamma-ray223

spectrum in the MC not fully reproducing the data. The N50 distributions for data
and MC had di erent widths which may support these reasons.

Ne ective for Nickel Source
Source Position
Mean
Gaussian Width
Data MC DataMC(cm)(hits) (hits) (hits) (hits)(35, -70, 0)41.29 42.18 12.59 10.91(35, -70, 1200)
41.87 41.48 11.98 10.87(35, -70, 1600)
41.08 39.59 11.18 10.20(35, -1200, -1200) 41.43 41.21 12.05 10.36(35, -1200, 0)41.15 41.53 12.45 10.83(35, -1555, -1200) * 38.43 38.12 11.79 9.93
(35, -1555, 0) *38.94 38.63 11.68 9.99
* denotes the source as outside the ducial volume
Table 7.13: Means and widths of Ne ective from nickel data and MC
As with the N50 distributions, the Ne ective mean values do not precisely agree
between Monte Carlo and data. These two points together indicate that the input
parameters are not yet entirely correct. They are close however. Probably the
inputs that need to be \tweaked" a bit still are the water attenuation and scatteringand the PMT angular acceptance.

2247.4.4 Energy from Ne ective
We have shown that the Ne ective distributions from the Monte Carlo simulated
nickel source and from the real nickel calibration source match fairly well. Ideally,
we would use the LINAC data to tell us how to get from Ne ective to electron totalenergy in MeV. One problem with this approach is that the LINAC data is taken
only at one position in the detector and with only one direction. Even though ourenergy scale (Ne ective) is fairly uniform over the detector volume, we do not want
to introduce a potential bias to the energy scale.
Also, there are still questions about the proper interpretation of the LINAC
data which impact the energy calibration. When the rst LINAC data was taken
in December 1996, it was discovered that the end cap obstructed the paths of afairly large percentage of the C erenkov photons (on the order of 10% at low energies). Due to the geometry and the path length di erence between 15 MeV and5 MeV electrons, the fraction of light which is shadowed by the beam pipe is energy
dependent. A new ange was designed to reduce the shadowing and was installed
for the January LINAC run. The shadowing is much smaller than before, but still
non-negligible.
For these reasons, we have chosen to perform the \absolute energy calibration"using the events simulated by the tuned Monte Carlo program. We will use the
LINAC data as a sanity check on both the energy calibration and the systematic
error assigned to the energy scale. We generated monoenergetic electron eventswith isotropic directions and vertices uniformly distributed throughout the ducial
volume. For these event samples, the Super-Low Energy trigger was implemented
in the MC. This way little bias is introduced by the trigger eciency at low energies.
225

The Ne ective distributions for each generated electron energy are t to a Gaussian.
The mean values from the t are graphed versus electron energy in Figure 7.9.
We t the data points in Figure 7.9 to both a straight line and to a quadratic.
The 2 per degree of freedom for the quadratic t was approximately one. The
linear t yielded a 2 per degree of freedom almost an order of magnitude larger.
We use the best t quadratic relationship between Ne ective and the total electronenergy for each ducial volume used in this analysis:22.5 kton 2 = 1:23 Ne ective = ,7:7909 + 6:6665  Etotal , 0:0228  E2total
11.7 kton 2 = 0:80 Ne ective = ,7:4556 + 6:6514  Etotal , 0:01678  E2total(7.10)The non-linearity is believed to be caused by the incomplete accounting of multi-pe
PMT signals in Ne ective. We do have a heavier charge weighting for PMTs thatmeasure larger signals, but it is very simple. A PMT with 3 pe counts the sameas a PMT with only 2 pe This insucient charge weighting causes Ne ective to fallo at larger energies. So the best t is non-linear. This conclusion is supportedby the best t curve for the smaller ducial volume (11.7 kton). When the higher
energy events are con ned near the center of the detector, fewer PMT hits will havemulti-pe signals. The quadratic term will then be smaller for the 11.7 kton FV thanfor the 22.5 kton FV. This has indeed been observed. To estimate the variationin the conversion from Ne ective to total energy due to Ne ective not being uniform
across the volume, we also plot in Figure 7.9 some data points corresponding toMC events generated only at the center of the detector.

226

Neffective

Energy (MeV)

Figure 7.9: Correlation between Ne ective and total energy using MC events

7.4.5 Time Dependence of Ne ective
Two of the main components to our energy scale have already been described.
Nickel data taken in the middle of August 1996 helped us nalize our Ne ective calculation and tune the Monte Carlo water parameters. We then use the MC to tell
us how to get MeV from Ne ective. So for mid-August, we know and understand ourenergy scale fairly well.
What happens to our energy scale when the water transparency changes withtime? It is no longer right. A change in the absorption or scattering length willa ect the number of PMT hits detected (and Ne ective) for a given electron energy.
Our Monte Carlo does not have input parameters which are time dependent, so theenergy conversion from Ne ective to MeV will only be correct for data taken aroundthe same time as the nickel data. There are several di erent ways to account for
the time dependence of the energy scale.
1. Ignore it and simply ensure that our systematic error in the energy scale is227large enough to account for this e ect
2. Re-tune the MC parameters to nickel data taken each month (for example)
and get a time dependent conversion from Ne ective to MeV
3. Scale Ne ective by a time dependent multiplicative factor which equals one in
mid-August
4. Recompute Ne ective with a time dependent attenuation correction (Ai(t))
This last method is the correct thing to do. For this analysis, the necessary time
to develop an appropriate Ai(t) was not available. We resort to applying method#3: a time dependent scaling of Ne ective.
We need some way to determine the overall scaling factor for Ne ective. One
option might be to use the nickel data taken at a particular location. We could
compute the mean Ne ective for nickel data taken at various times with the source
positioned at the center (for example). If we normalized Ne ective to the mid-August
value, we could perform a t to the resultant points. The best t function could
then be used as the multiplicative scaling factor. Two problems crop up with thisidea. One is that we have periods of time where no nickel data was taken. The second is that the correction derived from data taken at a single place in the detector
would, strictly speaking, be an appropriate correction for events with vertices nearthat place. Since we are making an average correction to the events in the rst
place (because we did not go with option #4 above), we really need to derive thescaling factor in a way that averages over all positions in the detector.
Clearly we want to use the data somehow to derive the Ne ective scale factor.
We need a source of events in the solar neutrino energy range from which we have228

data at various times throughout the entire time period of the solar neutrino data
set. There is always spallation occurring in the detector. The spallation products
are a ne source to use for monitoring Ne ective. It might be preferable to select aparticular product isotope and monitor the Ne ective changes in that single decay.
That is not easy to do in practice and is not really necessary. We just need a wellde ned sample of events to use for this study.
We chose to use events occurring within 100 ms and 1.5 m of a previous muon.
The events are separated into monthly samples and the central region of the Ne ective
distributions are t to Gaussians. Figure 7.10 shows one of the distributions withthe best t. The t mean Ne ective values are plotted as a function of time in
Figure 7.11. The best t polynomial function is shown. Note that hNe ectivei fromthe peak to the valley changes on the order of 7%. If hNe ectivei is normalized tothe middle of August (when the nickel data was taken which the Monte Carlo was
tuned with) and inverted, the multiplicative scaling factor is obtained (shown in
Figure 7.12). On an event by event basis, we take the Ne ective computed for the
event, multiply by the correction factor appropriate for the date on which the event
occurred, and then convert to MeV (energy). At most, we scale Ne ective up by 3%
or down by 1.5%.

7.4.6 LINAC results
The LINAC data does not always consist of perfect, single electron events. The data
must be \cleaned" up in order to do a reliable energy calibration. The problem isthat the LINAC trigger can be generated when there 0, 1, 2, or more electrons in thesame bunch. If no electron is present, the trigger was caused by random noise in thetrigger counter (PMT and thin plastic scintillator). Noise is not a problem when229

Figure 7.10: Ne ective from selected spallation events in August

Figure 7.11: Time dependence of t Ne ective from selected spallation events

230

Figure 7.12: Time dependent scaling factor for Ne ective
the LINAC is producing high energy electrons, since the distribution of Ne ectivefrom noise events is quite separable from the LINAC electrons. At lower energies,
the noise and LINAC signal are much less separable. One electron is present in thebunch was the intended condition and is not a problem. Two electrons in the same1 s window can cause problems. First of all, the event will not t as well as single
electron events. An error in the vertex will cause Ne ective to be o from its well- t
value. The fact that there are two electrons depositing energy in the water meansthat a second bump will be present higher in the Ne ective distribution. The existenceof this second bump may skew a t to the primary (1 electron) Ne ective distribution.
So how should the data be \cleaned" to remove the noise events and the multiple electrons? Figure 7.13 shows the distribution of the time between triggers
for a LINAC run. The bump at 0.75 s appears to contain many of the noise
events. This feature can be removed by a tprev > 10 s cut. Since we know thatmany of the multi-electron events will have poor ts, we should consider using thet information to make a cut on these two electron events. A reasonable method231

#/binof accepting only good ts is to make a cut on the value of T0 from Combo t.
Figure 7.14 gives the T0 distribution for all the events during a LINAC run. The
acceptable range of T0's is indicated on the plot (750 - 900 ns).

#/binTime since previous event (ns)Time since previous event (ns)Figure 7.13: Time since the previous trigger from LINAC data
We apply these two cuts (tprev and T0) to the LINAC data, compute Ne ective
for each event, and t the resultant distribution to a Gaussian. The mean andwidth of Ne ective as a function of computed electron energy is given in Table 7.14.
We compare the LINAC results to the Monte Carlo values. Since this LINAC data
was taken in January 1997 and the MC was tuned to August 1996 nickel data, weneed to apply the scaling factor discussed in Section 7.4.5. Both the scaled andunscaled results are given in the table. Also displayed are the mean and widthof Ne ective for Monte Carlo events simulated at the LINAC beam energies. The
MC electrons were given vertices at the same location as the end of the LINAC
beam pipe. The electron directions pointed straight down. The end cap geometry
was not simulated so there is no shadowing of the C erenkov light for the MC events.
232

#/binT0 from Combofit (ns)Figure 7.14: T0 from Combo t applied to LINAC data

Ne ective for LINAC
Beam Energy
Mean
Gaussian Width
Data Scaled Data MC Data Scaled Data MC(MeV)(hits)(hits)(hits) (hits)(hits)(hits)
5.866
31.07
30.72
30.02 9.02
8.87
7.80
6.782
38.70
38.27
36.10 10.37
10.22
8.32
8.637
51.85
51.26
48.31 11.74
11.60
9.38
15.96699.91
98.80
93.84 14.77
14.68
12.63
Table 7.14: Ne ective results from LINAC data and MC233

From Table 7.14, we can see that the scaled LINAC data and the Monte Carlodo not perfectly agree even after the time dependent correction to Ne ective. The deviation in the mean Ne ective from scaled data to MC is 5%. This di erence could
be caused by several di erent things. The rst is the cleaning technique applied
to the LINAC data. By changing how the \single electron" peak is selected out
prior to tting, we can change the mean Ne ective by up to a few percent. Also, the
LINAC data occurs at the end of the time period for which our Ne ective correction
is valid. It is quite possible that when the month of February is included in the tof Ne ective versus date that the actual values of the correction factor on the date of
the LINAC data will change. Given the uncertainty in the validity of this LINAC
to MC comparison, we do not take this 5% di erence into account when computing
our systematic errors.
The fractional energy resolution measured using the LINAC data is fairly well
reproduced by the MC. Figure 7.15 shows the energy resolution measured using the
LINAC and MC events. The best t to the LINAC data yields a parameterization
for the energy resolution of the following form:

E = q17:5%= 55p:4%E
E
10 MeV

(7.11)

7.5 Radon
Radon gas creates background events in underground solar neutrino detectors[72].
Radon is a noble gas (222Rn) which easily di uses through materials. Radon is aproblem because it is radioactive with a half life of 3.8 days. The decay of radon
leads to a long chain of unstable elements whose decays result in many low energy
and emissions. The member of the chain with the highest energy decay is234

Energy Resolution (%)

Energy (MeV)

Figure 7.15: Reconstructed energy resolution using MC and LINAC data
214Bi:214Bi,!214 Po + e, + e

(7.12)

which has an end point energy of 3.26 MeV. The rest of the decays in the chain
have even less energy than this reaction. Although this end point energy (thelargest energy which the ejected electron may carry) is technically below SuperKamiokande's trigger threshold, uctuations in the number of detected C erenkov
photons will sometimes allow these events to trigger the detector. If radon gas isvery plentiful, Super-Kamiokande will trigger a lot just on the radon. Using theMC with a simplistic generator for the 214Bi decay, we estimate the Low Energy
trigger eciency to be on the order of 0.2% for 214Bi decays.
As construction of the detector took place, the radon content of each material
was measured [73]. From our in situ measurements, the radon content in the detector is  2:0  10,2 Bq/m3 or  5:4  10,4 pCi/l (compared to the Kamiokande-III
concentration of  0:1 Bq/m3 or 2:7  10,3 pCi/l). Given the trigger eciency,
this radon concentration does not even account for half of the Low Energy triggers.
235

Even though the radon level does not explain the trigger rate, we still get manybackground events produced by the radon decay daughters.
As far as we know, radon events are not preferentially clustered in particularareas of the detector volume. They are real events in the sense that an electron or gamma-ray produced C erenkov light which assisted in generating a SuperKamiokande trigger. With our current knowledge there is no real way to cut radon
events out of the data sample except to reduce the radon content in the real detector. Radon can enter Super-Kamiokande via the water system or di using infrom the air above the tank. The radon working group is developing methods toreduce the radon contamination in the detector and to monitor the radon level in
the Super-Kamiokande water and air.

7.6 \Flashers"
As we processed the data and monitored the data quality, we discovered sporadic
excesses in the number of \junk" events ending up in our data sample. These \junk"events were found by looking at distributions of the goodness of t computed by
Hayai and Combo t. We devised a cut on the goodness of the vertex t to remove alarge fraction of these new \junk" events. Figure 7.16 shows the normal distributionof the goodness of t from Hayai and the distribution containing these junk events.
After veri cation using the Monte Carlo, we make a cut at 0.5 to keep the good
events. We scanned the events failing this cut to try and identify the root sourceof the triggers. We repeatedly observed the same PMT hit pattern. This is usuallyindicative of having a \ asher" inside the detector. A \ asher" is a PMT whichintermittently emits light (usually generated by arcing inside the PMT). A \ asher"is almost always near the end of its life. It is possible to devise methods tag
236

no. of events/bin

potential \ asher" events on an event by event basis, but nothing of that sort has
been implemented in this thesis. We rely on the goodness of the Hayai t to reduce
the number of asher events in our nal solar neutrino sample.

Goodness of Hayai fit

Figure 7.16: \Flasher" cut using the goodness of Hayai t distributions

237

Chapter 8
Results

8.1 Data Set
On April 1, 1996 Super-Kamiokande became fully operational and started collecting data full time. As with any new experiment, it took a while to work out thelittle problems and understand what was going on with the detector as a whole.
The water needed time to be further cleaned by the water puri cation system so
the water transparency would stabilize. This rst data is therefore excluded fromthis solar neutrino analysis.
The nal data set used in this analysis contains the data from May 24, 1996
through February 10, 1997. This corresponds to Runs 1679 through 3523. There
are approximately 10 days of data from the beginning of August which we did notprocess because of a `TQ real' problem which set the PMT times to zero for all
the high charge PMTs. Approximately 251 calender days of data are containedin this data set. The vertex cut of Dwall  2 meters implies a ducial volume of
22.485 kton 1 (out of the 32.481 kton inner detector volume). The Cubist exposure
1

In this thesis, a ton refers to a metric ton or a cubic meter.

238

and e ective live time (for the 22.801 kton volume considered active by Cubist) are
given in Table 8.1. The full data set will be broken down into data collected atnight and during the day.

Data Set
All
Day
Night

Cubist Exposure E ective Live Time

3376.3 kton-days
1600.0 kton-days
1776.3 kton-days

148.2 days
70.2 days
77.9 days

Table 8.1: Exposure for nal data sample
These exposures make sense, given all the places where live time can be lost.
First of all, the detector is only live 85% of the time each week. The remainderof the time is spent on calibration, hardware tests and replacement, water transparency measurements, and ` asher' nding expeditions. The good run criteria
removes almost 20% of the subruns leaving the analysis live about 85% of the time.
Spallation and other Cubist cuts reduce the live time by another 15%. Putting allthese losses together yields an expected live time of about 154 days. The Cubist
exposure is then quite reasonable:
154 days = 251 days  0:85  0:85  0:85:

8.2 \Interactive" Cuts
After le ntuple processing, more cuts are applied to the data via NTUPLE cuts.
These cuts are done interactively using PAW so there is no output le created. The
cuts can be easily modi ed without the hassle of re-processing the entire data set.
If desired, a new NTUPLE can be written out with only the events after certain239

cuts. The spallation cuts are applied through the NTUPLE. If Cubist returned a
non-zero value, the event has not passed all the cuts. We also make the \ asher"cut (GOFh > 0:5) described in Section 7.6. The last cut is on the energy of theevent. We want to use the events in the energy range where we are con dent aboutknowing the eciencies and where the eciency is very high and at with energy.
If you use the range where the eciency is falling, it is important to know the shapeof the falling edge well. For this reason, we only consider events above an energy
threshold of 6.5 MeV.

8.3 Characteristics of Final Event Sample
We started out with raw data which had lots of problems and events which we
wanted to remove from the data set. We developed ltering software and a varietyof cuts designed to clean up the data and leave us with only viable solar neutrino
candidate events, our nal data sample. Figure 8.1 shows the t coordinate distributions from the nal sample events after the GOF and spallation cuts and with
Ereconstruct > 7 MeV. Note that the number of events per bin in the R2 plot rises atthe edge of the ducial volume. There is also a peak in the Z coordinate distribution
near the bottom of the tank. The t direction cosines for the same events are given
in Figure 8.2. Note that the x and y direction cosine (dx and dy) distributions
are pretty much at, while the z direction cosine (dz) distribution has a distinctly
non at shape. In addition, the Z and dz distributions are both asymmetric. The
nal sample has many events whose t vertex is near the edge of the ducial volume
or outside it and whose direction points towards the center of the detector. These
events are typically referred to as \gammas from the rock" and form an anisotropic
background for the solar neutrino signal. We know from measurements made by the
Kamiokande collaboration [74] that there are many gamma-rays emanating from240

the rock face. Some of these gammas will penetrate through to the inner detector
volume and generate a trigger. These \ s from the rock" will t near the wallwith directions pointing in. Also, radioactive impurities in the glass envelope of the
50 cm PMTs may generate gamma rays which trigger the detector. These events
will also have t vertices close to the inner detector walls (where the PMTs arelocated). The energy distributions for all events above 7.0 MeV passing the GOF
cut and the spallation cut are given in Figure 8.3.
Next we want to know if we can see a correlation between our events and theSun. Figure 8.4 displays example of our standard `solar peak' distributions after
the spallation cuts. The GOF cut and a 7 MeV energy threshold were applied. The
quantity histogrammed is:cos sun = ,d~event  d~sun(8.1)

where d~event is the t direction of the event and d~sun is the direction vector fromthe center of the Super-Kamiokande tank to the Sun (in the Super-Kamiokande
coordinate system). We expect a strong peak at cos sun = 1 for events initiatedby neutrinos coming from the Sun. Indeed, we see a clear peak from the Sun.
Figures 8.5 and 8.6 show the same cos sun distributions after breaking up the data
into day and night samples. Note that the backgrounds do not look at.

8.4 Signal Extraction Method
In order to compute a solar neutrino ux, we need some way to extract the numberof solar neutrino interactions in our nal data sample. We tried several di erent
methods and settled on a two step method of tting the background level and thenthe signal above the background. We took the shape of the background to be a241

X Coordinate (cm)# events per 10 cm bin
Y Coordinate (cm)2

# events per 10 cm bin

242

2

T0 (ns)2

R (cm )

Figure 8.1: Vertex coordinate distributions from nal sample

Z Coordinate (cm)# events per 1 m bin# events per 10 cm bin# events per 10 cm bin

# events per 0.01 bin# events per 0.01 bin

X direction cosine

Z direction cosine

243

Y direction cosine

Figure 8.2: Direction cosine distributions from nal sample# events per 0.01 bin

# events per 0.1 MeV# events per 0.1 MeV

Total Energy (MeV)

Total Energy (MeV)

Events per 0.025 bin

Figure 8.3: Energy distribution from nal sample (linear and semi-log plots)cosθsun for ALL data

Figure 8.4: Correlation between the Sun and nal sample event directions

244

Events per 0.025 bincosθsun for DAY data

Events per 0.025 bin

Figure 8.5: Solar peak for the day data with Ereconstruct > 7 MeV

cosθsun for NIGHT data

Figure 8.6: Solar peak for the night data with Erecontruct > 7 MeV

245

straight line with non-zero slope. A non- at background was implemented after
looking at the day and night cos sun distributions. For consistency, we let the slope
oat for the ALL data, even though the t to a at background gives a similar 2.
The background is intrinsically not at, as we have an excess of events near thebottom pointing up. The background level is determined by a simple 2 t to alinear background using the data with ,1  cos sun < +0:5. We then extrapolate
this best t line (over the full range of cos sun) to predict the background underneath the solar neutrino peak.
Once the number of background events in each bin is found, the excess events
can be t to the shape of cos sun predicted by the Monte Carlo for the current
energy threshold. Figure 8.7 shows the various cos sun MC shapes (normalized tounit area) used for the ts to the data. A 2 minimization is used to nd thetotal number of signal events above background. The statistical error in the total
number of signal events is obtained by varying 2 by one unit. Figure 8.8 shows
the minimum and the variations in 2 from the t to the full nal sample with
Ethreshold > 7 MeV.

8.5 Measured Solar Neutrino Event Rate
We use the described method of extracting the number of solar neutrino events foreach subset of the data which is of interest. Speci cally, we apply several di erent
energy thresholds to the nal sample. We also break up the data into day-only andnight-only event samples to look for a day/night di erence. Day is de ned to bewhen the Sun is above the horizon ((dsun )z  0) and night occurs when the Sun
is below the horizon ((dsun )z < 0). As a consistency check, two di erent ducial
volumes are used - the 22.5 kton volume previously mentioned and a 11.7 kton
246

Normalized Probabilities

cosθMC sun

2

χ Value

Figure 8.7: cos sun shapes predicted from the Monte Carlo

Extracted Number of Signal Events

Figure 8.8: 2 minimum for t to background + solar neutrino signal

247

volume (created by making a Dwall  5 meter cut). For each of these subsets ofdata, the t background and signal levels are given in Table 8.2 or Table 8.3.

22.5 kton ducial volume
Ethreshold BG level
BG slope
Signal Excess(MeV) (events) (ev./bin, 80 bins) (events)(events/day)
All data, 148.07 day sample
6.5 MeV 1382.0
14.6
2796  128.0 18.884  0.864
7.0 MeV 1027.5
12.7
2436  111.0 16.452  0.750
6.81757  86.0 11.866  0.518
8.0 MeV 621.9
10.0 MeV 171.2
4.2
737  47.0 4.978  0.317
Day data, 70.17 day sample
6.5 MeV 646.9-22.41330  86.0 18.155  1.226-14.91177  75.0 16.774  1.069
7.0 MeV 480.0
8.0 MeV 289.2-18.9
903  57.5 12.869  0.819
10.0 MeV 79.1
-7.0
364  31.0 5.188  0.442
Night data, 77.90 day sample
6.5 MeV 734.2
37.7
1462  94.5 18.768  1.213
7.0 MeV 546.6
27.9
1257  82.0 16.137  1.053
8.0 MeV 332.0
25.7
848  63.5 10.886  0.815
10.0 MeV 91.3
11.0
367  35.0 4.711  0.449
Table 8.2: 22.5 kton measured signal and background rates

248

11.7 kton ducial volume
Ethreshold BG level
BG slope
Signal Excess(MeV) (events) (ev/bin, 80 bins) (events) (events/day)
All data, 148.07 day sample
6.5 MeV 598.1
4.3
1466  85.5 9.901  0.577
4.71316  77.0 8.888  0.520
7.0 MeV 476.1
8.0 MeV 293.1
1.3
893  59.5 6.031  0.402
10.0 MeV 78.5
0.7
390  32.0 2.634  0.216
Day data, 70.17 day sample
6.5 MeV 278.9-9.4
683  57.5 9.734  0.819-7.3
604  51.0 8.608  0.727
7.0 MeV 221.5
8.0 MeV 136.2-9.3
415  39.0 5.914  0.556
10.0 MeV 35.4
-5.1
178  20.5 2.537  0.292
Night data, 77.90 day sample
6.5 MeV 318.5
14.7
776  63.5 9.962  0.815
7.0 MeV 253.6
13.0
704  57.0 9.038  0.732
8.0 MeV 156.0
11.2
474  44.5 6.085  0.571
10.0 MeV 42.0
5.6
211  24.0 2.709  0.308
Table 8.3: 11.7 kton measured signal and background rates

249

8.6 Eciency
In order to compare the measured rate of solar neutrino events to the SSM predicted
rate, we need to know the eciency of detecting solar neutrino events. The mostlogical way to gure out this eciency is to model precisely what happens to theneutrino interactions in the detector. Given this philosophy, we simulate many
(200,000) solar neutrino interactions in the Super-Kamiokande detector. To do this,we select an energy from the predicted spectrum (Figure 4.1) for each neutrino. Aninteraction point in the 32.5 kton inner volume is selected and the nal kinetic
energy of the scattered electron is chosen from the shape of the energy dependent
scattering cross section. The electron is tracked through the water and the detector
trigger is modeled. The majority of the solar neutrino induced events do not trigger
the detector at all. Once the triggers are generated, the simulated events are sent
through the software lters (lef1 and lef2). The \interactive" cuts are appliedalso, except for the spallation cut. The eciency is calculated:# remaining events vs. generated Etotal = # events generated
with E in full 32.5 ktons (before trigger simulation)(8.2)
Figure 8.9 shows this overall eciency as a function of generated electron energy
for several di erent applied energy thresholds. Note that the maximum eciency
attained is 70%. This is because the e ect of the ducial volume cut is included
in our de nition of eciency. The ratio of ducial volume (22.485 kton) to the fullvolume (32.481 kton) is about 70%.

8.7 SSM Expectation
To calculate the number of neutrino events expected per day from the Standard
Solar Model, we need the overall eciency of detecting and measuring a neutrino
250

Total Efficiency (trigger + software)

Generated Energy (MeV)

Figure 8.9: Total eciency versus generated energy
event, the neutrino-electron scattering cross section, the energy spectrum of theincident neutrinos, and the total calculated ux of solar neutrinos. All of this information has been discussed already (Sections 4.1.1 and 8.6), it just needs to beassembled together for the overall rate calculation.
The total rate of solar neutrino interactions in a perfect detector (Rperfect) is:
Z EmaxZ TmaxE ; Te) dT dE(8.3)
Rperfect = 0 Fssm (E ) 0 Ntarget d(dTe ewhere E is the neutrino energy, Fssm is the SSM calculated neutrino ux at energyE , Ntarget is the number of electron targets in the full inner detector volume, dTde isthe di erential scattering cross section for an electron-neutrino pair, and Te is the
kinetic energy of the scattered electron. The ineciencies and energy resolutionof the detector must be included in order to compare this expected rate to a realmeasurement. To do this:Z EmaxZ TmaxE ; Te)  (T ) dT dE(8.4)
R = 0 Fssm (E ) 0 Ntarget d(dTtotal ee ewhere total is the total eciency for an electron with kinetic energy Te to end
251up in the nal sample (given in Section 8.6). We use the cross section for e , escattering with the radiative corrections applied[75]. For  ,e and  ,e scattering,
Equation 4.1 is utilized. The neutrino spectrum is taken from Bahcall [59]. The
predicted solar neutrino event rates using the BP92 ux [7] of 8B neutrinos (5:69 
106 cm2s ) and the BP95 ux [4] (6:62106 cm2s ) are given in Table 8.4. Two di erent
sets of numbers are presented in the table. The rst section shows the rate ofsolar neutrino interactions in the Super-Kamiokande detector. The second section
includes the e ects of energy our detector's energy resolution and reconstruction the applied threshold is on Ereconstruct.
Perfect detector for all energies
Thresh. Egenerated (MeV)
0

Expected Event Rate in 22.5 kton (events/day)
BP92
BP95
317.6
369.5

Calculated Super-Kamiokande eciency
Thresh. Ereconstruct (MeV)
6.5 MeV
7.0 MeV
8.0 MeV
10.0 MeV

Expected Event Rate in 22.5 kton (events/day)
BP92
BP95
42.81
49.81
35.93
41.80
23.48
27.31
8.27
9.03

Table 8.4: SSM predicted solar neutrino event rates

252

8.8 Systematic Errors
In addition to the statistical error assigned to the measured signal, we will have asystematic error. Systematic uncertainties originate from a variety of places. Eachcontribution which we consider is presented along with the estimated magnitude of
the ux uncertainty. A summary is given at the end of the section.

8.8.1 Fiducial Volume
By looking at the vertex resolution di erence between data and Monte Carlo, we
can estimate the possible error in the total ducial volume of the detector. Table 6.7
shows that di erence to be about 4 cm (Monte Carlo is wider). The resultant error
in the ducial volume is:V = 2R2max Zmax ,2(Rmax ,4cm)2 (Zmax,4cm)
V
2R2max Zmax

Rmax = 1490 cm and Zmax = 1610 cm
 VV 22:5kton = 0:78 %Rmax = 1190 cm and Zmax = 1310 cm
 VV 11:7kton = 0:98 %(8.5)

Since the total number of observed neutrino events is directly proportional to thedetector volume, the error on the neutrino ux is also:
11.7 kton volume: (F )Volume = 0:98%:
22.5 kton volume: (F )Volume = 0:78%:(8.6)

8.8.2 Energy Scale
Since an energy threshold is applied to the data, it is important to know the magnitude of any possible shift in the energy scale. A scale shift may cause an energy cut
which was thought of as E > 7:0 MeV to really be E > 6:85 MeV. The uncertainty
in the energy scale has of several di erent sources. First of all, the input parameters253

to the Monte Carlo simulation were tuned such that the data taken with the nickel
source on one particular day agrees with the simulation of the source. If the gammaray production from the nickel source is not simulated accurately, the Monte Carlowill not produce the appropriate amount of light for a given electron energy. To
estimate the accuracy of the nickel gamma-ray simulation, we compared the on-siteand o -site nickel gamma-ray model. By using two di erent nickel gamma-ray simulations in conjunction with a single detector Monte Carlo, we look at the variationin the mean N50 caused by the di erent gamma-ray generators. A 0:5% di erence
was found between the two.
Table 7.13 shows the agreement between Ne ective for the Monte Carlo of thenickel source and the nickel data at various source positions. The maximal variation between the two is 3.1%, but that is not a fair estimate of the scale uncertainty.
To determine the rms deviation between MC and data, we calculate the weighted
mean deviation and the corresponding weighted rms. We weight by the uncertainty in the Ne ective di erences. By varying the range over which the Gaussian t
to Ne ective distribution is done, we can calculate the mean value of Ne ective (for thenickel data) to only 2%. We assign this 2% uncertainty as the weight to each of
the points. The calculated rms deviation in Ne ective between nickel data and nickel
MC is then 0.77%. Being more conservative, a systematic of 1% is quoted.
Lastly, we have the contribution due to the conversion from Ne ective to totalenergy. When we t Ne ective(E) (described in Section 7.4.4), we calculate errors on
the t parameters. By propagation of errors, we can estimate the uncertainty inthe conversion as a function of energy. This uncertainty is approximately 8  10,3%
above 7 MeV. If three errors are summed together in quadrature, a total error on254the energy scale of 1.12% is found.

Uncertainty
Cause
0.5%
Gamma-ray simulation from nickel source
1.0%
Agreement between nickel data and MC
8  10,3 % Conversion from Ne ective to total energy
1.12%
TOTAL E (added in quadrature)
Table 8.5: Contributions to energy scale uncertainty
The systematic error on the solar neutrino ux (F ) is not equal to the energy
scale systematic. To estimate F , we use our program which calculates the total
expected rate of solar neutrinos given the detector eciency. Purposely, we insert ashift in the energy scale (both upward and downward shifts to check for symmetry)and study how the predicted rate above a 7 MeV threshold changes with the energy
scale shift. We extract the ux uncertainty:(F )Energy Scale = 2:6  EE (%) = 2:6  1:12%(F )Energy Scale = 2:91%:(8.7)

8.8.3 Time Dependence of Energy Scale
We need to evaluate the uncertainty in the ux due to the time dependent correction applied to Ne ective. We do this by varying the functional form of the correction
as a function of date, using the modi ed function to scale the Ne ective values of thedata, and observing the corresponding change in the measured neutrino ux. We
acquire the reasonable range of functional forms by performing many di erent ts
to the spallation product Ne ective distributions and to the time variation of thehNe ectivei. We t Ne ective to a single Gaussian and to a double Gaussian. We also
255try binning the data monthly versus weekly.
We select as maximum and minimum limits the two functions which envelope
the correction function we actually used. By using these limits to correct the
Ne ective and calculate the measured solar neutrino ux, we estimate an uncertainty
in the ux of:(F )Time Dependence = 2:0%:(8.8)

8.8.4 Energy Resolution
If our Monte Carlo does not reproduce the energy resolution of the real detector, ourprediction of the number of expected events above a particular threshold will be o .
The energy resolution describes the spread in observed energies given a particular
generated (or real) energy. When a spectrum of energies is observed by a detector
with nite energy resolution, the shape of the spectrum changes. If the Monte Carlo
has a di erent energy resolution than the data, the measured spectrum shape will
be di erent from the MC prediction. The ux above a particular threshold energy
will also di er between the MC and the data. To estimate the change in theux due to the energy resolution, we determine the energy resolution curves (seeFigure 7.15) which bracket the LINAC data (approximately 56%  5%) and assume
that these curves are characteristic of 2 errors in the resolution. We use these three
resolution curves to generate the shape of fake eciency functions for use in the
SSM predicted rate calculation. The variation in the predicted event rates above
7 MeV was 1:27% at the 2 level. The 1 error therefore corresponds to:(F )Energy Resolution = 0:64%:

256

(8.9)

8.8.5 Signal Extraction
When we extract the number of solar neutrino excess events, we introduce several
places for potential errors. We t the cos sun distribution to the shape predicted by
the Monte Carlo. What if this shape is not representative of the real shape producedby the data? To mimic this problem, we t the data with a threshold of Ethreshold
applied using the Monte Carlo shapes corresponding to Ethreshold  1 MeV. We canthen look at the di erence in the measured ux from using a shape corresponding
to a 1 MeV shift in energy (to get the ux di erence per MeV shift). To computethe actual error, we scale the ux uncertainty per MeV shift by the systematic error
in the energy scale (1.12%). The net result is(F )Signal Shape = 0:25%;(8.10)

the ux uncertainty due to the incorrect cos sun shape.
In addition to using the correct shape for the cos sun distribution, the background level must also be correct. If the background level is mis t or undergoes
large uctuations, the signal above background will be nearly impossible to t reliably. To estimate the maximum magnitude of this potential error, we varied theslope of the background level by 1 and observed how the extracted signal above
background changed. This is a conservative estimate of the maximum value forthe ux error due to the extrapolation of the background shape under the solar
peak. We have already assumed that the shape is consistent with a straight line.
By varying the slope by 1, we are estimating the ux error higher than might beconsidered reasonable. The deviation in the total number of signal events directly
tells us the error in the ux due to variations in the background level. The ux
uncertainties are given in Table 8.6 for several di erent energy thresholds, data
samples, and ducial volumes. These systematic uncertainties are due to the sta257

tistical accuracy of the points included in the background t. They will decrease
with more statistics. They also will go down with an improved t to the functional
form of the background.
Data Sample Fiducial Volume Ethreshold (F )BG Fit
All
22.5 kton
6.5 MeV
3.25%
All
22.5 kton
7.0 MeV
3.16%
All
22.5 kton
8.0 MeV
3.30%
22.5 kton
10.0 MeV 3.87%
AllDay
22.5 kton
7.0 MeV4.50%
Night
22.5 kton
7.0 MeV
4.50%
All
11.7 kton
7.0 MeV
4.03%
Day
11.7 kton
7.0 MeV
5.96%
Night
11.7 kton
7.0 MeV
5.47%
Table 8.6: Systematic ux uncertainty due to B.G. slope

8.8.6 Scattering Cross Section
The uncertainty is fairly small in the scattering cross section. The major contributing value is the uncertainty of 0.2% on sin2 W . The ux error is conservatively takenas:(F )Cross Section = 0:5%:(8.11)

8.8.7 Total Systematic Error
Each of the contributions to the systematic error on the solar neutrino ux has beenpresented. These errors are typically combined together so that a single systematic258

uncertainty is quoted for the ux. It is standard practice to add the component
errors in quadrature to yield a 1 total ux error. Although there are reasonablearguments against such practice, we have no other way of interpreting the meaningof the systematic error. For those who prefer to handle systematic errors in adi erent way, Table 8.7 provides a summary of all the contributions considered. A
shortened summary of the total error (adding in quadrature) is given in Table 8.8.
Contribution

Energy Error Flux Systematic Error

Fiducial volume
Nickel gamma-ray simulation
0.5%
MC/data agreement
1.0%
Ne ective to MeV conversion 8.0 10,3%
Net Flux error
Time dependence
Energy resolution
Signal shape
Background Fit
e + e cross section

0.78% - 0.98%

2.6%  Energy error
2.0%
0.64%
0.25%
3.16% - 5.96%
0.5%

Table 8.7: Components of the total systematic error on solar neutrino ux

8.9 Measured Solar Neutrino Flux
Tables 8.9 and 8.10 display the solar neutrino ux results and the data/SSM ratios
for the two ducial volumes analyzed. Note that the data/SSM ratios are not equal
to 1.0, indicating that we are observing fewer solar neutrinos than predicted. Also,
there is an energy dependence to the data/SSM ratio. This could be caused by a259

Sample
All
All
All
All
Day
Night
All
Day
Night

Volume22.5 kton
22.5 kton
22.5 kton
22.5 kton
22.5 kton
22.5 kton
11.7 kton
11.7 kton
11.7 kton

Ethreshold Total Systematic Error
6.5 MeV
4.94%
7.0 MeV
4.88%
8.0 MeV
4.97%
10.0 MeV
5.37%
7.0 MeV
5.84%
7.0 MeV
5.84%
7.0 MeV
5.51%
7.0 MeV
7.05%
7.0 MeV
6.64%

Table 8.8: Total systematic error on solar neutrino ux
systematic problem in the energy scale or by the neutrino spectrum being distorted(as may happen in neutrino oscillations).

8.10 Measured Di erential Energy Spectrum
To further explore the apparent energy dependence of the data/SSM ratio, we examine the di erential energy spectrum of the data. Figure 8.10 shows the backgroundsubtracted energy distribution of the nal sample events above 6.5 MeV. The background subtraction was performed by assuming the region with cos sun  0:5 (S)contains the solar neutrino signal plus background and ,1  cos sun < 0:5 (B) has
background only. We assume the background level is at (see Section 8.4) withcos sun and simply subtract S , B3 energy bin by energy bin. The result is the data
distribution shown in Figure 8.10. The last bin contains all events above 14 MeV.
Statistical errors only are given on all three plotted distributions.
260

Ethreshold

22.5 kton Fiducial Volume




FData
FSSM BP92

FData
FSSM BP95 (statistical error)  (systematic error)
All data
6.5 MeV 0.441  0.020  0.022 0.379  0.017  0.019
7.0 MeV 0.458  0.021  0.022 0.394  0.018  0.019
8.0 MeV 0.504  0.025  0.025 0.434  0.021  0.021
10.0 MeV 0.602  0.038  0.032 0.517  0.033  0.028
Day data
6.5 MeV 0.443  0.029
0.381  0.025
7.0 MeV 0.467  0.030  0.027 0.401  0.026  0.024
8.0 MeV 0.548  0.035
0.471  0.030
10.0 MeV 0.627  0.053
0.539  0.046
Night data
6.5 MeV 0.438  0.028
0.377  0.024
7.0 MeV 0.449  0.029  0.026 0.386  0.025  0.023
0.399  0.030
8.0 MeV 0.464  0.035
10.0 MeV 0.569  0.054
0.489  0.047
Table 8.9: Ratios of measured  uxes in 22.5 kton to the SSM predictions

261

Ethreshold

11.7 kton Fiducial Volume




FData
FSSM BP92

FData
FSSM BP95 (statistical error)  (systematic error)
All data
6.5 MeV 0.446  0.026
0.384  0.022
7.0 MeV 0.477  0.028  0.026 0.410  0.024  0.023
8.0 MeV 0.500  0.033
0.426  0.021
10.0 MeV 0.614  0.050
0.528  0.043
Day data
6.5 MeV 0.439  0.037
0.377  0.032
7.0 MeV 0.462  0.039  0.033 0.397  0.034  0.028
8.0 MeV 0.486  0.046
0.418  0.039
10.0 MeV 0.591  0.068
0.508  0.059
Night data
6.5 MeV 0.449  0.037
0.386  0.039
7.0 MeV 0.485  0.039  0.032 0.417  0.034  0.028
0.426  0.028
8.0 MeV 0.500  0.033
10.0 MeV 0.632  0.072
0.543  0.047
Table 8.10: Ratios of measured  uxes in 11.7 kton to the SSM predictions262

# events/MeV

Reconstructed Electron Energy (MeV)

Figure 8.10: Di erential energy spectra from the data and Monte Carlo prediction
Also given in Figure 8.10 is the SSM predicted spectrum. This distribution
comes from a Monte Carlo simulation of solar neutrinos with the predicted energy
distribution. The same background subtraction is applied to the MC as with thedata. The BP95 SSM distribution has been scaled to contain the predicted number of events our analysis would see over 148.2 live days. The third distribution
displayed in Figure 8.10 is the SSM spectrum scaled down by the observed integral
data/SSM ratio above a 7 MeV threshold (given in Table 8.9). Observe that thescaled down SSM and the data do not appear to have the same shape.
Since the prediction of a distorted energy spectrum is one of the keys to newneutrino physics, we want to further study the shape of the di erential energy spectrum. We can plot the ratio of the observed spectrum to the predicted spectrum.
If the neutrino spectrum is not distorted, the data/SSM ratio will be constantwith energy. Figure 8.11 shows the data/SSM ratio as a function of reconstructed
electron energy. The last bin contains all events above 14 MeV. The error bars
263

Data / BP95 SSM per 1 MeV Energy bin

indicate the statistical errors only. The systematic errors as a function of energy
have not yet been evaluated. Given these statistical errors, the probability that
this distribution ts to a at line is <1% (2 = 22.3, # DOF = 8).

Reconstructed Electron Energy (MeV)

Figure 8.11: Spectral shape of the data relative to the SSM prediction
The shape (slope) of the distribution in Figure 8.11 is greatly a ected by energy
dependent systematic errors which have not yet been evaluated. We have evaluatedthe e ect of these energy errors on the integral ux above various thresholds. The
contribution to the systematic errors on the di erential energy ux will be di erent. These systematics are currently under study and will not be presented here,
therefore Figure 8.11 should always be considered cautiously.

264

Chapter 9Interpretation and Conclusions

9.1 Comparison with On-Site GroupAs was mentioned previously, this dissertation describes only one of the solar neutrino analyses being performed by the Super-Kamiokande collaboration. A second
independent group based at the experimental site (On-Site group) also analyzes
the low energy data. The only thing the two groups have in common is that theyboth have access to the same calibration data and both lter and analyze the sameraw data. The philosophies driving the two groups are remarkably divergent. This
leads to very dissimilar ltering algorithms and analysis techniques. The fact thatthings are so di erent has made performing direct comparisons between the twogroups quite challenging. On the other hand, the same result from two independent analyses signi cantly increases the con dence in the robustness of the result.
The On-Site Low Energy group does most of their analysis o -line and in semireal time. A farm of Sun workstations grabs the data out of memory (where the`TQ real' process places the data) and starts ltering. The lter operates in several
stages and includes some `junk' cuts, a vertex tter and ducial volume cut, anda single muon tter. They apply good run criteria, implement spallation cuts, and265

calculate energies using a di erent de nition of Ne ective from this analysis. Noneof the details will be given here as they will be described in another dissertation [76].
Table 9.1 contains a summary of the On-Site groups' solar neutrino ux results
and the results presented in this dissertation. The total ux given in the table isthe total number of 8B neutrinos at all energies that must be coming from the Sun
in order to produce the measured signal in Super-Kamiokande above the energy
threshold. It is assumed that the neutrinos have the theoretically predicted energy
spectrum. The current On-Site data sample contains 201.6 days and is larger thanour data sample of 148.2 days. Note that one group has asymmetric errors while
the other uses equal  errors (taken as the largest of the asymmetric values).

Total Flux Results
Ethreshold Volume Our FData
On-Site FData(MeV) (kton) (106 cm2s )(106 cm2s ) (statistical error)  (systematic error):09 +0:14
6.5
22.5 2.51 0:11 0:13 2.65 +0,0:08 ,0:10:11 +0:13
6.5
11.7 2.54 0:15
2.62 +0,0:10 ,0:09:09 +0:15
7.0
22.5 2.61 0:12 0:13 2.70 +0,0:08 ,0:10:11 +0:15
7.0
11.7 2.71 0:16 0:15 2.68 +0,0:11 ,0:10
Table 9.1: Comparison of independent solar neutrino ux results
Table 9.2 gives the fractional day/night ux di erences as measured by the
On-Site group and as given in this dissertation (for comparison purposes). Our
systematic errors on the fraction have not been studied yet. Some of the contributions to the day and night ux uncertainties will cancel; others will not.
266

Day versus Night Fluxes
D,N
Ethreshold Volume
D+N(MeV) (kton)
This Thesis
On-Site
6.5
22.5 -0.017  0.047 +0.004  0.031  0.017
6.5
11.7 -0.012  0.059 -0.048  0.040  0.017
7.0
22.5 +0.019  0.046 +0.004  0.033  0.017
7.0
11.7 -0.024  0.058 -0.046  0.043  0.017
Table 9.2: Comparison of independent day/night ux di erences
These ux and day/night results results and those from the On-Site group arein good agreement. Although the two groups are using completely di erent vertex
tters, energy reconstruction, and event selection, getting the same answer fromboth groups boosts our con dence in the results from this experiment.

9.2 Comparison with Previous Results
In order to gauge the impact of these new solar neutrino results, a comparison ismade against the most recent published results from the Kamiokande experiment,
our predecessor. The Kamiokande results are shown in Table 9.3. Note that theresults presented in this dissertation agree with the previous results, but have muchsmaller errors.

267

Previous Results from Kamiokande (680 m3):25
6 
Total Flux (E> 7 MeV) [15]2.82 +0,0:24  0.027 10 cm2 s
D,N (E> 9:3 MeV & E> 7:5 MeV) [77]+0.08  0.11  0.03
D+N
Table 9.3: Prior experimental solar neutrino results

9.3 Neutrino Oscillation Interpretation
One of the proposed explanations to the apparent lack of solar neutrinos is neutrino avor oscillations, possibly enhanced by the MSW mechanism. The basic
concepts behind neutrino oscillations and the MSW mechanism are discussed in
Section 1.6.6. Within this framework, the two oscillation parameters, sin2 2# andm2, determine what the measured ux should be. The most straightforward way
to gure out which values of the parameters yield solar neutrino uxes which areconsistent with our measurement is to compute the predicted event rate in SuperKamiokande for every set of parameters. Allowed sets of parameters will yielduxes within the errors on our measured ux and the SSM predictions. A contour
plot (`oscillation plot') can then be made showing the allowed regions of parameter
space.
We need to compute the predicted event rate our analysis would measure formany di erent sets of oscillation parameters. Our method requires the calculationof the energy dependent e survival probability out of the Sun (P (E )) for each setof mixing parameters. The survival probability can then be multiplied by the SSM
e ux (Fssm (E )) to yield the oscillation modi ed e spectrum. From this point
on, we follow the calculation described in Section 8.7. The predicted event rate

268

Rosc is:Z EmaxRosc = 0

Z TmaxPosc(E )Fssm (E ) 0

E ; Te)  (T ) dT dE
Nelec d(dTtotal e
e 
e

(9.1)

where Nelec is the number of electrons in the full inner volume of Super-Kamiokande,d(E ;Te) is the di erential cross section for scattering between a neutrino of energy
dTeE and an electron with kinetic energy Te, and total is the total eciency including
the ducial volume selection for an electron with kinetic energy Te to end up in the
nal sample (given in Section 8.6). Using the above general formula and particularsurvival probability functions, we will compute the expected event rates in SuperKamiokande for every set of oscillation parameters which we consider.

9.3.1 Vacuum Oscillations
We rst consider vacuum neutrino oscillations. In order to calculate Rvac, we needto determine the survival probability Pvac(E ). From Section 1.6.6, we know thesurvival probability for detecting a e with energy E after traveling a distance r:"2
Pvac(e ! e) = 1 , sin2 [2#] sin2 4Emhrc


#

(9.2)

We directly use this equation to estimate the loss in the e signal as the neutrinos
travel out of the Sun or from the Sun to the Earth. Figure 9.1 shows an example ofthe energy dependence of Pvac over the solar neutrino energy range. The probability
Pvac(E ) oscillates more rapidly than the sampling energy bin size used to plot thefunction; Pvac(E ) in the region below 2 MeV always oscillates between 0.4 and 1.
We use Equation 9.1, the probability Pvac(E ), and the travel distance of theneutrino to compute Rvac. When we consider oscillations occurring inside of theSun, we need to remember that all neutrinos are not created at the center of theSun. To properly account for the range in neutrino path lengths required to exit
269

Vacuum Oscillation νe Survival Probability

Neutrino Energy (MeV)

Figure 9.1: Vacuum oscillation survival probability
the Sun, we should integrate over the radial probability distribution (shown in Figure 9.2) for the 8B neutrino production. After the neutrinos leave the Sun, we
assume that they all travel the same distance before being detected on Earth. The
Earth-Sun distance changes by 2% with the Earth's location along its orbit. We
have not accounted for this variation in this calculation.
To determine the allowed regions in vacuum oscillation parameter space, we
compute Rvac(m2; sin2[2#]) for sets of oscillation parameters. We then make aplot showing which parameter values yield an expected ux which is within errorsof our measurement. This analysis was performed using our ux measurement corresponding to Ereconstruct > 7 MeV. Figures 9.3 through 9.5 show the parameterregions allowed at the 90% con dence level (CL) when the various errors are combined together in di erent ways. The measured ux has statistical and systematic
uncertainties. Uncertainties also exist for the predicted ux and were given in Table 1.1 (we use the BP95 ux and corresponding uncertainties). For Figure 9.3,
we compute the 90% CL using only the statistical error on the measurement. If270

B ν Production Probability
8Radius/Solar RadiusFigure 9.2: Radial dependence of the probability to produce a 8B neutrino

22∆ m (eV )we assume that the three errors are independent and add them in quadrature, we
get the allowed region shown in Figure 9.4. If we take the worst case and add thethree errors linearly, we get the region given in Figure 9.5. Note that in much of
the parameter space shown in the Figures, the MSW e ect must be considered.

2

sin 2θ

Figure 9.3: Allowed vacuum oscillation parameters using stat only.

271

2

2

∆ m (eV )2

sin 2θ

22∆ m (eV )2 +  2 +  2 )1=2.
Figure 9.4: Allowed vacuum osc. parameters using (stat
syst
theo

2

sin 2θ

Figure 9.5: Allowed vacuum osc. parameters using (stat + syst + theo).

272

9.3.2 MSW Enhanced Oscillations
The computation of the allowed regions in the oscillation parameter space for MSW
oscillations involves much more computation than the vacuum oscillation case. To
compute the survival probability Pmsw(E ), we need to numerically integrate thetime evolution of the neutrino wavefunction as it travels out of the Sun. The
wavefunction time evolution is given in Equation 1.11 with H reduced down to:2
2
26 1
H = 21p m1 +2 m2 64

3
0 77
5

0 1



2
1 m2 66 A
2p 2 4, cos 2#sin 2#

3
sin 2# 77
5

cos 2#

(9.3)

23

3

Electron Density in the Sun (10 e / cm )where A is the contribution to the Hamiltonian induced by the forward  , e scattering (the matter term added by Wolfenstein). A is proportional to the electron
number density Ne at the location of the neutrino. Figure 9.6 shows the variationin Ne as a function of the distance from the core of the Sun.

Radius/Solar RadiusFigure 9.6: Radial dependence of the electron number density
The rst term contributes an overall phase to the wavefunction and can therefore be neglected from the mixing probability. To perform the actual integration,
273

MSW Oscillation νe Survival Probability

we consider this to be a one-dimensional problem. It is assumed that the neutrino
traveled outwards along a radial path from the production point to the surface of
the Sun. We break up the total distance traveled into small intervals. For eachinterval, we compute the change to the real and imaginary components of the mass
eigenstate wavefunctions (j1i and j2i). The corresponding evolution for the weakforce eigenstates (jei and jxi) is computed. When the neutrino exits the Sun, we
can compute the resultant survival probability Pmsw(E ) assuming only the MSW
enhancement of the oscillations in the Sun. An example of Pmsw (E ) is given in
Figure 9.7.

Neutrino Energy (MeV)

Figure 9.7: MSW oscillation survival probability at the Sun's surface
After the neutrino reaches the edge of the Sun, we stop using the matterenhanced oscillation probability. We continue to evolve the neutrino wavefunction
assuming vacuum oscillations as the neutrino travels to the Earth. Once it arrives
at the Earth, we can compute the survival probability for the neutrino to be detected in the jei state.
274

As with the vacuum solution, Figures 9.8 through 9.10 show the MSW parameterregions allowed at the 90% con dence level (CL) for di erent error combinations.
Figure 9.8 uses only the statistical error. If we add them in quadrature, we get theallowed region shown in Figure 9.9. For linear error addition, we get the region
given in Figure 9.10. To enable comparisons with previous experimental results
and interpretations, we also give the contours assuming the older SSM, BP92, inFigures 9.11 through 9.13. The contours of the allowed regions implied from theseresults are in good agreement with the previously published contours.

9.3.3 Di erential Energy Spectrum
When attempting to extract the MSW parameters which best t the di erential
spectrum (Figure 8.11), the e ect of the energy resolution can not be forgotten.
The combination of the SSM spectral shape and the detector resolution leads to adi erence in the relative shapes of the post-MSW spectrum and the SSM spectrum:Fmsw (Egenerated) 6= Fmsw(Ereconstruct)
FSSM(Egenerated) FSSM(Ereconstruct)
The generated electron energy distributions (from both SSM and MSW a ected
neutrinos) must be folded with the energy resolution function in order to correctly compare the predicted shape distortion with the measurement from SuperKamiokande.
A correct oscillation interpretation of the spectral shape of the data can not be
performed without the proper inclusion of the systematic errors. The systematic
errors on the di erential energy spectrum have not been given in this dissertation.
The study of these systematics is ongoing. Therefore, an oscillation interpretationof the spectrum is not presented here.
275

2

2

∆ m (eV )2

sin 2θ

22∆ m (eV )Figure 9.8: Allowed MSW parameters using stat only.

2

sin 2θ

2 +  2 +  2 )1=2.
Figure 9.9: Allowed MSW parameters using (stat
syst
theo

276

2

2

∆ m (eV )2

sin 2θ

22∆ m (eV )Figure 9.10: Allowed MSW parameters using (stat + syst + theo).

2

sin 2θ

Figure 9.11: Allowed MSW parameters using BP92 and stat only.

277

2

2

∆ m (eV )2

sin 2θ

22∆ m (eV )2 +  2 +  2 )1=2.
Figure 9.12: Allowed MSW parameters using BP92 and (stat
syst
theo

2

sin 2θ

Figure 9.13: Allowed MSW parameters using BP92 and (stat + syst + theo).

278

9.4 Implications
Super-Kamiokande has made a more accurate measurement of the solar neutrino
ux and has con rmed the apparent de cit in the total ux of neutrinos from theSun. The measured ux is 2.61 0:12 (stat) 0:13 (syst) 106 cm2s using the data
above Ethreshold > 7 MeV. The measurement is low compared to the Standard Solar
Model calculations (BP95) of 6.62 106 cm2s for the 8B ux.
It is apparent from the measured uxes from the DAY and NIGHT data samples, that we have no statistically signi cant day/night ux di erence. The large
angle MSW oscillation solution predicts a day/night ux di erence (the `day/nighte ect') which can be as large as a 50%. The current data sample does not havethe statistical accuracy to rule out the large angle solution yet. After 3 years ofoperation, the statistical errors should be reduced by a factor of 2. To improve thestatistical accuracy on the day/night measurement further, work must be done tosigni cantly reduce the background level while maintaining or increasing the totaleciency for saving the solar neutrino events.
The next step for Super-Kamiokande will be an in depth study of the energy
distribution of the solar neutrinos and the energy dependent systematic errors. We
can not actually measure the neutrino energies, but we measure the electron energies after the  , e scattering. We can compare the shape of the measurement
to the shape of the predicted spectrum. We would look for any visible spectral
distortions which would indicate new neutrino physics (such as MSW-enhanced
oscillations). Such a distortion is predicted by the nonadiabatic MSW avor oscillation solution. No changes to the Standard Solar Model will induce a change inthe energy spectrum for the neutrinos. Unaccounted for systematics in the energy279

scale and the energy resolution can mock the spectral distortion typically associated with neutrino oscillations. These systematics must be studied and reduced
before a meaningful interpretation of the di erential energy spectrum measured bySuper-Kamiokande can be made. Using both the day/night ux di erence and themeasured energy spectrum, Super-Kamiokande should provide strong evidence foror against neutrino avor oscillations.
The other two new solar neutrino detectors, SNO and Borexino, are not yet taking data. When they turn on, what burning questions will they need to answer? A
neutral current measurement by SNO would be a powerful addition to our current
base of knowledge. SNO's neutral current measurement would explicitly measure
the total number of neutrinos (of all 3 avors) reaching the SNO detector fromthe Sun. Even if Super-Kamiokande were to assert which of the possible explanations to the Solar Neutrino Problem was most supported by the Super-Kamiokande
data, an independent con rmation would still be needed to convince the world-widescienti c community. SNO could provide this con rmation by demonstrating thefraction of neutrinos which are e, although not in the next year or two due to theirschedule.
Borexino's measurement of the 7Be ux would directly address the \second
Solar Neutrino Problem". Prior to Super-Kamiokande results and recent theoreticalimprovements to the Standard Solar Model, reasonable agreement between theexisting solar neutrino measurements seemed to require a very small or negativeux of 7Be neutrinos. It remains to be seen if this 7Be requirement still holds whenSuper-Kamiokande results are combined in with the others. Either way, Borexino
should be the rst detector to observe the 7Be neutrinos explicitly.
280

9.5 Future WorkThe results presented in this dissertation are the rst solar neutrino results fromthe Super-Kamiokande experiment. There is plenty of work still to be accomplishedand many physics studies that may be performed using the Super-Kamiokande Low
Energy data. The immediate tasks at hand are:

 Veri cation of and improvement in the accuracy of our absolute energy calibration:
The energy scale is one of the two largest contributors to the systematic
error in the ux. If we can improve the agreement between the Monte Carlosimulation and the calibration data, we can reduce our uncertainty in theenergy scale. The contribution to the overall ux systematic error can then belowered. The LINAC and titanium source data will provide needed constraints
for our energy calibration.

 Investigation into a more appropriate shape for the background t in thecos sun distributions for ALL, DAY, and NIGHT data samples:
We have approximated the shape of the background as a straight line whichis extrapolated under the solar neutrino peak. We know that the exposureof Super-Kamiokande to the Sun is not the same during day and night. We
also know that we do not have an isotropic background. Obtaining the correctfunctional t to the background will require a study of the detector's exposure
to the Sun and the background distributions. By improving the shape of thet, we should further reduce the systematic error on the ux.
281 Addition of reasonable cuts which remove problematic background events:
Our ability to reduce the background must improve. We will continue tocollect additional solar neutrino candidate events. We will also work to reduce
our systematic errors. The best way to improve the statistical signi cance ofSignalour solar neutrino signal is to improve the pBackgroundfor our data set. We
need to lower the background level to improve the signi cance of our signal.

 Continued re nement of the Monte Carlo simulation program:
Recently, the High Energy Analysis group determined that some of the tuned
parameters in the Monte Carlo detector simulation did not reproduce several
important features in the high energy regime. Since both analysis groups use
a single simulation program, we must work to determine a new, improved setof input parameters.

 Study of the allowed regions in oscillation parameter space produced by theALL, DAY, and NIGHT uxes:
In this dissertation, we have only discussed the parameter regions allowed by
the total ux measurement above 7 MeV. Further work should continue using
the results corresponding to other energy thresholds. Also, we should accountfor the possible matter enhanced oscillations occurring near the Earth's core.
The di erences between the day and night uxes are the key to possible
regeneration in the Earth. Excluded regions in the oscillation parameter
space based on the day/night di erence need to be studied.

282 Production of a solar neutrino induced electron energy spectrum with systematic errors relative to the expected shape from theoretical particle physics:
The spectrum is the next experimental key available to Super-Kamiokande
which may indicate the source of the apparent solar neutrino de cit. If SuperKamiokande should measure a spectral distortion, new neutrino physics would
be required as an explanation. For example, a change in the spectral shapeis predicted by the nonadiabatic MSW oscillation solution. The energy dependent systematic errors must be included when the spectrum shape is interpreted.

 Demonstration of Super-Kamiokande's ability to properly measure an electron energy spectrum:
In order for any solar neutrino spectral measurement to be believed, we mustshow our ability to correctly measure a distribution of energies from someknown sources. A comparison of the measured energy spectrum and the
expected shape for spallation products and a decay calibration source should
prove the reliability of the measurement and analysis techniques.

283

Appendix A
Zebra BanksThe Super-Kamiokande data format is a set of zebra banks [44]. A zebra bank isa block of information with some space set aside for `links' to neighboring zebrabanks. The rest of the space contains data in a particular format. Zebra banks are
typically created in a mother-daughter environment so that a new `child' bank islinked with an existing `mother' bank. The routines to read, write, modify, create,
and whatever else you want to do with zebra banks were written and supported by
CERN. A map of the zebra banks in a data le is like a road map in a big city, it
tells you where the interesting data is located. The nice thing about zebra les isthat the directions remain constant, even if a new `street' is added along the way
to the destination. If the data was stored in an array, you would need to know if
an extra piece of information got added in the middle of the array in order to index
the array correctly. That type bookkeeping is hidden from the zebra user.
Super-Kamiokande's data contains many di erent zebra banks. Table A.1 lists
the various banks that are found in the data, the relationship between various
banks, and what information is contained in the bank. Tables A.2 through A.6
detail the information stored in many of the banks and the type of variables whichhold that information.
284

Bank Mother

Contents

EMB
Main structural link for event
HEAD EMBHeader information
AHEA EMB
Anti-header information
TQ
EMB
PMT data (On-Site format)
EVIN EMBTime of previous event
HDRI EMBPMT charge calibration information
CALI EMB Inner detector PMT data (O -Site format)
CALO EMB Outer detector PMT data (O -Site format)
USSK EMB Structural link for all O -Site created banks
USMC USSK
O -Site MC information
TRAK USSK
Generic track storage bank
MCPT TRAK
MC particle non-track information
LEF1 USSK
lef1 lter information
THR1 USSK
THR1 t parameters
THR2 USSK
THR2 t parameters
FSTM USSKFSTMU t parameters
HAYA USSK
Hayai t parameters
LEF2 USSK
lef2 lter information
MBOY USSK
Muboy t parameters
COMB USSK
Combo t t parameters
CUBE USSK
Cubist tag and exposures
Table A.1: Names of zebra banks and information contained in each bank285

Fieldrun moderun
sub runevent
yr mth day
hr min sec
clock48
trg idtrg event counter
event ag
tko statusservers

Storage Description
int
int
int
int
int
int
int[3]
int
int
int
int[2]
int[56]

mode of run
run number
sub run number
event number
y*10000 + m*100 + d from computer clock
h*10000 + m*100 + s from computer clock
48 bit clock
trigger type from TRG
TRG event counter
event ag
TKO statusserver (workstation) status

Table A.2: Description of HEAD bank286

FieldStorage Description

local to gps
gps sec

int
int

gps usec
local trig
local bip

int
int
int

tdc to trg1
tdc to trg2
tdc to trg3
tdc to trg4
fscc busy
calib version

int
int
int
int
int
int

50 MHz clock to interpolate GPS clock# seconds from the GPS clock since January 1,
1970 in a time zone 9 hours West of UT# microseconds from the GPS clock
local clock at time of trigger
local clock at end of Busy In Progress signal from
FSCCs
tdc to trg time in Hut 1
tdc to trg time in Hut 2
tdc to trg time in Hut 3
tdc to trg time in Hut 4
fscc busy ags
version # of the applied OD calibration constants

Table A.3: Description of AHEA bank287

FieldStorage

Description

ngood
int
# \good" hit tubes
nbad
int# \bad" hit tubes
tube struct[ngood]
PMT data
struct contains:
numberint
tube number
statusint
status wordtimeoat
PMT time in ns
chargeoat
PMT charge in \photoelectrons"
Table A.4: Description of CALI and CALO banks288

Fieldversioncut version
date
run date
class
trash
time since ped
tot ID hit
inner max hits
time inner maxhits
tot OD hit
outer max hits
time outer maxhits
inner charge
track goodness
through goodness
zenith cosine

Storage Description
int
int
int
int
int
int
int
int
int
oat
int
int
oat
oat
oat
oat
oat

version # of lef1 code
version # of cut parameters
date lef1 was compiled
date lef1 was executed on the data
event classi cations from lef1
tag returned from Trashmantime [s] since end of last pedestal period
total # ID PMT hits
max. # ID hits in 200 ns residual window
beginning time of the 200 ns ID window
total # OD PMT hits
max. # OD hits in 200 ns residual window
beginning time of the 200 ns OD window
total charge in ID
goodness of t from anis track routine
total time residual from THR2 t
z direction cosine from THR2 t

Table A.5: Description of lef1 bank289

Fieldversioncut version
date
run dateclassclass same as lef1
goodbadminbiasupgoingtime since mu

Storage Description
int
int
int
int
int
int
int
int
int
oat

version # of lef2 code
version # of cut parameters
date lef2 was compiled
date lef2 was executed on the data
event classi cations from lef2
ag = 1 if class has not changed from lef1
good&bad data ag for subrun
ag = 1 if minimum bias event
ag = 1 if upgoing muon event
time in s since the last muon

Table A.6: Description of lef2 bank290

References[1] J. Bahcall, Neutrino Astrophysics, Cambridge University Press, Cambridge,
1989.
[2] See for example [4] or S. Turck-Chieze and I. Lopes, Astr. Jour., 408, 347(1993).
[3] Totsuka, Y., University of Tokyo (ICRR) Report ICRR-Report-227-90-20(1990).
[4] J. Bahcall and M. Pinsonneault, Rev. Mod. Phys., 67, 781 (1995).
[5] J. Bahcall and R. Ulrich, Rev. of Mod. Phys., 60, 297 (1988).
[6] W. F. Huebner, et.al., \Astrophysical Opacity Library," Los Alamos Scienti cLaboratory Report No. LA-6760-M, 1977.
[7] J. Bahcall and M. Pinsonneault, Rev. Mod. Phys., 64, 885 (1992).
[8] R. Davis Jr., Phys. Rev., 97, 766 (1955).
[9] J. Bahcall and R. Davis Jr., Essays in Nuclear Astrophysics, Cambridge University Press, Cambridge, 1982.
[10] R. Davis Jr., D. Harmer, and K. Ho man, Phys. Rev. Lett., 20, 1205 (1968).

291

[11] J. K. Rowley, B. T. Cleveland, and R. Davis Jr., Proc. Conf. on
Solar Neutrinos and Neutrino Astronomy (Homestake, S.D. 1984), eds.
M. L. Cherry, K. Lande, and W. A. Fowler, AIP Conf. Proc. 126 (AIP, New
York, 1985)[12] B.T. Cleveland et.al., Nucl. Phys. (Proc. Suppl.), B38, 47 (1995).
[13] K. S. Hirata et.al., Phys. Rev., D44, 2241 (1991).
[14] K. Inoue, Ph.D. Thesis, Univ. of Tokyo (1993).
[15] Y. Fukuda et.al., Phys. Rev. Lett., 77, 1683 (1996).
[16] A. Abazov et.al., Phys. Rev. Lett., 67, 3332 (1991).
[17] P. Anselmann et. al, Phys. Lett., B285, 376 (1992).
[18] R. Wink et.al., NIM, A329, 541 (1993).
[19] GALLEX Collaboration, Phys. Lett., B327, 377 (1994).
[20] J. N. Abdurashitov et.al., Nucl. Phys. (Proc Supp.), B38, 60 (1995).
[21] N. Hata, S. Bludman, and P. Langacker, Phys. Rev., D49, 3622 (1994).
[22] V. Castellani et.al., Phys. Rev., D50, 4749 (1994).
[23] V. Castellani, S. Degl'Innocenti, and G. Fiorentini, Astr. Astrophysics, 271,
601 (1993).
[24] C. Arpesella, Nucl. Instr. and Meth., A350, 327 (1994).
[25] P. Anselmann et.al., Phys. Lett., B342, 440 (1994).
[26] A. Cumming and W. Haxton, Phys. Rev. Lett., 77, no. 21, 4286 (1996).
292

[27] L. Wolfenstein, Phys. Rev., D17, 2369 (1978).
[28] S. P. Mikheyev and A. Y. Smirinov, Nuov. Cim., 9, 17 (1986).
[29] T.K. Kuo and J. Pantalone, Rev. Mod. Phys., 61, 937, (1989).
[30] N. Hata and P. Langacker, Phys. Rev. D, 50, 632 (1994).
[31] G. T. Ewan et.al., \Sudbury Neutrino Observatory Proposal," Report No.
SNO-87-12 (1987) (unpublished).
[32] T. Kovacs et.al., Solar Phys., 128, 61 (1990).
[33] D. Chen, private communication.
[34] Y. Fukuda et.al., \Development of the Data Acquisition System for SuperKamiokande," Super-Kamiokande Report SKAM-95-03 (1995).
[35] R. Claus et.al., NIM, A261, 540 (1987).
[36] A. T. Suzuki et.al., \Improvement of 20-Inch Diameter PhotomultiplierTubes," KEK Preprint 92-50 (1992).
[37] Y. Fukuda et. al., \Development of the Data Acquisition System for SuperKamiokande," Super-Kamiokande Report SKAM-95-03 (1995).
[38] M. Shiozawa, M.S. Thesis, Univ. of Toyko (1994).
[39] TKO Speci cations, KEK Report 85-10, November 1985.
[40] J. Flanagan and M. Masuzawa, \Study of Super-Kamiokande Inner Detector
Front End Electronics," (1994).
[41] LeCroy spec sheet at http://www.lecroy.com/, April 1996.
293

[42] Z. Conner et. al., \Monte Carlo Results of Trigger Schemes," SuperKamiokande Report SKAM-93-03 (1993).
[43] M. Shiozawa, personal communication.
[44] \Zebra, Overview of the ZEBRA System," CERN Program Library Q100 and
Q101 (1995).
[45] T. Haines, Z. Conner, et.al., \Super-Kamiokande Calibration: An Interim Report," (1994).
[46] See the Super-Kamiokande Collaboration Meeting Notes from November 1995,
April 1996, and July 1996 for descriptions of the xenon calibration system.
[47] Z. Conner et.al., \Status Report of Laser Calibration System," (1995).
[48] K. Inoue, Ph.D. Thesis, Univ. of Tokyo (1993).
[49] H. S. Park, Ph.D. Thesis, University of Michigan (1985).
[50] A. Melissinos, Experiments in Modern Physics, Academic Press Inc., New
York, 1966.
[51] Nucl. Data Tables, A3, 369 (1969).
[52] Neutron Sources: For Basic Physics and Applications, Pergamon Press, New
York, 1983, p. 7.
[53] K. Inoue and Y. Suzuki, \Improvement of Ni(n, )Ni' Calibration Source forthe Delayed Coincidence Method," Super-Kamiokande Report SKAM-94-07(1994).
[54] J.F. Briesmeister, \MCNP: A General Monte Carlo N-Particle Transport
Code," LA-12625-M.
294

[55] M. Nakahata and K. Nishikawa, \Electron LINAC for the Calibration of SuperKamiokande," Super-Kamiokande Report SKAM-93-04 (1993).
[56] M. Morita, Beta Decay and Muon Capture, W.A. Benjamin, Inc., Reading,
Massachusetts, 1973, p. 276.
[57] T. Suzuki, D.F. Measday, and J.P. Roalsvig, Phys. Rev., C35, 2212 (1987).
[58] E.K. Warburton, D.E.Alburger, and D.J. Millener, Phys. Rev., C29, 2281
(1984).
[59] J.N. Bahcall et.al., \Standard Neutrino Spectrum from 8B Decay," IASSNSAST 95/47.
[60] L. B. Okun, Leptons and Quarks, North-Holland Publishing Company, New
York, 1982, p. 138.
[61] W.R. Nelson, H. Hirayama, and D.W.O. Rogers, \The EGS4 Code System,"
SLAC-Report-265 (1985).
[62] D.W.O. Rogers, NIM, 227, (1984) 535.
[63] Z. Conner, \Low Energy Electrons With EGS4," Super-Kamiokande Report
SKAM-93-02 (1993).
[64] \GEANT Detector Description and Simulation Tool," CERN Program Library
W5013 (1994).
[65] R.C. Smith and K.S. Baker, Appl. Opt., 20, 177 (1981).
[66] J.D. Jackson, Classical Electrodynamics, John Wiley and Sons, New York,1975.
[67] F. Goebel, M.S. Thesis, State Univerity of New York at Stony Brook (1996).
295

[68] H. Press et.al., Numerical Recipes in Fortran, Cambridge University Press,
New York, 1992.
[69] \PAW - Physics Analysis Workstation," CERN Program Library Q121 (1995).
[70] \HBOOK Reference Manual," CERN Program Library Y250 (1995).
[71] R. Firestone, Table of Isotopes, John Wiley & Sons, Inc., New York, 1996.
[72] M. Nakahata, Ph.D. Thesis, University of Tokyo (1988).
[73] K. Matsumoto and Y. Suzuki, \Measurement of Rn originating from the20inch PMT glass and other materials used i the Super-Kamiokande," SuperKamiokande Report SKAM-94-03 (1994).
[74] Y. Oyama, Kamiokande Internal memo (1984).
[75] J.N. Bahcall, M. Kamionkowski, and A. Sirlin, Phys. Rev., D51, 6146 (1995).
[76] Y. Koshio, Ph.D. Thesis, University of Tokyo (soon to be completed).
[77] K.S. Hirata et.al., Phys. Rev. Lett, 66, 9 (1991).

296