Measurement of Electron Neutrino Appearance with the MINOS Experiment

343 Pages·2009·4.39 MB·English

FER MIL AB-T HESIS-2009-17
A Meas ure me nt of Electr o n Ne utri no A p peara nce wit h t he MI N O S
Ex peri me nt
A dissertation presented
by
Joshua Ada m Alpern Boeh m
to
The Depart ment of Physics
in partial fulfill ment ofthe require ments
forthe degree of
Doctor of Philosophy
inthe subject of
Physics
Harvard University
Ca mbridge, Massachusetts
May 2009
c 2009 - Joshua Ada m Alpern Boeh m
All rights reserved.
Thesis advisor Author
Prof .Gary Feld man Joshua Ada m Alpern Boeh m
A Meas ure me nt of Electro n Ne utri no Ap peara nce wit h t he MI N O S Ex peri me nt
A bstr act
MI N OS is a long-baseline t wo-detector neutrino oscillation experi ment that uses a high intensity
muon neutrino bea mtoinvestigatethe pheno menon of neutrino oscillations. By measuringthe neu-
trinointeractionsin a detector nearthe neutrino source and again 735 k m a wayfro mthe production
site, itis possible to probethe para meters governing neutrino oscillations. The majority ofthe ν
µ
oscillateto ν but a s mallfraction may oscillateinsteadto ν . Thisthesis presents a measure ment of
τ e
theν appearancerateinthe MI N OSfar detector usingthe firstt wo years of exposure. Methodsfor
e
constrainingthe far detector backgrounds usingthe near detector measure ments are discussed and
atechnique for esti matingthe uncertainty onthe background and signal selection are developed. A
1.5σ excess overthe expected background rateis found providing a hint of ν appearance.
e
iii
C o nt e nts
T itle Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Ackno wledg ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1 Introduction 1
2 Neutrino Physics 4
2.1 History ofthe Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 The Weak Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 The S U (2) Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Mass Ter ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Fer mion Representationin S U (2) . . . . . . . . . . . . . . . . . . . . . . 12
2.2.4 Glasho w- Weingberg-Sala m Theory . . . . . . . . . . . . . . . . . . . . . 13
2.2.5 Flavor Changing Interactions. . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.6 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Ti me Evolution ofthe Neutrino . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Conversionto Flavor Basis . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Three Flavor Neutrino Mixing . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Matter Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.5 Neutrino Oscillation Analysis Probabilities . . . . . . . . . . . . . . . . . 27
2.4 Evidence for Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.1 Solar Neutrino Oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 At mospheric Neutrino Oscillations. . . . . . . . . . . . . . . . . . . . . . 31
2.4.3 Measure ments of θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
13
3 The MI N OS Experi ment 36
3.1 Nu MI Bea m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 The MI N OS Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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Contents v
3.2.2 Scintillator Asse mbly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.3 Detector Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.4 Triggering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Detector Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 MI N OS Monte Carlo Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.1 Si mulation ofthe Bea m . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.2 Si mulation of Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . 58
3.4.3 Detector Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.4 Lo w Pulse Height Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4.5 Hadronic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 Current Status ofthe Experi ment . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Electron Event Selection 70
4.1 Event Topologyin MI N OS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.2 Sho wer Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.3 Reconstructed Event Energy . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Data Quality Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.1 Bea m Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.2 Detector Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Event Quality Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.1 Fiducial Volu me Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.2 Mini mu m Activity Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.3 Spill Ti ming Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.4 Cos mic Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.5 Largest Event Cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.4.6 Co mparison of Data and Si mulation . . . . . . . . . . . . . . . . . . . . . 88
4.5 Preselection Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5.1 Event Based Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.2 Track Based Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5.3 Energy Based Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.5.4 Su m mary of Preselection Cuts . . . . . . . . . . . . . . . . . . . . . . . . 93
4.6 Topological Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.6.1 Longitudinal Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.6.2 Transverse Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.6.3 Sho wer Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.7 Electron Identification Algorith ms . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7.1 A N N Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7.2 L E M Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.8 Perfor mance ofthe Selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.9 Identification of ν C C Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . 105
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Contents vi
5 Near Detector Data 109
5.1 Uncertaintiesin Near Detector Si mulation . . . . . . . . . . . . . . . . . . . . . . 110
5.2 Co mparison Bet ween Near Data and Si mulation . . . . . . . . . . . . . . . . . . . 110
5.2.1 Preselection Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.2 Topological Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2.3 Near Detector Electron Event Candidates . . . . . . . . . . . . . . . . . . 115
5.2.4 Data and Si mulation Agree mentinthe ν C C Selection. . . . . . . . . . . 119
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5.3 Horn On and Horn Off Data Separation Method . . . . . . . . . . . . . . . . . . . 121
5.3.1 The Horn On/ Off Method . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.3.2 Syste matics Uncertaintiesinthe Horn On/ Off Method . . . . . . . . . . . 124
5.3.3 The Horn On/ Off Event Type Separation . . . . . . . . . . . . . . . . . . 126
5.4 Muon Re moval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.4.1 Description ofthe Muon Re moval Algorith m . . . . . . . . . . . . . . . . 129
5.4.2 Muon Re moval Data Separation Technique . . . . . . . . . . . . . . . . . 133
5.4.3 I mple mentation ofthe Muon Re moval Separation Method . . . . . . . . . 139
5.4.4 Syste matic Uncertaintiesinthe Muon Re moval Separation . . . . . . . . . 141
5.4.5 Separation of Near Data Usingthe M R C C Technique . . . . . . . . . . . . 143
5.5 Co mparison ofthe Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6 Esti mation of the Signal Efficiency 146
6.1 Muon Re moval and Electron Addition Algorith m . . . . . . . . . . . . . . . . . . 147
6.2 Analysis Using M R E Sa mples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.2.1 Muon Re moval with Electron Quality Cuts . . . . . . . . . . . . . . . . . 151
6.3 Co mparison of M R E data and Si mulation . . . . . . . . . . . . . . . . . . . . . . 153
6.3.1 Original Event Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.3.2 Track Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.3.3 Sho wer Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.3.4 Topological Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.3.5 ν Selection Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
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6.3.6 Su m mary of M R E data and Si mulation . . . . . . . . . . . . . . . . . . . 164
6.4 Deter mination ofthe ν Signal Selection Efficiency . . . . . . . . . . . . . . . . . 166
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6.4.1 Efficiencies as Deter mined bythe M R E Sa mples . . . . . . . . . . . . . . 166
6.4.2 Efficienciesinthe Standard Monte Carlo . . . . . . . . . . . . . . . . . . 167
6.4.3 Predicted ν C C Signal Data Efficiency . . . . . . . . . . . . . . . . . . . 168
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6.5 Uncertaintyinthe Signal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.5.1 Syste matic Uncertaintiesinthe M R E Esti mation . . . . . . . . . . . . . . 171
6.5.2 Syste matic Uncertaintyinthe Electron Si mulation . . . . . . . . . . . . . 175
6.5.3 Su m mary of Syste matic Uncertainties . . . . . . . . . . . . . . . . . . . . 176
6.6 Analysis of Far M R E Sa mples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.7 Validation of Far Detector M R E Sa mples . . . . . . . . . . . . . . . . . . . . . . 178
6.8 Far Detector M R E ν Signal Selection Efficiency . . . . . . . . . . . . . . . . . . 178
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6.8.1 Far Detector Based Predicted ν C C Signal Data Efficiency. . . . . . . . . 180
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6.9 Su m mary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Contents vii
7 Prediction of Far Detector Rates 182
7.1 Far/ Near Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.1.1 Prediction fro m Near Detector Backgrounds. . . . . . . . . . . . . . . . . 183
7.1.2 Prediction of ν and Oscillated ν Event Rates . . . . . . . . . . . . . . . 188
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7.2 Inputstothe Extrapolation Method . . . . . . . . . . . . . . . . . . . . . . . . . . 192
7.3 Predicted Far Detector Event Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8 Uncertainties on the Far Detector Prediction 198
8.1 Uncertaintiesinthe Physics Si mulation . . . . . . . . . . . . . . . . . . . . . . . 200
8.1.1 Bea m Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.1.2 Cross Section Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.1.3 Hadronization Model Uncertainties . . . . . . . . . . . . . . . . . . . . . 202
8.1.4 Averaged Particle Multiplicities and Dispersion . . . . . . . . . . . . . . . 206
8.1.5 Intranuke Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.1.6 Single Particle Interaction Uncertainties . . . . . . . . . . . . . . . . . . . 209
8.2 Uncertaintiesinthe Energy Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.2.1 Absolute Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . . . . 210
8.2.2 Relative Energy Calibration Uncertainty . . . . . . . . . . . . . . . . . . . 211
8.2.3 Hadronic/ E M Energy Scale Uncertainty . . . . . . . . . . . . . . . . . . . 212
8.2.4 Additional Uncertaintiesinthe Calibration Chain . . . . . . . . . . . . . . 213
8.3 Uncertaintiesinthe Detector Model . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.3.1 Relative Event Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
8.3.2 Effects fro m Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
8.3.3 Lo w Pulse Height Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 217
8.3.4 Uncertaintiesinthe Crosstalk Model. . . . . . . . . . . . . . . . . . . . . 218
8.4 Syste matics Associated with ν and Signal ν Events . . . . . . . . . . . . . . . . 219
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8.4.1 ν C C Selection Syste matics . . . . . . . . . . . . . . . . . . . . . . . . . 219
µ
8.4.2 M R E Signal ν Efficiency Error . . . . . . . . . . . . . . . . . . . . . . . 220
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8.4.3 ν Selection Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
τ
8.5 Syste matic Uncertainty ofthe Predicted Rates . . . . . . . . . . . . . . . . . . . . 220
8.5.1 Calculation of Syste matic Errors fro m Extrapolation . . . . . . . . . . . . 235
8.5.2 Calculation of Syste matic Errors fro m Input Data . . . . . . . . . . . . . . 237
8.5.3 Calculation ofthe Total Syste matic Error . . . . . . . . . . . . . . . . . . 238
9 Far Detector Data 242
9.1 The Far Detector Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
9.2 Far Detector Data Sidebands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
9.2.1 Anti-PI D Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
9.2.2 M R C C Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.2.3 M R E Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9.2.4 Near-PI D Sideband . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
9.3 Far Data ν Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
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9.4 ν → ν Oscillation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
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9.4.1 Unified Analysis (Feld man- Cousins) Based Contours . . . . . . . . . . . . 263
9.5 Results ofthe ν Appearance Analysis . . . . . . . . . . . . . . . . . . . . . . . . 269
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Contents viii
9.5.1 I mpact of Other Oscillation Para meters . . . . . . . . . . . . . . . . . . . 272
9.5.2 Potential Future Li mits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
9.5.3 Possible I mprove ments for Future Analysis . . . . . . . . . . . . . . . . . 276
9.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
A Three Neutrinosin Matter 289
A.1 Properties ofthe Oscillation Probabilities . . . . . . . . . . . . . . . . . . . . . . 291
A.2 Expansions Used forthe ν Appearance Result . . . . . . . . . . . . . . . . . . . 293
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A.2.1 Expansionto First Orderin α . . . . . . . . . . . . . . . . . . . . . . . . 295
A.2.2 Expansionto First Orderin sinθ . . . . . . . . . . . . . . . . . . . . . . 303
13
A.2.3 Neutrino oscillation for mulato second orderin α and sinθ . . . . . . . . 310
13
A.3 Analysis Neutrino Appearance Probabilities . . . . . . . . . . . . . . . . . . . . . 311
A.4 Accuracy ofthe approxi mations . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
B Validation of Far M R E Sa mples 316
B.1 Variables Relatedtothe M R E Process . . . . . . . . . . . . . . . . . . . . . . . . 316
B.2 Reconstruction Quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
B.2.1 Track Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
B.2.2 Sho wer Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
B.3 PI D Input Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
B.4 PI D Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
B.5 Su m mary of Far M R E Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
C Alternative Oscillation Analysis Approaches 324
C.1 Si mple χ 2 Derived Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
C.2 Feld man- Cousins Analysis with Pseudo-experi ments . . . . . . . . . . . . . . . . 327
C.2.1 Pseudo- Experi ment Method A . . . . . . . . . . . . . . . . . . . . . . . . 331
C.2.2 Pseudo- Experi ment Method B . . . . . . . . . . . . . . . . . . . . . . . . 332
C.2.3 Pseudo- Experi ment Method C . . . . . . . . . . . . . . . . . . . . . . . . 332
List of Fi g u r es
2.1 The possible weakinteractions ofthe neutrino. . . . . . . . . . . . . . . . . . . . 8
2.2 Exa mple of a standard neutrinointeraction with a nucleon. . . . . . . . . . . . . . 18
2.3 The possible neutrino mass ordering. . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 The flux of 8B solar neutrinos measuredin S N O. . . . . . . . . . . . . . . . . . . 31
2.5 The zenith angle distribution for Super K events. . . . . . . . . . . . . . . . . . . . 32
2.6 Contours forthe best fit values ofthe at mospheric oscillation para meters. . . . . . 33
2.7 90 % exclusion contours forthe C H O O Z experi ment. . . . . . . . . . . . . . . . . 34
3.1 Thelayout ofthe Nu MI bea mline . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Calculated rate of ν - C Cinteractionsinthe near detector. . . . . . . . . . . . . . . 39
µ
3.3 Distribution of parent hadronstothe bea m ν content. . . . . . . . . . . . . . . . . 41
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3.4 The MI N OS far detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 The MI N OS near detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 A single scintillator strip sho wnin cuta way. . . . . . . . . . . . . . . . . . . . . . 47
3.7 The far detector scintillator configuration forthe U direction. . . . . . . . . . . . . 47
3.8 The four different scintillator configurations usedinthe near detector. . . . . . . . 48
3.9 The stopping po wer of muonsinthe MI N OS calibration detector.. . . . . . . . . . 54
3.10 The response ofthe calibration detectorto pions and electrons. . . . . . . . . . . . 55
3.11 Co mparison of near detector datato original and fit Monte Carlo. . . . . . . . . . . 57
3.12 The near detector distribution of strip energies. . . . . . . . . . . . . . . . . . . . 60
3.13 The pixelto plane mapping for a M64 and M16 P M T. . . . . . . . . . . . . . . . . 62
3.14 Data/ M C co mparison of non-track hits associated with a cos mictrack. . . . . . . . 62
3.15 Results of near detector crosstalktuning . . . . . . . . . . . . . . . . . . . . . . . 63
3.16 Results of far detector crosstalktuning . . . . . . . . . . . . . . . . . . . . . . . 64
3.17 K N O scaling distributions for νp and ν n interactions. . . . . . . . . . . . . . . . . 67
3.18 Nucleon p2 and nucleon x distribution data. . . . . . . . . . . . . . . . . . . . . 68
T F
3.19 The perfor mance ofthe Nu MI bea m since May 2005. . . . . . . . . . . . . . . . . 69
4.1 A charged current and neutral currentinteraction. . . . . . . . . . . . . . . . . . . 71
4.2 A si mulated quasi-elastic ν C Cinteractioninthe far detector.. . . . . . . . . . . . 72
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4.3 T wo candidate ν C Cinteractionsinthe far detector. . . . . . . . . . . . . . . . . 73
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4.4 Event display of si mulated N Cinteractionsinthe far detector . . . . . . . . . . . . 73
4.5 Event display of a si mulated ν -like N Cinteractioninthe far detector. . . . . . . . 74
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ix
List of Figur es x
4.6 An ev ent display sho wing an event containing both atrack and a sho wer. . . . . . . 76
4.7 Reconstructed energy as a function ofthetrue hadronic and E M energy . . . . . . 80
4.8 Diagra m ofthe fiducial volu me regions . . . . . . . . . . . . . . . . . . . . . . . 83
4.9 Far detector energy spectra before and afterthe mini mu m activity cut . . . . . . . 85
4.10 Far detector spillti me before and afterthe mini mu m activity cut . . . . . . . . . . 87
4.11 Reconstructed vertex distributions forthe near and far detectors. . . . . . . . . . . 90
4.12 Contiguous planes with greaterthan 0.5 M E U per planeinthe far detector . . . . . 91
4.13 Length oftrackin planesinthe far detector . . . . . . . . . . . . . . . . . . . . . 92
4.14 Nu mber oftracklike planesinthe far detector . . . . . . . . . . . . . . . . . . . . 92
4.15 Reconstructed andtrue energy distribution of preselected far det. M C events . . . . 95
4.16 Sho wer rise and fall fit para meters distributions of far detector M C events . . . . . 96
4.17 Fraction of event energy containedin a windo w of 2, 4 or 6 planes . . . . . . . . . 97
4.18 Sho wer radius co mputed fro m sho wer width and 90 % contain ment . . . . . . . . . 98
4.19 Fraction of event energyinthe sho wer core andlongitudinal energy . . . . . . . . 99
4.20 Sho wer dispersion para meter and fraction of energyinthe 8 hottest strips . . . . . 99
4.21 Distribution ofthe A N N discri mination variable . . . . . . . . . . . . . . . . . . . 101
4.22 Thethreeinput variablestothe L E M PI D . . . . . . . . . . . . . . . . . . . . . . 102
4.23 Distribution ofthe L E M discri mination variable . . . . . . . . . . . . . . . . . . . 103
4.24 The F O M and SF O M calculated as a function of a cutin PI D . . . . . . . . . . . . 105
4.25 The fourinput variablestothe k N N algorith m.. . . . . . . . . . . . . . . . . . . . 107
4.26 Distribution ofthe k N N discri mination variable . . . . . . . . . . . . . . . . . . . 108
4.27 Purity and efficiency ofthe k N N selection . . . . . . . . . . . . . . . . . . . . . . 108
5.1 The fractional syste matic uncertainty onthe A N N and L E M distributions . . . . . 111
5.2 Data and M C co mparison ofthe preselection variables . . . . . . . . . . . . . . . 112
5.3 The ratio of datato M C forthe preselection variables . . . . . . . . . . . . . . . . 113
5.4 The reconstructed energy spectru m ofthe preselected event sa mple . . . . . . . . . 114
5.5 Data and M C co mparison ofthe fraction energyin a narro w road . . . . . . . . . . 116
5.6 Data and M C co mparison ofthe sho wer radius. . . . . . . . . . . . . . . . . . . . 116
5.7 Data and M C co mparison ofthe sho wer dispersion variable . . . . . . . . . . . . . 117
5.8 Data and M C co mparison ofthe sho wer fall fit para meter . . . . . . . . . . . . . . 117
5.9 Data and M C co mparison ofthe fraction of ν events matches . . . . . . . . . . . 118
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5.10 Data and M C co mparison ofthe mean y of matched events . . . . . . . . . . . . . 118
5.11 Data and M C co mparison ofthe mean matched charge . . . . . . . . . . . . . . . 119
5.12 The near detector data and M C distribution of A N N and L E M . . . . . . . . . . . 120
5.13 The near detector energy distribution for A N N and L E M selected events . . . . . . 121
5.14 Reconstructed energy distribution for events selected as ν C C candidates . . . . . 121
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5.15 Thetrue neutrino energy of eventsinthe Horn On and Horn Off data . . . . . . . . 122
5.16 The reconstructed energy of eventsinthe Horn On and Horn Off data . . . . . . . 123
5.17 Horn On/ Off ratios for ν C C and N C events . . . . . . . . . . . . . . . . . . . . 125
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5.18 Horn On/ Off ratios after successive cutlevels . . . . . . . . . . . . . . . . . . . . 127
5.19 Horn On/ Off separated spectra forthe A N N and L E M selections . . . . . . . . . . 128
5.20 Purity and co mpleteness forthe muon re moved events. . . . . . . . . . . . . . . . 132
5.21 An event before and after muon re moval which si mulated an N C event . . . . . . . 132
5.22 An event before and after muon re moval which si mulated an ν event . . . . . . . 133
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