Experimental Studies on Low Energy
Electron Antineutrinos and Related
Physics
Dissertation Submitted toTsinghua University
in partial fulfillment of the requirement
for the degree ofDoctor of Philosophy

inPhysicsby
Wan Linyan

Dissertation Supervisor : Professor Chen Shaomin

December, 2018

Abstract

Abstract
Electron antineutrinos within the energy range of several to several hundreds of
MeV are composed of those from supernovae or past supernovae, the Earth, reactors, andatmospheric neutrinos. They provide a unique probe into the dynamic of sources as well
as new phenomena beyond the Standard Model of particle physics. One of the interactions
with the largest cross section for neutrino detection in this energy range is inverse beta
decay (IBD), which produces a positron and a neutron. The detection of neutron is crucial
for the separation between signal and backgrounds. This thesis presents studies based on
the analysis of low energy signal and neutron production from neutrino interactions.
• We used LEDs to calibrate the water scattering and absorption properties for the water Cherenkov detector Super-Kamiokande (SK). We employed radioactive sources
to correct the bias introduced by the long-term gain increase of PMTs, and implemented a new algorithm to the energy reconstruction process, all of which reduced
the systematics as a consequence.
• With SK-IV data of 2,778 days, a search for SRN signal has been performed bydetecting the neutron capture signal. We improved the neutron tagging algorithm
by reconstructions of the neutron capture vertex based on time-of-flight subtracted
PMT hit time and the primary vertex respectively, and optimized the determinationof multi-variate cut. The signal-background discrimination power of the algorithm
was significantly enhanced, and the signal eﬃciency was increased from 8.8% to19.3%. The SRN candidates were compared with the expectations of backgrounds
including reactor neutrinos, spallation backgrounds, atmospheric neutrino induced
backgrounds, and accidental coincidence. The result was consistent with null signal
hypothesis. An upperlimit was derived, giving the best limits for the SRN search.
• Atmospheric neutrinos interact with oxygen nuclei in water, producing gammas
and neutrons, which imposes an important background for SRN detection by the
mis-identification of gammas as positrons. Based on the SRN sample except for
Cherenkov angle cut, we obtained NCQE candidates with Cherenkov angle > 50◦ .
The mean NCQE cross section from atmospheric neutrinos on oxygen was measured+0.49(sys.)) × 10−38 cm2 , consistent with the theoreticalto be (0.95 ± 0.12(stat.)−0.32

prediction.

IIAbstract• We performed a calculation on geoneutrinos fluxes generated in the Earth and analyzed the oscillation impact with both vacuum approximation and MSW eﬀect.
Considering the backgrounds of reactor neutrinos and (α, n) interaction, an prediction has been made for the geoneutrino and U/Th ratio sensitivities in a liquid
scintillator detector at the Jinping underground lab in Sichuan, China. These measurements will provide powerful constraints on the radiogenic heat budget of the
Earth as well as tests on Earth models.
Key words: neutrino; supernova relic neutrino; atmospheric neutrino; geoneutrino

IIIContents

Contents
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Neutrinos Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Neutrinos in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 The Inverse Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 The Neutral Current Quasi-Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Neutrinos from Diﬀerent Sources and Related Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Overview of Neutrino Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Supernova Relic Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Geoneutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 2 The Super-Kamiokande Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Photo-Multiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 ID PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.2 OD PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Water and Air System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Electronics and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Electronic System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Online DAQ and Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 3 Calibration and Reconstruction at SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1 Detector Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.1 PMT Response Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1.2 Water Transparency Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.3 Energy Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Detector Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.1 Cherenkov Photon Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2.2 Photon propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2.3 PMT and Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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3.3 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.1 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.2 Direction Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.4 Cherenkov Angle Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.5 Muon Fitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Chapter 4 Data Reduction at SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 First Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Spallation Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 External Event Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4 Solar Event Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 Cherenkov Angle Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Multi-Event Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6.1 Pre/Post Activity Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6.2 Multi-ring Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7 Muon/Pion Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7.1 Pion Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.7.2 Charge/Hit Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.8 Summary of Reduction Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chapter 5 Selection of Correlated Neutrons at SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Neutron Tagging Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.1 Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.2 Discriminating Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1.3 Multivariate classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2 Significance Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 Systematic Study with the Am/Be Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4 Validation with Cosmogenic 9 Li Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.5 Cut Optimization and Eﬃciency Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Chapter 6 SRN Analysis and Result at SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.1 Accidental Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.2 Atmospheric NC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.3 Atmospheric CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
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6.1.4 Spallation Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.1.5 Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2 Candidate Events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3 Model-Independent Upper Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Chapter 7 NCQE Analysis at SK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1 Introduction and Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1.1 Atmospheric NCQE as the SRN Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.2 Further Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 Monte-Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.1 Atmospheric Neutrino Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.2 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.3 Other NC Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2.4 MC Reconstruction and Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3 Data Reduction and Neutron Tagging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.1 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.2 Neutron Tagging for NCQE Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4.1 Candidate Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4.2 Cross section Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.4.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.5.1 Discussion on Future Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Chapter 8 Geoneutrino Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.1 Geoneutrino Intensity and Energy Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
8.2 Geo ν̄e Flux Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
8.2.1 Earth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.2.2 Oscillation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
8.3 Liquid Scintillator Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.3.1 Scintillation Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8.3.2 Detector Response Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.3.3 A Proposed Experiment at Jinping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.4 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
8.4.1 Reactor Neutrino Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
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8.4.2 Other Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8.5 Sensitivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.5.1 Predicted IBD Spectrum at Jinping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8.5.2 Sensitivity for Geoneutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.5.3 BSE Model Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.6 Further Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.6.1 Requisites for the Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.6.2 Earth Core Fission Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Chapter 9 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Acknowlegement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Resume and Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

VIIChapter 1

Chapter 1

Introduction

Introduction

This chapter first introduces general properties of neutrinos, then reviews the neutrino interactions, emphasizing on the inverse beta decay and neutral current quasi-elastic
scattering. A discussion on diﬀerent neutrino sources and related physics is presented,
focusing on supernova relic neutrinos and geoneutrinos, including the dynamics of supernovae and Earth, and the present experimental status.

1.1 Neutrinos Properties
Less than a century from its discovery, neutrinos are nowadays significantly pushing
forward the progress of fundamental physics governing our universe. Named by theirelectrical neutrality and tiny masses, neutrinos were first postulated by Wolfgang Pauliin 1930 to explain the continuous electron energy spectrum in nuclear β-decay. His
neutrino solution to the energy and momentum crisis was to propose that the β-decay of
the nucleus is a three-body process involving the nucleus, the electron, and the neutrino [1] .
This postulation was confirmed experimentally by C. Cowan and F. Reines in 1956 withthe discovery of electron anti-neutrinos from the nuclear reactor [2] .
1.1.1 Neutrinos in the Standard Model

Neutrinos are only subject to weak interaction. It is experimentally well-establishedthat there are 3 generations of neutrinos, νe, νµ, ντ , coupling to the corresponding 3 generation leptons e, µ, τ. Experiments on Large Electron-Positron Collider (LEP) reported
the final electroweak measurements performed with data taken at the Z resonance, whichconstrained the number of light neutrino species to be 2.9840 ± 0.0082 [3] . This result

requires only 3 generations of active neutrinos, and any further generation of neutrinos
has to be non-conventional neutrinos, for example, sterile neutrinos which do not haveelectroweak interaction.
The absolute value of neutrino mass remains unknown so far, though the upper limitsof νe have been obtained by β−decay measurements at eV level [4] . Still, the non-zeromass of at least 2 generations of neutrinos along with neutrino mixing can be derived
from the fact that neutrinos oscillate among the 3 generations [5,6] . This contradicts the1Chapter 1

Introduction

massless prediction within the Standard Model [7] , marking neutrinos as the only particle
showing deviation from SM so far.
1.1.2 Neutrino Oscillation

Experiments provide compelling neutrino oscillation evidences compatible within
the present frame work of 3-generation neutrino mixing, although there are some experimental hints for the hypothetical sterile neutrinos that interact only via gravity and do notinteract via any of the fundamental interactions [8–10] .
1.1.2.1 Vacuum Oscillation

Neutrino mixing indicates that the mass eigenstates are not flavor eigenstates, i.e.,
the neutrino mixing matrix U is not diagonal. Denoting the mass eigenstates as ν1 , ν2 ,and ν3 , and the flavor eigenstates as νe , νµ , and ντ , the matrix U is parameterized by three
mixing angles between diﬀerent generations of neutrinos and the CP phase,*.
U = ..
.

1c23, −s23 c23+/ *.
s23 // × ..
/ .
-s13 e−iδc p + * c12 s12
+/
// ..
//
1
// × .. −s12 c12
/
c13
1
- ,
-

c13

, −s13 e−iδ c p*.
= .. −s12 c23 − c12 s13 s23 eiδ c12 c23 − s12 s13 s23 eiδ
.
c12 c13s12 c13, −s12 c23 − c12 s13 c23 eiδ

c12 s23 − s12 s13 c23 eiδ

s13 e−iδ +/c13 s23 // ,/c13 c23 -(1-1)

where si, j and ci, j represent the sine and cosine of a mixing angle between the i-th andj-th generations respectively.
The survival probability of an electron antineutrino νe with energy E propagatingover a baseline L can thus be written as
Pαβ (E, L) =

∑∑
i

j

e−i M̃i, j × Um (i, α) †Um ( β, i)Um (α, j)Um ( j, β) †,(1-2)

where α and β indicate the initial state and the final state respectively, M̃i, j = ∆Mi2j L/2E,
with the oscillation distance L and the energy E, and ∆Mi j is the neutrino mass diﬀerence
between the ith and jth generations. Um is the eigenmatrix of neutrino mass mixing matrix
A = U × M × U † , where M is the neutrino mass matrix, Mi j = δi j × ∆Mi j , and U is theneutrino oscillation matrix.

2Chapter 1

Introduction

1.1.2.2 Matter Eﬀect

The presence of propagating medium can change drastically the pattern of neutrino
oscillations due to the weak but existing interaction between neutrinos and the particles
forming the medium. In case of matter oscillation, the Hamiltonian of the neutrino system
in matter Hm diﬀers from the Hamiltonian in vacuum H0 , Hm = H0 + Hint , with Hint
describing the interaction of neutrinos and particles such as the electrons, protons andneutrons in the medium matter. The eﬀect of matter in neutrino oscillations is usuallycalled Mikheyev-Smirnov-Wolfenstein (MSW) oscillation eﬀect, or matter eﬀect [11] .
The mixing matrix for the MSW oscillation of neutrinos changes from vacuum
oscillation as′= A11 + V,
A11

(1-3)

with the additional term V representing the chemical potential,√
V = 2 2G F ne Eν,(1-4)

where G F is the Fermi constant, ne is the electron density, and Eν is the neutrino energy.
Therefore, the neutrino mixing angle in matter can be written as
sin 2θ m = √ (tan 2θ
,)Ne 2
2
1 − Neres + tan 2θ

(1-5)

where Neres is the eﬀective density, referred to as resonance density,
Neres =

∆m2 cos 2θ
.
√
2E 2G F

(1-6)

If Ne ≪ Neres , Eq. (1-5) reduces to vacuum oscillation, and θ m ≈ θ. On the contrary,

if Ne ≫ Neres , the presence of matter greatly suppresses neutrino oscillation, θ m ≈ π/2.
Based on this eﬀect, neutrino tomography is feasible with a high luminosity source anda high electron density environment. Typical examples include using solar neutrinos
propagating through the Sun to probe solar interior, or using geoneutrinos to probe theEarth.
3

Chapter 1

Introduction

1.2 Neutrino Interactions
Main neutrino interaction channels vary within a wide range dependent on the neutrino energy and matter properties. The typical neutrino interactions from low energy
neutrinos to high energy neutrinos include coherent scattering, neutrino capture, inverse
beta decay, low energy nuclear interactions, neutral current quasi-elastic scattering, resonant pion production, kaon production, deep inelastic scattering, and ultra-high energy
interactions [12] .
In this thesis, we emphasize on the two neutrino quasi-elastic interaction with nucleons, inverse beta decay and neutron current quasi-elastic scattering, in the context ofwater target. As an illustration, Fig. 1.1 shows the eﬀective interaction cross section as afunction of the incident neutrino energy in a large water Cherenkov detector for various
reactions [13] .

Figure 1.1 Eﬀective cross sections for neutrino interactions in a water Cherenkov detector,
including corresponding energy resolution and threshold eﬀects [13] .

1.2.1 The Inverse Beta Decay

One of the channels with the largest cross sections for low energy neutrinos is inverse
beta decay (IBD) interaction [14] . The cross section for IBD interaction is more than one
order greater than those for other reactions, as shown in Fig. 1.1 and Fig. 1.2.

4

σ [m2]

Chapter 1

Introduction

×10-45
3
2.5
2
1.5
1
0.5
0

0

5

10

15

20

Neutrino energy [MeV]
Figure 1.2

Cross section for IBD interaction as a function of incident neutrino energy.

Inverse beta decay is the simplest neutrino nuclear interaction, in which an electron
antineutrino ν̄e scattered on a proton p, producing a positron e+ and a neutron n,ν̄e + p → e+ + n.

(1-7)

In a typical Cherenkov or scintillation detector, the positron is detected immediately by
Cherenkov radiation or scintillation light and is referred to as the primary event, or prompt
event, and the neutron is detected by its capture after thermal propagation, referred to as
the delayed event. If the capture occurs on a hydrogen nucleus, a 2.2 MeV γ ray will thenbe emitted with a lifetime of ∼ 200µs,
n + p → d + γ.

(1-8)

In the MeV level of low energy range, the energy of the out-going positron of an IBD
event can be written as a function of incident neutrino energy approximated to the 0thorder,
Te+ = Eν̄e + m p − mn − me+ . = Eν̄e − 1.8MeV.

(1-9)

In IBD events, antineutrinos are usually detected by identifying e+ , or sometimes by atime-correlated signal between a prompt signal and a delayed signal. This feature provides
a distinct signature against backgrounds, and will thus increase the sensitivity for IBD
5

Chapter 1

Introduction

signals. In some cases where a 2.2 MeV γ does not exceed the energy threshold andwill not trigger a signal, for example a water Cherenkov detector, the neutron capture
signal can be selected by associating the prompt signal through neutron tagging, as to be
discussed in Chapter 5.
1.2.2 The Neutral Current Quasi-Elastic Scattering

Neutral current quasi-elastic interaction (NCQE) with 16 O is found to be one of the
major channels in water based neutrino detectors for neutrinos with several hundred MeV
energy [15] . The interaction processes can be written asν +16 O → ν +15 O + n + γ ′ s,

ν +16 O → ν +15 N + p + γ ′ s,

(1-10)

in which neutrinos knock out one or multi-nucleons from oxygen, and the residual nuclei
de-excites, emitting γ’s. The number and energies of these γ’s depend on the final statesof excitation energy levels and corresponding branching ratios. The produced γ ray thenpropagates in water and can be detected by the Cherenkov light of the secondary electron
or positron mainly through Compton process and pair production. The recoil proton isusually below the Cherenkov threshold and becomes invisible, while the recoil neutron canbe captured on hydrogen, releasing a 2.2 MeV photon that can be tagged, and mimicking
an IBD signal.
Theoretical predictions have been given for both low energy case and high energy
case, the latter of which applies to T2K neutrino beam and atmospheric neutrino withenergy of GeV or sub-GeV [15] , as shown in Fig. 1.3. This cross section has been measured
from T2K neutrino beam, reporting a result in agreement with the theoretical prediction [16] .
Still, the cross section on oxygen from atmospheric neutrinos has not yet been studied
before, which remains as a backgrounds for many rare signal searches in water Cherenkov
detectors.

6

Chapter 1

Introduction

Figure 1.3 Cross section for NCQE interaction as a function of incident neutrino energy, citedfrom Ankowski’s model [15] .

1.3 Neutrinos from Diﬀerent Sources and Related Physics
Neutrinos are generated in various physics processes and come from a variety ofsources. In this section, we first briefly review the neutrino sources, and then focus on
both the supernova relic neutrinos and the geoneutrinos with IBD signature.
1.3.1 Overview of Neutrino Sources

Neutrinos originate from various sources, including cosmic relic neutrinos from therelic of the Big Bang [17] , supernova neutrinos from the collapsed supernova explosions,
solar neutrinos from the Sun, atmospheric neutrinos from the cosmic-ray interactions in
the air, accelerator neutrinos from accelerators, reactor neutrinos from nuclear reactors,
and geoneutrinos from the decay-chain of 238 U and 232 Th inside the Earth.
These neutrinos have very diﬀerent properties on energy spectra, flavor composition,and directional distribution, and thus can be distinguished in most cases. The energy ofneutrinos ranging from several eV for the cosmic relic neutrinos [18] to several PeV fromsome extra terrestrial neutrino source [19] .
Owing to the fact that neutrino interaction with matter is very weak, neutrinos can beused as a probe into the dynamics of these neutrino sources, especially when the sources
are far away or heavily shaded.

7

Chapter 1

Introduction

1.3.2 Supernova Relic Neutrinos

Supernova relic neutrinos (SRNs) are the neutrinos emitted from past supernova
bursts everywhere in the universe. In this section, we will first introduce supernova bursts,
especially core-collapse supernovae, and the dynamics driving them. Then we discuss onsupernova neutrinos and supernova relic neutrinos, emphasizing on the neutrino spectraand flux predicted by diﬀerent models. Finally the present status of SRN search in diﬀerent
experiments is covered.
1.3.2.1 Supernova Overview

For historical reasons, supernovae are classified into type I and II by their light
spectroscopic characteristics instead of their trigger scheme, as shown in Fig. 1.4. To
remedy for that, supernova categories are further divided into sub-categories, where TypeIa supernovae are believed to be triggered by the thermonuclear disruption of white dwarf
stars in binary systems, and Type Ib, Ic and II supernovae are generated by the gravitational
collapse of the core of massive stars.
Core-collapse supernova burst is an important topic in supernova astronomy and starevolution as well as in neutrino physics. The progenitors of core-collapse supernovae are
typically with larger mass than type Ia. When the mass of a progenitor satisfies M ≳ 8M⊙ ,where M⊙ denotes one solar mass, after its burning out, a gravitational collapse will be

triggered. Most of energy from a core-collapse supernova burst is carried away by theemission of a large number of neutrinos. The term supernova in the following context
refers to core-collapse supernovae unless otherwise explained.

8

Chapter 1

Figure 1.4

Introduction

The classification scheme of supernovae [20] .

Core-collapse supernova bursts can be driven by diﬀerent causes dependent on theprogenitor mass and metallicity, but the early phases of the burst producing neutrinos
are quite similar [21] . The explosive processes related to the neutrino emission can besummarized as below [20,22,23] .
• Photo-disintegration.
As the density and the temperature in the core climbs during the star collapse,
electron capture on nucleus
e− + N (Z, A) → N (Z − 1, A) + νe,(1-11)

becomes favorable, further reducing the electron degeneracy pressure in supportof the gravitational force inside the iron core and accelerating the core collapse.
Though some νe ’s are generated in this stage, the amount is negligible compared tothe total emission. These neutrinos, together with the neutrinos emitted in the presupernova stage through pair production, can escape freely from the core, possible
to be used as an early warning for a close-by supernova burst, but the amount of
neutrinos is not significant in supernova relic neutrino analysis.
• Neutrino trapping.
The inner and outer parts of star core begin to evolve diﬀerently. In the inner part,the collapse is homologous, with the collapsing velocity v ∝ r, and it takes the sametime for all parts collapse, while the density increases at the same rate everywhere.
In the outer part, however, the collapse is quasi-free fall, v ∝ 1/r 2 . When the density
9Chapter 1

Introductionof the inner part of the core reaches 1011 − 1012 g·cm−3 , electron neutrinos begin to

be trapped in a so-called neutrinosphere by the nuclei through coherent scattering,the cross section of which follows σcoh ∝ A2 . This neutrinosphere is defined byradius asRν ≈ 1.0 × 107 cm

(

)
Eν
.
10MeV

(1-12)• Neutrino burst.
The inner core continues to collapse until the density exceeds the nuclear limit(∼ 1014 g·cm−3 ), enabling the repulsive nuclear pressure to halt the collapse andto drive a shock wave outwards. Nuclei are then dissociated into free protons
and neutrons by the shock wave, emitting a huge number of electron neutrinos
through the process of electron capture on protons e− + p → n + νe , enabling
the previously trapped νe ’s to decouple from the nuclei. This process of electron

neutrinos emission and free is called the prompt electron neutrino burst, with thepeak luminosity exceeding 1053 erg·s−1 for a few ms.
Besides, neutrinos of all flavors are produced thermally in the collapsed region via
both neutral current (NC) and charged current (CC) processes,
e− + e+ → ν + ν̄,N + N → N + N + ν + ν̄,e± + N → e± + N + ν + ν̄,(1-13)γ ∗ → ν + ν̄,and additional νe /ν̄e ’s are produced by CC interactions,e− + p → n + νe,
e+ + n → p + ν̄e .

(1-14)• Delayed explosion.
The shock wave loses energy, and calculations show that it will not be able to reachthe star surface in most cases. Instead, it is generally supposed that the explosion
is relayed by neutrinos depositing energy through a so-called delayed explosion
mechanism ∼1 second later than a prompt explosion.
10Chapter 1

Introduction

Finally after cooling down, what remains of the progenitor will form either a neutron staror a black hole, depending on the its mass and metallicity.
1.3.2.2 Supernova Relic Neutrinos

Supernova bursts with neutrino observations are rare, expected at the rate of 2∼3
per century [24] , while the accumulated supernova relic neutrinos throughout the historyof universe can make a sensible probe into the dynamics of supernova burst as well as
many other topics. To shed light on the supernova explosion mechanism, other than
waiting for the burst neutrinos from the centennial supernova within our galaxy, SRNs
from past supernovae should be thoroughly studied. Since 1987A, many calculations of
SRN flux have been available, giving diﬀerent results based on diﬀerent hypotheses forthe explosion mechanism [25–34] .
A general SRN spectrum prediction at the observatory can be given by [35] ,dN(Eν ) = c
dEν

∫ ∞
0

RS N (z)(1 + z)

dN (Eν (1 + z)) dt| |dz,dEν
dz(1-15)

where dN/dEν is the energy spectrum from one supernova explosion, assumed to beuniversal in supernovae of diﬀerent masses, RS N is the core-collapse supernova rate atredshift z, the detected energy Eν from a neutrino is Eν (1 + z) at production due to theredshift, and t is the cosmic time following the Friedmann equation,√dz= −H0 (1 + z) Ωm (1 + z) 3 + ΩΛ,
dt(1-16)

where H0 is the Hubble constant, Ωm is the cosmic matter density, and ΩΛ is cosmologicalconstant.
Rate of Core-collapse Supernovae
The rate of core-collapse supernovae used to be calculated from the cosmochemistry[25,26]and the time variance used to be given by the cosmochemical evolution [27–29] .

In recent SRN models [30–34] , however, the estimation of supernova rate is based on the starformation rate (SFR) with a rather good accuracy compared to other parameters in SRN
spectra prediction.

11

Chapter 1

Introduction

The core-collapse supernova rate as a function of SFR can be written as [32]∫ 50
8RS N (z) = ρ̇∗ (z) ∫ 100

Φ(m)dmmΦ(m)dm
0.1,(1-17)

where RS N (z) is the supernova rate at redshift z, ρ̇∗ (z) is the SFR density, Φ(m) is theinitial mass function. The integral limits are the mass ranges of stars that lead to corecollapse. Below 8M⊙ , the progenitor tends to evolve into a dwarf, while above 50M⊙ , theprogenitor tends to form a black hole directly without an explosion [21] .
Supernova Neutrino Spectra
The supernova neutrino emission flux and spectra remain a mystery, with manymodels proposed but none of them providing very high precision or has been verified.
The average of neutrino energy can be estimated by the total amount of gravitationalbinding energy liberated in a supernova explosion
) −1
(
)2 (
3 GMN2 S
MN S
RN S
53
∼ 3 × 10erg,
Ebind ∼
5 RN S
1.4M⊙
10km(1-18)

where MN S is the mass of a neutron star and RN S is the radius. Energy estimations basedon the only available neutrino data from a supernova so far, the SN 1987A in the Large
Magellanic Cloud ∼50 kpc away, showed consistency with the above calculation [36,37] .
However, due to the small statistics, where only 11 neutrinos have been detected from SN
1987A by Kamiokande II [38] and 8 by IMB [39] experiments, the explosion mechanism has
not yet been well-established with SN neutrino data. An example of neutrino luminosityand average energy from a numerical simulation in a supernova explosion with the delayed
explosion mechanism by Totani et al. is shown in Fig. 1.5 [40] .

12

Chapter 1

Introduction

Figure 1.5 The first 1.5 s evolution of neutrino luminosity and average energy from a numericalsimulation [40] .

As Eq. (1-13) indicates, most neutrinos are emitted in pairs, presumably carrying
equivalent amount of energy among neutrino flavors. However, only some simulation
results show equal partitions for the luminosities of all flavors [40] , while significant deviations are seen in others [41] . A commonly accepted hierarchy on the average neutrinoenergy among the species is⟨Eνe ⟩ < ⟨Eν̄e ⟩ < ⟨Eνx ⟩,(1-19)

with the average energy [40,42] ,⟨Eνe ⟩ ≈ 13MeV,⟨Eν̄e ⟩ ≈ 16MeV,(1-20)⟨Eνx ⟩ ≈ 23MeV.
The energy spectrum of supernova neutrinos for each flavor is assumed to follow theFermi�Dirac (FD) distribution with diﬀerent temperatures and a zero potential [29] ,dN
1
120 E 2
= L 4 4 E/T,
dE
7π T e+113(1-21)

Chapter 1

Introduction

where T ≈ ⟨E⟩/3.1514 is the eﬀective neutrino temperature and L is the total luminosity.
This requires an approximation that the neutrino emission in a supernova burst is thermal,
which is not true due to the energy dependence of the interaction cross sections. Figure 1.6
shows the energy spectrum from the same simulation as Fig. 1.5 by Totani et al. [40] , where
the zero-potential FD distribution cannot describe the numerical simulation very well.

Figure 1.6

Energy spectrum of ν̄e [40] .

From Eq. (1-21), a more realistic pinched Fermi�Dirac (FD) distribution can beextended to parameterize the supernova neutrino spectrum for a given flavor predictedfrom most models [41] ,
dN
1
1 E2
=L
,
dE
F (η) T 4 e E/T −η + 1(1-22)

where η is the pinching parameter and F (η) is a normalization function. The neutrino
emission can then be characterized by the total flux Lν , the thermal temperature of emissionTν , and the pinching parameter η. Of these three parameters, no one depends sensitively
on the supernova mass, thus enabling the assumption in SRN calculation Eq. (1-15) thatSN spectra are not sensitive to the core-collapse supernova properties. Some recent SRN
models also take into consideration the change of neutrino spectrum of a certain generation
during its propagation through the universe because of oscillation [31,32] .
14

Chapter 1

Introduction

Future detections of a nearby core collapse supernova by the present large neutrino detectors including Super-Kamiokande, IceCube, SNO+, etc will greatly enhance
our knowledge on the supernova explosion mechanism and the supernova neutrino spectrum [43,44] .
SRN Models
Some representative SRN models and predictions are summarized in Ref. [45] andRef. [46] . The predictions for supernova relic neutrino rate and emission spectrum from thevarious models diﬀer due to their assumptions on the supernova rates, the modifications
on FD distribution, whether oscillation eﬀect is considered or not, and the processes ofsupernova explosions.
In late 20th century, the discussion has been focused on the estimation of supernova
rate, when constant SN rate model [25] , cosmic gas infall model [27] , chemical evolution
model [28] , and population synthesis model [26] were proposed. Totani and his collaborators
first assumed in the constant SN rate model in 1995 that the supernova rate was a constant,then updated with the population synthesis model that the supernova rate was timedependent, derived from galaxy evolution based on the population synthesis method.
Malaney et al. proposed that the supernova rate should be calculated from the redshift
evolution of cosmic gas, and Hartmann et al. proposed the calculation of SFR fromcosmic chemical evolution. Later, with the experimental search on SRN, a star formation
rate constraint model [33] was proposed by Kawasaki et al. to obtain the supernova ratefrom SFR constrained by the SRN result from Super Kamiokande [47] .
Another concern on the insuﬃcient FD-distribution-based description of the emission
spectrum resulted in the heavy metal model [29,30] proposed by Kaplinghat et al., in order todescribe the spectrum by the universal metal enrichment history. Later in 2008, Horiuchi
et al. proposed the HBD 6 MeV model [32] , predicting the neutrino emission spectrum witha pinched FD distribution with eﬀective temperatures between 4-6 MeV This is further
extended to a universal emission model for diﬀerent temperatures [48] .
Large mixing angle (LMA) model [31] by Ando et al. in 2002 is the first SRN model
to introduce the neutrino oscillation eﬀect. In 2009, Lunardini et al. proposed the failed
SN model [34] , in which the flux was more significant and the neutrino spectra were harderconsidering the failed supernova explosions.

15

Chapter 1

Introduction

1.3.2.3 Experimental Search

Supernova relic neutrinos contain all species of either neutrinos or anti-neutrinos.
The largest cross section for neutrino experiments in this ∼ 10 MeV region is inverse beta
decay, which produces a positron and a neutron. In this section, we concentrate on the

search for SRN signal in a large water-Cherenkov detector, together with the present statusof SRN search from diﬀerent experiments in the world.
Cherenkov Radiation
Charged particles with a speed exceeding the light speed in medium emit Cherenkov
radiation. The Cherenkov threshold is determined by the refractive index of a medium.
For electrons in pure water, the threshold is 0.76 MeV, while for muons, it is 157 MeV.
Cherenkov photons are usually ultra-violet, decreasing as the wavelength increases.
Compared to scintillation light, which is also widely employed in low energy neutrino
experiments, Cherenkov radiation has a lower light yield, but retains the directional
information, which is important for solar neutrino detection etc. For an IBD event, thedirection of the incident neutrino is already lost in the positron production stage. Still, thedirectional information can help to suppress backgrounds such as solar neutrinos in SRN
detection.
A typical light yield with regard to the electron kinetic energy is shown in Fig. 1.7.
This process will be described in detail in Section 3.2.1 with quantitative explanation.

Figure 1.7

Typical Cherenkov Yield for electrons in water versus electron energy.

16Chapter 1

Introduction

Backgrounds for SRN
Backgrounds for the SRN search in Super Kamiokande include the atmosphereneutrinos, neutral current events, the spallation backgrounds induced by the incident
cosmic muons, and reactor neutrinos.
Atmosphere νµ /ν̄µ ’s CC
Atmospheric νµ /ν̄µ ’s can interact with water via the CC processνµ + n → µ− + p,

(1-23)

ν̄µ + p → µ+ + n.

(1-24)

andIn this analysis, the first process does not contaminate the data sample due to the absenceof direct neutron and the negligible yield of secondary neutron in low energy region.
Similarly, the atmospheric νe background does not produce neutrons and will not betagged.
In the second process, however, the daughter electron from the Michel decay of themuon and neutron may fake an IBD signal. The muons as reaction products here may
have energy below the Cherenkov threshold, and is called invisible muons. These muonsdecay to positrons mimicking the primary signal [49] , and may coincide with the neutron
produced to form an irreducible background at Super Kamiokande even with the neutron
tagging technique.
Atmosphere ν̄e ’s CC
The very low end of atmospheric ν̄e spectrum overlap with the SRN detection window,
and the CC background from atmospheric ν̄e ’s has exactly the same signature as the SRN
signal, forming another irreducible background in this analysis. Atmospheric ν̄e within
the energy range of SRN sample is believed to be very low and is predicted by sometheoretical models. However, the spectrum in lower end is not clearly studied and no
experimental result is available, introducing additional systematic uncertainty to the SRN
search.
Neutral current events
The dominant NC process in this energy region is mainly the NC quasi-elastic
scattering with nuclei, knocking out nucleons from the nuclei and leaving excited nuclei
17

Chapter 1

Introduction

which may emit low energy γ’s. An example of quasi-elastic scattering process can be
written as:ν +16 O → ν +15 O + n + γ,

(1-25)

where the actual interaction takes place between the neutrino and a nucleon bounded in
the nuclei in the initial state. The nucleon in the final state is freed and continues topropagate in water, sometimes triggering secondary processes in water. Most of the NC
events can be removed by a Cherenkov angle cut while the residual become backgroundin our SRN sample. This background will be discussed in detail in Chapter. 7.
Reactor neutrinos
Reactor neutrinos are ν̄e ’s overlapping the lower end of the SRN energy spectrum,
producing exactly the same signal as SRN IBD. After the Fukushima Daiichi nuclear
disaster [50] in 2011, nuclear power plants in Japan were shut down and only some of them
resumed operation from 2016. The reactor neutrinos from these nuclear reactors and also
from the nearby South Korea reactors become irreducible backgrounds in the data sample.
The energy of reactor neutrinos is known to be below 10 MeV. However, some reactor
neutrino events may still leak into the SRN signal region via the energy resolution eﬀect.
Spallation
In the energy range of SRN detection, the dominant backgrounds are spallationinduced radioactive isotopes, including 12 B and 16 N with very large yields per day, as
well as 9 Li and 8 He, which are accompanied by neutron production. For neutron tagging
detection, 9 Li can decay into β − n with a branch ratio of (50.8 ± 0.9)% [51] , faking the
IBD signal.

Spallation cuts based on the time and spacial separation of the muon precedent intime flow will reduce the spallation backgrounds. The knowledge of the backgroundpattern is important in this reduction, and a precise measurement on the yield of 9 Li inwater has been carried in Ref. [52] .
Accidental backgrounds
Any single event in the energy window of SRN that does not accompany a neutron
signal will be a source of accidental background, especially the remaining solar neutrinos
from the solar angle cut, and the radioactive isotopes induced by spallation. The fakeneutron signal arises from mis-tagging. The reduction of this backgrounds mostly depends
on the improvement in the neutron tagging algorithm.
18

Chapter 1

Introduction

Present Status
Supernova relic neutrinos are not observed yet, despite many experimental eﬀorts,
mainly from the neutrino experiments KamLAND and Super Kamiokande (SK). Figure 1.8 shows the 90% upper limit for SRN ν̄e flux from KamLAND [53] , SK-I/II/III [49]and SK-IV results [54] , respectively. The predicted flux for SRN from the constant rate
model which gives the largest SRN event rate is also plotted for comparison, as shown inshadow in Fig. 1.8. The present analysis results from barely exclude any SRN models.

Figure 1.8 The ν̄e flux upper limit from KamLAND [53] in black, SK-I/II/III [49] in blue and
SK-IV results [54] in red. The flux of SRN using the constant SN rate model is plotted in shadow.

KamLAND
KamLAND is a large liquid scintillator detector with 0.6 kiloton fiducial volume,
initially designed for the detection of neutrinos, and has recently upgraded to KamLANDZEN with a xenon ball inside the scintillator looking for double beta decay [55,56] . The
relatively high photon yield and the much lower energy threshold of KamLAND enables
the direct detection of neutron capture signal, thus sensitive to SRN IBD events. Figure 1.9
shows the positron energy spectrum of the final ν̄e sample in KamLAND [53] . The dominantbackground is the NC events from atmospheric neutrinos. Due to the inability to performparticle identification between electrons and gammas, KamLAND cannot tell the NC
events from IBD events. No statistically significant signal is found, and KamLAND gives
19Chapter 1

Introduction

the best upper limit of flux below 17.3 MeV.

Figure 1.9

The prompt positron energy spectrum for the final ν̄e sample at KamLAND [53] .

SK-I/II/III
Figure 1.10 shows the positron energy spectrum of the final ν̄e sample in SK-III [49] ,typical for the SK-I/II/III analysis. The energy threshold in SRN detection window was
set at 17.3 MeV to reject spallation background. Neutron tagging was not employed in thisstudy due to the limit of the front end electronics and trigger system. As Fig. 1.10 shows,the major backgrounds in this SRN analysis are νµ CC, νe CC, µ/π and NC events fromatmospheric neutrinos, all of which are induced by the atmospheric neutrinos. Amongthem, the decay electrons/positrons from the invisible muons produced by the νµ CC isdominant. A fitting of the four backgrounds and relic signal MC is performed on three
data samples of diﬀerent Cherenkov angle, and no statistically significant signal is found.
SK-I/II/III gives the best upper limits for SRN above 17.3 MeV.

20

Chapter 1

Figure 1.10

Introduction

The distribution of positron energy for the final ν̄e sample at SK-III [49] .

SK-IV
Figure 1.11 shows the positron energy spectrum of final ν̄e sample in the previous
analysis at SK-IV [54] . In SK-IV, the DAQ system was changed and the new front end
electronics QBEE enabled the software trigger to collect data for the neutron tagging.
The SRN analysis SK-IV performed the coincidence events search to identify the IBD
signals. With neutron tagging, many of the spallation backgrounds that do not produce
neutrons were greatly suppressed, and the energy threshold for this analysis was lowered
down to 13.3 MeV. The major backgrounds in this neutron tagging SRN search include
the spallation background, atmospheric ν̄e events, and the decay electrons from invisible
muons from atmospheric ν̄µ ’s, among which the spallation background dominates. No
statistically significant signal was found, and model independent upper limits of flux are
extracted for each MeV bin.

21

Chapter 1

Figure 1.11
SK-IV [54] .

Introduction

The distribution of positron energy for the final ν̄e sample in previous analysis at

1.3.3 Geoneutrinos

Geoneutrinos are ∼ MeV anti-neutrinos from the Earth interior. In this section, we

first introduce the energy budget and bulk silicate Earth models. Then we discuss themechanism of geoneutrino production and the importance of its detection and measurement. Finally, a review of the present status of geoneutrino studies in diﬀerent experiments
is presented.
1.3.3.1 Energy Budget of the Earth

Understanding the Earth energy budget is crucial, in that it defines the driving power
for the Earth activities closely related to the living life, including the mantle convection,plate tectonics, and the geodynamo which describes the magnetosphere protecting theplanet from the fatal cosmic radiations [57] . For this aim, many fundamental geologicalquestions have to be answered, as they touch on the geological formation, the chemicalcomposition and layering of the Earth.
TW

To begin with, the Earth surface heat flow is currently estimated to be 46 ± 3[58,59]. Among them, part of the driving power comes from the initial inheritanceof primordial energy since the formation of the planet, released by the accretion as well
22

Chapter 1

Introduction

as the gravitational diﬀerentiation of metal elements sinking to the planet center. The
determination of Earth energy budget will answer the question whether this primordial
energy is exhausted or not. Besides the primordial energy, the other part of the driving
power comes from the radiogenic heat of the natural decay chains of the potassium,
thorium and uranium, also known as the heat producing elements (HPE).
HPEs are believed to reside mainly in the silicate shell of the Earth, also known as bulk
silicate Earth (BSE). BSE refers to the composition of five reservoirs: the DM(Depleted
Mantle), the EM (Enriched Mantle), the CC (continental crust), the OC (oceanic crust),
and the LM (lithospheric mantle), as shown in Fig. 1.12 [60] .

Figure 1.12 A schematic drawing of the structure of the Earth structure [60] . The labels are
explained in the text.

The predictions for the chemical composition of the BSE are model-dependent.
These predictions can be summarized into three classes of distinct predictions for theradiogenic energy (Q):• a) the low-Q models with Q ∼ 11 ± 2 TW, represented by the cosmochemical
models [61] ;• b) the medium-Q models with Q ∼ 20 ± 4 TW, represented by the geochemical
models [62] ;• c) the high-Q models with Q ∼ 33 ± 3 TW, represented by traditional geodynamical
models [63] .

Besides the power budget of primordial energy and radiogenic heat, J. M. Herndon
et al. also proposed a natural self-sustaining fission reactor mechanism at the core of the23Chapter 1

Introduction

planet to explain for the Earth magnetic field and its long-term variation [64] . This is an
exotic hypothesis not widely accepted by the community of geologists.
1.3.3.2 Geoneutrinos

The abundance of HPEs and their distributions inside the Earth are key ingredientsto understand the radiogenic heat from the Earth. One of the methods from the geologicalside is to drill a deep borehole and measure the chemical composition of the sample
taken from it. This method is restricted by the present drilling technique which allows for
only ∼13 km beneath the surface, while the crust typically extends to ∼35 km. Anotherapproach is from the seismic tomography, which employs surface wave and free oscillation
data as well as body wave travel times to resolve the structure of the Earth. However,this approach is sensitive to the density of the Earth layers rather than the abundance ofelements.
A direct measurement can be performed by measuring the product of radioactive
decays, and the only decay product that can reach from the interior of the Earth to thesurface is geoneutrinos. Geoneutrinos are electron antineutrinos ν̄e ’s from the decay chainof HPEs. They serve as a unique probe into the interior of the Earth, benefiting from theextremely weak interaction between neutrinos and matter. An example of geoneutrino
map from the Earth is shown in Fig. 1.13 [60] .

Figure 1.13 Geoneutrino flux at Earth�s surface [60] . The definition of unit TNU will be coveredin Chapter 8.

By detecting the geoneutrino flux, the total amount of HPEs can be derived. The
diﬀerent energy spectrum among geoneutrinos from potassium, uranium, and thorium
24

Chapter 1

Introduction

can be used to obtain the HPE ratios. Furthermore, taking into account the oscillationeﬀect, a tomography of the BSE using geoneutrinos may be feasible. Present BSE models
mainly diﬀer on the description for the Earth mantle. Though lacking the direction
information, a precise determination of geoneutrino flux and energy spectrum could allow
the identification of mantle geoneutrinos [65] , thus discriminating between diﬀerent BSE
models.
The hypothesis of Earth core reactor, or Earth core fission processes [66] , will also
contribute to the geoneutrino flux. The energy spectra of these neutrinos resembles the
spectrum of reactor neutrinos. Since their energy distribution reaches beyond the higher
end of the geoneutrinos from radioactive decay, and thus can be distinguished. In following
context, we discuss mainly on geoneutrinos from radioactive decay, and refer to them asgeoneutrinos. A discussion on Earth core fission neutrinos is included in Section 8.6.2.
1.3.3.3 Experimental Search

Geoneutrino detection has become practical with the recent development of neutrino
detectors [67–72] .
KamLAND performed the first experimental search of geoneutrinos in 2005 [67] .
Assuming a constant Th/U mass ratio at 3.9, the number of geoneutrinos observed at
90% confidence interval was [4.5, 54.2]. Later in 2011, after accumulating 2,135 daysof data, KamLAND published a positive observation with higher significance [68] . The
long-term shutdown of Japanese nuclear reactors from 2011 resulted in a much higher
signal to background ratio in KamLAND, and KamLAND claimed to have observed[69]. The main background is still reactor
116+28−27 geoneutrino events, as shown in Fig. 1.14

neutrinos from outside Japan, while other backgrounds include the contribution from
13

C(α, n) 16 O and accidental coincidence.

25

Chapter 1

Figure 1.14

Introduction

Final geoneutrino data sample observed by KamLAND in 2013 [69] .

Borexino is another liquid scintillator detector that performed experimental studies
on geoneutrinos [73,74] . In 2010, Borexino published the first observation of geoneutrinos
at more than 3σ confidence level [70] . A following up paper in 2013 attempted to fit
the uranium and thorium components individually, though the result was not statisticallysignificant [71] . In 2015, Borexino reported geoneutrino observation by 5.9σ exclusion ofnull hypothesis, as shown in Fig. 1.15 [72] .

26

Chapter 1

Figure 1.15

Introduction

Final geoneutrino data sample observed by Borexino in 2015 [72] .

Geoneutrino measurements should be interpreted with input from geology community to provide information inaccessible by conventional methods [57] . Figure 1.16 shows
the observation from KamLAND and Borexino compared to the expectations from diﬀerent BSE models. Both studies disfavor the exhausting of primordial energy (the intercept
point at the y-axis), yet cannot distinguish among BSE models due to the large uncertainty.

Figure 1.16 The horizontal bands show the geoneutrino observation from KamLAND (left) andBorexino (right). The oblique lines show the expected geoneutrino signal as a function of radiogenic heat. The colored oblique bands show the expectations from diﬀerent BSE models [69,72] .

The uncertainties in both experiments are dominated by statistical uncertainty, contributed mainly by the low statistics and the high reactor neutrino background. In addition,
the ratio of uranium and thorium in geoneutrinos is a nother critical issue that should be
resolved. All the present measurements assumed a fixed chondritic U/Th ratio, and no27

Chapter 1

Introduction

measurement of this value has ever been successful. Future large experiments such as
SNO+ [75] , JUNO [76,77] , HANOHANO [78] , and Jinping [79] will push forward the solution
for these issues.

28

Chapter 2

Chapter 2

The Super-Kamiokande Detector

The Super-Kamiokande Detector

This chapter discusses the Super-Kamiokande detector, including the detector
overview, the mechanism to detect signal, and the key systems related to the operation of
the experiment.
The author contributed to the detector maintenance of ID and OD PMTs, the datataking shift, and the preparation work for upgrading.

2.1 Detector Overview
Located in a cavity of Kamioka mine in Mt. Ikenoyama, Gifu Prefecture, Japan [80] ,Super-Kamiokande (SK) is the successor of the famous Kamiokande experiment which
endeavored the neutrino observation from supernova SN1987 [38] .
Inside the Kamioka mine, SK shares with other low-background experiments under
1,000 m overburden of rock (2,700 m.w.e.), which reduces the cosmic ray muons by about
5 orders of magnitude, down to 2.2Hz at SK. To further shield the natural radioactivities
from the surrounding rock, reinforced concrete of 40-50/ cm was painted to cover thewall of the experimental hall. Above the hall holding the SK detector tank, a large dome
was built for the storage of electronics, with holes on given places that enable in-situ
calibration without opening the tank. This area, as well as other experimental places
where collaborators are supposed to work within, was painted by a polyurethane material
named ‘Mineguard’ to reduce the radon contamination from the surrounding rock in the
air. Figure 2.1 shows the schematic view of the detector.

29

Chapter 2

The Super-Kamiokande Detector

Figure 2.1 A schematic layout of Super-Kamiokande detector and its position inside the
Ikenoyama mountain.

The Super-Kamiokande detector tank is a cylinder 41.4 m in height and 39.3 m indiameter, holding 50 kiloton pure water. A layer of black sheet at 2 m from the tankwall separates optically the detector into two concentric cylinders of an inner detector(ID) and an outer detector (OD), leaving 32 kiloton water in ID. The ID is currently
viewed by 11,129 20-inch photomultiplier tubes (PMTs) distributed with an interspace of
70 cm as the main detection part, while the OD has a looser distribution of 1,885 8-inch
PMTs to veto the cosmic ray muons. These PMTs and their cables are housed by thesame supporting frame at ID edge covered with black polyethylene terephthalate sheets,or simply called black sheet, to prevent optical leak between ID and OD, as shown in
Fig. 2.2.

30

Chapter 2

Figure 2.2

The Super-Kamiokande Detector

The frame structure of the PMT support system in the SK tank.

Inside the SK tank, neutrinos are detected through the interaction in water, producing
charge particles or secondary charged particles which emit detectable Cherenkov photons.
SK is the largest water-Cherenkov detector with energy threshold down to several MeVs,
allowing for various purposes of studies to be performed, including atmospheric neutrinos,
solar neutrinos, supernova (relic) neutrinos, and neutrinos from man-made sources suchas accelerators or nuclear reactors. SK is also competitive in its initial design purpose of
nucleon decay, as well as indirect dark matter search.
The running period of SK can be divided into four phases, from SK-I to SK-IV.
The detector first began operation in April, 1996, with 11,146 PMTs in ID forming aphoton coverage of ∼ 40%. This operation continued till July, 2001, when the detector
was stopped for maintenance such as faulty PMT replacement, and the time between isreferred to as SK-I. During the water re-filling in tank after the maintenance, an accident
in which one of the ID PMTs imploded resulted in a chained reaction with a shock-wave
that destroyed all the ID PMTs underwater then. In 2002, SK resumed operation after a
31

Chapter 2

Table 2.1

The Super-Kamiokande Detector

A summary of SK running periods.

SK Period

SK-I

SK-II

SK-III

SK-IV

Begin
End
Livetime (days)
No. ID PMTs
No. OD PMTs
Photocoverage
Front-end Electronics
Trigger

Apr. 1996
Apr. 2001
1489.2
11,146
1,885
40%
ATM
HardwareOct. 2002
Oct. 2005
798.6
5,182
1,885
19%
ATM
HardwareJul. 2005
Aug. 2008
518.1
11,129
1,885
40%
ATM
HardwareSep. 2008
1775.6
11,129
1,885
40%
QBEE
Softwareredistribution of the remaining ID PMTs above water to allow even coverage of the tankwith a photon coverage of merely ∼ 19%. To prevent the catastrophe of implosion, every

PMT was protected with an acrylic cover and a fiberglass reinforced plastic (FRP) case. In
Oct. 2005, SK opened its tank again to mount the new PMTs produced during SK runningin the tank, and the running period between is referred to as SK-II. After the installation,
SK continued operation with a coverage of ∼ 40% till Jul., 2008, called SK-III. In Aug.,

2008, after calibration and upgrading of the electronics and the data acquisition system,
SK started to run again and continues till today. This phase is referred to as SK-IV. A
summary of livetime and diﬀerences between SK-I - SK-IV periods is included in Tab. 2.1.

2.2 Cherenkov Radiation
When the speed of a charged particle is greater than the speed of light in medium,it radiates Cherenkov photons in the forward region within a cone pattern of Cherenkov
angle θ c along its path. For a charged particle with relative speed β and the medium
refractive index n(λ) dependent on the Cherenkov photon wavelength λ, the Cherenkov
angle θ c can be calculated as:cos θ c =

1
,
βn(λ)

(2-1)

The refractive index of SK water is about 1.33 at 589 nm, therefore, for ultra relativistic
particles with β ≈ 1, the Cherenkov angle θ c ≈ 42◦ . The energy threshold for Cherenkov
32

Chapter 2

The Super-Kamiokande Detector

light Ethr is calculated byEthr = √m
1 − (1/n) 2

,

(2-2)

where m is the mass of the charged particle. For the physics event of interest, electrons
with their small mass are usually ultra-relativistic and their Cherenkov angles peak at 42◦ ,while heavier particles such as µ’s and π’s tend to have lower Cherenkov angles. Further
discussion is included in Section 3.2.1.

2.3 Photo-Multiplier Tubes
2.3.1 ID PMTs

The ID PMTs are 20-inch PMT (R3600) [81] developed by Hamamatsu Photonics, thestructure of which is shown in Fig. 2.3.

Figure 2.3

An overview of the Hamamatsu R3600 PMT.

The photo-cathode is made of bailkali (Sb-K-Cs). The sensitive wavelength region
is between 300 ∼ 600 nm, with the maximum quantum eﬃciency ∼ 20%, as shown in
Fig. 2.4.

33

Chapter 2

Figure 2.4
length [81] .

The Super-Kamiokande Detector

The quantum eﬃciency of the Hamamatsu R3600 PMT as a function of wave-

Photons collected by the photo-cathode emit single or multiple photo-electrons (p.e.)
via the photoelectric eﬀect, and these p.e.’s are then amplified with a gain factor ∼ 107 by
the 11 chain dynodes.

During the propagation from the cathode to the first dynode, p.e.’s are driven by theelectrical field and are easily diverted out of the way by the Earth’s geomagnetic field. To
compensate this eﬀect, 26 Helmholtz coils were deployed surrounding the detector wall,
reducing the external magnetic field from 450 mG to 50 mG.
The PMT dark noise in SK-I was ∼3.5 kHz at a threshold of 0.25 p.e. and has now

increased to ∼5.2 kHz, partially due to radioactivity from the additional acrylic cover andthe FRP case applied from SK-II on.
2.3.2 OD PMTs

The OD PMTs are covered by a wavelength shifting acrylic plate. The incoming
photons are absorbed and re-emitted with a longer wavelength to better match the peak
quantum eﬃciency of the PMT, increasing overall collection eﬃciency by 50%. This
compensates the relatively low coverage but impairs the time resolution due to the absorption and re-emission mechanism. Fortunately, since the OD PMTs are used as a vetocounter only, the worse time resolution does not aﬀect its functionality.

2.4 Water and Air System
Water System
34

Chapter 2

The Super-Kamiokande Detector

It is crucial to maintain the SK tank water at a constant and high level of purity
for the propagation of photons. The absorption and scattering in the tank water must be
kept as low as possible to ensure both suﬃcient photon statistics and good time response.
Radioactive isotopes in water may form a significant background in low energy detection
and should also be eliminated. Besides, the water quality has to be stable and constantly
monitored, so as not to contaminate the data sample with any detector-level abnormality.
The fresh water to be purified and filled into the tank comes from two streams inside
the Kamioka mine, supplied by the natural rain and snow melt in the mountain. The water
is then pumped through a purification system and is continuously circulated through apurification system with a flow of ∼ 60 tons/hour, as shown in Fig. 2.5 [82] .

Figure 2.5

A schematic of the water purification system in SK [82] .

Various filters and systems are employed to remove contaminants, including an ion
exchanger, a vacuum degasifier and membrane degasifier to remove the radon gas, a size
specific filters and an ultra filter (UF), and a reverse osmosis (RO) filter. Water entrance
in the bottom of the tank and removal points in the top of tank have been calculated andcarefully chosen to reduce convection as much as possible, keeping water uniformity. To
further reduce convection driven by thermodynamics, heat exchangers (HE) are used tomaintain the supply water at a constant temperature of ∼ 13 ◦ C, with a variation of 0.01◦

C [82] . This low temperature, as well as a UV sterilizer, suppress any potential bacterial

growth. Still, nonuniformity of water temperature is observed, indicating better water
quality in the tank bottom, as shown in Fig. 2.6.

35

Chapter 2

The Super-Kamiokande Detector

Figure 2.6

Water temperature in SK tank.

Air Purification
The natural mine air is radon-rich from the surrounding rocks produced by naturaluranium decays, imposing a background for low energy detection and also potential healthrisk due to inhalation. The air flow has a seasonal variation, which causes the diﬀerent
radon contamination level of ∼ 30 Bq/m3 in winter and ∼ 1500 Bq/m3 in summer [83] .

A special air supply system consisting of a large air blower, air filters and a heatexchanger is installed at the entrance of the mine to supply fresh air from outside with arate of 70 m3 /min, thus keeping the radon (Rn) concentration as low as ∼ 50 Bq/m3 . To

further reduce Rn concentration in the tank, a special Rn free air system was developed
to keep the input Rn concentration to the tank at 0.06 ± 0.05 mBq/m3 [82] .

2.5 Electronics and Data Acquisition
Atop the SK tank in the experimental dome, there are four electronic huts hosting
the high voltage power supplies and the electronic system, and a central hut hosting thetrigger system and the control electronic.
2.5.1 Electronic System

In 2008, Super-Kamiokande experiment installed a new electronic system which
tend to remove the use of hardware trigger [84] . In this system, all the data recorded by36

Chapter 2

The Super-Kamiokande Detector

the PMTs are output. A more sophisticated software trigger is implemented in the online
data acquisition system. The front-end electronics uses new QBEE system (QTC-BasedElectronics with Ethernet), where QTC refers to an ASIC developed as a high-speed
charge (Q)-Time converter. One QBEE module takes input from 24 PMTs at most withstable observance and fast digitization, which allows a software-based trigger system witha merger PC located in the central hut, as shown in Fig 2.7.

Figure 2.7

A schematic showing the trigger system used in SK-IV.

During the digitalization in QBEE, the PMT charge is still integrated but with three
input channels of diﬀerent gains 1, 1/7, and 1/49, thus to improve the charge resolution
for a wider range of 0.2 to 2500 pC. The output from the QTC modules is then sent to the
TDCs to measure the pulse width and digitalized later by an FPGA with the charge andtiming information, before being sent to the front-end PCs which pass the hit information
onto the merging PCs. Finally, the merge PC applies the software trigger thresholds toevery event with diﬀerent trigger width and determines whether to store or remove theselected event on disk.
2.5.2 Online DAQ and Trigger

Diﬀerent trigger thresholds drive the classification of signal: Super Low Energy(SLE), Low Energy (LE) and High Energy (HE) triggers. The thresholds for these types
depend on diﬀerent SK periods, and the thresholds in SK-IV are shown in Table 2.2. The
minimum threshold of SLE at 31 PMT hits approximately defines the SK energy thresholdat 3 MeV for electrons.
The trigger threshold as well as trigger time is diﬀerent from previous periods in37

Chapter 2

The Super-Kamiokande Detector

Table 2.2

A summary of QBEE triggers.

SK-IV triggers

Hits/200ns Threshold

Event Width (µs)

OD
SLE
LE
HE
SHE
AFT

22
34→31
47
50
70→58
SHE w/o OD[-0.5, 1.0][-5, 35][-5, 35][-5, 35][35, 535]

SK-IV. Diﬀerent trigger types do not share the same trigger width to eﬃciently use thedisk space, as SLE triggers are too frequent to expand their time width, while HE trigger
are rare enough and related pre- or post-activities are of interest in atmospheric neutrino
analysis. The time window is 40 µs for LE or HE triggers. For SLE triggers, it is 1.5 µs.
Besides, a special high energy (SHE) trigger was first introduced in SK-IV to enable theneutron capture signal tagging, with relative high threshold (lowered to 58 hits in Sep.
2011). If an SHE trigger does not accompany an OD trigger, i.e., it’s not an apparent
muon event, an additional ‘After Trigger’ (AFT) is issued. The 500 µs of data following
the AFT trigger will saved for future analysis of neutron captures. The corresponding
trigger thresholds and trigger window widths are shown in Table 2.2.

38

Chapter 3

Chapter 3

Calibration and Reconstruction at SK

Calibration and Reconstruction at SK

This chapter covers the detector calibration, simulation, and reconstruction. For eachsection, we will introduce the global picture of the system in the SK collaboration, whileemphasizing on the contributions from the author.

3.1 Detector Calibration
Calibration quantitatively measures the detector performance, providing crucial parameters and systematic uncertainty for data analysis. Depending on the level of measured
items, the calibration performed at SK can be split into three categories: PMT calibration,water transparency calibration, and energy scale calibration.
On detector calibration, the author was responsible for the nickel related analysis
of QE update and top bottom asymmetry estimation, as well as the water transparency
measurements by laser and by decay electron. The author also took part in related
hardware work.
3.1.1 PMT Response Calibration

PMTs provide timing and charge information, which are used in both energy andposition reconstructions.
PMT charge is usually parameterized as the product of two factors: the PMT gain
and quantum eﬃciency. Gain refers to the conversion factor from the generated numberof p.e.’s on the cathode to the charge output of the PMT in pico Coulomb (pC). Quantum
eﬃciency (QE) by definition refers only to the ratio of p.e.’s emitted from the cathode to
the number of incident photons. However, since the first-dynode collection eﬃciency can
not be isolated from the measurement of QE, we define the QE here as the ratio of p.e.’scollected by the first dynode to the number of incident photons on the cathode.
For the low-energy events, most PMT hits are single p.e., and the QE calibrationis critical, while for the high energy events, where charge information is required to get
the exact number of p.e.’s on a single PMT, gain calibration is also crucial. Since the
PMTs used at SK are mostly from the same model with only the diﬀerence in production
batches and the fluctuations PMT by PMT, an ‘absolute gain’ is defined as the average
amplification factor for all PMTs, while a ‘relative gain’ is used for the individual PMT
39

Chapter 3

Calibration and Reconstruction at SK

diﬀerence. The overall QE is absorbed in a ‘COREPMT’ parameter to be mentioned in
LINAC calibration, and the ‘QE table’ refers to a normalized QE factor PMT by PMT.
3.1.1.1 High Voltage

PMTs must work under proper and relatively uniform high voltage to produce similar
output charge for the same incident photons. At SK, this high voltage value is adjusted by
the response to an isotropic light source: scintillation light.
A scintillator ball is placed at the center of SK tank as a permanent fixture, and istriggered by the light produced from a xenon (Xe) lamp passes through an optical fibre,
as shown in Fig. 3.1.

Figure 3.1 A sketch of the high voltage calibration by a scintillator ball triggered by a Xe lamp.
The red dots illustrate positions of the pre-calibrated reference PMTs.

To compensate for the geometric acceptance, 420 reference PMTs were calibrated
one by one before the PMT installation into the tank and distributed uniformly as shownin Fig. 3.1. The HV input for each PMT was adjusted to match its charge output with the
pre-calibrated PMT’s in the same geometrical location.
3.1.1.2 Relative Gain

The normalized ‘relative gain’ is determined by a laser system with two setups
generating flashes of diﬀerent intensity. The light source is a nitrogen laser emitting
photons whose wavelengths are shifted by a dye to match the PMT response spectrum.
The emitted photons then pass through an optical fiber to a diﬀuser ball near the tankcenter, as shown in Fig. 3.2.
40

Chapter 3

Figure 3.2

Calibration and Reconstruction at SK

The overview of the timing calibration system.

The two intensities give diﬀerent diﬀerent hit patterns. The high-intensity flash
illuminates every PMT with multiple photons and the low-intensity flash fires only several
PMTs, and thus enabling a reasonable assumption of a single photon hit. Denoting the
PMT id as i, the high-intensity flash gives the charge Q obs (i) and low-intensity flash gives
the number of events that records an over threshold hit Nobs (i), i.e., the hit frequency. The
geometrical acceptance and QE are therefore cancelled out:
Q obs (i) ∝ Is × a(i) × ϵ qe (i) × G(i)Nobs (i) ∝ Iw × a(i) × ϵ qe (i)(3-1)

where Is and Iw are the average intensities of high and low intensity flashes, respectively,a(i) is the acceptance of ID-PMT i, ϵ qe is the QE, and G(i) is the PMT gain. The overall‘gain’ G(i) relies on the precision of laser intensity, but the relative gain can be directly
derived as,
G(i) =

Q obs (i),Nobs (i)Fnorm
41

(3-2)

Chapter 3

Calibration and Reconstruction at SK

where Fnorm is a normalization factor. The distribution of relative gain at SK is shown in
Fig. 3.3.

Figure 3.3

Distribution of the relative gain of PMTs at SK.

3.1.1.3 Absolute Gain

The calibration of the absolute gain value is carried with a nickel (Ni) source emitting
isotropic γ’s of 9 MeV from the neutron capture 58 Ni(n, γ) 59 Ni, where the neutrons are
emitted from a 252 Cf source [85] . For uniformity, the Ni-Cf source is shaped as a sphericalmelon ball, and deployed at the tank center for the absolute gain calibration. The γ’s
intensity and energy is so low that the average charge produce by every event is only 0.004
p.e./PMT, and thus ensure with Poisson statistics that more than 99% of the hits produce
only single p.e. on a PMT.
The relative gain value and dark hits eﬀect should be corrected before deriving theabsolute gain. The first item is corrected by dividing the charge with the relative gain
obtained as described in Section 3.1.1.2. To account for dark hits, an on- and oﬀ-time
windows are defined by the expectation whether a PMT could possibly be hit by thesource, and the data in the oﬀ-time window is considered as dark noise to be subtracted
from the on-time data. The charge distribution from all ID PMTs after correction is shown
42

Chapter 3

Calibration and Reconstruction at SK

in Fig. 3.4, where a linear extrapolation is applied to represent the region below the 0.3
pC threshold.

Figure 3.4

The single p.e. distributions with a linear extrapolation under 0.3 pC.

Averaging from this single charge distribution gives the conversion factor from pC
to single p.e. as 2.658 pC / p.e. in SK-IV. A long-term gain increase has been observedat SK as well as many other experiments using PMT as photo sensor. No clear reason has
been identified, and a correction is included in data analyses run by run to account for thiseﬀect.
3.1.1.4 Quantum Eﬃciency

The normalized QE table is crucial for the reconstruction of low energy events. QE
is measured by the Ni-Cf used in the absolute gain calibration so that the intensity of lightsource is low enough to satisfy Eq. (3-1). This time the acceptance as well as the solid
angle has to be corrected. While the latter can be directly calculated, a Monte-Carlo (MC)simulation is used to predict the number of photons arriving at each PMT. The QE tableis calculated by counting the number of observed hits in data and taking the ratio between
the observed hits to the predicted number of hits from MC, with an overall normalization
to remove the dependence of the absolute light intensity.
43

Chapter 3

Calibration and Reconstruction at SK

The setup for MC is important to obtain a proper QE table, and it should take
into consideration the water transparency and the nonlinearity of the transparency toreproduce the acceptance in data. In SK-IV, the water transparency variation inside thetank is modeled by a piecewise linear function established by measuring the temperature
profile throughout the ID. Details will be covered in Section 3.1.2.4. Previously in SK-IV,
the QE table was produced using SK-III data during the water convection period, when
the nonuniformity of water was believed to be zero. However, a recent study showedthat the QE table had a ϕ direction nonuniformity, which is related to the convection and

1.03

1.03

1.02

1.02

1.01

1.01

1.01

1
0.99

QE value

1.03
1.02
QE valueQE value

circulation of water, as shown in Fig. 3.5.

1
0.99

1
0.99

0.98

0.98

0.98

0.97
−2000

0.97
0

0.97
0

−1000

0
Z [cm]

1000

2000

1

2

3

4

5

6

φ

500

×
1000 1500 2000 2500 3000
2
2
R [cm ]

Figure 3.5 Previous QE table used in SK-IV in z (left), ϕ (middle), r (right) direction. Systematic
nonuniformity was observed.

Now a new QE table has been calculated using the nickel data without water convection, so as to avoid the nonuniformity in ϕ direction. The expected nonuniformity
in z-direction is included in MC to compare with data, while the solid angle is directly
corrected analytically for both data and MC,
N ′ = Nobs (i) × R(i) 2 /α(θ(i)),(3-3)

where Nobs (i) is the observed hit in i-th PMT, R(i) is the distance from the i-th PMT
to the event vertex, θ(i) is the incidence angle of a photon to the PMT and α is thecorresponding solid angle. Some position dependence remains even after this acceptancecorrection, including the angular acceptance on the PMT surface, the reflection fromneighboring surfaces, the scattering and absorption by the water, etc. These eﬀects arecompensated in MC. Finally after normalization, the relative QE of the ID PMTs is
obtained as shown in Fig. 3.6. This quantity is tabulated and used in the MC simulations.

44

Calibration and Reconstruction at SK
1.03

1.03

1.02

1.02

1.01

1.01

1.01

1
0.99

QE value

1.03
1.02
QE valueQE value

Chapter 3

1
0.99

1
0.99

0.98

0.98

0.98

0.97
−2000

0.97
0

0.97
0

−1000

0
Z [cm]

1000

2000

1

2

3

4
φ

5

6

500

×
1000 1500 2000 2500 3000
2
2
R [cm ]

Figure 3.6 Present QE table used in SK-IV in z (left), ϕ (middle), r (right)-direction. Good
uniformity is observed except for the z-direction, where the water quality nonuniformity is still
not well-understood.
3.1.1.5 Timing Calibration

Hit time is the only information used in the vertex and direction reconstructions of
the low energy events. The response time of a readout channel depends mainly on the
PMT transit time, the length of a PMT signal cable, the processing time of electronics,
and the time-walk eﬀect due to the dependence of rise time on the pulse amplitude.
In the timing calibration, the light source is the same nitrogen laser as that used in
the relative gain calibration shown in Fig. 3.2. The diﬀuser ball is again placed near thecenter of the tank. The directional nonuniformity of the photon emission time is measured
and observed to be within 0.2 ns.
Due to the correlation between the time response and pulse height, i.e., charge, thecalibration gives a 2-dimensional table. The time of flight (ToF) must be subtracted
from the recorded hit time, which introduces an uncertainty of ±50 ns. The timing

distribution in every of the 180 bins on the charge axis is parameterized as an asymmetric
Gaussian function and evaluated with the same data set. The smoothed 2-dimensional
TQ distribution is then fitted by a piecewise polynomial function. The function with fitted
parameters is then used in MC.
3.1.2 Water Transparency Measurement

Three kinds of water transparency measurements are performed at SK, namely thewater laser measurement for the scattering and absorption of photon in water, the throughmuon measurement for the eﬀective total attenuation length in the high energy physics
group, and the decay-electron measurement for the eﬀective total attenuation length in the
low energy physics group.
This section discusses the water laser measurement and the decay-electron measurement only, since the topics for this thesis are concentrated on the low energy physics.
45

Chapter 3

Calibration and Reconstruction at SK

Also discussed is the water transparency nonuniformity in the z-direction, i.e., top-bottom
asymmetry in water.
3.1.2.1 Water Laser Measurement

The attenuation length in water is obtained by combining the measurements on the
scattering and absorption of the optical photons. By definition, the scattering coeﬃcientis measured by the hits scattered oﬀ the direction of the input light, and the absorption
coeﬃcient can be measured by the total light intensity. However, this is not practical for an
in-situ monitoring. At SK, using several mono-direction light sources with well-known
wavelengths, we compared the timing and spatial distributions of the light with thosefrom MC, and extracted the light absorption and scattering coeﬃcients as functions ofwavelength.
Experimental setup
The light source in this measurement referred to as the water laser system, is acombination of dye and N2 lasers of wavelengths 337, 375, 405, 445 and 473 nm. The
laser beam is directed into SK tank via the optical fibers connected to injectors in diﬀerent
positions, as shown in Fig. 3.7. There are 7 injection positions for the laser beam, with
2 on the top endcap and 5 on the barrel region in a vertical line. The present water laser
analysis uses only data from one of the top injectors (called new-top) beaming down. Data
from other injectors, especially from the position on the barrel beaming horizontally, havethe potential to resolve the top-bottom asymmetry in SK tank water, and recently a newgroup starts to analyze the horizontal laser data.

46

Chapter 3

Figure 3.7

Calibration and Reconstruction at SK

Schematic view of the water laser system.

Analysis method
In the water laser analysis, the SK tank is divided into 7 sections, namely, the top
endcap, barrel 1 through 5 from top to bottom, and the bottom endcap. After the water
laser event selection by the calibration trigger attached, PMT hits are extracted from thedata file with charge and hit time information. To avoid the inclusion of saturated PMTs,
the hits in the cluster region facing the beam are rejected, which, for the new-top injector,
is in the bottom endcap. The remaining hits are then corrected for the ToF and filled witha weight of PMT charge in 7 hit-time histograms, which correspond to the 7 sections of
the SK tank.
The laser intensity is a nuisance parameter which impacts the sensitivity of this study.
However, it is not easy to measure the laser intensity. Although a measurement of total
charge in the cluster region facing the light beam can provide a reference value to tune
the water laser intensity in MC, this value is aﬀected by the saturation eﬀect of PMTs.
Besides, it is not realistic to reproduce MC for every intensity measured. To eliminate thefluctuation of laser intensity in the water laser analysis, the 7 hit-time histograms should
be normalized to remove the impact of laser intensity. Consequently, this water laser
measurement is not very sensitive to the absorption parameter.
Many MC samples are generated with diﬀerent sets of scattering and absorption
parameters. The deviation of these 7 histograms between data and a MC sample is47

Chapter 3

Calibration and Reconstruction at SK

calculated by a χ2 test. To ensure suﬃcient statistics, the range for calculation in thehistogram is changed for each region. The input parameter set for the MC sample with theminimum χ2 is determined to be the measured water scattering coeﬃcients. An exampleof the fitting histograms is shown in Fig. 3.8.
1500

1600

1700

1800

1900

1600

1700

1800

1900

1600
1600

1700
1700

1800
1800

1900
1900

1600
1600

1700
1700

1800
1800

1900
1900

1600

1700

1800

1900

1600
1600

1700
1700

1800
1800

1900
1900

1600

1700

1800

1900

1600

1700

1800

1900

0.004
0.003
0.002
0.001
1500
0.004
0.003
0.002
0.001
1500
1500
0.004
0.003
0.002
0.001
1500
1500
0.004
0.003
0.002
0.001
1500
0.004
0.003
0.002
0.001
1500
1500
0.004
0.003
0.002
0.001

1500
0.004
0.003
0.002
0.001
1500

Figure 3.8

An example of water laser data (black points) and MC (red line) fit.

3.1.2.2 Calibration result

At SK, the input parameters are defined as those for the absorption αabs (λ), thesymmetric scattering αsym (λ) described by 1 + cos2 θ, and the asymmetric scattering
αasy (λ) described by 1 + cos θ, where θ defines the angle between the incident direction
and the reflected direction. The water transparency can be obtained as
L(λ) =

1.
αabs (λ) + αsym (λ) + αasy (λ)

48

(3-4)

Chapter 3

Calibration and Reconstruction at SK

For the 5 wavelengths available in water laser data, these three parameters are fit withpolynomials of λ −1 to obtain the wavelength dependent curves,
P1
+ C,
λ4
P1
P5
αsym = 4 × (1 + ),
λ
λ2
)
(
P7
2
αasy = P6 × 1 + 4 × (λ − P8 ) ,λαabs = P0 ×

(3-5)

C = P0 × P2 × (λ/500) P3, λ ≤ 464nm,
where P0 ∼ P8 are the fitting parameters. These polynomial function definitions are

empirical and do not exactly represent real physical properties [86] . The functions used inpresent SK simulation were calibrated in 2009 and are shown in Fig. 3.9

Figure 3.9

The calibration of water scattering parameters in 2009 [86] .

As shown in Fig. 3.10, the symmetric scattering parameter shows a good stability
over time, while the sensitivity is relatively poor for the absorption parameter and theasymmetric scattering parameter. The slight increasing trend of water parameter is dueto the uncorrected threshold eﬀect in hits due to the gain increasing as described in
Section 3.1.1.3.

49

Absorption (m)Chapter 3

Calibration and Reconstruction at SK

0.014
0.012
0.01
0.008
0.006
0.004
0.002

Symmetric (m)

0

2009

2010

2011

2012

2013

2014

2015

2016

2017
Year

2009

2010

2011

2012

2013

2014

2015

2016

2017
Year

2010

2011

2012

2013

2014

2015

2016

2017
Year

0.02
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0

Asymmetric (m)

-3

0.6

×10

0.5

0.4

0.3

0.2

0.1

0

2009

Figure 3.10

Water parameter stability over time.

3.1.2.3 Decay-electron Measurement

Although the water laser calibration can provide 5 diﬀerent water transparency
values for the 5 available diﬀerent wavelengths, it is desired to measure the eﬀective watertransparency directly for Cherenkov photons. Since water transparency keeps changing
inside the SK tank on a daily basis due to the water circulation, etc., a daily sample
with suﬃcient statistics is necessary for the calibration. The 2.2 Hz muon rate indicatethat many muons are stopped inside the SK tank, and quickly decay to produce Michelelectrons. These decay-electrons radiate Cherenkov photons with the well-known Michel
spectrum and is therefore suitable for the water transparency calibration.
Data selection
Unlike the water laser data where events are selected directly by the calibration trigger,
decay-electron events have to be selected with certain criteria to remove the backgrounds:
50

Chapter 3

Calibration and Reconstruction at SK

1. 3.0 µsec ≤ ∆t ≤ 8.0 µsec, where ∆t represents the time diﬀerence between theparent muon and the daughter decay-electron candidate;

2. L wall > 2 m, where L wall is the distance between the reconstructed vertex of the decay
electron candidate event and the ID wall, i.e., the fiducial volume for decay-electron
events is 22.5 kiloton;
3. |⃗x µ − ⃗x e | < 250 cm, where ⃗x µ is the reconstructed stopping point of cosmic ray
muon and ⃗x e is the reconstructed decay electron candidate vertex.

Analysis method
After the event selection, the distance r between the ith PMT and the decay electron
candidate is calculated. All the ID PMTs are grouped by r and divided into 60 bins. Aniis calculated aseﬀective hit for every PMT Neﬀ’i
Neﬀ’
= (Xi + ϵ tail − ϵ dark ) ×1
Nall
Rcover××,
Nnormal S(θ i, ϕi ) QEi(3-6)

where Xi is the gain corrected occupancy of a PMT to account the eﬀect of multiple
1)/x i , and x i is the ratio of the number of hit PMT’s to thephotoelectrons, Xi = log( 1−xitotal number of PMT’s in a 3 × 3 patch around the i-th PMT; ϵ tail and ϵ dark are correction

factors respectively for the tail eﬀect and dark noise; Nnormal accounts for the bad tubes

and dead channels; Rcover corrects the acceptance of the candidate vertex to the i-th PMT,
i.e., solid angle; QEi is the QE table value for the i-th PMT. More details are explainedi
is calculated for every r bin, andin the context of Eq. (3-21). Then the average of Neﬀ’i
) is plotted against r, as shown in Fig. 3.11. This histogram is fitted by a linearln(Neﬀ’function within the range from 1,200 cm to 3,500 cm. The inverse of the fitted slope bydefinition is the attenuation length.

51

ln(Nieff’)

Chapter 3

Calibration and Reconstruction at SK

1.5

1.45
1.4
1.35
1.3
1.25
1.2
1.15
1.1
0

500

1000

1500

2000

2500

3000

3500
r [cm]i versus r (blue solid), fitted by a linear function within
Figure 3.11 A typical histogram of Neﬀ’
the range from 1,200 cm to 3,500 cm (red solid). The fitting range is indicated by a black dottedline.

Result and validation
Since SK is under a rock shielding of 2,700 m.w.e., the number of decay-electron
events from muons per day are still limited. To ensure the stability of fitting, two methods
have been adopted. The first is to fix the intercept on the y-axis, which used to cause aproblem in obtaining the water transparency due to the gain increase in SK-IV, but has
been fixed by tuning the conversion factor C, which describes the threshold eﬀect, andconverts the gain increase into the hit increase. The calculation of C will be covered in
Section 3.3.3.2. After the fix, the y-intercept is so stable that can be regarded as a constant
1.499, as shown in Fig. 3.12. The second method is to take a ±7-day running average ofwater transparency. Figure 3.13 shows the water transparency evolution with time. The
variation of the water transparency is observed within 10% throughout the SK-IV period.

52

Y Intercept

Chapter 3

Calibration and Reconstruction at SK

1.8
1.6
1.4
1.2
1
0.8

1000

1500

p0

1.499 ±0.0002129

p1−6.87e−07 ±2.087e−07

2000

2500

3000

3500

4000
elapsed day

Water Transparency (m)Figure 3.12 Stability of fitted y-intercept after the threshold eﬀect correction. X-axis is theelapsed day from the beginning of SK-IV. A good stability over SK-IV period is observed.

200
180
160
140
120
100
80
60
40
20
0

1000

1500

2000

2500

3000

3500

4000
elapsed day

Figure 3.13 Water transparency evolution with time. A ±7-day average is used in this figure.
X-axis is the elapsed day from the beginning of SK-IV. Water transparency varies within 10%.
i
The sum of Neﬀ’
, Neﬀ , is a direct indicator of event energy, as will be discussed in

Section 3.3.3.1. The calculation of Neﬀ is sensitive to the water transparency, and thus astable Neﬀ in some sense verifies the estimation of water transparency. Figure 3.14 shows
the average Neﬀ of the decay-electron spectrum with a good stability.

53

Neff

Chapter 3

Calibration and Reconstruction at SK

283
282
281
280
279
278
277
276
275

Figure 3.14line).

2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Year

Neﬀ evolution with time. Blue lines indicate 0.5% deviation from average value (red3.1.2.4 Top-bottom Asymmetry

A top-bottom asymmetry (TBA) has been observed in SK data, i.e., after all of theabove calibration results corrected in a controlled sample, top PMTs still do not get as
many hits as bottom PMTs do. The most possible reason is that the water transparency is
not uniform throughout the tank, and the water quality has a z-dependence, thus causing
the TBA eﬀect. As shown in Fig. 2.6, the water temperature is varying along the z-axis.
A z-dependent water transparency model is constructed to accommodate this eﬀect,
αabs (λ, z) = αabs (λ) × (1.0 + βz)(z ≥ −1, 100cm),

αabs (λ, z) = αabs (λ) × (1.0 − 1, 100 β) (z ≤ −1, 100cm),(3-7)

where β is the slope in the unit of cm− 1, an indicator for the top-bottom asymmetry level.
This z-dependent water transparency is shown in Fig. 3.15, in three diﬀerent parameter
sets. Only αabs is modelled with z-dependence, while both scattering parameters are
assumed to be constant.

54

Z / cm

Chapter 3

Calibration and Reconstruction at SK

2000
TBACD: 4

1500

Abs: 1.0

1000
500
0

TBACD: 10
Abs: 1.0
TBACD: 10−500

Abs: 1.1

−1000
−1500
−2000
0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25 1.3
Absorption

Figure 3.15 Three examples of z-dependent water model parameter sets. Labels and the corresponding models are in the same color. The scattering component is assumed to be constant,while the absorption component stays as a constant below -11 m and increases linearly above.

A top-bottom asymmetry parameter (TBA) is constructed as
TBA =< top > − < bottom >,< barrel >(3-8)

where <region> represents the mean hit rate of PMTs in each region corrected by acceptance and gain increasing only, without any relative QE, water transparency or dark noisecorrection. TBA is monitored by the Xe laser data discussed previously in the high voltage
calibration and the Ni-Cf source data used in absolute gain calibration and QE calibration.
The time variation of TBA over the SK-IV period is shown in Fig. 3.16, with blue points
measured by the Xe lamp and red points measured by the monthly Ni-Cf calibration. Bothshow a good agreement.

Figure 3.16 TBA time variance in SK-IV. Blue points are measured by the Xe lamp and red
points measured by the monthly Ni-Cf calibration. Both show a good agreement.
55

Chapter 3

Calibration and Reconstruction at SK

To relate this phenomenal TBA parameter to the water slope β, the hit map from thenickel data is fitted by diﬀerent β values in MC, where the hit number is again corrected byacceptance only. This χ2 fitting was carried with 10 randomly chosen runs in 2009-2010
and a conversion function from TBA to β was constructed as
β = (−0.163 × TBA2 − 3.676 × TBA) × 0.01.

(3-9)

A validation with recent run data was done and the result agreed with the previous function.
3.1.3 Energy Calibration

The calibration of absolute energy scale directly determines the energy for low energy
events at SK. To calibrate the absolute energy scale, a linear accelerator for single electronenergy calibration (LINAC) and a deuterium-tritium neutron generator (DT) are regularly
performed on SK.
3.1.3.1 LINAC Calibration

LINAC is short for the LINear ACcelerator installed above the SK tank, with whichdata are taken at various positions inside the fiducial volume, tracking detector responsein the variables relevant to physics studies [87] .
LINAC overview
This accelerator was initially designed for medical purposes in 1978 and later modified and installed at SK in 1996. Figure 3.17 shows the present setup, where LINAC
is fixed in a tunnel near the dome above the SK tank. The electron beam generated by
the accelerating gun is tuned in direction by the steering magnet D1-4 before reaching
diﬀerent positions in the tank. The electron energy is calibrated by a germanium detector
with keV-level resolution. To exclude multi-electron events, besides software-level cuts,a special collimator is used to control the number of electrons entering the transportation
tube. The beam intensity is tuned to very low level, with only 10% triggers containing
any electrons. This ensures ∼ 1% multi-electron event ratio.

56

Chapter 3

Calibration and Reconstruction at SK

Figure 3.17 The LINAC and its beam line at the SK detector. The 22.5 kiloton fiducial volume
is indicated by a dashed line. Circled numbers mark the positions for the previous calibration in2016.

Data taking
During SK-IV, LINAC calibrations were performed 5 times, in 2009, 2010, 2012,2016, and 2017, respectively. The beam positions are limited by the length and conjunctionof the beam pipes as well as the calibration hole locations. An arbitrary combination of
three calibration holes along the x-axis at -12 m, -6 m and -4 m, and three depths along
the z-axis at -15 m, 0 m and 15 m are used in sequence for the calibration data taking.
The electron energy ranges from 4.4 MeV to 18.0 MeV.
Analysis result
To analyze the LINAC calibration data, Monte Carlo samples with most of theparameters measured by other calibration sources were produced to tune the overall
energy response factor, or COREPMT. COREPMT is determined by a comparison of thepeak positions in the Neﬀ distributions between data and MC.
LINAC calibration in 2016 determined this COREPMT to be ∼0.87. The diﬀerencesof Neﬀ between data and MC with the tuned COREPMT in diﬀerent positions were treatedas the systematic uncertainty introduced by position dependence, as shown in Fig. 3.18.
This energy scale variation is below 1%.

57

Chapter 3

Figure 3.18
energies.

Calibration and Reconstruction at SK

Data and MC diﬀerences in 2016 LINAC calibration for various positions and3.1.3.2 DT Calibration

Though diﬀerent injection positions are possible, electrons produced by the LINAC
are still limited in direction: the beam goes only downward, thus unable to accommodate
the angular dependence which is calibrated by the DT calibration [88] .
DT overview
The DT generator emits 14.2 MeV neutrons via
3

He +2 H →4 He + n.

(3-10)

This neutron interacts with oxygen to produce 16 N by
16

O + n →16 N + p.

(3-11)

The 16 N then decays to 16 O, producing a 6.1 MeV γ ray and a 4.3 MeV β (66%), or a 10.4
MeV β (28%),16

N →16 O + e− + ν̄e .
58(3-12)

Chapter 3

Calibration and Reconstruction at SK

The half-life of 16 N is 7.13 seconds.
Since the beta energy is not monochronic, these beta rays cannot be directly used
for the absolute energy calibration. However, the flexibility of the DT device and theuniform direction of β’s and γ’s from the 16 N decay provide a unique measurement on the
directional and positional dependence of energy scale, which allows a systematic study of
low energy analysis.
Data taking
A sketch of the DT calibration is shown in Fig. 3.19 [88] .

Figure 3.19

The schematic view of DT calibration method [88] .

The data taking procedures can be summarized as:
1. As pad a) of Fig. 3.19 shows, the DT generator is first lowered to the assigned
position by a crane.
2. Then, as pad b) shows, the generator is fired, producing ∼3 million neutrons interacting with oxygen.

3. On pad c), the generator is lifted immediately after firing by the crane, 2 m above
the initial position where it is filled with 16 N to avoid making any shadow.
4. No data is taken in the above steps until step 3 is completed to avoid electronicnoise. This data taking lasts for 40 seconds.
The above cycle is repeated ∼25 times at a single location to accumulate ∼ 300,000 16 N
events for further analysis with reconstruction tools and MC comparison.
Analysis result
The position and directional dependence of the energy scale calibrated by the DT
59

Chapter 3

Calibration and Reconstruction at SK

data is shown in Fig. 3.20.

Figure 3.20 The position (left) and direction (right) dependence of the diﬀerence of eﬀective hit(Neﬀ ) peak between the data and MC simulation. Left: The horizontal axis shows the z-position[m]. Right: The horizontal axis shows the cosine of the zenith angle.

Figure 3.21 shows the stability of energy scale from the DT data set in SK-IV. The
fluctuation is within 0.3% level during the SK-IV phase.

Figure 3.21
phase.

The stability of energy scale obtained by the DT calibrations during the SK-IV

3.2 Detector Simulation
MC simulation is used for most the analysis and the calibration, as well as thesystematic estimation. At SK, MC is separated into the detector- and physics-level.
For SK, the oﬃcial simulation package has a generator for atmospheric neutrino related
physics in higher energy range for the interaction calculation, while for low energy physics
especially for SRN study, the spectra of positron and neutron produce from IBD interaction
are manually set.
60

Chapter 3

Calibration and Reconstruction at SK

The oﬃcial simulation package at SK is referred to as SKDetSim, which is basedon GEANT 3.21. Most physics processes are simulated by GEANT 3 packages, whilesome of the crucial processes such as photon propagation in water are customized withcalibration results.
The author’s contribution to the SKDetSim package includes maintenance for photon
propagation simulation and unit test with nickel data.
3.2.1 Cherenkov Photon Production

Charged particles with energy beyond the Cherenkov light emission thresholdmEthr = √,1 − (1/n) 2(3-13)

generate Cherenkov light in a cone with an open angle θ c ascos θ c =1,nβ(3-14)and the diﬀerential number of the Cherenkov photons per unit length travelled per unit
wavelength isd2 N
1
2πz 2 α2πz 2 α 2(1−sin θ c,
=
)
=
dλdx
λ2
β 2 n2 (λ)λ2(3-15)

where n is the refractive index in SK water, m is the mass of the charged particle, β is thevelocity of the charged particle in unit of vacuum light speed c, z is the particle charge
in unit of e, α is the fine structure constant, and dx is the infinitesimal range of travelinglength.
The refractive index n is determined with considerations including water temperature,
water pressure, etc. For a typical n value at SK, the thresholds of the Cherenkov emission
for common charged particles in physics analysis are summarized in Table 3.1.
For faster simulation, the actual number of photon generated is less than N (typicallyN/3), thus to save the simulation time of photons which will not arrive on PMTs due tocoverage etc.

61

Chapter 3

Table 3.1

Calibration and Reconstruction at SK

Thresholds of Cherenkov radiation for charged particles at SK.
Particle

Energy threshold [MeV]

e±
µ±
π±

0.767
157.4
207.9

3.2.2 Photon propagation

Some of generated Cherenkov photons will be reflected or absorbed by water itself
and impurities inside even after purification and cooling. The overall attenuation eﬀect
can be written as
I (x) = I0 (λ) exp(−x/L(λ)),(3-16)

where I (x) is the light intensity after a travel length of x, I0 (λ) is the initial light intensity,and L(λ) is the attenuation length of the medium. The attenuation length representing thewater transparency is parameterized at SK with three wavelength-correlated water coeﬃcients: absorption coeﬃcient αabs , Rayleigh scattering α ray and Mie scattering αmie . Mie
scattering only diﬀers from Rayleigh scattering by the target molecule size and mechanism
rather than the behavior, and thus is diﬃcult to distinguish. At SK, these two scattering
components are combined and divided into a symmetric scattering coeﬃcient αsym , including mainly the Rayleigh scattering and also the contribution from the symmetric partof Mie scattering, and an asymmetric scattering parameter αasy including the asymmetricpart of Mie scattering. Therefore, the total attenuation length in MC simulation can be
defined as
L MC (λ) =1αabs + αsym + αasy,(3-17)

corresponding to the calibration explained in Eq. (3-4).
The reflection of Cherenkov photons by the detector structure such as the surfaceof PMT, the black sheet and so on, was also measured and accommodated in the MC
simulation [86] .

62

Chapter 3

Calibration and Reconstruction at SK

3.2.3 PMT and Electronics

In SKDetSim, when a photon reaches the PMT surface, it is either reflected, ortransmitted through, or absorbed by the cathode. The probability for each process depends
on the incident angle as well as the wavelength, and is accounted in SKDetSim. The photon
can generate a photoelectron only when the it is absorbed by the cathode. Figure 3.22
illustrates these three processes on a PMT surface.

Figure 3.22

A sketch of the PMT response for an incident photon in SKDetSim.

The probability of the i-th PMT to absorb an incident photon and emit a p.e. isdefined as
Probi (λ) = Eﬀ(λ) × Probobs (λ, θ) × COREPMT × QEi,

(3-18)

where Eﬀ(λ) is the overall quantum eﬃciency of the 20-inch PMT with wavelength
dependence, Probobs (λ, θ) is the probability of absorption process for a given incident
angle θ, COREPMT is the overall scale factor to correct the average quantum eﬃciency,
and QEi is the relative QE for the i-th PMT. The dependence of quantum eﬃciency on
the position of incident photon on PMT surface is not included in the current version of
SKDetSim, though a relevent study is still ongoing.
Finally, when the number of p.e.’s are determined, the corresponding charge iscalculated and compared with the threshold of the electronics.

63

Chapter 3

Calibration and Reconstruction at SK

3.3 Event Reconstruction
At SK, low energy events are defined as the events with less than 1,000 hit PMTs.
Unlike high energy reconstruction tools which consider both time and charge information,
low energy reconstruction tools use mainly timing information and hit patterns. This isdue to the fact that most low energy events only produce single p.e. on each hit PMT.
In this section, we will first introduce vertex reconstruction and direction reconstruction, then focus on the energy reconstruction and the correction of threshold eﬀect
in it. Cherenkov angle reconstruction is an important tool for particle identification in
Cherenkov detectors, and we will describe its algorithm. Finally, the muon reconstruction
tool, which is used to identify incoming muons and following spallation events, is alsopresented. The author was responsible for the threshold eﬀect correction of the energy
reconstruction analysis.
3.3.1 Vertex Reconstruction

The typical travel distance for 10 MeV electrons and positrons in water is ∼ 10 cm,

less than the corresponding vertex resolution ∼50 cm. Therefore, the electron or positron
can be assumed to radiate Cherenkov light at a still point.

In the low energy analysis, BONSAI [89] is the mostly adopted vertex reconstruction
tool, since it can give the best vertex resolution. The ToF-subtracted time residual ∆t i on
the i-th PMT is defined as∆t i = t i − ToF(⃗x ) − t 0,

(3-19)

where t i is the original hit timing on the i-th PMT, ⃗x and t 0 are the candidate pair of vertex
and Cherenkov light emission time, and ToF is the time of flight for photons from thecandidate vertex to the hit PMT. The probability density function (PDF) for ∆t for signal
is obtained from LINAC. The PDF for PMT dark noise is assumed to be flat. BONSAI
looks for the best-fit ⃗x and t 0 pair by maximizing the likelihood function constructed fromthe time residuals of given hits and gives an evaluation of the fit.
3.3.2 Direction Reconstruction

Direction reconstruction in water Cherenkov detectors is based on the Cherenkov
ring pattern. For relativistic electrons, the Cherenkov angle distribution peaks at 42◦ . Due
64Chapter 3

Calibration and Reconstruction at SK

to the multi-scattering eﬀect, this angle is diluted, especially for charged particles withenergies close to the Cherenkov threshold.
Direction reconstruction at SK requires a vertex reconstruction result as an input. A⃗ is constructed as:
likelihood function L( d)
⃗ =
L( d)

N20
∑
i

log( f (cos θ dir,i, E)) ×

cos θ i,a(θ i )

(3-20)

where N20 refers to the number of hits satisfying −20 ns < ∆t < 20 ns, θ dir,i refers
to the angle between the incident particle direction d⃗ and a vector pointing from thereconstructed vertex to the i-th hit PMT, f (cos θ dir,i, E) refers to the expected distributionof θ dir,i dependent on the particle energy E due to multi-scattering, θ i is the solid angle ofthe i-th PMT’s surface to the reconstructed vertex, and a(θ i ) corrects for the acceptance.
We obtain the distribution of f (cos θ dir,i, E) by MC simulation. This reconstruction looks
for the best-fit of d⃗ by maximizing the likelihood function.
The typical angular resolution at SK for a 10 MeV electron is ∼ 25◦ .
3.3.3 Energy Reconstruction

For the Cherenkov process in low energy region, number of Cherenkov photons
follows a monotonic response to the incident particle energy, as shown in Fig. 1.7. Due tothe low photon yield for low energy events, single p.e. is assumed for most of PMT hits.
The incident particle energy can thus be approximated to be proportional to the numberof PMT hits.
3.3.3.1

Neﬀ Calculation

As Eq.( 3-6) suggests, several corrections are needed to obtain the corresponding‘eﬀective hit’ value of a PMT hit. The eﬀective hits within a 50 ns residual time window
are then summed up with a correction of water transparency to obtain a variable named
Neﬀ , which will be converted to energy,
)
(
1
Nall
Rcoveri
Neﬀ’
×= Xi + ϵ tail − ϵ idark ××,
Nnormal S(θ i, ϕi ) QEi
(
)}
N50 {
∑
ri
i
Neﬀ =
Neﬀ’ × exp,
λ(run)
i=1
65(3-21)

Chapter 3

Calibration and Reconstruction at SK

in which the variables are:• Occupancy Xi
It’s not easy to decide whether the i-th hit PMT generates a single p.e. or more, evenwith charge information, due to the resolution. To account for the case of multiple
p.e.’s, the hit information from PMTs in a 3×3 patch surrounding this candidate
PMT i is also collected. Assuming the same hit probability for these 9 PMTs, wedefine an occupancy Xi to estimate the number of p.e.’s generated by the i-th PMT
based on the Poisson statistics as
Xi = − log(1 − x i )/x i, x i < 1
Xi = 3.0,

xi = 1(3-22)

where x i is the ratio of hit PMTs surrounding the i-th hit PMT. This occupancy needs
further correction for the gain increase, as will be addressed in Section 3.3.3.2.
• Tail hits correction ϵ tailScattering, absorption/re-emission, and reflection dilute the time resolution, leavingsome tail hits behind the 50 ns window. These tail hits are corrected by the term
ϵ tail .
• Dark noise correction ϵ idark
As discussed in Section 3.1.1.3, dark noise is estimated by the hits in the oﬀ-time
window, and ϵ idark corrects the dark noise on a run-by-run and PMT-by-PMT basis.
• Bad PMTs Nall /Nnormal
Though the 11,146 PMTs (Nall ) were initially installed in the tank in SK-I, thenumber of properly operating PMTs now in SK-IV is only 11,129 (Nnormal ). This
term is corrected for consistency with previous SK periods.
• Photocoverage Rcover /S(θ i, ϕi )The acceptance and photocoverage is corrected by this term, where θ i and ϕ represent
the incident angle and azimuth angle, respectively. S is the photocathode coverageof i-th PMT, and R is the overall photo-coverage.
• PMT quantum eﬃciency QEi
This QE has the same definition as discussed in Section 3.1.1.4.
• Water transparency λ(run)ito Neﬀ , the exponential term exp (r i /λ(run)) applies the correction for
From Neﬀ’

the water transparency. Here, r i refers to the distance between the reconstructed
66

Chapter 3

Calibration and Reconstruction at SK

event vertex and the i-th hit PMT, and λ(run) refers to the water transparency as afunction of run number. The measurement of λ is described in Section 3.1.2.3.
3.3.3.2 Threshold Eﬀect Correction

Due to the long-term increase of PMT gain mentioned in Section 3.1.1.3, Neﬀ isobserved to have an increasing trend for all the calibration data sets. This is due to the‘threshold eﬀect’ where the increase of gain results in more hits which exceed a fixed
threshold. To correct this threshold eﬀect, we parameterize the gain increase and assign
a conversion factor C between the gain increase and hit increase,
FG (k, run) = (Gt (k, run) − G0 )/G0,

FN (k, run) = (Nt (k, run) − N0 )/N0,(3-23)FN (k, run) = FG (k, run) × C,

where G0 is the gain for the reference run at the beginning of SK-IV, Gt is the PMT gain
for the current run, estimated by the oﬀ-time window charge from an independent study.
PMTs are grouped by production year and denoted by k to tag their batch. The conversion
factor C is assumed to be uniform over time and for diﬀerent PMT batches, even though
the gain increasing amplitudes vary. Since the gain increase does not exceed 20% throughout the SK-IV period, the correlation of hit increase and gain increase can be treated aslinear.
The occupancy Xi in the Neﬀ calculation is modified as
Xi (x i ) → Xi (x i (QE j ))/(1 + FG × C),(3-24)

where x i is corrected for the QE of j-th PMT in the 3×3 patch surrounding i-th PMT, andthe threshold eﬀect is quantified as FG × C, where G is the relative gain increase and C isa conversion factor. Similarly, ϵ dark is also corrected byϵ dark = ϵ dark /(1 + FG × C)

(3-25)

This conversion factor is estimated by tuning the y-intercept of Fig. 3.11 to a constantover time. As a crosscheck, Neﬀ for diﬀerent calibration data samples (decay electron,
nickel, DT, LINAC) is recalculated and confirmed to be stable, an example of which is
67

Chapter 3

Calibration and Reconstruction at SK

shown in Fig. 3.14. The stability of Neﬀ grouped by PMT batches is also confirmed,
validating the assumption of uniform C over time and over diﬀerent PMT batches. The C
value in SK-IV is finally determined to be 0.226 for the data.
3.3.3.3 Energy Calculation

The energy of the incident particle is reconstructed as a polynomial function of Neﬀ
to the 4th order for E < 25 MeV and to the 2nd order for E > 25 MeV,
Erec =
Erec =

4
∑
i=0
2
∑

ai (Neﬀ ) i ,Erec < 25MeV(3-26)ai (Neﬀ ) ,iErec > 25MeV

i=0

where Erec is the reconstructed energy and ai is the i-th order coeﬃcient determined by
LINAC calibration. For 10 MeV electrons, the energy resolution is about 14%.
In principle, the Neﬀ based energy reconstruction method will also work for events
below the detection threshold of ∼ 4 MeV, though with much worse resolution due to thenonlinearity of Cherenkov radiation.

3.3.4 Cherenkov Angle Reconstruction

The removal of the non-electron/positron backgrounds in SRN samples requires
particle identification information. At SK, due to the mass diﬀerence of charged particles
and the mechanism of Cherenkov light emission, particle identification is done by the
Cherenkov angle. In the energy range of SRNs, the positrons of IBD candidates areultra-relativistic with a Cherenkov angle at 42◦ , while for muons and pions it becomes
smaller due to their heavier mass. The PMT hits induced by γ-rays are isotropically acrossthe detector, thus showing a much diﬀerent hit pattern and cannot fake a 42◦ Cherenkov
ring.
Hits from a candidate event within a residual time window of 15 ns are combinedin 3-hit sets so that every set uniquely defines a cone with an opening angle. These
opening angles are filled to a histogram and forms a distribution, which does not havea well-defined shape. A 7-bin sliding sum is calculated and the maximum center bin istaken as the peak of this distribution, and thus defines the Cherenkov angle of this event.
This Cherenkov angle is used to reject non-electron/positron backgrounds such as muons,68Chapter 3

Calibration and Reconstruction at SK

pions and γ’s.
3.3.5 Muon Fitter

The main backgrounds for the SRN search are spallation products induced by thecosmic ray muons. These events are correlated with precedent muons in space and time,and can be rejected by likelihood construction dependent on the muon type and track. A
precise reconstruction of muon events is crucial in suppressing the spallation backgrounds.
3.3.5.1 Muboy

A muon reconstruction tool named Muboy [90,91] is applied to fit the events with morethan 1,000 p.e.’s, since these events are very likely to be cosmic ray muons. Cosmic
ray muons at SK are classified into 4 categories, namely single through-going muons,
stopping muons, multiple muons and corner clipper muons. Muboy can fit multiple tracks
simultaneously and find the most likely category for the muon candidate. It also evaluates
the quality of the fit by goodness. All of the above information is used in the spallation
likelihood calculation.
The muon rate at SK is 2.2 Hz, while the time window for HE events is 40 µs. If an
HE time window is already open, for the time being, another incoming muon will be notregistered as a trigger again. The rate of the un-registered second muon is found to be ∼100 / day. To get back these untagged muons, a software trigger in Muboy is implemented
to check the already found muon candidates.
3.3.5.2 Brute Force Fitter

As indicated by the goodness value, Muboy may give a poor fit due to exotic hit
patterns or extremely low/high number of hits. These cases account for 1.4% of the total
fit. A brute force fitter (BFF) is developed as an alternative to refit these muons which
failed the Muboy fit (goodness < 0.4). It performs a grid search for the entry and exit
points in the ID surface.
Even though BFF is extremely slow and can only fit the single-through muons
due to the algorithm, about 75% of the failed muons from Muboy can be successfullyreconstructed by BFF.

69

Chapter 3

Calibration and Reconstruction at SK

3.3.5.3 Energy Loss

Energy loss per track length (dE/dx) for energetic muons may have peaks along thepath, and may thus be closely related to the spatial distribution of spallation events. To
calculate the energy loss for a given muon, the muon track is first reconstructed. Binned
by 50 cm along this track, for every bin, the ToF-timing information of every hit PMT iscalculated to look for the hits whose incident photons are most likely to be emitted fromthis bin, as shown in the left panel of Fig. 3.23. Recently, a likelihood calculation method
is employed to smooth the dE/dx spectrum, as shown in the right panel of Fig. 3.23. Thisnew method is expected to improve the spallation reconstruction.

Figure 3.23 Energy loss binned along the same muon track using the old (left) and new (right)
calculation method respectively.

70

Chapter 4

Chapter 4

Data Reduction at SK

Data Reduction at SK

As discussed in Section 1.3.2.3, the search for SRN can use IBD events because of its
large cross section. To select IBD events, in the absence of a 100 % detection eﬃciencyof neutrons due to the SK detector properties, a careful and eﬃcient reduction of theprompt events is required. For an easier demonstration, the term energy E in this chapter
is limited to reconstructed energy Erec . For SRN signal, it is the positron kinetic energy
plus the annihilation energy.
The author performed the data reduction for the data collected in 2014 − 2018 during

SK-IV, improved the multi-event cut, and re-calculated the estimated eﬃciency for an
SRN spectrum.

4.1 First Reduction
First reduction, or precut, is a series of basic requirements to select the physics events
against non-physics events, such as those due to PMT flashers and detector calibrations.
This cut reduces the sample size significantly, facilitating further studies.
Bad Run Cut
A typical run at SK contains 24-hour data, with ∼80,000 subruns which last for

1-minute each. During the data taking, runs are labelled as normal run or test run, thelater of which is usually during the calibration or with a hardware problem.

At the oﬄine stage, normal runs are further examined on a subrun basis by eye scanof low energy analysis group members and experts. If a normal run has either of thefollowing problem:• run time < 5 min,• beginning of run < 15 min after a high voltage (HV) recovery,• hardware problems recorded by shift person or expert,• evident distortion in event distribution tracing back to a change recorded by shift
person or expert,
it is tagged as a bad run. Generally, only the good run data are used in physics analysis.
Fiducial Volume Cut
Most radioactive backgrounds is from the surrounding rock and detector wall (steel
frame and PMT surfaces), and are likely to be reconstructed close to the tank wall.
71

Chapter 4

Data Reduction at SK

In addition, the nonuniformity is enormous at the tank edge even after the acceptancecorrection, due to the reflection on surfaces and the much larger time resolution of PMT
for extreme incident angles. To eliminate these eﬀects, a fiducial volume cut of 200 cm
from the tank wall is applied.
Goodness Cut
Primary events are reconstructed by BONSAI, as described in Section 3.3. BONSAI
evaluates the goodness of fit by GV and DirKS, which represent the quality of vertex reconstruction and direction reconstruction respectively. Based on these goodness values, ovaQ(One dimensional variable of Vertex and Angular reconstruction Quality) is constructed
as ovaQ = GV2 −DirKS2 . The first reduction requires GV > 0.4 and ovaQ > 0.25.
Calibration Events Cut

Some calibration data requires test runs, such as the nickel calibration and DT
calibration as discussed in Section 3.1. Other calibration data, however, are taking during
normal runs with periodical calibration triggers. By rejecting events tagged with thecalibration triggers, we eliminated the possible contamination from calibration data into
the SRN search sample.
Noise Events Cut
PMT noises tends to have lower charges than those for the true hits. By requiring
N (Q < 0.5 p.e.)/Nall < 0.55, a large fraction of noise events are removed.
OD CutAn OD trigger indicates an incoming muon, thus the event cannot be a SRN candidate.
In case the OD trigger does not function properly, events with OD hits > 19 are removed.
Muon Time Cut
The muon rate at SK is ∼ 2 Hz. Energetic muon deposits energy inside the tank, witha large number of secondary tracks and hits, which are likely to be reconstructed as low
energy events. To eliminate these backgrounds, all the events within 50 µs after a muon
event are rejected.

4.2 Spallation Cut
Spallation products form the main background in lower energy range for SRN searchat SK, both in the spectrum analysis, and in the neutron tagging analysis. The backgroundin neutron tagging analysis originates from 9 Li production and the mis-tagged accidental
coincidence from cosmic ray induced spallations. Previous studies [49] used four variables
72

Chapter 4

Data Reduction at SK

to construct a likelihood to reject the spallation-like events.
Spallation Backgrounds
Cosmic-ray muon induced spallation backgrounds in the detectable energy range at
SK are listed in Table. 4.1. The imperfect energy reconstruction could smear the endpointof spallation energy distribution, thus contaminating higher energy SRN samples up to
24 MeV, below which spallation cuts are applied.
Table 4.1

Summary of cosmic-ray muon induced spallation radioactivities at SK [51,92] .

IsotopeMean life [s]Decay mode

Ekin [MeV]Primary process

11 Be
4

19.9

11.51
9.41+2.1(γ)(n,α + 2p)

16 N
7

10.3

β−
β− γ
β−
β− γ

10.44
4.27+6.13(γ)

(n,p)

15 C
6

3.53

9.77
4.51+5.30(γ)(n,2p)

8 Li
3
8B
5
16 C
6
9
3 Li

1.21
1.11

β−
β− γ
β−
β+

∼13.0
∼13.9

(π − ,α+2 H+p+n)(π + ,α + 2p+2n)

∼4
∼13.6

1.08
0.26

9
C
6
8 He
2

0.18

β − +nβ−β− γβ + +p

12 Be
4
12 B
5
13 B
5
14 B
5
12 N
7
13 O
8
11 Li
3

(π − ,n+p)(π − ,α + 2p+n)

∼10
3∼5

(n,α + 4n)

0.17

β− γ

9.67+0.98(γ)(π − ,3 H+4p+n)

0.034

β − +nβ−11.71(π − ,α+p+n)

0.029
0.025

β−
β−

13.37
13.44

(n,α+p)(π − ,2p+n)

0.02
0.016

β− γ
β+

14.55+6.09(γ)
16.38(π + ,2p+2n)

0.013
0.012

β + +pβ−β − +n8∼14
20.62(µ− ,µ− + π − +p+2n)(π + ,5p+π 0 + π + )(n,3p)∼16

Spallation Likelihood
The spallation cut is constructed by the following procedures.
First, as described in Section 3.3.5.1, muons are classified into four categories ofsingle through muons, stopping muons, multiple muons, and corner clipper muons.
Then, four variables are constructed to describe the correlation between the incoming
73

Chapter 4

Data Reduction at SK

muon and the primary event of an IBD candidate:• d t , the time diﬀerence between the primary event and the preceding muon;• l t , the transverse distance between the primary event and the preceding muon track;• l n , the longitude distance between the primary event and peak position of the dE/dx
distribution along the muon track.
• Qpeak , the peak value of dE/dx binned by 50 cm along the muon track.
Third, a spallation sample and a random sample are prepared by setting a cut on
the time diﬀerence dt. The spallation sample requires 0 > dt > −30 s preceding the
primary event and random sample requires 0 < 0 < 30 s after the primary event. The

spallation sample distribution is then subtracted by the random sample. For diﬀerent
samples, diﬀerent distribution of the four discrimination variables can be observed andthe likelihood function can be constructed, thus evaluating the possibility of the primary
event to be spallation-like or signal-like. Typical distributions for spallation events andnon-spallation events for the single through muons are shown in Fig. 4.1.

Figure 4.1

Distributions of d t , l t , l n and Qpeak using the single through muon [45] .
74

Chapter 4

Data Reduction at SK

A spallation likelihood L spall is thus constructed as:
L spall =

∑

log

i

PDFispall
PDFirandom

,

(4-1)

where i represents one of the four discriminating variables. The distribution of thespallation likelihood for both the spallation data sample and the random sample is shownin Fig. 4.2.

Figure 4.2

Distributions of the spallation likelihood using the single through-going muons [46] .

Performance
The spallation cut is performed on the output of likelihood function, and is changedfor diﬀerent muon categories and primary event energy. A random event sample isgenerated by randomly choosing vertex, adverting the sign of dt, while keeping the otherinformation of the SRN sample with regard to muons. This random sample is used toevaluate the eﬀect of the spallation cuts on the SRN signals. The eﬃciency for SRN signal
in diﬀerent energy ranges for the spallation cuts are listed in Table 4.2.

75

Chapter 4

Table 4.2

Data Reduction at SK

SRN eﬃciency with spallation cuts.

Energy range

Eﬃciency in SK-IV

Eﬃciency in SK-I/III

18-24 MeV
14-18 MeV
12-14 MeV
11-12 MeV
8-11 MeV

89.8%
80.5%
72.1%
61.2%
51.3%

89.7%
80.3%

4.3 External Event Cut
Higher energy γ’s from radioactive backgrounds outside the tank or from the tankwall can travel further into FV, contaminating the data sample even after applying the FV
cut. The distance between the reconstructed vertex and the point of entry on the tank wall
calculated from the reconstructed vertex and inverted direction is called as eﬀwall. The
distributions of eﬀwall for the data and MC SRN signal are shown in Fig. 4.3.

Figure 4.3

Distributions of eﬀwall for the data (black line) and the SRN signal (red line) [46] .

The incoming event cut is therefore set at 300 cm for E > 22 MeV, 450 cm for
12 MeVE < 22 MeV, and 600 cm for E < 12 MeV.

76

Chapter 4

Data Reduction at SK

4.4 Solar Event Cut
Solar neutrinos are detected at SK by the electron scattering on electrons ν+e → ν+e.

Though without a neutron, the higher energy solar neutrinos can still leak into our final
SRN sample through accidental coincidence with its relatively high luminosity. The angle
between the reconstructed direction of an event to the sun direction at the time of the event
is called θ sun . The distribution of θ sun for solar neutrinos at ∼ 10 MeV quite stands out

from the flat distribution of the SRN signals, providing an easy way to tag and reject solar
neutrinos, as shown in Fig. 4.4.
htemp
Entries36569
Mean
0.8997RMS
0.1716

bscossun
9000

160

7000

140

6000

120

5000

100

4000

80

3000

60

2000

40

1000

20
-1

-0.5

Figure 4.4

00.5

Entries
13464
Mean -0.006043
RMS
0.5756

180

8000

0

htemp

bscossun {bsenergy>16}

0

1
bscossun

-1

-0.5

0

0.5

1
bscossunDistributions of cosθ sun for the solar MC (left) and the SRN MC (right).

Since the energy of the solar neutrinos is below 16 MeV, we reject events with cosθ sun
greater than 0.9 and energy lower than 16 MeV. Remaining solar neutrino background dueto the resolution eﬀect is expected to be removed by the neutron tagging.
This cut will be one of the main diﬀerent cut between the neutron tagging analysis
and spectral analysis of SRN search. For the neutron tagging analysis, this cut can beloosened because solar neutrinos do not have neutrons and contribute to the final sample
only by accidental coincidence.

4.5 Cherenkov Angle Cut
Atmospheric νµ /ν̄µ will generate muons via charged current interaction, which canbe mis-reconstructed as electrons in the energy range of several tens of MeV, when themuon energy is around 100-500 MeV. For relativistic e± ’s ∼ 10 MeV, the Cherenkov angleis ∼ 42◦ , while for these muons, the Cherenkov angle tends to be lower.

On the other hand, background events with multiple γ’s, or an electron and a γ, asmany spallation events do, usually have larger Cherenkov angles for the isotropic light77

Chapter 4

Data Reduction at SK

emission of γ’s.

Figure 4.5

Distributions of Cherenkov angle for the data (black line) and LMA MC (red line) [46] .

Figure 4.5 shows the Cherenkov angle for the data and the simulated SRN signal,
from which the Cherenkov cut is determined to be 38◦ < θC < 50◦ .

4.6 Multi-Event Cut
The prompt signal in an IBD event should be a single event in a 1.3 µs time interval, while the CC backgrounds from atmospheric neutrinos tend to be multi-events, forinstance, a decay electron from a muon. To remove these events, we apply multi-event
cuts from the aspects of both space and time.
4.6.1 Pre/Post Activity Cut

Invisible muons with energy lower than the Cherenkov threshold can not be detected
at SK, and the following decay electrons or induced spallations will escape from the muonor spallation cuts. Cosmic-ray muons are unlikely to have such low energy with the rockoverburden of SK. Instead, invisible muons are more likely to be produced by atmosphericνµ /ν̄µ ’s. Decay electrons from these invisible muons can be removed if the atmospheric
neutrino generates a prompt gamma when interacting with an oxygen. For the [-5, 0] µs
78

Chapter 4

Data Reduction at SK

precedent time range covered by an SHE trigger, the distribution of number of hits within
a 15 ns sliding time is shown in the left panel of Fig. 4.6. Events with N15 > 11 are called
pre-activity events, and are removed from the final sample.

3

6

Entries

Entries

×10

Entries 200000

0.16

×10
35

0.14

30

0.12

25

0.1

Entries 200000

20

0.08
15
0.06
10
0.04
5

0.02
0
0

2

4

6

8

10

12

0
0

14 16 18 20
maximum N15

5

10

15

20
25
30
maximum N15

Figure 4.6 Distributions of N15 in 5µs random trigger (left) and in 35µs trigger. The latter has
wider distribution due to the existence of 2.2 MeV γ.

Visible muons produced by atmospheric νµ /ν̄µ ’s can be mis-reconstructed with
Cherenkov angle > 38◦ , leaking into the SRN sample. The decay electron signal fromsuch muons produces a second peak, which is used to tag these muons after the primary
event in the time range [0, 35] µs recorded by the SHE trigger. Using a similar number of
hit in a 15 ns sliding window, the distribution of N15 after the primary event is shown in
the right panel of Fig. 4.6. Due to the existence of 2.2 MeV γ, this distribution is shiftedto the right and spread wider than the left panel. Post-activity events are thus defined by
N15 > 19, and are removed from the SRN sample.
The event displays of a pre-activity and a post-activity event example are shown in
Fig. 4.7.

79Chapter 4

Data Reduction at SK

Figure 4.7 Event display for an example of a pre-activity event (left) and a post-activity event(right) [45] .

4.6.2 Multi-ring Cut

A positron only generates one Cherenkov ring in the tank while backgrounds fromatmospheric neutrinos tend to undergo multi-processes and produce multiple charged particles, thus producing multiple rings. A simple ring counting will cause signal eﬃciency
loss due to some poor reconstructed positron ring and the fuzziness in ring pattern itself
for low energy positrons. Instead of counting ring numbers, the angle between rings aretaken as the cut parameter, requiring θ ring < 60◦ for any two rings inside an event, using
the ring counting tool in Ref [93] .

4.7 Muon/Pion Cut
The residual muon and pion events after the Cherenkov angle cut will remain in thedata sample, and further reduction is required.
4.7.1 Pion Cut

The Cherenkov angle cut removes most non-electron backgrounds by the relativityof the particle. However, this cut does not reject high energy pion. The Cherenkov angle
distribution of these pions tends to peak at 42◦ with a sharper than SRN positrons due tothe higher energy and less multi-scattering. To account for the width of Cherenkov angle
distribution, the ratio of hits number within ±3◦ around the Cherenkov angle peak over80

Chapter 4

Data Reduction at SK

the number within ±10◦ , called πlike , is constructed. Events with πlike > 0.58 are regarded
as pion-like events, and are removed from the SRN sample.

4.7.2 Charge/Hit Cut

In addition to the above non-electron particle cut, muons and pions are further
rejected by the charge and hit distribution within 50 ns as a function of reconstructedenergy E [45] . Such distributions for e’s, µ’s and π’s are shown respectively in Fig. 4.8.
Events with Q50 /N50 ≥ 2.0 + 0.0025 × E are tagged as µ/π’s, and are removed from the
SRN sample.

Figure 4.8 The distribution of Q50 /N50 as a function of the reconstructed energy E for e’s, µ’s
and π’s obtained from the simulated atmospheric neutrinos [46] .

4.8 Summary of Reduction Eﬃciency
The reduction eﬃciency is evaluated by SRN MC sample, and the eﬃciency value
may vary slightly according to the energy profile of the SRN model. Table 4.3 showsthe eﬃciencies evaluated by the LMA model. It should be noted that these eﬃciencies
are evaluated in sequence as listed in Table 4.3. The accumulated signal eﬃciency is the
product of individual eﬃciencies.
81

Chapter 4

Data Reduction at SK

Table 4.3 Data reduction eﬃciencies evaluated by LMA model. Detailed calculations explainedin the text.
Reduction

Eﬃciency

First reduction
Spallation cut
External event cut
Solar cut
Cherenkov angle cut
Pre/post activity cut
Multi-ring cut
pi cutCharge/hit cut

>99%
77.1%
92.8%
97.2%
88.6%
99.8%
99.5%
99.2%
99.8%

82

Chapter 5

Chapter 5

Selection of Correlated Neutrons at SK

Selection of Correlated Neutrons at SK

For antineutrinos in the SRN search window, the neutron energy from IBD is usually
lower than 1 MeV. The energy and angular distribution can be explicitly calculated to
first order as P. Vogel and J. F. Beacom demonstrated [14] . The convolved neutron energy
distributions for diﬀerent SRN model are shown in Fig. 5.1. These neutrons propagating ina.u.

water are quickly thermalized and eventually captured by the oxygen or hydrogen nucleus.

LMA
Const SN
Cosmic gas
Chemical evolution
Heavy metal
Population synthesis
HBD 6 MeV
Kaw(star formation)
Failed SN

10

1

10-1

10-2

10-3
0

0.5

Figure 5.1

1

1.5

2

2.5
3
Energy / MeV

Energy of neutrons produced in IBD events.

In the above energy range, neutron capture on hydrogen has a cross section of ∼0.33

bars, much larger than the ∼0.19 millibar cross section on oxygen. Therefore, we assume
the neutrons are ∼ 100% captured by hydrogen as Eq. (5-1).
n + p → d + γ(2.2MeV)(5-1)

The neutron capture lifetime is measured to be 204.8 µs [94] . Before being captured,
neutrons are constantly losing energy and changing directions by scattering. The distance
between the capture vertex of a thermal neutron and the primary vertex where the neutron
83

Chapter 5

Selection of Correlated Neutrons at SK

is generated is usually negligible compared to the vertex resolution in SK (∼50 cm).
Figure 5.2 shows the typical distance between the capture vertex and the primary vertex
in the direction of neutron emission for diﬀerent incident antineutrino energy model
simulated using Geant4.9.6 [95] .

60000

LMA
Const SN
Cosmic gas
Chemical evolution
Heavy metal
Population synthesis
HBD 6 MeV
Kaw(star formation)
Failed SN

50000

40000

30000

20000

10000

0
-400

Figure 5.2

-200

0

200

400

600
Ls / mm

Distance between the capture vertex and the primary vertex.

The 2.2 MeV γ emitted from a neutron capture on hydrogen can be used to tag
neutrons, giving a power to discriminate IBD signals over the background of radioactive
isotopes and spallations. Since the 2.2 MeV γ is below the trigger threshold of SK, a special
trigger scheme is adopted to record their information. As introduced in Section 2.5.2, for
2.2 MeV γ’s outside the usual 35 µs HE time window, a 500 µs time window of the AFT
trigger is opened right after an HE trigger without an OD trigger. After extracting the
AFT data and combining with the preceding HE data, we developed a neutron tagging
technique to look for the associated 2.2 MeV γ signals.
The neutron tagging technique, also known as Ntag, was first introduced to SK
in 2009 by H. watanabe and H. Zhang [96] , and further developed by Y. Zhang [46] and T.
Irvine [97] towards higher signal eﬃciency and purity either in the low neutrino energy data
sample to search for SRN signals or in the high energy atmospheric neutrino interactions
to distinguish anti-neutrinos from neutrinos. This section presents the author’s workin developing neutron tagging technique for the SRN search with 2.2 MeV γ vertex
reconstruction, the tuning of the neural network, validations with diﬀerent samples, aswell as the optimization of the cut value for the SRN sample.
The four-vector momenta and vertex positions for both the 2.2 MeV γ and the84Chapter 5

Selection of Correlated Neutrons at SK

prompt positron are obtained from toy-MC. Then the generator-level information is sent
to SKDetSim for the detector-level simulation. Dark noise is only simulated to 5 µs after
the primary trigger, and afterwards dummy trigger, i.e., a constant calibration trigger that
does not coincide with any physics events, is used as backgrounds to add into the puredata sample from MC, thus unbiased from the actual backgrounds in the experiment.

5.1 Neutron Tagging Algorithm
To distinguish 2.2 MeV γ signals from backgrounds, a comprehensive understandingof signal and background characteristics is crucial. For signal, a 2.2 MeV γ is expected
to produce all the PMT hits within a narrow timing (ToF-subtracted) window, and thesehits are expected to be anisotropic. The neutron capture vertex should be close to theneutrino vertex, and the energy of the hits, though diﬃcult to fully reconstruct, should
correspond to ∼ 2.2 MeV. Dominant backgrounds in this energy range include naturalradioactivities from the surrounding rock and detector material, radon contamination intank water, PMT dark noise, etc. These background sources have diﬀerent characteristics,
as natural radioactivities from the surrounding usually produce hit clusters, and dark noise
tends to produce isotropic hits in random patterns.
In searching for the 2.2 MeV γ’s, we first look for timing peaks within the trigger data
right after the primary event. Then we calculate a set of 22 variables for each candidate.
These variables are then sent into a neural network, where the output is used to determine
the likelihood of the neutron capture signal.
5.1.1 Pre-selection

First, all the PMT hits within the given certain time range are ToF-subtracted to theprimary vertex, as introduced in Section 3.3. This time range is constrained by the AFT
trigger time of 535 µs as well as after pulses from the primary event, which contaminate
the time range close to the primary event. Therefore, a time range from 0.05 µs to 535 µs is
chosen to select 2.2 MeV γ candidates at a cost of ∼ 7% eﬃciency loss. Figure. 5.3 shows
the time distribution with ToF-subtraction for the 2.2 MeV γ’s [45] . From this distribution,
we chose a 10 ns window to search for the candidate cluster hits.

85

Chapter 5

Selection of Correlated Neutrons at SK

Figure 5.3 Time distributions for 2.2 MeV γ candidates with ToF subtracted for true primaryvertex (solid line) and reconstructed primary vertex (dashed line) [45] .

Figure 5.4 shows the distribution of number of hits within a 10 ns sliding window
for 2.2 MeV γ and background noise. In this figure, we required
N10 > 7

(5-2)

where N10 is the number of hits in the 10 ns sliding window. The candidate time t 0 isdefined as the timing of the first hit in N10 . To avoid double counting of the same neutron
capture event and maximizing the discrimination over background, the candidate needs
a further check for a wider window to t 0 + 20 ns. The hits within this 20 ns window isregarded as from the same neutron, and the set of hits with the max N10 sliding within the
20 ns window is taken as the 2.2 MeV γ candidate. Outside the t 0 + 20 ns, hits are treatedas separate candidates.
To remove energetic backgrounds in the SHE+AFT trigger range, an upper limit on
the number of hits is applied as
N10 ≤ 50,

N200 ≤ 100,
86

(5-3)

Chapter 5

Selection of Correlated Neutrons at SK

where N200 is the number of hits in ±100 ns around t 0 .

There are 35.4% of true neutron capture events remaining the above cuts, with 1.6

background events tagged on average for each neutrino event.
5.1.2 Discriminating Variables

After the pre-selection, candidates are processed to calculate 22 variables. Thesevariables are chosen to cover most of the distinctive diﬀerences between signals andbackgrounds, and can be classified into hit pattern (N10 , N300 , Nc , Nlow , NhighQ , Nlowθ ,Nback , ϕr ms , θ mean , and θ r ms ), charge information (Qr ms and Q mean ), time information(Tr ms , minTr ms (3), and minTr ms (6)), and reconstruction related (N Fwall , δTr ms , δN10 ,BSwall , BSener gy , F Pdist , BFdist ). Later in this subsection we will show the signalbackground comparison for each variable. To make figures easier to read, we scaled
background to 22% = 35.4%/1.6 so that the total number of signals and backgrounds isthe same in each figure.
5.1.2.1 Number of hits in 10 ns: N10

This variable is required to be above 7 and used as a cut in the pre-selection.
Figure 5.4 shows a comparison of N10 between signal and background. Unlike those forthe accidental background, N10 tends to have a larger number for signal.

12000
10000
8000
6000
4000
2000
0

8

10

12

14

16

18

20

22
N10

Figure 5.4 N10 distributions for both the neutron capture signal (blue) and the background (red).
See text for more details.

87Chapter 5

Selection of Correlated Neutrons at SK

5.1.2.2 Number of clustered hits: Nc

Due to the spatial distribution around the detector wall, hits from many backgrounds,
such as radioactive contaminants in the PMT glass, or PMT flashings, are found to havea cluster pattern, both in time and space. For 2.2 MeV γ signals, however, the fiducial
volume cut for the primary events requires the vertex to be more than 2 m away from thetank wall. The neutron capture vertices are therefore rarely close to the tank wall to cause
a set of clustered hits, as shown in Fig. 5.5.
The direction of a hit is defined by a vector pointing from a vertex to a hit PMT.
However, due to the less hits, the neutron vertex is poorly or even not reconstructed, andwe use the primary vertex instead to calculate the direction of hits.
For all N10 hits in a 2.2 MeV γ candidate, if the angle between a pair of hit vectors
is less than 14.1◦ , these hits form a cluster of Nc = 2. If an additional hit is within 14.1◦
of any hit in a cluster, it adds up to the cluster hit count Nc . We expect the number of hits
in a cluster Nc for the background to be larger than that for signal.
10000
8000
6000
4000
2000
0
0

2

4

6

8

10

12

14

16
Nc

Figure 5.5 Nc distributions for both the neutron capture signal (blue) and the background (red).
See text for more details.
5.1.2.3 Number of hits on low probability PMTs: Nlow

For a neutron capture vertex, even thought the direction of emitted γ is not predictable,
the geometric acceptance and attenuation can still give diﬀerent hit probabilities for the
PMTs. If most of the hits in a candidate have very low hit probability, this candidate is88

Chapter 5

Selection of Correlated Neutrons at SK

very likely to be a background event. The hit probability for the i-th PMT is calculated asAi ∝F (θ i ) Ri /L
e
Ri2

(5-4)

where F (θ i ) is the acceptance of i-th PMT for the incident angle θ i (collection eﬃciency
and quantum eﬃciency assumed to be uniform on θ i ), Ri is the distance from the vertex
to the i-th PMT, and L is the light attenuation length in water. Similar to the calculationof Nc , instead of neutron capture vertex, the primary vertex is employed in determinationof Ri .
The number of hits with low hit probability Nlow is obtained by first defining a groupof high hit probability PMTs for each primary event, which consist of PMTs totaling the
top x% of hit probabilities for all PMTs listed from high to low. If a hit PMT is notincluded in this group, this hit is counted as low probability hit.
However, this cut causes a position nonuniformity. When a primary event is relatively
close to the tank wall, the distribution of high hit probability PMTs is highly concentrated,while for a primary vertex in the tank centre, all PMTs will be assigned a similar hit
probability. To compensate for this nonuniformity, the percentage of hit probability
ranking required to be high probability, x%, varies throughout the tank, as shown in
Fig. 5.6. Nlow assuming random distribution of primary vertices inside the fiducial
volume is shown in Fig. 5.7. We expect a smaller Nlow for 2.2 MeV γ signals.

Figure 5.6
tank [45] .

A map of required total hit probability (x%) based on the primary vertex position in89

Chapter 5

Selection of Correlated Neutrons at SK

7000
6000
5000
4000
3000
2000
1000
0
0

2

4

6

8

10

12

14

16 18
Nlow

Figure 5.7 Nlow distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
5.1.2.4 Number of hits in 300 ns: N300

The N10 cut removes many low energy backgrounds. However, for high energy
backgrounds, such as the PMT flashing or high noise channels, N10 can be large andmay contaminate the signal sample. The crucial feature to distinguish signal from thesebackgrounds will be the number of hit in a wider time window, N300 . The hits of a neutron
capture event are usually fully contained within a 10 ns window, while for these highenergy backgrounds, the noise eﬀect will continue in a longer time range, thus forming alarger, more disperse pattern, as shown in Fig. 5.8.

Figure 5.8 Upper figure shows a typical neutron capture event, and lower figure shows a hypothetical background signal to be rejected. The blue markers correspond to the PMT dark noise,and the red markers represent a signal or a PMT flasher [45] .
90

Chapter 5

Selection of Correlated Neutrons at SK

We expect a smaller N300 for signals, as shown in Fig. 5.9.
2000

1500

1000

500

0
0

10

20

30

40

50

60
N300

Figure 5.9 N300 distributions for both the neutron capture signal (blue) and the background (red).
See text for more details.
5.1.2.5 Hit vector RMS: ϕr ms

We calculates the RMS of the azimuthal angle of the hit vectors ϕr ms for each 2.2
MeV γ candidate. Unlike neutron capture on gadolinium or lithium, the neutron capture
on hydrogen emits only a single 2.2 MeV γ. This single γ is expected to deposit most of
its energy in one direction, though the actual hits will spread as the γ interacts with water.
On the contrary, the PMT dark noise tends to form a random hit pattern, and have a larger
ϕr ms , as shown in Fig 5.10.

1600
1400
1200
1000
800
600
400
200
0
0

20

40

60

80

100 120 140 160 180
phiFigure 5.10 ϕr ms distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
91Chapter 5

Selection of Correlated Neutrons at SK

5.1.2.6 The mean value and RMS of the opening: θ mean and θ r ms

Here we define an opening angle θ i to describe the angle between the i-th hit vector
and the sum of all hit vectors for a candidate. θ mean is the mean value of the opening angle
θ i . For the 2.2 MeV γ induced Compton electrons, θ mean should peak around 42◦ , whilebackground events are more likely to have a clustered hit pattern and a smaller θ mean , asshown in Fig. 5.11. On the other hand, θ r ms , the RMS of the opening angle θ i , can tell acluster faked N10 peak from a true 2.2 MeV γ peak by its unreasonably narrow distribution
against the wider multiple-scattering induced distribution, as shown in Fig. 5.12.
1000
800
600
400
200
0
0

10

20

30

40

50

60

70
thetamFigure 5.11 θ mean distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

800
600
400
200
0
0

10

20

30

40
thetarms

Figure 5.12 θ r ms distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
92Chapter 5

Selection of Correlated Neutrons at SK

5.1.2.7 Number of backward hits: Nback

The 2.2 MeV γ tends to lie mostly in the forward direction, since Compton electrons
emitted Cherenkov light with the directional information, while for dark noise the hits
tend to be uniformly distributed. The number of PMT hits with θ i > 90◦ is referred to as
Nback . We expect Nback to be smaller for signal, as shown in Fig. 5.13.

8000
6000
4000
2000
0
0

5

10

15

20
Nback

Figure 5.13 Nback distributions for the neutron capture signal (blue) and the background (red).
See text for more details.
5.1.2.8 Number of hits with low θ : Nlowθ

Similar to the situation of Nback , the Cherenkov hits from Compton electrons scattered by true 2.2 MeV γ’s are also unlikely to have really low number θ i ’s, while radioactive
backgrounds on PMT windows or from the tank wall tends to form a cluster, producing
hits with much lower θ i ’s. The number of hits with θ i < 20◦ is defined as Nlowθ . We
expect Nlowθ to be smaller for signal, i.e., N10 − Nlowθ to be larger, as shown in Fig. 5.14.

93

Chapter 5

Selection of Correlated Neutrons at SK

5000
4000
3000
2000
1000
0
−5

0

5

10

15

20
25
Nlowtheta

Figure 5.14 N10 − Nlowθ distributions for both the neutron capture signal (blue) and the background (red). See text for more details.
5.1.2.9 Charge mean and RMS: Q mean and Qr ms

Though for low energy analysis in SK, PMT charge usually cannot provide muchinformation, in neutron tagging processes where we take into consider the actual performance of every PMT channel, the charge distribution may still give a hint on the possibilityof a hit to be from signal or from electronic noises. Q mean and Qr ms are defined respectively as the mean and the RMS of the number of p.e.’s for a candidate. For noisy channels
or PMT sparkling events which produce enough hits to mimic a 2.2 MeV γ events, it isvery likely that these channels have higher gain than usual PMTs and thus have higher
Q mean and wider Qr ms , as shown in Fig. 5.15 and Fig. 5.16.

1000
800
600
400
200
0
0

0.5

1

1.5

2

2.5
Qmean

Figure 5.15 Q mean distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
94

Chapter 5

Selection of Correlated Neutrons at SK

800
600
400
200
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
Qrms

Figure 5.16 Qr ms distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
5.1.2.10 Number of hits with high charge: NhighQ

The number of hits with more than 3 p.e.’s for a candidate is defined as NhighQ . Dueto the same reason as mentioned above, noisy channels tend to have a higher gain and thus
if a PMT gets unreasonably high charge, it’s more likely to be from a noisy channel thanthat from a signal event. The distribution of NhighQ is shown in Fig. 5.17.
8000
7000
6000
5000
4000
3000
2000
1000
0
0

5

10

15

20

25
NhighQ

Figure 5.17 NhighQ distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
5.1.2.11 Hit time RMS: Tr ms

Though the timing information has been used in the pre-selection to select 2.2 MeV
γ candidates at a 10 ns cut, hits from true 2.2 MeV γ’s tend to concentrate in this 10 ns
95

Chapter 5

Selection of Correlated Neutrons at SK

time window. Without scattering, hits from 2.2 MeV γ’s are expected to arrive on PMTs
at exactly the same ToF-subtracted time, and thus the width of the time distribution is
simply determined by the PMT timing resolution, which is ∼ 3 ns for those with charge∼ 1 p.e. at SK [80] . Variable Tr ms is the RMS of the timing of all N10 hits, as shown in
Fig. 5.18. We expect a smaller Tr ms for 2.2 MeV γ signals.

800
600
400
200
0

1

2

3

4
Trms

Figure 5.18 Tr ms distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
5.1.2.12 Minimum RMS of hit time: minTr ms (3) and minTr ms (6)Due to the inevitable PMT dark noise, even when a candidate originates from a 2.2
MeV γ, it may still have several hits from the noise and result in a smeared Tr ms . To
eliminate the influence from these noisy hits, a minimal Tr ms based on only part of thecandidate hits is reconstructed as minTr ms (x), where x is the considered number of hits
from the total N10 , as shown in Fig. 5.19.

Figure 5.19 A scheme for the construction of minTr ms . Clusters of 3-6 hits with minimal
Tr ms are shown for a candidate with N10 = 9. Possible background in this candidate will notcontaminate the minTr ms [97] .

Among possible x choices from 2 to 7, we use minTr ms (x) with x = 3 and x = 6 forthe neural network inputs, as shown in Fig. 5.20 and Fig. 5.21.
96

Chapter 5

Selection of Correlated Neutrons at SK

1000
800
600
400
200
0
0

0.2

0.4

0.6

0.8

1
1.2
minTrms3

Figure 5.20 minTr ms (3) distributions for both the neutron capture signal (blue) and the background (red). See text for more details.

1000
800
600
400
200
0
0

0.5

1

1.5

2

2.5

3

3.5
4
minTrms6

Figure 5.21 minTr ms (6) distributions for both the neutron capture signal (blue) and the background (red). See text for more details.
5.1.2.13 Neut-Fit variables: N Fwall , δN10 and δTr ms

Neutron Fit (Neut-Fit) is a vertex fitter developed by Tristan Irvine [97] . This fitter
performs a grid searching for the best vertex which minimize the Tr ms for all the hits froma candidate,√Tr′ms =

∑ N10i

(t i − t mean ) 2
,
N10

97

(5-5)

Chapter 5

where t mean =

∑ N10
i

Selection of Correlated Neutrons at SK

t i /N10 , and t i is the hit timing on the i-th PMT after the ToF subtraction

to the grid vertex. This process repeats with a finer precision until 0.5 cm. The Neut-Fit
reconstructed vertex is heavily biased towards the primary vertex due to the initial choiceof the N10 hits, which is determined by the ToF subtracted time to the primary vertex.
With Neut-Fit, the reconstructed neutron capture vertex and the goodness of the fit
can be used to discriminate the 2.2 MeV γ signal from background. The distance between
the Neut-Fit vertex and the nearest tank wall is defined as N Fwall . The neutron vertex ismore likely to be close to its primary vertex, and Neut-Fit tends to be biased towards theprimary vertex. Therefore, for 2.2 MeV γ’s, the reconstructed vertex should satisfy thefiducial cut applied to the primary vertex, i.e., the candidate should not be reconstructednear the ID wall, as shown in Fig. 5.22.

5000
4000
3000
2000
1000
0
0

200 400 600 800 1000 1200 1400 1600 1800
NFwallFigure 5.22 N Fwall distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

The minimal Tr′ms Neut-Fit obtained for the best vertex tends to be smaller than Tr ms
for the primary vertex for neutron capture signal events. For backgrounds, however, theyusually do not originate from a single source or a source outside the fiducial volume,thus having larger Tr′ms values. Comparing Tr ms from diﬀerent vertices, the variableδTr ms = Tr ms − Tr′ms is constructed to discriminate between signals and backgrounds, as

shown in Fig. 5.23.

98

Chapter 5

Selection of Correlated Neutrons at SK

1400
1200
1000
800
600
400
200
0
−3

−2

−1

0

1

2

3
4
DTrms

Figure 5.23 δTr ms distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

As shown in Fig. 5.3, we can find that with ToF subtracted to the reconstructedprimary vertex, some hits from the 2.2 MeV γ may still spread outside the 10 ns window.
Sliding another 10 ns window in 40 ns around the neutron candidate, and re-performing′− N10 isthe ToF subtraction with regard to the Neut-Fit vertex, a new variable δN10 = N10′
should be smaller
constructed, as shown in Fig. 5.24. For the 2.2 MeV γ signal, this N10′
should not have such athan N10 , while for backgrounds without a single source, N10

improvement from N10 .
14000
12000
10000
8000
6000
4000
2000
0
−2

0

2

4

6

8
N10d

Figure 5.24 δN10 distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

99

Chapter 5

Selection of Correlated Neutrons at SK

5.1.2.14 BONSAI fit variables: BSwall and BSenergy

BONSAI fit is an unbiased low energy fitter as described in Section 3.3. It is
optimized for low energy events, but requires at least 10 hits to perform the vertex fitting,and is extremely slow when the input hits exceeds 1000 hits. To account for that, for each
2.2 MeV γ candidate, BONSAI fit is performed on the surrounding 1.3µs of data; if thenumber of hits in a 1.3µs time window exceeds 1000, the selection window is narrowed
to 325 ns surrounding the 10 ns candidate; if the number is still exceeding, the event is
too noisy to be a good neutron capture event, and is dropped.
BSwall is the distance between the reconstructed BONSAI vertex and the nearest ID
wall. Similar to N Fwall , BSwall removes backgrounds reconstructed near the ID wall, andis independent of N Fwall due to the diﬀerence in reconstruction algorithm, as shown in
Fig. 5.25.

6000
5000
4000
3000
2000
1000
0

0

500

1000

1500
BSwallFigure 5.25 BSwall distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

BSener gy is the eﬀective number of hits for the candidate event, representing theenergy. As explain in Section 3.3, the energy of low energy events are first reconstructedby the eﬀective number of hits, and then converted to energy (MeV) by an energy scaling
function. For 2.2 MeV γ events, however, the energy scaling function under 3 MeV is notproperly calibrated at SK. In this case, a variable BSenergy is defined to be the eﬀective
number of hits, to represent the energy of a candidate event. The mono-energetic 2.2 MeV
γ is expected to have a sharper peak in the BSenergy distribution, as shown in Fig. 5.26.

100

Chapter 5

Selection of Correlated Neutrons at SK

12000
10000
8000
6000
4000
2000
0
0

5

10

15

20

25

30

35
40
BSenergy

Figure 5.26 BSenergy distributions for both the neutron capture signal (blue) and the background(red). See text for more details.
5.1.2.15 Fit agreement variables: F Pdist and BFdist

The diﬀerence between vertices reconstructed by diﬀerent methods can be used toevaluate the goodness of neutron fit and the likelihood for the hits within a candidate tooriginate from the same source.
F Pdist is the distance between the Neut-Fit neutron vertex and the primary vertex
reconstructed by BONSAI. As we have shown in Fig. 5.2, SRN IBD neutrons do nottravel far from the neutrino interaction point before being captured. The primary vertex
reconstructed by BONSAI is proved to be more reliable for the higher energy and more
apparent Cherenkov ring [89] . If a Neut-Fit reconstructed neutron vertex is close to its
BONSAI reconstructed primary vertex, the candidate is more likely to be a 2.2 MeV γ
signal, as shown in Fig. 5.27.

101

Chapter 5

Selection of Correlated Neutrons at SK

7000
6000
5000
4000
3000
2000
1000
0
0

1000

2000

3000

4000
FPdistFigure 5.27 F Pdist distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

BFdist is the distance between neutron vertices reconstructed by BONSAI and NeutFit. Due to the diﬀerence of algorithm and input hit set where BONSAI takes 1.3 µs andNeut-Fit takes a set biased 10 hits, these two reconstructions will diﬀer if the candidate isaccidentally chosen from longer-lived backgrounds, as shown in Fig. 5.28.
3000
2500
2000
1500
1000
500
0
0

1000

2000

3000

4000

5000
BFdistFigure 5.28 BFdist distributions for both the neutron capture signal (blue) and the background(red). See text for more details.

5.1.3 Multivariate classification

Multivariate classification is a machine learning based technique for pattern recognition. Derived from the training events separated in both classes or even events from asingle class, a classifier can determine the mapping function describing a decision bound102

Chapter 5

Selection of Correlated Neutrons at SK

ary. A Toolkit for Multi-Variate Analysis TMVA has been implemented in the widelyused in high energy physics area analysis framework ROOT [98] . In this analysis, after
comparing several classifier, we decided to use a feed-forward Multi-Layer Perceptron(MLP) in TMVA to maximize the separation between signal and backgrounds.
In this analysis, MLP was trained with 10,000,000 events hybrid with both theMC simulated 2.2 MeV γ signal and the dummy trigger backgrounds. There were
20,458,451 candidates selected, in which 3,507,630 candidates were true 2.2 MeV signals,
and 16,950,821 were backgrounds. To avoid over-training, this sample was split randomly
into a training sample with 3/4 of the candidates and a testing sample with 1/4 of thecandidates. The tunable parameters in a MLP include signal and background weight(fixed at 1), number of iteration cycles, and the node pattern. After several trials andconsidering the time consumed, the number of cycles was determined at 1,000 and thenode pattern was chosen as 22:18:8:1 (input variables : hidden layer 1 : hidden layer 2: output). The output node represents the MLP calculated similarity of a candidate to a
training 2.2 MeV γ signal or a training background, to be used as a cut in latter stage.

5.2 Significance Curve
The eﬃciency of 2.2 MeV γ-ray selection is defined to beϵ=True neutrons that are tagged as candidates,
All neutron captures(5-6)

And the background rate as
R=

Dummy triggers tagged as candidates.
All dummy triggers(5-7)

The pre-selection is a rigid cut and its eﬃciency is calculated from MC simulation andthe dummy trigger data, as shown in Table 5.1.
Table 5.1

Neutron tag pre-selection eﬃciency

Signal (MC)/ event

Background (dummy trigger)/ event (500µs)

35.4%

160.1%In the neural network selection, however, these eﬃciencies are dependent on the103

Chapter 5

Selection of Correlated Neutrons at SK

1-dimensional MLP cut. To compare with the previous neutron tagging study in LOWE
group, this MLP cut is set at a point that the background level is the same as the previous
study, as shown in Table 5.2. Two diﬀerent energy regions are separated by the level ofbackgrounds, where below 14.3 MeV the spallation backgrounds dominate and the cut
must be set tighter to remove the backgrounds. A significant improvement on the neutron
tagging eﬃciency is observed. The eﬃciency in the low-energy region is nearly doubled,
while it also increased by ∼40% in the high-energy region. A comparison for the improved
and the previous neutron tagging method versions can be directly observed in Fig. 5.29.
For Eν̄e > 14.3 MeV, the neutron tagging with a loose cut (∼ 25% signal eﬃciency and∼0.3% accidental background level) was applied, while for Eν̄e < 14.3 MeV, the neutron

tagging with tight cut (∼19% signal eﬃciency and ∼0.065% accidental background level)
was applied.

Table 5.2

A comparison of neutron tag eﬃciency with the previous study [46]Signal (MC)/ event
ImprovedOldEν̄e <14.3 MeV
Eν̄e >14.3 MeV

19.1%

10.2%

0.065%

25.2%

18.1%

0.3%

Background efficiency / 160.1%

NTag version

10−1

10−2

Combined ntag
LOWE ntag
Cut for sample 1
Cut for sample 2

10−3

0.2

Figure 5.29

Background (dummy trigger)/ event (500µs)

0.4

0.6

0.8
1
Signal efficiency / 35.5%

A comparison of neutron tag eﬃciency with the previous study [46]104Chapter 5

Selection of Correlated Neutrons at SK

5.3 Systematic Study with the Am/Be Source
To study the systematic uncertainty on the neutron tagging technique, we took neutron
capture data in 2009 and 2016 with the neutron emitting calibration source of Am/Be.
Experimental Setup
Figure 5.30 shows the Am/Be source embedded in the center of a 5 cm cube of
bismuth germanate oxide (BGO) scintillator. The emission of neutron is through thefollowing processes with a prompt γ as the primary event,
α +9 Be →12 C∗ + n,
12C∗ →12 C + γ(4.43MeV), prompt(5-8)

n + p → d + γ. delayed

where the incident α is emitted from 241 Am. A minor branch directly to the ground stateof 12C produces a neutron without time correlation and is counted as background. The
prompt γ triggers SHE signal, after which the AFT will cover 93% probability range ofa neutron capture . On one hand, the existence of BGO compensated the low Cherenkov
photon yield for 4.43 MeV γ’s; on the other hand, it may shade or distort the propagationand capture of neutron in water.

Figure 5.30

A photo of the Am/Be source.

The Am/Be source is placed via 2 diﬀerent calibration holes into 3 diﬀerent locations
during the calibration data taking to study the position dependence of neutron tagging
eﬃciency. Table 5.3 lists the detailed positions. During the data taking at position A, a 10
Hz random trigger data is also taken to evaluate both the source related and the accidental
105

Chapter 5

Selection of Correlated Neutrons at SK

background levels.
Table 5.3

Am/Be source positions.

Am/Be source

X position (cm)Y position (cm)

Z position (cm)A (Center)
B (Y-12)C (Z15)

35.3
35.3
35.3

-70.7
-1201.9
-70.7

0.
0.
1500.

Data Selection
This selection caters for the goodness of event, before any neutron selection is applied.
Events passing these selection criteria are counted as Am/Be events.
1. For the primary event: 750 < total p.e. < 1,050 at source A; 850 < total p.e. < 1,
150 at source B; 900 < total p.e. < 1, 150 at source C;
2. For the AFT event: if N200 > 50, the whole event is rejected;
3. Time diﬀerence between any two events is greater than 1.5 ms, to avoid events
overlap.
Eﬃciency Validation
Am/Be were taken twice in SK-IV, namely 2009 and 2016. SK hardware properties
such as water quality and PMT gain, were changed significantly during this period andthose diﬀerences are considered in MC production. Therefore, the diﬀerence between
2009 and 2016 result should be included in the systematic uncertainty.
In the Am/Be data analysis, the number of true 2.2 MeV neutron capture eventswas calculated by fitting the time distribution of tagged neutrons with an exponential
distribution plus a constant component representing the backgrounds. As shown in
Fig. 5.31, the time distribution of Am/Be data (black points) in position A (centre) was
fitted (red line), with the left panel showing for 2009 Am/Be data and right panel for 2016.
The best-fit parameters of τ and eﬃciency are listed in Table 5.4. Similarly, for position
B (Y-12) and position C (Z12), the time distributions are shown in Fig. 5.32 and Fig. 5.33
respectively. The best-fit results are listed in Table 5.5 and Table 5.6. The diﬀerence of
signal eﬃciency between the MC and the Am/Be source is assigned as the systematic
uncertainty of neutron tagging eﬃciency, which is 10%.

106

Chapter 5

Selection of Correlated Neutrons at SK

800

hta
21100
191
152.8

700
600
500
400

Number of events / 10 μ s

Number of events / 10 μ s

hta
EntriesMean
Std Dev

900

EntriesMean
Std Dev

800

19652
191.3
152.9

700
600
500
400
300

300

200

200

100

100
100

200

300

400

500

600

700

800
� T (μ s)

100

200

300

400

500

600

700

800
� T (μ s)

Position A

MC

2009

2016

ϵS
τ

19.1±0.2%

18.3±0.2%
203.9µs

17.9±0.2%
206.7µs

hta
Entries
6999
Mean
188.4
Std Dev
152

300
250
200
150

Number of events / 10 μ s

Number of events / 10 μ s

Figure 5.31 The time distribution of Am/Be data (black points) in position A (centre) is fitted(red line), with the left panel showing for 2009 Am/Be data and right panel for 2016 data.
Table 5.4 Comparisons of eﬃciencies and fit neutron lifetimes between MC simulation, the2009, and the 2016 Am/Be data at position A.

hta
Entries
6933
Mean
189.1
Std Dev
150.4

250

200

150

100

100

50

50

100

200

300

400

500

600

700

800
� T (μ s)

100

200

300

400

500

600

700

800
� T (μ s)

Figure 5.32 The time distribution of Am/Be data (black points) in position B (Y-12) is fitted (redline), with the left panel showing for 2009 Am/Be data and right panel for 2016 data.
Table 5.5 Comparisons of eﬃciencies and fit neutron lifetimes between MC simulation, the2009, and the 2016 Am/Be data at position B.
Position B

MC

2009

2016

ϵS
τ

23.4±0.2%

20.7±0.4%
197.7µs20.9±0.4%
210.7µs

Table 5.6 Comparisons of eﬃciencies and fit neutron lifetimes between MC simulation, the2009, and the 2016 Am/Be data at position C.
Position C

MC

2009

2016

ϵS
τ

24.6±0.2%

23.3±0.5%
197.2µs

22.7±0.5%
198.9µs

107Selection of Correlated Neutrons at SK
hta
Entries
7142
Mean
187.2
Std Dev
151.4

300
250
200
150

Number of events / 10 μ s

Number of events / 10 μ s

Chapter 5

hta
Entries
6118
Mean
183.1
Std Dev
148.6

250

200

150

100
100
50

50

100

200

300

400

500

600

700

800
� T (μ s)

100

200

300

400

500

600

700

800
� T (μ s)

Figure 5.33 The time distribution of Am/Be data (black points) in position C (Z15) is fitted (redline), with the left panel showing for 2009 Am/Be data and right panel for 2016.

5.4 Validation with Cosmogenic 9 Li Sample
A 9 Li sample can be obtained by SK normal run data with the same first reduction
and neutron tagging as those used in the SRN search. Tagging neutrons in the 9 Li sample
not only measures the 9 Li yield at SK, but also validates the neutron tagging techniqueitself.
We applied the neutron tagging method to the 9 Li sample corresponding to 1886
days live-time. The cut was set at the background level of 0.065% for E < 14.6 MeV.
The distribution of time diﬀerence between the tagged neutron and the prompt β signal isshown in Fig. 5.34. Also shown is the prompt energy distribution.
Due to the limited statistics in the present 9 Li sample, two diﬀerent fits were performed, either with a fixed background estimated from accidental level, or with a fixed
lifetime of τ = 204.8 µs [94] . With a fixed background level, the neutron tagging lifetime
was fit to be τ = 251.5 ± 33.1 µs, and the number of tagged β + n 9 Li events was
246.6±23.2, as shown in Fig. 5.34. With a fixed neutron lifetime at τ = 204.8 µs, thefitted number of tagged β + n 9 Li events was found to be 214.0±25.6, agreeing with thefixed background level result within 1 σ. Compared to described in Ref. [46] , an obvious
improvement from the previous fitting in both the lifetime result of neutron tagging andthe uncertainty on the 9 Li yield evaluation.

108

Selection of Correlated Neutrons at SK

160

Events/1 MeV

Entries / 25μs

Chapter 540

data
accidental bkg
expected

140

35

120

30
100
25
80
20
60

15
10

40

5

20

0

100

200

300

400

0
8

500
� T(μs)

9

10

11

12

13
14
15
Energy (MeV)

Figure 5.34 Neutron tagging result for 9 Li sample of 1886 days in SK-IV. The left figure shows
the time diﬀerence between the tagged neutron and the primary event. The right figure shows theenergy of primary events with tagged neutrons.

5.5 Cut Optimization and Eﬃciency Evaluation
Previously in this section we applied the neutron cut by two steps: the pre-selection
cut and the multi-variable analysis cut, also called the neural network cut, or MLP cut.
The pre-selection is a stand-alone cut, while the neural network cut is applied as a stepfunction, with 2 distinct cuts below and above the energy 13 MeV, or neutrino energy
14.3 MeV. It works under the assumption that the background rates changes drasticallybelow and above 13 MeV. Further optimization is performed to take into consideration
the expected backgrounds and signals in each energy bin.
To determine a cut, only MC result can be used to provide eﬃciency and significanceinformation. Background rates within each energy bin are estimated by MC, with morediscussion in Section 6.1. For the signal estimation, due to the very low SRN flux expectedfrom SRN models, and to avoid the model-dependence, we assume null signal here, justto obtain optimized values for the neutron cuts. In this case, the upper limit can be derived
as a function of the neural network cut value. Two examples are shown in Fig. 5.35 forthe 11 MeV bin and the 17 MeV bin. The optimized MLP cut values are 0.98 and 0.55,
respectively.

109

Chapter 5

Selection of Correlated Neutrons at SK

80

Upperlimit [cm-2s-1]

Upperlimit [cm-2s-1]

100

60
40
20
0
0.1

0.2

0.3

0.4

0.5 0.6
MLP value

0.7

0.8

0.9

1

2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.1

0.2

0.3

0.4

0.5 0.6
MLP value

0.7

0.8

0.9

1

Figure 5.35 The upper limit calculated as a function of the MLP cut value for the 11 MeV binand the 17 MeV bin.

Using the same method for each energy bin between 8 MeV and 30 MeV, the optimized
cut values were obtained, and the eﬃciency was evaluated from the SRN MC sample, as
shown in Fig. 5.36. The previous step function used as the neutron tagging cut is also
shown in blue lines on the left figure, with overall signal eﬃciency at 8.8% [46] and 44
events remaining. After optimization, the cut values and eﬃciencies are shown in black
points, with overall signal eﬃciency at 19.3% and 29 events remaining. The overall signal
eﬃciency and background rejection is significantly improved.

1
0.9

0.9
MLP efficiency

MLP cut

0.8
0.7
0.6
0.5
0.4

0.8
0.7
0.6
0.5

0.3
0.4

0.2
10

15
20
Energy [MeV]

25

30

10

15

20
Energy [MeV]25

30

Figure 5.36 The cut values and corresponding eﬃciencies as a function of energy before andafter the optimization.

110

Chapter 6

Chapter 6

SRN Analysis and Result at SK

SRN Analysis and Result at SK

This chapter presents the author’s work in SRN analysis. We give the backgroundestimation, the SRN candidate events at SK-IV, and the upper limit for SRN flux.

6.1 Background Estimation
Table 6.1 summarizes the estimation for each background in the final SRN sample.
The method to evaluate the background are also listed. Detailed descriptions will bepresented in the following sections.
Table 6.1

Background estimation in the final SRN sample.

Components

Number of Events

Estimation Method

Accidental
Atm. NC
Atm. CC
Li9
Reactor14.2 ± 1.2
10.0 ± 4.1
5.6 ± 1.2
3.3 ± 0.9
0.7 ± 0.2

Ntag algorithm
NC sample
MC
Spallation sample
KamLAND data

Total

33.7 ± 4.6

6.1.1 Accidental Backgrounds

Accidental backgrounds are single signals that accidentally form a coincidence pair
to mimic the IBD event. This background mainly arises from the low light yield of
neutron capture signal in water. To keep a reasonable signal eﬃciency, we have to tolerate
the accidental contamination in the data sample. This background has been explained indetail in Chapter 5.
The systematic uncertainty on the estimation of this background is purely from theneutron tagging method itself, and was evaluated as 10%.
6.1.2 Atmospheric NC

Atmospheric neutrinos contaminate the final data sample through the NC and CC
channels, which produce events with similar signatures as IBD events. NC background111

Chapter 6

SRN Analysis and Result at SK

can be estimated from MC, as to be discussed in Chapter 7. To reduce the dependence on
nuclear interaction models, we employed a data-driven side-band method instead in thisanalysis.
The mechanism of NC interaction from atmospheric neutrinos on oxygen will be
explained in Chapter 7. The signature of NC events is the de-excitation γ’s. The deexcitation γ’s are sometimes accompanied by neutrons knocked out from the oxygen
nucleus, forming a coincidence signal mimicking the IBD pair. For the low energy γ
events or multi-γ events, the Cherenkov angle of the primary event is expected to bereconstructed above 42◦ , as explained in Section 7.3.1.1. Therefore, the side-band above42◦ can be used as a control sample to evaluate the atmospheric NC backgrounds inthe data sample. To avoid the resolution eﬀect of Cherenkov angle reconstruction, theside-band used for NC estimation is defined as the Cherenkov angle range [78◦, 90◦ ]. The
contamination of atmospheric NC in the SRN data sample is shown in Fig. 6.1.

10
9
8
7
6
5
4
3
2
1
0

10

15

20

25

30

Energy [MeV]
Figure 6.1

The energy spectrum for atmospheric NC events in the SRN sample.

The uncertainty for NC background is 41% as estimated by the NC analysis in
Chapter 7, averaging between the upper and the lower uncertainty ranges.
6.1.3 Atmospheric CC

The charge current interaction of neutrinos on a proton is rather well understood,
and in this case we estimate this background by MC. Atmospheric charged current backgrounds originate from low energy ν̄e ’s and ν̄µ ’s in atmospheric neutrinos. For ν̄e ’s, thisbackground directly comes from the IBD interaction. The cross section as well as the correlation between the incident neutrino energy and the positron energy follows discussion
112

Chapter 6

SRN Analysis and Result at SK

in Section 1.2. The contribution of ν̄e ’s in the SRN sample is shown in Fig. 6.2. For ν̄µ ’s,
however, the prompt signal in the coincidence pair is actually the decay electron from themuon produced via CC. To produce a muon, the neutrino energy Eν must be above 105.7
MeV. Furthermore, if the muon is an invisible muon in water, i.e., its energy is below theCherenkov threshold of muons in water, it will pass the reduction cuts. In this case, theneutrino energy is required to be less than 160 MeV. The contribution of ν̄µ ’s in the SRN
sample is shown in Fig. 6.3.

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

10

15

20

25

30

Energy [MeV]
Figure 6.2

The energy spectrum for atmospheric CC from ν̄e ’s in the SRN sample.

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

10

15

20

25

30

Energy [MeV]
Figure 6.3

The energy spectrum for atmospheric CC from ν̄µ ’s in the SRN sample.

The uncertainties are mainly due to the atmospheric neutrino flux prediction as
well as the neutron tagging eﬃciency evaluation. Above 160 MeV, the atmospheric
neutrino energy spectrum is well-described by theoretical models [99,100] and constrained
113

Chapter 6

SRN Analysis and Result at SK

by measurements [101] . However, the spectrum below 160 MeV has not yet been measured,and this analysis employs a simulation from FLUKA [102] , which give a prediction assuming
an approximately flat extension [103] .
6.1.4 Spallation Backgrounds

Most spallation backgrounds induced by cosmic ray muons do not produce neutrons,
and are thus classified as accidentals. The only spallation background leaking into thefinal data sample is from 9 Li, which can emit a beta and a neutron, perfectly mimicking
the signature of IBD signal.
This background is estimated by a spallation sample as explained in Section 5.4. By
tagging the neutron in the spallation sample, and applying the eﬃciencies of other cuts,
we evaluated the number of spallation events in the final sample. More details can befound in Ref. [52] . The systematics are mainly from the statistics of the spallation sample
as well as the data reduction procedures.
6.1.5 Reactor Neutrinos

Reactor neutrinos originate from nuclear power plants near the Kamioka Observatory.
The reactor operation data can be found in the IAEA data base [104] . The contribution fromreactor neutrinos can be calculated taking into consideration the oscillation eﬀect, as we
did in Chapter 8.
To follow the data-driven style of background estimation in this analysis, we estimatedthe reactor neutrino background by the IBD data provided by KamLAND, another neutrino
experiment at the Kamioka Observatory. They can provide the reactor neutrino flux ona daily basis covering the entire SK-IV period. We integrated the flux and scaled it
according to the live-time by diﬀerent energy ranges with diﬀerent live-times.
The systematic estimation followed the previous analysis [46] .

6.2 Candidate Events
In this analysis, we employed 2,778 (1,886) days of data from 2008 to 2018 in
SK-IV. In the whole 2,778 days of data, events within the energy window [11.3, 31.3]
MeV were analyzed. Due to the modification of software trigger system in 2011, theenergy threshold for an SHE trigger was lowered from 70 hits to 58 hits, enabling the114

Chapter 6

SRN Analysis and Result at SK

neutron tagging analysis for the [9.3, 11.3] MeV region. Therefore, 1,886 days of data
were analyzed for this energy range.
After the data reduction and neutron tagging, in the final sample for the SRN analysis,
29 events were observed, in good agreement with the expectation of 33.7±4.6 background
events. Figure 6.4 shows the energy distribution of these events against the expectationsof backgrounds. The time diﬀerence between the primary event and the neutron signal isshown in Fig. 6.5. The statistics is not significant, and the fitted neutron capture lifetimein Fig. 6.5 is τ = 204 ± 130 µs, consistent with the expected neutron capture lifetime inwater [94] . Therefore we validated the estimation of the number of accidental background

Entries/1 MeV

in the final SRN sample.

Observed
Accidental bkg
ATM ν μATM ν eLi9
reactor ν eNC
LMA model
population sys
heavy metal

8
7
6
5
4
3
2
1
0

10

Figure 6.4

15

20

25
30
Energy (MeV)

The energy spectrum for SRN sample.

6.3 Model-Independent Upper Limit
The number of observed events was statistically consistent with the null-signal hypothesis. In the absence of signal, an upper limit of SRN flux was derived. To comparewith results from other experiments, we estimated the upper limit for 90% C.L..
Based on present background estimations, this upper limit can be calculated in amodel-independent way, setting diﬀerent limits for diﬀerent energy bins. The upper limit
115

Entries / 25μs

Chapter 6

SRN Analysis and Result at SK

6
5
4
3
2
1
0

Figure 6.5

100

200

300

400

500
� T(μs)The neutron capture time distribution for SRN sample.

in each bin was derived by Rolke method [105] . It suits the case of a Poisson distributed
signal with a Poisson or Gaussian distributed background, thus caters for the systematics inthe background estimation. Moreover, the eﬃciency was also modeled with a Binomial ora Gaussian distribution. We used the Rolke method implemented in the ROOT toolkit [106]in our estimation for the upper limit.
The upper limit for the number of events in each bin was interpreted into the upper
limit for the SRN flux by
ϕ90 =

N90
,
T · Np · σ̄ I BD · ϵ(6-1)

where ϕ90 refers to the upper limit of the SRN flux and N90 refers to the upper limit ofnumber of events calculated by the Rolke method. T is the live-time for the data sample
used in this bin, either 1,886 days or 2,778 days. Np is the number of target protons
calculated from the fiducial mass, Np = 1.5 × 1033 . σ̄ I BD is the IBD cross section, and ϵis the total signal eﬃciency.

The previous SRN flux upper limit was mainly constrained by KamLAND in thelower energy range below 16 MeV and by SK-I/II/III result above 16 MeV, as shownin Fig. 6.6. Compared to the previous experimental results, this analysis gives a better
constraint below 16 MeV, and comparable upper limit with the SK spectrum analysis
116νe flux upper limit (cm-2 s-1 MeV-1)

Chapter 6

SRN Analysis and Result at SK

103
KamLAND 2343 days
SK-IV 960 days
SK-IV 1890 days
SK-IV 2778 days
SK-I/II/III 2853 days

102

10

1

10-1
10

Figure 6.6

15

20
25
30
Neutrino energy (MeV)

Upper limits derived by diﬀerent experiments and analyses.

above 16 MeV.

117

Chapter 7

Chapter 7

NCQE Analysis at SK

NCQE Analysis at SK

Neutral current interactions from atmospheric neutrinos on 16 O forms one of the
major backgrounds for the supernova relic neutrino search in water Cherenkov detectors
like Super-Kamiokande. This background in SRN search is found to be dominated by
the quasi-elastic (NCQE) scattering with nucleons inside 16 O nuclei. In this section we
first introduce the NC channels including NCQE, and then describe the Monte-Carlosimulation for atmospheric neutrino NC channels. Using the features provided by MC,
we can extract the NC sample from data and compare them against MC. Finally we present
a measurement of NCQE cross section for atmospheric neutrinos in SK-IV.

7.1 Introduction and Motivation
NC signal events in the SRN search window (8-30 MeV) must contain a primary
event and a delayed 2.2 MeV neutron capture event. If the neutron capture is absent, it may
still form a background by accidental coincidence but will not be classified as NC and will
be included in accidental background. The main contribution in NC backgrounds is fromNCQE channel. The primary trigger of an NCQE event is typically from a de-excitation
gamma of the oxygen nucleus, and leaks into the SRN sample via the resolution eﬀect of
Cherenkov angle reconstruction. The delayed neutron is usually a true neutron knocked
out by the incident neutrino. This will be further discussed in the section for the event
simulation.
The idea of this study came after we tuned the neutron tagging cut bin by bin in
the SRN search. By optimizing neutron tagging eﬃciency to the expected backgrounds
for SRN, the eﬃciency in the lower energy range is decreased and the eﬃciency in thehigher energy range is increased compared to the previous study at SK. The backgrounds
in the lower energy range include reactor neutrinos (extending to ∼10 MeV), cosmogenic
spallation 9 Li (reaching ∼15 MeV), and accidental backgrounds of which the primary

events are spallation singles (spreading the whole region but concentrate in below 15
MeV). The backgrounds in the higher energy range include atmospheric neutrino induced
CC ( ν̄e and ν̄µ ) and NC. The physics mechanism of CC is clear, and the uncertainties in

estimation are relatively low, while for NC, the previous SRN study at SK assigned 100%
uncertainty for its estimation.
118

Chapter 7

NCQE Analysis at SK

NC background was found to be the second largest background source in the search
for SRN, next to accidental background, as discussed in Section 6.1. It requires a detailed
study in NC and its main contamination channel in SRN sample, i.e., NCQE. This study
is also crucial for the future SRN search, especially if SK is going to be loaded withGadolinium [107] . With Gd, the neutron tagging does not introduce as much accidental
background as without Gd, while the NCQE backgrounds usually produce true neutrons,
thereby not reducible. This measurement will also pave the way for SRN detection inHyper-K [108] . Further possible applications of this measurement are described in the endof this section.
7.1.1 Atmospheric NCQE as the SRN Background

Neutral current quasi-elastic interactions of atmospheric neutrinos with 16 O produces
de-excitation γ’s and emitted nucleons, which can be used as signatures to identify these
events. The process can be written asν +16 O → ν +15 O + n + γ ′ s,

ν +16 O → ν +15 N + p + γ ′ s.

(7-1)

For high energy incident neutrinos, the emitted nucleons from the primary process typically have several hundred MeVs of energy and can continue to collide on other 16 O nuclei.
This is called as secondary processes, which will produce secondary γ’s and nucleons by
the decay of excited 16 O.
Because of the emission of low energy γ rays and the production of neutrons mimicking IBD signal pairs, NCQE events are the major component of NC backgrounds withinthe "golden" SRN search window of 8-30 MeV. In scintillator detectors, NCQE events
will form an irreducible background due to the inability to identify signals of positron andγ’s. In Cherenkov detectors, however, the majority of NCQE γ’s can be distinguished bytheir larger Cherenkov angles, though a considerable amount of remnant can still leak into
the SRN sample through the reconstruction resolution. NCQE γ’s sneak into the SRN
sample above 8 MeV through the single high energy de-excitation channels, the energy
resolution eﬀect, and multiple γ’s from secondary processes. Based on the Cherenkov
angle distribution, we present a study of atmospheric neutrino NCQE events detection
and cross section measurement.
119Chapter 7

NCQE Analysis at SK

7.1.2 Further Applications

NCQE channel is also important for the low energy case. With energy region from
20 to 30 MeV, NCQE can be used to detect supernova burst neutrino [109] . Because thischannel is NC, it provides additional flavor information on SN neutrinos and thereby helps
to constrain diﬀerent SN models [110,111] .

7.2 Monte-Carlo Simulation
Monte-Carlo (MC) simulation of atmospheric neutrino events was done in two stages.
First, an event generator models the interactions of atmospheric neutrinos in water. The
atmospheric neutrino flux is taken as the input for this step and the output is a series offinal state particles. For example, in the case of NCQE channel, the output could be ade-excited nucleus, a de-excitation γ, and a knocked nucleus. Then, subsequent particle
is tracked within ID and the detector response is simulated.
This analysis used the oﬃcial MC sample by the atmospheric neutrino analysis groupat SK. This sample was generated for 500 years of live-time with the SK-IV detector setup,
including both the FC (full contained) and the PC (partial contained) events. The UPMU
(upward-going muon neutrino) sample is not necessary in this study, since these events
enter the tank as muons and will be removed by the OD trigger and spallation reduction.
7.2.1 Atmospheric Neutrino Flux

Super-Kamiokande performed a comprehensive study of atmospheric neutrino fluxin the energy region from sub-GeV up to several TeV in Kamioka Observatory [101] . The
measured observables include flux, energy spectrum, and directionality. All these measurements are in good agreement with the theoretical prediction from Honda et.al [99,100] .
In this thesis, we took the HHKM model as the input for the atmospheric neutrino model,
which is also the default atmospheric neutrino model in the MC sample, i.e., no weightis applied. For the systematic study, the flux uncertainty is taken from the previous SK
measurement, as shown in Fig. 7.1. The neutrino ratio uncertainty is derived from thetheoretical prediction of Honda model. The neutrino-antineutrino ratio used in this study
is shown in Fig. 7.2.
We do not consider atmospheric neutrinos above TeV level due to the negligible flux.
For atmospheric neutrinos below 160 MeV (the lowest bin in SK atmospheric neutrino
120

Chapter 7

NCQE Analysis at SK

Flux [cm-2×sec-1×sr-1 ×GeV-1]

0.4
0.35

atmospheric νe

0.3

atmospheric νμ

0.25
0.2
0.15
0.1
0.05
0
1

Atmospheric neutrino flux measured at SK.

ν/ νν μ/ ν μνe/ νe

1

10

Ratio

Ratio

Figure 7.1

Energy [GeV]1ν/ νν μ/ ν μνe/ νe1

10Energy [GeV]1

10Energy [GeV]

Figure 7.2 Atmospheric neutrino-antineutrino ratios predicted by Honda models HHKM06 (left)and HHKM11 (right).

measurement [101] ), no experimental data is available, and a simulated result from FLUKA
is used [103] .
7.2.2 Neutrino Interactions

Atmospheric neutrino interactions with constituents of water molecules at SK issimulated by the NEUT generator [112] . In general, there is no up-to-date publication orinternal technical note for NEUT. The following description of the neutrino interactions isa review based on several previous SK/T2K collaborators’ PhD thesis [113,114] and a directcontact with NEUT author Hayato [112] .
7.2.2.1 NCQE Simulation

Based on Ankowski’s model [15] , the NCQE cross section on oxygen in NEUT is
simulated by a oxygen spectral function model [115] with the BBBA05 form factor [116] ,121

Chapter 7

NCQE Analysis at SK

taking into consideration the Pauli blocking eﬀect at pF = 225 MeV/c. NEUT well
reproduces the Ankowski result [15] , and also provides additional information on kinematics
which cannot be directly subtracted from the model. The nucleon breakdown crosssections as a function of neutrino energy for neutrinos and anti-neutrinos are shown in
Fig. 7.3.

Cross section [10-38 cm2]

0.3
0.25
0.2
0.15
nu_p
nu_n
nub_p
nub_n

0.1
0.05
0
0

Figure 7.3
energy.

2

46Energy [GeV]8

10

Nucleon breakdown cross sections for the NCQE process as a function of neutrino

The remnant excited oxygen nucleus exists with a single hole in 1p1/2 , 1p3/2 or 1s1/2
state in the simple shell model. Among these final states, the excitation energy levels
with gamma emission (and corresponding gamma emission branching ratio) for the state
1p3/2 include 6.32 MeV (86.5%) or 9.93 MeV (4.9%) in the case of a proton knock-out,
and 6.18 MeV (86.9%) in the case of a neutron knock-out. Therefore, the main signature
for NCQE events is a ∼ 6 MeV gamma. The de-excitation channels in single-hole states
are summarized in Fig. 7.4. Other decay channels include further nucleon emission.
The de-excitation from the state 1s1/2 is complicated with both de-excitation gamma andadditional nucleon emission. We used the data from the 16 O(p, 2p) 15 N experiment RCNPE148 [117] . Continuum states are assumed to have no gamma emission, while the normal
gamma emission assumption is also calculated and included in the systematic study.
7.2.2.2 Detector Simulation

The following processes of transportation, Cherenkov light emission, possible secondary processes, and the detector response are simulated in the GEANT3 [118] based SK
detector simulation package SKDETSIM. In this study, we used the ATMPD group oﬃcial
122Chapter 7

Figure 7.4

NCQE Analysis at SK[113] .
De-excitation modes of 16 O proton hole (p3/2 ) −1
p and neutron hole (p3/2 )n states

MC. The gain increasing was not implemented in this version, and the gain variation indata was taken into account by the LOWE group reconstruction tool.
The secondary process is illustrated in Fig. 7.5. For the secondary gamma production,
there is no available experimental data yet, and the simulation was done by the GCALOR
package of GEANT3 [119] . In the GCALOR,the simulation package NMTC and MICAP areused for hadronic reactions covering the energy of knock-out nucleons in NCQE processes
from atmospheric neutrinos. NMTC simulates protons in all energies and neutrons above
20 MeV, while MICAP simulates neutrons below 20 MeV. Some discontinuity is seen at
the cutoﬀ and taken as the systematic uncertainty.

Figure 7.5

An illustration for NCQE primary and secondary processes [114] .

7.2.3 Other NC Channels

In principal, all the NC channels were included in our MC. The second leading NC
channel after NCQE in the MC sample is single pion (NC1π), dominated by NC1π fromdelta resonance. The third place goes to the multi-pion production channel. The primary
signals from these events are de-excitation gamma’s after pion absorption on oxygen. If the123Chapter 7

NCQE Analysis at SK

produced pion is absorbed before going out of the nucleus, it will be simulated by NEUT.
When the produced pion goes out of the nucleus and propagate in water before being
absorbed by another oxygen nucleus, it will be simulated in SKDETSIM, i.e., GEANT3
packages.
7.2.4 MC Reconstruction and Reduction

The reconstruction of MC was done by the lowe group reconstruction tools. BONSAI[120]

was employed for the vertex reconstruction. The energy reconstruction was

performed by calculating the so-called Neﬀ, i.e., the eﬀective hits for an event, as discussed in Section 3.3.3.1. Afterwards, the low energy events were processed with theCherenkov reconstruction tool by combining every 3 hits to derive open angles and tolook for the peak of open angle distribution.
The MC reduction was performed in the same way as the data reduction except forthe spallation cut and the solar cut. For MC, due to the independence of the atmospheric
neutrino MC from muon events, the spallation cut was directly applied as the event weight,
i.e., only eﬃciency was multiplied to calculate the number of events.

7.3 Data Reduction and Neutron Tagging
A sample with 2,778 (1,886) days live-time at SK-IV was used in this analysis. The
upper bound of energy for the NC sample was set at 30 MeV, where the de-excitation
gamma can hardly reach even with the energy resolution eﬀect and where the atmosphericcharged current (CC) background also starts to increase as the energy approaches theMichel peak of the decay electrons from muons.
7.3.1 Data Reduction

One of the main motivations for the atmospheric neutrino NC study is to determine
the NC events in the SRN search. In SRN study, many strict reductions were applied toremove possible backgrounds, and most of them also worked to make a clean NC sample,
as described in Chapter 4. Similarly, these cuts were applied to select NCQE events fromthe low-energy data sample except for the Cherenkov angle cut.

124Chapter 7

NCQE Analysis at SK

7.3.1.1 Cherenkov Angle Cut

The algorithm of Cherenkov angle reconstruction has been described in Chapter 3.3.
The Cherenkov angle of an electron above the threshold is 42◦ , while for a pion or muons
below 30 MeV, the opening angle is less than 42◦ . On the contrary, the Cherenkov light
distribution of NCQE de-excitation gamma’s is more uniform, and the corresponding
opening angle is consequently reconstructed above 50◦ , as shown in Fig. 7.6.

Figure 7.6

The distributions of reconstructed Cherenkov angles for e’s, µ’s, γ’s and π’s.

The angle distribution after the neutron tagging required can be seen in Fig. 7.7,
together with MC predictions. Therefore, taking into consideration the resolution eﬀect,
we applied a Cherenkov angle cut of 50◦ , which results in the eﬃciency of ∼ 86%.
7.3.2 Neutron Tagging for NCQE Events

NCQE events for GeV and sub-GeV neutrinos are likely to knock out a nucleon fromthe nucleus. Knocked-out neutrons will propagate in water and thermalize. This process
is invisible in the sense of Cherenkov light. The thermalized neutrons are then captured
on hydrogen, emitting delayed 2.2 MeV gammas, which can be used to tag the NCQE
events.
The algorithm for the neutron tagging is the same as the one described in Chapter 5125Chapter 7

NCQE Analysis at SK

30
Data
non-NC
NC non-QE

25

NCQE

20
15
10
5
0

20

30

40

50

60

70

80

90

θC
Figure 7.7 Cherenkov angle distributions for both the data and the MC expectation. All cuts areapplied, except for the Cherenkov angle cut.

except for the treatment of the neutron travel distance. Since the TOF-subtracted time
is corrected with regards to the primary vertex, the distance between primary vertex
and neutron capture vertex becomes crucial in the determination of the neutron tagging
eﬃciency. For IBD neutrons from SRN neutrinos, the neutron energy is sub-MeV, and thetypical drift distance is less than 5 centimeters away from the primary vertex. However,for neutrons in the NC events, the neutron energy can reach up to several hundreds MeV,
as shown in Fig. 7.8. The neutron tagging eﬃciency was correlated with the simulationof drift distance. Since the present SKDETSIM may not well simulate the neutron
propagation process, a comparison between a GEANT4 toy-MC and SKDETSIM was
performed, as shown in Fig. 7.8. The neutron tagging eﬃciencies for diﬀerent steps indiﬀerent simulation setups are shown in Table. 7.1. The diﬀerence between GEANT4 and
SKDETSIM was assigned as the systematic uncertainty.
Table 7.1

Neutron tagging eﬃciencies for diﬀerent steps in diﬀerent simulation setups.
Process

Pre-cut

NN (15 MeV)SRN
NC (GEANT4)
NC (SKDETSIM)

35.4%
29.3%
27.7%

71.1%
60.8%
57.7%

The neutron capture time for the NC sample after all reductions is shown in Fig. 7.10.
126Chapter 7

NCQE Analysis at SK

nmom[0] {nneutron==1}

nmom[1] {nneutron==2}
htemp
Entries
8721
Mean
494.4
RMS
256.9

600

htemp
Entries
2539
Mean
380.6
RMS
196.1

220
200
180

500
160
140

400

120
300

100
80

200

60
40

100

20
0
0

500

1000

1500

2000

0
0

2500
nmom[0]

200

400

600

800

1000 1200 1400 1600 1800 2000 2200
nmom[1]Figure 7.8 Neutron momentum from primary (left) and secondary (right) processes. Bumps inthe low energy region is due to the neutrons emitted from the de-excitation of oxygen.
sqrt(pow(CaptureX,2)+pow(CaptureY,2)+pow(CaptureZ,2))
htemp
Entries
1068
Mean
1008
RMS
898.3

60

50

40

30

20

10

0
0

1000

2000
3000
4000
5000
6000
sqrt(pow(CaptureX,2)+pow(CaptureY,2)+pow(CaptureZ,2))

Figure 7.9 Distance from neutron production vertex to capture vertex. Left: toyMC using
GEANT4 (primary only, mm, QGSP_BERT_HP + NeutronHP); right: skdetsim using GEANT3(all processes, default, cm).

There are 89 remaining events in total, including true neutron events and accidental
background events. The accidental event rate was estimated by using the same tagging
criteria on the random trigger sample, and was calculated to be 13.7 events in this NC
sample. Fitting the time diﬀerence distribution with an exponential signal and a fixed
accidental background level, we obtained the total events with neutron as 75.3±9.4 and thelife-time as 219.5±47.2 µs, which is in good agreement with the expectation 204.7 µs [121] .
Using a fixed τ at 204.7 µs and fitting the time distribution again as a cross-check, we
obtained 68.5 ± 12.1 events with neutrons, which is statistically consistent with the result
from the fixed background fitting. Neutron multiplicity comparison between data and MC
is shown in Fig. 7.11. Good agreement is observed.
The total reduction eﬃciency for NCQE gamma events within [8, 30] MeV scaled to
2,778 days live-time is shown in Fig. 7.12. The main eﬃciency loss is due to the spallation
cut and the neutron tagging. These cuts are tuned bin by bin towards the best significance127Entries / 25μs

Chapter 7

NCQE Analysis at SK

18
16
14
12
10
8
6
4
2
0

100

200

EntriesFigure 7.10

300

400

500
� T(μs)Neutron tagging time distribution.

1

0.5

0

1

2

3

4
5
6
Neutron multiplicity

Figure 7.11 Neutron multiplicity in data (black points) and MC (red histogram). The uncertainties assigned to points are statistical while these assigned to histogram are the 10% intrinsic
neutron tagging uncertainty.
128

Chapter 7

NCQE Analysis at SK

at the null-signal expectation, putting an energy dependence on the final eﬃciency.

Efficiency

0.1

0.05

10

15

20
Energy [MeV]25

30

Figure 7.12 Reduction eﬃciency scaled to 2,778 days livetime. The energy dependence mainly
comes from spallation cut (50% to 100%), ntag (4% to 22%), and the livetime diﬀerence (72% to100%).

7.4 Analysis
The 89 events in our final data sample are from NCQE, NC other channels, neutron
backgrounds including leakage from reactor neutrinos and spallation, and accidental
backgrounds. To evaluate the contribution from non-NC and NC non-QE events, and to
derive the NCQE cross section, we carried out a further analysis using both the MC andthe data from the side-band region in the Cherenkov angle distribution.
7.4.1 Candidate Events

The vertex distribution in our NC sample is shown in Fig. 7.13. As expected, a good
uniformity is observed. The energy distribution is shown in the upper panel in Fig. 7.14.
The energy dependence of the signal eﬃciency is shown in Fig. 7.12.
In addition to the accidental background, non-NC backgrounds in the data sample
include the leakage from spallations, the reactor neutrinos, as well as the atmospheric
neutrino CC. The spallation background was estimated using a spallation data sample
derived by the local proximity in both time and space [52] . The same cuts as in the NC
study was then applied on this data sample. Consequently, the spallation background wasestimated to be 0.5, mainly contributed by the cosmogenic 9 Li background.

129Chapter 7

NCQE Analysis at SK

y [cm]

hvertex_xy
Entries
89
Mean x33.22
Mean y-4.043
RMS x
770.8
RMS y
702.2

1500
1000

hvertex_rz_py
Entries
89
Mean
-63
RMS
1032

2

500
0

1

-500
-1000
-1500
-1500

-1000

-500

0

500

1000

Events/1 MeV

Figure 7.13

0

1500
x [cm]

-1500

-1000

-500

0

500

1000

1500

Vertex distributions of the NC sample.

Data
NCQE
Single pion
Multi pion
Non-NC
Accidental

12
10
8
6
4
2
0

10

15

20

25
30
Energy (MeV)

Figure 7.14 Energy distribution of the NC sample. The data is shown in black points withstatistical uncertainty. The yellow histogram shows the accidental backgrounds. The red histogramshows the MC expectation of the NCQE events. The green and blue histograms represent the pionchannels of NC backgrounds, and the black histogram shows the non-NC background.

130Chapter 7

NCQE Analysis at SK

Background from the reactor neutrinos are IBD positrons and their Cherenkov angle
distribution is well understood. This background leaks into the NC sample through theeﬀect of Cherenkov angle resolution and was estimated to be 0.1 event.
Atmospheric neutrino CC backgrounds include νe CC and νµ CC. Their contribution
was evaluated from the same MC batch as that for the NC events. Due to the neutron
tagging cut, the leakage into the NC sample must originate from anti-neutrinos. Thisbackground was estimated from MC at 0.4 event for νe CC and 0.3 event for νµ CC. The
non-NC backgrounds are summarized in Table. 7.2.
Excluding the non-NC backgrounds, the total NC events in the data sample is estimated as 74.0 ± 9.4, which can be compared against MC predictions in NCQE and other
NC channels, as listed in Table. 7.3.
Table 7.2

Table 7.3

Break-down of background sources and contributions in the NC sample.
Components

EventsNC dataAccidental
Spallation
Reactorν̄e CC

74.0
13.7
0.5
0.1

ν̄µ CC

0.4
0.3

Final sample

89

Predictions for the processes in MC. A comparison to the NC data is also given.
Components

EventsNCQE
Single πMulti π’s
DIS

58.0
23.1
2.4
0.0

MC
NC Data

83.5
74.0 ± 9.4

131Chapter 7

NCQE Analysis at SK

7.4.2 Cross section Calculation

The NCQE cross section was measured by comparing the data and the MC expectatheory> can be expressed as:tion. The theoretical prediction < σNCQE∫ 10 GeV ∑theory< σNCQE>=

160 MeV

i=ν,ν̄

theoryϕi (Eν ) × σi (Eν )NCQE
dEν

∫ 10 GeV ∑160 MeV

i=ν,ν̄

ϕi (Eν )dEν(7-2)

= 1.14 × 10−38 cm2,
where ϕi (Eν ) is the atmospheric neutrino flux at neutrino energy Eν , σi (Eν ) is thecorresponding theoretical cross section, and i sums for neutrino and anti-neutrino species.
The energy integral was performed between 160 MeV and 10 GeV, above which theatmospheric neutrino flux is trivial, and below which the NCQE gamma cross section
with a neutron is negligible. The systematic uncertainty introduced by this energy cutoﬀ
was evaluated and included in the systematic analysis in following context. The measured
cross section is therefore expressed as:
observed>≈< σNCQE

exp
obs
obs
obs
Ntot
− Nacc− Nothers− NNCothers
exp
NNCQE

theory× < σNCQE>(7-3)=(0.95 ± 0.12stat. ) × 10−38 cm2,
obs
obs
refers to the observed number of events in the final reduction sample, Nacc
where Ntot

refers to the accidental background without a true neutron, and was evaluated from theobs
refers to the non-NC backgrounds, including spallation,
random trigger data. Nothers
exp
refers to the expected number of NC non-QE
reactors, atmospheric CC, etc. NNCothers
exp
refers to the expected number of NCQE events.
backgrounds. NNCQE

7.4.3 Systematic Uncertainties

Atmospheric neutrino flux uncertainty varies for diﬀerent energy bins, as discussed
in Ref. [101] . In this paper, a conservative estimation at 18% was taken in the energy range[160 MeV, 10 GeV]. The uncertainty of atmospheric ν/ν̄ ratio was estimated at 5% fromthe theoretical model [99] .
The non-QE NC cross sections had 18% uncertainty [16] . The spectroscopic factors
132Chapter 7

NCQE Analysis at SK

and the gamma emission branching ratios determines the uncertainty from the primary
simulation [114] . By removing and restoring all secondary gamma’s from the simulation [114] , the uncertainty from the secondary process was estimated to be 13% by the T2K
group. Although the atmospheric neutrino energy range is much wider than the T2K
beam, the decrease in the flux towards high energy tail is exponential scale. The central
value of primary neutrons from atmospheric neutrinos do not essentially tend to be higher
than that from T2K ν’s. The neutron energy distributions from both study were checked
to be in good agreement. In this case, the 13% uncertainty was found to be valid as aconservative estimation.
Data reduction besides neutron tagging imposed a 3% systematic uncertainty, as in
the SRN analysis [46] . The neutron tagging eﬃciency had 10% intrinsic uncertainty fromcalibration (Am/Be) and MC for low-energy neutrons, as discussed in Section 5.3. NC
neutron drift distance simulation further introduced 10% uncertainty on the neutron tagging eﬃciency, as given in Table. 7.1. The cutoﬀ at 10 GeV imposed ∼ 0.1% uncertainty

using simulation with the measured high energy atmospheric neutrino flux [101] . The cutoﬀ
at 160 MeV introduced less than 0.7% uncertainty, which is estimated by simulation withthe theoretical prediction of low energy atmospheric neutrino flux [103] . The evaluation ofobs.
non-NC (reactor, 9 Li, CC, etc) leakage into the NC sample introduced ∼ 21% to Nothers

However, due to the small ratio of events from the non-NC background, this uncertainty
was estimated to be ∼ 0.2% to the total cross section. All the uncertainties are listed inTable. 7.4.

Table 7.4

Uncertainties in the NCQE measurement
NCQE

νatm flux
ν/ν̄ ratio
Cross section
Primary γ’s
Secondary γ’s

NC others
18%
5%

10%
13%

Data reduction
Neutron drift
Neutron tagging
Others

18%
3%
13%
3%
10%
10%
0.7%

133

Chapter 7

NCQE Analysis at SK

A toy-MC was used to derived the uncertainty envelope for the cross section, and theresult is shown in Fig. 7.15. The 68% confidence level region is [0.59, 1.49] × 10−38 cm2 ,+0.49(sys.)) × 10−38 cm2 .
and the cross section is measured to be (0.95 ± 0.12(stat.)−0.32

12000
10000
8000
6000
4000
2000
0
0

Figure 7.15
MC.

0.5

1

1.5

2
2.5
[10-38 cm2]

3

3.5

4

The uncertainty envelope for NCQE cross section measurement, as a result of toy

7.5 Results and Discussion
We used 2,778 (1,886) days live-time of SK-IV data in a fiducial volume of 22.5
kiloton water detector and applied a strict reduction to remove possible backgrounds
from spallation and accidental coincidence. Within the 8-30 MeV energy window, we
observed 89 events compared with theoretical prediction of 83.5 events and 15.0 expected
non-NC background events of accidental coincidence and spallation. The flux-averaged
NCQE cross section measured is 0.95 × 10−38 cm2 with a 68% confidence interval of+0.49(sys.)) × 10−38 cm2 for atmospheric neutrinos from 160 MeV to 10 GeV.
(±0.12(stat.)−0.32

This measurement can be compared with a theoretical prediction of 1.14 × 10−38 cm2 .
7.5.1 Discussion on Future Improvement

The measurement is aﬀected by systematic uncertainties, including the atmosphericflux, other NC process cross section, primary and secondary process simulation, as wellas the neutron tagging eﬃciency. The flux measurement can be improved with future
Cherenkov detectors such as Hyper-Kamiokande [108] . The cross section for other NC
processes can be improved by the T2K oﬀ-axis near detector ND280 [122,123] and other134

Chapter 7

NCQE Analysis at SK

nuclear experiments such as MiniBooNE [124] and MINERvA [125] . For the simulation ofprimary and secondary processes, the gamma ray emission experiment at RCNP will start
to shed light soon when the neutron beam energy is tuned [126]The statistics in this analysis is mainly limited by the neutron tagging eﬃciency. The
present eﬃciency in pure water is relatively poor and is only ∼ 20%. When SK is updated

to SK-Gd [107] , the eﬃciency is expected to increase to about 90%, which can reduce therelative uncertainty caused by the neutron tagging eﬃciency.

135

Chapter 8

Chapter 8

Geoneutrino Study

Geoneutrino Study

This chapter covers a grid-calculation based geoneutrino simulation and the sensitivity study in a liquid scintillator detector, based on a publication by the author of thisthesis [127] . First we present the simulation of geoneutrino spectra and intensity at the
production point, then calculate flux at detection point considering both the Earth modeland the oscillation eﬀect of geoneutrinos. An introduction to a proposed liquid scintillator
detector follows, based on which we calculate the expected backgrounds and the sensitivity to geoneutrino flux and the Th/U ratio. The interpretation is also included. In the lastsection, we briefly discuss on the Earth core fission neutrinos.

8.1 Geoneutrino Intensity and Energy Spectra
Heat producing elements genearte geoneutrinos not only by isotopes themselves, butalso by the decay products in the same decay chain, i.e., the decay chain starting from thelong-lived isotope 232 Th with τ12 = 14.0 × 109 year, from 238 U with τ12 = 4.47 × 109 year,
and the isotope 40 K with τ12 = 1.28 × 109 year:
238
232
235
40
40

U →206 Pb + 8α + 6e− + 6ν̄e + 51.698 MeV,Th →207 Pb + 7α + 4e− + 4ν̄e + 46.402 MeV,
U →208 Pb + 6α + 4e− + 4ν̄e + 42.652 MeV,

(8-1)

K →40 Ca + e− + 4ν̄e + 1.311 MeV (89.3%),
K + e− →40 Ar + νe + 1.505 MeV (10.7%).

The νe ’s from the K-shell electron capture of 40 K are diﬃcult to detect due to the smaller
cross section of ν − e scattering compared to IBD applicable for ν̄e ’s. In the following

discussion, we consider ν̄e ’s from beta decays only.

A general energy formula for the energy spectrum of allowed beta decays can be
written as,
dN (Ee ) =G2F |M | 2
F (Z, Ee )(Emax − Ee ) 2
3 ℏ7 c 52π√×Ee2 − me2 c4 Ee dEe,
136

(8-2)

Chapter 8

Geoneutrino Study
G 2 |M | 2

where dN refers to the density of event at electron energy Ee , 2πF3 ℏ7 c5 is the shape function
for allowed decays, F (Z, Ee ) represents the Fermi function describing the electrical field of
the isotope nucleus, and Emax is the maximum electron energy allowed by the conservationof total energy. The energy of the emitted geoneutrino Eν̄e is then given by(8-3)

Eν̄e = Emax − Ee .

The antineutrinos from all the individual beta decays in a decay chain compose thegeoneutrino spectrum for an HPE. The spectra and rates from all the decay branches of the
HPEs have to be considered and calculated to estimate the overall geoneutrino intensity
and spectrum. Figure 8.1 shows the spectra of geoneutrinos from diﬀerent HPEs. The
spectra are generated with GEANT4 [95] and checked by diﬀerent references. A few percent
diﬀerence is found for 238 U geoneutrino spectrum between the GEANT4 simulation and
S. Enomoto’s calculation [128] . This diﬀerence shows up around 1 MeV and will not exceed
the 1.8 MeV threshold for IBD, and thus will not influence the detection. Actually, amongthe ν̄e ’s produced from the beta decays of HPEs, only those from the decay chains of 232 Th
and 238 U will exceed the reaction threshold of 1.8 MeV for IBD, while the ν̄e ’s from 40 K
are below 1.5 MeV, unable to be detected through IBD channel.
102
232

Th
K
235
U
238
U

Intensity / keV / decay

40

10

1

10−1
0

500

1000
1500
2000
2500
3000
Electron antineutrino energy [keV]

3500

Figure 8.1 The geoneutrino energy spectra produced by HPEs are simulated with Geant4. Theν̄e ’s are produced in the decays of 238 U, 232 Th, 40 K and 235 U. νe from 40 Kchain are not shown.

Due to the 1.8 MeV IBD threshold, the only contribution to the detectable geoneutrinosignal by IBD interaction are from the isotope 214 Bi and 234 Pa from the 238 U decay chain,and 212 Bi and 228 Ac from the 232 Th decay chains [129] . The energy spectra of geoneutrinos
137

Chapter 8

Geoneutrino Study

from the HPE uranium and thorium have diﬀerent distributions, with the 238 U geoneutrinos
extending to a maximum end point of 3.3 MeV, while the 232 Th geoneutrinos do not exceed
the energy of 2.25 MeV. From this diﬀerence, the uranium and thorium geoneutrinos canin principal be fitted individually to obtain the Th/U ratio, which in theoretical calculation
BSE models give m(232 Th)/m(238 U) = 3.9 globally [60] .

8.2 Geo ν̄e Flux Calculation
The calculation of geoneutrino flux and spectrum at the detection site involves theinitial energy spectrum at each production point, the distribution of HPEs in the world ona grid basis, the spheric wave propagation, and the oscillation eﬀect. Integrating over theabove factors, we derived a general formula of the geoneutrino energy spectrum ϕ(E) as
below
ϕi (E)dE =Xi λ i N Anν (i)µ∫i
Ai (⃗r ) ρ(⃗r )×
Pee (E, L) f i (E)d⃗r dE,
4πL 2

(8-4)

where by sequence X stands for the natural isotopic mole fraction of the HPE isotope i,
λ stands for the decay constant of i, N A refers to the Avogadro constant, µ refers to thestandard atomic mole mass for i, and nν is the average number of ν̄e ’s emitted per decay
from i. These parameters are either constants or dependent on the isotope i only, invariant
on the production location. A(⃗r ) refers to the locally variant abundance for i, and ρ(⃗r )stands for the density, also locally variant. These parameters are taken from the Earthmodel used. L stands for the linear distance from the production point to the detection
site, Pee stands for the neutrino survival probability, the calculation of which is included
in Section 1.1.2, and f (E) stands for the normalized ν̄e energy spectrum for the HPE i,
as shown in Fig. 8.1. These parameters are related to the neutrino oscillation.
The total flux ϕi is then obtained by integrating the energy spectrum,∫ϕi =

ϕi (E)dE=

Xi λ i N A
inν (i)⟨Pee⟩µi∫

Ai (⃗r ) ρ(⃗r )
d⃗r,
4πL 2

(8-5)

i
where ⟨Pee
⟩ represents the average ν̄e survival probability, calculated by integrating over138

Chapter 8

Geoneutrino Study

the normalized energy spectrum of HPE i and its abundance distribution in the Earth.
8.2.1 Earth Model

To obtain the locally variant density of the Earth, a reference model describing the
BSE is required. A group of geologists built a 1◦ × 1◦ topological map of the Earth crust,
named CRUST1.0 [130] . In CRUST1.0, every 1◦ × 1◦ cell is split in depth into 8 layers

of profiles, namely water, ice, upper, middle, and lower sediments, and upper, middle,

and lower crusts. Some of the layers may have 0 depth depending on the local structure,whether the cell locates in the ocean or in the mountains. In each layer, CRUST1.0
provides the density ρ(⃗r ) used in Eqs. (8-4) and (8-5), as well as some other information
less relevant to this study. For the mantle however, the determination of boundaries andlayers are diﬃcult, not to mention the density and locally variant density distribution.
The seismic tomography can be used to obtain these information, and in this analysis we
employ the model from Huang et al [60] . In general, the mantle is divided into three layersof continental lithospheric mantle, depleted Mantle, and enriched mantle. In each mantle
layer, the density is assumed to be uniform due to the mantle convection.
The abundance of HPEs Ai (⃗r ) is assumed to be uniform for every HPE in eachgeological layer. Diﬀerent BSE models mainly on this abundance, and in this analysis
we take the abundance assumptions from Ref. [131] , which employs the medium-Q BSE
model.
The Earth model parameters are set at the best precision of 1◦ × 1◦ , but this is still

too rough for the 1/r 2 propagation of geoneutrinos and the oscillation eﬀect. To facilitate
the computation, the 1◦ × 1◦ cell is further divided into grids to calculate the distance L aneutrino would propagate.

The main uncertainty introduced by this Earth model is from the assumption of HPE
abundance, i.e., the uncertainties from the BSE models themselves. From a previous
study [131] , the uncertainty from Earth model on the total expected geoneutrino flux is+12.6%−12.3% , and ±15.0% for the crustal geoneutrinos.

8.2.2 Oscillation Analysis

Geoneutrinos oscillates following the three generation scheme of neutrino oscillation,
as discussed in Section 1.1.2.1. However, it is worth further discussion on the variant
propagation length L for every production point, and on the propagation underneath the139Chapter 8

Geoneutrino Study

Earth surface.
8.2.2.1 Vacuum Oscillation

Following the notations in Section 1.1.2.1, we employ the oscillation parameters θ i j
and ∆Mi j from Ref. [132] , considering both the central values and uncertainties. The default
neutrino mass hierarchy is set as inverted hierarchy, while the case of normal hierarchy isalso discussion and included as an uncertainty.
i⟩ as in Eq. (8-5), is obtained by the
The average survival probability of ν̄e ’s, or ⟨Peei(E),
integral of energy dependent survival probability Pee

∫
i
⟨Pee
⟩=

(8-6)

i
Pee
(E) f i (E)dE,

iwhere Pee(E) is averaged over the HPE distributions in the Earth, considering the oscil-lation from every grid ⃗r to the detection site at the distance L,
∫
i
Pee
(E) =

Pee (E, L) · Ai (⃗r ) ρ(⃗r )/(4πL 2 )d⃗r∫.
Ai (⃗r ) ρ(⃗r )/(4πL 2 )d⃗r

(8-7)

i
(E) as a function of
The notation is the same as Eq. (8-5). The survival probability Pee

geoneutrino energy is shown in Fig. 8.2.

0.58
0.57

P ee

0.56
0.55
0.54
0.53
0

0.5

1

1.5
2
2.5
Neutrino Energy [MeV]3

3.5

i as a function of geoneutrino energy E. The
Figure 8.2 Geoneutrino survival probability Peemagenta points represents for uranium, blue points for thorium, and green points for potassium.
The red line shows the total geoneutrino energy spectrum in arbitrary units, and the black line
shows the IBD event energy spectrum, also in A.U..

140

Chapter 8

Geoneutrino Study

From the calculation, an average survival probability for geoneutrinos ⟨Pee ⟩ can bei(E) by the HPE energy spectrum. Applying
derived by averaging the energy dependent Peei⟩ can also
the IBD cross section as a weight, another ’eﬀective’ survival probability ⟨Pee′be calculated, as listed in Table 8.1.

Table 8.1 The survival probabilities for geoneutrinos of diﬀerent HPEs averaged ⟨Pee ⟩ and′eﬀectively averaged ⟨Pee ⟩ .
⟨Pee ⟩′⟨Pee ⟩

40 K

232 Th

235 U

238 U

Total

0.554

0.553

0.553

0.554

0.553

0

0.560

0

0.563

0.562

8.2.2.2 Uncertainty Introduced by Oscillation Parameters

The uncertainties from the neutrino oscillation parameters θ i j ’s and ∆Mi j ’s as citedfrom Ref. [132] will introduce uncertainties in the expected geoneutrino fluxes. The CP termδ and the hierarchy are also taken as uncertainty sources. Table 8.2 gives the estimation of
uncertainties propagated from oscillation parameters into the calculation of geoneutrino
fluxes.
Table 8.2 The central values, relative uncertainties, and corresponding relative uncertainties
propagated to the geoneutrino flux of neutrino oscillation parameters. For ∆Mi j ’s, the unit is
eV. For CP term δ and mass hierarchy MH, the uncertainty column corresponds to the parameterboundaries.
Parameter

Value

Uncertainty

Flux
uncertainty

θ 12

0.584

+2.6%
−2.4%

+1.8%
−1.7%

+1.8%
−1.7%

θ 13

0.149

±0.2%

±0.2%

θ 23
∆M21

0.785
7.53×10−5

±0.0%

±0.0%

∆M32
δ
MH

2.51×10−3
0
IH

+2.7%
−2.8%
±6.4%
±2.4%
±2.4%
±1.5
NH

±0.1%
±0.0%
±0.0%
±0.0%

Crustaluncertainty

±0.1%
±0.0%
±0.0%
±0.0%

The total uncertainty introduced by neutrino oscillation parameters is +1.8%−1.7% , mainly141

Chapter 8

Geoneutrino Study

contributed by the uncertainty from θ 12 . It is still negligible compared to the +12.6%−12.3%

uncertainty introduced by the Earth model now. However, with the future progress in thetheoretical predictions of the BSE models, the uncertainty from the Earth model is likely
to be further reduced and this in turn will require a better measurement of θ 12 .
Figure 8.3 shows the correlation between the uncertainty of θ 12 with the propagateduncertainty into the geoneutrino flux. The red solid lines stand for the central value ofθ 12 and the corresponding expected geoneutrino flux. The blue dotted lines represent
the 1σ uncertainty range, as listed in Table 8.2. The precision of measurement on θ 12
is expected to be improved with present and future experiments for solar and reactor
neutrinos, including JUNO [77] and Hyper-K [108] . The sensitivity study of JUNO claims±0.3% uncertainty on θ 12 after accumulating suﬃcient statistics. This prediction is shownin Fig. 8.3 by red dotted dashed lines, and the corresponding uncertainty in the geoneutrino
flux is expected to be ±0.2%.

Deviation from central value [%]

3
2
1
0
-1
-2
-3

0.56

0.57

0.58

0.59

0.6

0.61

θ 12

Figure 8.3 The correlation between the predicted geoneutrino flux and θ 12 . The red solid lines
stand for the central value of θ 12 and the corresponding expected geoneutrino flux, the blue dottedlines represent the 1σ uncertainty range in present experimental measurement, and the red dotteddashed lines stand for the predictions from JUNO [77] .

The MSW eﬀect, as discussed in Section 1.1.2.2, is also calculated for the geoneutrinos. Using the same method as described above, we expect +0.3% deviation on thegeoneutrino flux when considering the MSW oscillation instead of the vacuum oscillation.

142

Chapter 8

Geoneutrino Study

8.3 Liquid Scintillator Detector
The energy range of geoneutrinos is between 0 to 3.3 MeV. The low energy signalof geoneutrinos requires high light yield to ensure good energy resolution. Also, due tothe low cross section of neutrinos, the detector must be large enough to ensure suﬃcient
statistics. Liquid scintillator is a suitable material for the geoneutrino detection, as it ischeap and has relatively high light yield.
Compared to water Cherenkov detectors such as SK, the low light yield will not allow
geoneutrinos to trigger any event at SK, while in a liquid scintillator experiment where
the trigger threshold is usually below 3 MeV, geoneutrinos can be naturally detected.
The deficit of liquid scintillation light compared to water Cherenkov light is that liquid
scintillation light does not carry the direction information of the primary particle. In
geoneutrino analysis, however, the directional information has already been lost during
the IBD process, and thus water will not outperform liquid scintillator.
KamLAND and Borexino have succeeded in performing geoneutrino analysis withliquid scintillator detectors.
8.3.1 Scintillation Light

In a liquid scintillator, a positron with several MeV can generate both scintillation
photons and Cherenkov photons. The process of Cherenkov light production has been
discussed in Section 3.2.1.
Unlike water Cherenkov photons, scintillation photons are emitted isotropically. The
process of scintillation light production can be described by the empirical function called
Birks’ law [133] ,
dE/dx
dYs
,
=A
dx
1 + k B · dE/dx(8-8)

where dYs /dx refers to the photon yield per distance propagated by the positron, A stands
for a normalization constant, k B represents the Birks’ constant, which is dependent on the
scintillator property. dE/dx refers to the energy loss of the positron at the energy E. Thisdependence causes the nonlinearity of the scintillation light yield, as shown in Fig. 8.4.

143

Chapter 8

Figure 8.4

Geoneutrino Study

The nonlinearity of scintillation light yield as a function of the true energy.

8.3.2 Detector Response ModelAn energy response model should be able to describe the relation between the incident
particle and the output electronic data and reconstruct the incident particle energy fromthe output, taking into consideration the nonlinearity and nonuniformity of the detector.
The energy response of a liquid scintillator detector is important in the reconstruction ofneutrino energy, especially in the case of a low-energy neutrino due to the nonlinearity oflight emission around 1 MeV.
A generic energy response function can be written as [134]

Eobs (⃗x, Einit, Edep ) = E0

N
∑

{ [
(
)]}
,
Ri Oi ⃗x, Y Einit, Edep

(8-9)

i=1

where Eobs refers to the observed energy as a function of the initial energy of the incident
particle Einit , the deposited energy Edep , and the scintillation point ⃗x . E0 stands for a scale
factor to convert the readout from N channels of electronics to energy, R refers to thesingle channel electronics response, O refers to the optical response, and Y refers to thephoton yield including Cherenkov photons and scintillation photons.
Some approximations can be applied to simplify Eq. (8-9) in the sense to make it morecomputationally eﬃcient. First, the wavelength diﬀerence between Cherenkov photons
and scintillation photons is neglected. Due to the low light yield of Cherenkov photon
compared to scintillation photon, this approximation is feasible. Second, the position
144

Chapter 8

Geoneutrino Study

dependence of the electronics response is neglected. This is actually not an approximation,
but a requirement for the calibration and correction on each channel. Finally, the opticalresponse is decoupled into two parts: photocoverage, and phototransmission. It does
not work mathematically, but statistically this decoupling is feasible. The basic idea isthe high light yield of scintillator, due to which the yielded photon number actually falls
into a Gaussian distribution following the large number law. After these approximations,Eq. (8-9) is modified as][
Eobs (⃗x, Einit, Edep ) = E0 · R · C(⃗x )T (⃗x ) · Ys + f YC (Einit, Edep ),(8-10)

where Y is split into Ys and YC , namely the scintillation component and the Cherenkov
component, the optical response O is decoupled into photocoverage C and phototransmission T, and R is decoupled from other components to be an independent electronics
response term. A schematic view of this model is shown in Fig. 8.5.

Figure 8.5

A schematic flowchart of the proposed detector response model.

The photon yields Ys and YC can be analytically expressed as in Eq. (8-8) and in
Section 3.2.1. For the optical responses of phototransmission, first we start with the
Beer’s law:
T (λ, l) = exp(−l/L(λ)),(8-11)

where l represents the distance between the scintillation point and the PMT, L(λ) repre145

Chapter 8

Geoneutrino Study

sents the wavelength dependent attenuation length, and T (λ, l) is the survival probability.
Then the phototransmission response T (⃗x ) can be written as)(nl i (⃗x )
1∑
,
exp −
T (⃗x ) =n i=1
L(8-12)

where ⃗x is the scintillation point, n is the number of emitted photons, and l i is the distancetravelled by the i-th photon from ⃗x to the photosensors, or more precisely, to a continuous
surface that contains the photosensor surface. The ratio of the photosensor surface on that
continuous surface is defined as the photocoverage. To decouple the phototransmission
and the photocoverage, Eq. (8-12) can be expanded and regrouped as
)k
∞ (
∑
1
−
mk (⃗x ),T (⃗x ) = 1 +
L
k=1
n
]
1 1 ∑[l i (⃗x ) k ,mk (⃗x ) = ·n k! i=1(8-13)

where mk (⃗x ) is a moment term dependent only on the detector geometry. From Eq. (813), the precision of the approximation of finite moment terms is limited by the ratio ofl i /L. If l i /L is small enough, i.e., the case where attenuation does not dominate the photopropagation, the first moment term m1 (⃗x ) is suﬃcient to calculate T (⃗x ).
The above scheme is summarized into a pseudocode example to explain the procedures for this energy response model.
1. Uniformly place vertices inside the detector volume.
2. For each vertex, generate hypothetical photons isotropically, and trace the distance
between it and the continuous surface that contains the photosensor surface. Scattering or absorption should not be included here.
3. Record the portion of photons arriving at photosensors and the total number ofphotons, and the ratio is the photocoverage.
4. Calculate the moment term mk (⃗x )’s according to Eq. (8-13), and mk (⃗x )’s are
suﬃcient to describe the detector setup and phototransmission.
Since the moment term mk (⃗x )’s are only dependent on the detector geometry, invariant with the photo-properties of the scintillator, they will not require update unless thegeometry of the detector is changed, or the reflectivity of some material is modified.
Therefore, mk (⃗x )’s can be made into look-up tables, and the application of this scheme
146

Chapter 8

Geoneutrino Study

into calibration will be swift, without the need to perform a detector-level simulation.
This energy response model can naturally accommodate multi-volume detectors with
diﬀerent attenuation lengths in diﬀerent parts. Following the formality of Eq. (8-13), thephototransmission moments for a 2-volume detector can be derived as
)
)k
(

∞ (
∑
 1 k
1

m
(⃗
x
)
+
−
m
(⃗
x
)
T (⃗x ) =1 +
−
1,k
2,k
 L
L

1
2
k=1 
)a (
)b
∞ (
∑
1
1
−
−
m ab (⃗x ),
+
L1
L2
a,b

n
]k
1 1 ∑[
m j,k (⃗x ) =l j,i (⃗x ) ,n k! i=1n] []1 1 1 ∑[
l 1,i (⃗x ) a l 2,i (⃗x ) b ,m ab (⃗x ) =n a! b! i=1(8-14)

where j takes the value 1 or 2, and l 1,i + l 2,i = l i . In this case, the k-th order moment term
consists of m ab where a ≥ 0, b ≥ 0, a + b = k. It is straight forward to expand Eq. (8-14)

into more than 2 volume detectors. Eq. (8-14) can also be used to fit a single detector withmore than one distinct attenuation terms, i.e., scattering and absorption. Incorporating
Eq. (8-14) back into Eq. (8-10), this model can accommodate two volumes with not only
distinct attenuation length, but also diﬀerent yields and electronic scales.
A detailed discussion of the model and its application can be found in Ref. [134] . The
performance of this energy response model is expected to be less than 0.4% over a courseof 5 years for a cylindrical detector of radii and half-height at 5.65 m. This number is
suﬃciently low compared to the usual statistical energy resolution of liquid scintillator at
1 MeV, which is ∼ 4%.
8.3.3 A Proposed Experiment at Jinping

For the geoneutrino detection, as Fig. 1.14 and Fig. 1.15 shows, the largest backgroundcomes from the reactor neutrinos. Therefore, a geoneutrino observation site will havea significant signal background ratio if it locates somewhere far away from the nuclear
power plants and reactor sources.
The China Jinping Laboratory (CJPL, latitude at 28.15323◦ N, longitude at
101.7114◦ E), is located in a low background experimental site in the Jinping Mountain, Sichuan Province, China. The site is more than 900 km away from the closest
147

Chapter 8

Geoneutrino Study

reactors either in operation or under construction. A low-energy neutrino experiment at
CJPL will push forward the detection of geoneutrinos greatly.
The Jinping Neutrino Experiment (Jinping) is proposed to be built at CJPL, employing a kiloton-level detector of liquid scintillator or slow liquid scintillator [135] . The
expected fiducial mass for IBD is 3 kiloton, with a wide range of live-time and energy resolution scanned in a sensitivity study, to be discussion in Section 8.6.1. More sensitivity
studies on other physics topics and the assessments of the site as well as detector designs
can be found in Ref. [79] .

8.4 Backgrounds
The backgrounds for geoneutrino detection include electron antineutrino backgrounds which are irreducible due to the exactly same signal signature, and other backgrounds, sometimes can be distinguished by certain features.
8.4.1 Reactor Neutrino Background

Reactor neutrinos are electron antineutrinos covering the energy range of geoneutrinos. They form exactly the same signal signature of IBD as geoneutrinos. This backgroundcan be fitted by the distinct energy spectrum, extending above the 3.3 MeV geoneutrinoenergy boundary. Still, the statistical and systematic uncertainties introduced by reactor
neutrino background due to its large statistics and spectrum uncertainties can aﬀect thesensitivity of an experiment to the detection of geoneutrinos. The only way to reduce
this background is to move the neutrino detector away from the nuclear power plant, andJinping is the best neutrino observatory site so far in the sense of low reactor neutrino
backgrounds.
Reactor neutrinos are electron antineutrinos emitted from the beta decays of theradioactive isotopes in the fission fuel, 235 U, 238 U, 239 Pu, and 241 Pu. The neutrino spectrum
ϕ(Eν ) can be calculated by
Wth LF ∑ϕ(Eν ) = ∑f i Si (Eν ),i f i ei i

(8-15)

where Wth refers to the reactor thermal power and LF stands for the load factor of thereactor. These parameters can be found in the yearly booklet of the International Atomic
Energy Agency (IAEA) [104] . As a conservative estimation for geoneutrino sensitivity,
148

Chapter 8

Geoneutrino Study

we performed a small over-estimation for the reactor neutrino background by setting theload factor to 1.0 in this study. The fission fraction f i for the i-th isotope should follow∑
i f i = 1. In every fission of the i-th isotope, ei stands for the average energy released, andSi (Eν ) stands for the ν̄e spectrum [136,137] . The typical values for these fission parameters
can be found in Table 8.3.
Table 8.3

Fission fraction f i and average energy ei for the fissile isotopes.
Isotopefiei [MeV/fission]

235 U

0.58
0.07

202.36 ± 0.26
205.99 ± 0.52

238 U
239 Pu241 Pu0.30
0.05

211.12 ± 0.34
214.26 ± 0.33

Reactor neutrinos are also detected by IBD interaction. The event rate R(Eν ) can becalculated by the product of the flux ϕ(Eν ) and the IBD cross section σ(Eν ),R(Eν ) = ϕ(Eν ) × σ(Eν ).

(8-16)To directly compare between diﬀerent experiment material, masses, and live-times, auniversal geoneutrino unit called Terrestrial Neutrino Unit (TNU) is defined as 1 ν̄eevents detected by IBD interaction for 1032 protons in 1 year live-time. The event rates
of reactor neutrinos are shown in the unit of TNU in Table 8.4. Due to the diﬀerent
energy ranges of geoneutrinos and reactor neutrinos, we define [1.8, 10.0] MeV as theFull Energy Range (FER) for whole spectrum of reactor neutrinos, and [1.8, 3.3] MeV
as Signal Energy Range (SER) for the reactor neutrinos overlapping with the energy
range of geoneutrinos. The uncertainties listed in Table 8.4 are mainly introduced by
the oscillation eﬀect [138] , evaluated at 1.5% using the same method as in the calculationof geoneutrino oscillation eﬀect. The oscillation parameters and uncertainties are also
taken from Ref. [132] . Additional deviation from the central value listed can be contributedby considering the MSW oscillation, at the level of 0.5%. This is not considered as an
uncertainty source.
The reactor neutrino background is mainly contributed by reactors along the coastlineof China, as Fig. 8.6 shows.

149

Chapter 8

Table 8.4
Event rate
(TNU)
FER
SER

Geoneutrino Study

Reactor neutrino rates in diﬀerent energy ranges at Jinping.
Constructed
China
OthersUnder construction
China
Others

8.9 ± 0.2
2.4 ± 0.1

6.3 ± 0.1
1.5 ± 0.0

10.6 ± 0.1
2.3 ± 0.0

2.0 ± 0.0
0.6 ± 0.0

Total
27.8 ± 0.4
6.8 ± 0.1

Reactor Neutrinos [TNU]1210China, in Operation
China, Under Construction

8

Other, in Operation
6

Other, Under Construction

4
2
0
0

2000

Figure 8.6

4000
6000
8000
10000
Distance from Jinping [km]12000

Reactor neutrinos from around the world.

8.4.2 Other Backgrounds

Backgrounds other than ν̄e ’s may be reducible, but usually cannot be totally removed
from the data sample. In the case geoneutrino detection, the backgrounds include thecosmogenic background 9 Li and fast neutron, the natural radioactivity background (α, n),and solar neutrinos.
Cosmogenic backgrounds originate to the muons from cosmic rays trespassing thedetector. They collide on the carbon nuclei and break them apart. Among these spallation products, 9 Li isotopes decay with a correlated β − n signal, mimicking the IBD
signature. Muons from cosmic rays can also produce fast neutrons. These fast neutrons
colliding on other nuclei to produce a fast signal, and thermalize before being captured
on hydrogen. This process also produces a pair of correlated signals. The rate of cosmogenic backgrounds directly depends on the muon rate at the detector. At Jinping, the6,720 w.m.e. (water meter equivalent) overburden shielded the detector from the cosmic
rays, and the muon rate there is as low as (2.0 ± 0.4) × 10−10 /(cm2 · s) [79] . Assuming asimple veto of 2 s muon veto time window, the live-time loss is expected to be only 1.1%.
Benefiting from the extremely low muon rate at Jinping, the 9 Li background is estimatedto be (0.02 ± 0.01)/3 kilotons/1,500 days, while the fast neutron background is calculated
150

Chapter 8

Geoneutrino Studyat ≤ 0.04/3 kilotons/1,500 days.

The background from natural radioactivity comes from both inside the detector andoutside the detector, the latter of which usually comprises of the leakage of MeV γ’s,
and can be rejected by a fiducial volume cut. This background leaks into the geoneutrino
data sample by (α, n) reactions and accidental coincidence. Accidental coincidence inlarge volume detectors are usually negligible after applying a simple fiducial volume
cut [79] . The (α, n) reaction however, does mimic the IBD signal by a coincidence ofprompt α and a delayed neutron capture. The α comes from the natural decays fromthe long-term decay chains, especially from 210 Po. If we assume the same level of 210 Po
contamination as Borexino [70] , Jinping is expected to have (1.7 ± 0.1)/3 kilotons/1,500

days (α, n) backgrounds.

Solar neutrinos also form a possible background for the detection of geoneutrinos,
with the elastic scattering process:ν + e → ν + e.

(8-17)

This process has relatively low cross section compared to IBD, and the electron will notcoincide with a neutron to form a correlated pair of signals, thus it produces a background
only by accidental coincidence, which is negligible compared to the other backgrounds.
To summarize the above discussion, Jinping will have up to 1.8/3 kilotons/1,500
days non-ν̄e backgrounds in SER, negligible compared to the reactor neutrino backgroundat (60.4 ± 0.9)/3 kilotons/1,500 days. In the following sensitivity study, we will consider
only the reactor neutrino background.

8.5 Sensitivities
This section covers the result of simulation, the predictions of sensitivity study, andthe implementation on the geological models. In this section, we assumes a 3-kiloton√
liquid scintillator with a 500 p.e./MeV energy resolution (corresponding to 4.4%/ Evis ).
The live-time is taken as 1,500 days, corresponding to 5 years running with some deadtime for calibration. All these parameters have been scanned, and related studies can befound in Section 8.6.1.

151

Chapter 8

Geoneutrino Study

8.5.1 Predicted IBD Spectrum at Jinping

Figure 8.7 shows the expected IBD events at Jinping. Corresponding numericalresults for signal events are included in Table 8.5, in which the geoneutrinos are divided
into Th/U and crust/mantle. The comparison between geoneutrino signal and reactor

Events / 50 keV / 3 kilotons / 1500 days

neutrino background is listed in Table 8.6.
50
Expected IBD Events
Reactor neutrinos

40

Geoneutrinos from 238U
Geoneutrinos from 232Th

30
20
10
0
0

1

2

3
4
5
6
Neutrino Energy [MeV]

7

8

9

Figure 8.7 The simulation of IBD events at Jinping. The magenta dashed line shows thecontribution from 238 U, the blue dotted dashed line shows the contribution from 232 Th, the grayshadow shows the reactor neutrino background, and the black line shows the sum.
Table 8.5

Geoneutrino flux at Jinping in the unit of TNU.

Geo ν̄e (TNU)

Crust

Mantle

BSE

Th
U
Th+U

10.6 ± 0.8
38.4 ± 6.6
49.0 ± 7.3

2.1 ± 0.5
8.3 ± 2.3
10.4 ± 2.7

12.7 ± 1.0
46.7 ± 6.7
59.4 ± 7.6

Table 8.6 Geoneutrino signals and reactor neutrino backgrounds expected at Jinping. The setup
is a 3-kiloton detector for a live-time of 1,500 days, with an energy resolution at 500 p.e./MeV.
238 U

Event Rate ( TNU )Total Events

46.7
414.5

Geoneutrino
232 Th
Total
12.7
113.6

152

59.4
527.3

Reactor
FER
SER
27.8
246.8

6.8
60.4

Chapter 8

Geoneutrino Study

8.5.2 Sensitivity for Geoneutrinos

To evaluate the sensitivities of geoneutrino flux and Th/U ratios at Jinping, we
performed toy Monte Carlo simulations. First, we randomly sampled from the total
spectrum in Fig. 8.7 based on the statistics of 3 kiloton × 1,500 days by 50 keV binning.

Next, the spectrum is fitted by the expectations of U, Th and reactor spectra simultaneously
using maximum likelihood method. The fitting is limited in the energy range Ev ∈[1.8, 6.8] MeV. The procedure of sampling and fitting was repeated 10,000 times to avoid
fluctuations. The fitting function is written as[]
N (E) =N Rgeo RU f˜U (E) + (1 − RU ) f˜Th (E)+ N (1 − Rgeo ) f˜R (E),

(8-18)

where N (E) stands for the number of events in the sampled spectrum within the energy
bin E, N refers to the total number of IBD events, Rgeo is the fraction of geoneutrinos
among all the IBD events, and RU is the fraction of geoneutrinos from 238 U among thetotal number of geoneutrinos. The expectations of U, Th and reactor spectra are calculatedby the oscillated ν̄e spectra weighted by the IBD cross section, and f˜(E)’s stand for thenormalized spectra for 238 U, 232 Th, and reactors respectively, denoted by the subscripts U,
Th, and R. The free fitting parameters in this function are N, Rgeo , and RU .
The total number of geoneutrino events is(8-19)

Ngeo = N · Rgeo,
and the Th/U ratio in the measured IBD events at Jinping can be written as
R(Th/U)IBD = (1 − RU )/RU .

(8-20)The mass ratio of the HPE thorium and uranium in the BSE can then be derived as
′

U
⟩ σ̃U
⟨Pee
XU λ U nν (U) µTh·,
R(Th/U)m =R(Th/U)IBD · Th′
⟨Pee ⟩ σ̃Th XTh λ Th nν (Th) µU(8-21)

where σ̃’s stands for the eﬀective cross section of HPE i,
∫
σ̃i =

∫
σ(E) f i (E)dE/
153

f i (E)dE.

(8-22)

Chapter 8

Geoneutrino Study

For the BSE model used in the prediction of geoneutrinos at Jinping [131] , the Th/U
geoneutrino ratio R(Th/U)IBD = 0.27, and the HPE mass ratio R(Th/U)m = 4.1.
Fixing the reactor neutrino spectrum and set the reactor neutrino rate as a freeparameter, we obtained the sensitivities to the geoneutrino flux and the Th/U ratio, assummarized in Table 8.7.
Table 8.7

Geoneutrino sensitivities at Jinping.

Measurement

Precision (%)

Ngeo
R(Th/U)IBD

4.6%
26.3%

8.5.3 BSE Model Test

The BSE models diﬀer on the HPE abundance in mantle and give diﬀerent predictions for the geoneutrino flux. With the geoneutrino measurement precision at Jinping,
the distinguishing power on BSE models is plotted in Fig. 8.8. This figure is diﬃcult tounderstand due to the cross-over of geological information and the experimental measurement. Basically, the horizontal axis shows the radiogenic heat, the vertical axis showsthe expected geoneutrino flux, the oblique lines and bands represent the theoretical prediction on the correlation between x and y, and the horizontal structure represents theexperimental measurement.
The horizontal solid line stands for the expected geoneutrino measurement at Jinping,
and the gray band within the horizontal dashed lines represent the uncertainties. The
oblique solid line shows the response between the radiogenic heat and the expected
geoneutrino flux under the assumption of a fixed potassium, thorium, and uranium ratio.
The starting point of the oblique solid line marks the geoneutrino flux and radiogenic
heat from the crust at 49.0 TNU and 7.4 TW. The oblique dashed lines represent theuncertainties introduced by the crustal geoneutrinos. Diﬀerent colored bands stand for
diﬀerent BSE models, with blue for the low-Q [61] , green for the medium-Q [62] , and redfor the high-Q model [63] . The horizontal width of the bands indicates the theoreticaluncertainties of these models, and the corresponding intercepts on the y-axis represent theuncertainties in the prediction of geoneutrino flux. As the geoneutrino flux calculation
employs the medium-Q model, the horizontal solid line intercept with the oblique solidline at the center of green band representing medium-Q model.
154

Geo-neutrinos observed [TNU]

Chapter 8

Geoneutrino Study

80
70
60
Low Q

50

Medium Q
40
0

High Q
5

10

15
20
25
30
Radiogenic heat [TW]35

40

Figure 8.8 The theoretical predictions on the correlation between the radiogenic heat and the
expected geoneutrino flux, and the expected experimental measurement precision. Further explanations included in the text.

Besides the experimental measurement uncertainty in the horizontal dashed lines andthe model uncertainty, the main uncertainties plotted in Fig. 8.8 actually come from thecalculation of crustal geoneutrinos. As mentioned in Section 8.2, the crustal geoneutrino
uncertainties are contributed by the Earth model (±15.0%) as well as the oscillation
parameters (+1.8%−1.7% ). The Earth model uncertainties originate from the fact that even thecrust is not thoroughly understood, due to the limitation of geological data. A more precise
global crust model will surely help to reduce of the uncertainty but is not a short-term
task.
About half of the geoneutrino events detected at the experiment site actually comewithin 300 km around the detector [131] . A precise crust map of the local environment
can reduce the uncertainty on the crustal geoneutrino flux significantly. Seismologicaland geological data around Jinping are abundant, owing to the studies on the earthquakes.
However, the crust around Jinping is very thick as it is located on the Tibetan Plateau,
which complicates the construction of a precise local model. A close collaboration
between physicist and geoscientists is required towards the aim. For future prospect on
the crustal geoneutrino uncertainties, if we expect an optimistic uncertainty of ±1.0% in the

Earth model and ±1.0% from the oscillation parameters (mainly θ 12 ), the oblique dashedlines will shrink to the oblique dashed dotted lines in Fig. 8.8, significantly increasing thediscrimination power of geoneutrinos towards the BSE models.
155

Chapter 8

Geoneutrino Study

8.6 Further Discussion
In this section, we first discuss on detector requisite for the geoneutrino detection,then presents the test on the hypothesis of the Earth core fission neutrinos.
8.6.1 Requisites for the Detector

We scanned the detector parameters including live-time and energy resolution to
obtain their influence on geoneutrino flux and Th/U ratio sensitivities. The live-time isexpressed in kiloton × days, so it is equivalent to target mass.

Figure 8.9 shows the geoneutrino flux and Th/U ratio sensitivities against the reso-

lution and target mass. The left figure shows the sensitivity against energy resolution andthe right figure shows the sensitivity against the target mass. The black points show thesensitivity on Th/U ratio, and the blue points show the sensitivity on geoneutrino flux.
The lines are simply spline interpolations.
The precisions of both measurements are sensitive to the target mass and less sensitive
to the energy resolution as far as this is a kiloton level detector and the light yield is at thelevel of scintillation light (∼ 100 p.e./MeV). Therefore, on a practical basis, and also tosatisfy the requisites of other studies especially for solar neutrinos [139] , the detector setup
of a liquid scintillator experiment at Jinping is assumed to be 3 kiloton fiducial mass for
IBD, 1,500 days live-time, and 500 p.e./MeV resolution.
80

80
70

Geo-ν

60

U/Th ratio

50
40
30

Sensitivity [%]Sensitivity [%]

70

50
30
20

10

10
0
0

200 300 400 500 600 700 800 900 1000
Energy Resolution [p.e.]

Figure 8.9

U/Th ratio

40

20
0

Geo-ν

60

1000
2000
3000
4000
Target Mass [ton ×1500 days]

5000

Geoneutrino sensitivity and detector requisites. Explanations can be found in text.

8.6.2 Earth Core Fission Neutrinos

The hypothesis from J. M. Herndon et al. claims that there are natural fission reactors
in the inner core of the Earth. These reactors are also called geo-reactors. Due to the156

Chapter 8

Geoneutrino Studysmall size of the inner core compared to other layers of the Earth, the distribution ofgeo-reactors does not influence the predicted ν̄e flux or spectrum.
To sustain the Earth magnetic field and its variation, the total thermal power ofgeoneutrinos must be between 3 and 30 TW. Besides, the fuel of such a long-term
self-burning reactor should compose of 74.6% 235 U and 24.9% 238 U [140] . From thisassumption, the energy spectrum of ν̄e ’s from geo-reactors should resemble the spectraof reactor neutrinos from nuclear power plants.
Borexino [71] and KamLAND [69] have set an upper limit of 4.5 TW and 3.7 TW
respectively for the thermal power of earth core fission reactors with 95% confidence
level. Similarly, at Jinping we performed the analysis and obtained the upper limit by the
CLs+b method [141] . With the proposed 3 kiloton detector, it takes Jinping only 300 days
to excluded the 3 TW geo-reactor hypothesis by setting an upper limit of 1.4 TW at 95%
confidence level.

157

Chapter 9

Chapter 9

Summary and Outlook

Summary and Outlook

This section presents the summaries and discussions on the prospects of the threestudies in this thesis.

9.1 Summary
Based on the low energy signal and neutron production from neutrino interactions, we
presented three studies, namely the SRN search, the atmospheric ν−O NCQE interaction
measurement, and the geoneutrino sensitivity simulation.
The detection of SRNs will shed light on star formation and supernova burst mechanism as well as the neutrino physics. However, SRNs have not yet been observed. In
this thesis, SRNs are searched for in a 2,778-day data sample in SK-IV, a Cherenkov
detector via IBD channel. We optimized the neutron tagging technique by two partial
reconstruction methods on the neutron vertices and tuned the cut towards the best significance. The total SRN signal eﬃciency is improved from 8.8% to 19.3%. By tagging
the neutron product, we found 29 SRN candidates in the energy range of [9.3, 11.3] MeV,
with 33.7 ± 4.6 events expected. This is consistent with null-signal hypothesis, and amodel-independent upper limit is derived for every energy bin.

The atmospheric ν−O NCQE interaction forms a crucial background to the SRN
and other rare signal searches using the IBD channel, due to the γ − n signal it produces,

mimicking the IBD β − n pair. This cross section is not well-known, and was firstmeasured by the T2K collaboration, but the T2K neutrino beam profile is diﬀerent from theatmospheric neutrino profile. This thesis presents a direct measurement of the atmospheric
ν−O NCQE cross section based on the neutron tagging and the detection of the deexcitation γ from the residual nuclei. The NCQE cross section is measured to be (0.95 ±+0.49(sys.)) × 10−38 cm2 , averaged over the atmospheric neutrino energy range
0.12(stat.)−0.32

between 160 MeV and 10 GeV. This result is consistent within uncertainties with thetheoretical prediction of 1.14 × 10−38 cm2 by the Ankowski model.

Geoneutrinos are also low-energy ν̄e ’s of which the main detection channel is IBD.

The detection of geoneutrinos can provide constraint on the Earth heat budget and resolve
the BSE HPE abundance which is diﬃcult to derive otherwise. The main background togeoneutrinos is the reactor neutrinos from man-made nuclear power plants, and the loca158

Chapter 9

Summary and Outlooktion of neutrino observatory is a key issue in the signal/background ratio. We simulated a
3-kiloton liquid scintillator detector at Jinping, calculated the expected geoneutrino flux
and reactor neutrino backgrounds there. The expected number of geoneutrino IBD eventsat Jinping for 1,500 days live time is 414.5 and the number of reactor neutrino backgroundwithin the signal energy window of [1.8, 3.3] MeV is 60.4. The sensitivities is 4.6%
towards the geoneutrino flux measurement, and 26.3% towards the Th/U ratio. To achieve
such a goal, several requirements on the detector design, including the detector size andthe energy resolution, are proposed.

9.2 Outlook
The common features of the three studies presented in this thesis include the low
energy signal + neutron signature.
Among them, the SRN study is a rare signal search, and the signal-background ratio
is important. For the SRN analysis, the background reduction is performed at a cost of
the signal eﬃciency loss. The optimization in the neutron tagging presented in this thesis
nearly doubled the signal eﬃciency of SRN signal. Still, further improvement can beachieved from the hardware level. The SK-Gd project [107] plans to load 0.2% Gd2 (SO4 )3
into the water tank of SK. The shorter lifetime and the greater energy of emitted γ’sreaching 8 MeV makes the neutron tagging in Gd loaded water much easier than in purewater. It is estimated that the neutron tagging eﬃciency will reach 90% [107] . The SK tankis now (2018) under refurbishment for the Gd loading. After the upgrading, the SK-Gd
project is promising to make an observation of SRN within 10 years of data taking.
The NCQE interaction from the atmospheric neutrinos will still form a strong background for the SRN search even with Gd loaded. Due to the suppression of accidental
background in SK-Gd phase, the NCQE background will become the major background,and a precise measurement of its cross section is crucial for the SRN search. The
present measurement on the NCQE cross section is mainly limited by systematic uncertainties from the atmospheric neutrino flux, the cross section for other NC processes,
the γ emission, and the neutron tagging. Future atmospheric neutrino experiments suchas Hyper-Kamiokande [108] , the neutrino beam-line detectors [122–125] , and related nuclear
experiments [126] will further constrain the systematic uncertainties.
The geoneutrino observation has been claimed by Borexino experiment [72] , and thenext goal, precise measurement, can be easily achieved by placing a kiloton level neutrino
159

Chapter 9

Summary and Outlook

experiment at Jinping. Further consideration is about the component of geoneutrinos,from the crust and the mantle. For the BSE model, the crustal abundance of HPEs can beextracted from drills, while for the mantle part, neutrinos are the only probe. In this case,observation of purely mantle neutrinos is a crucial topic. An oceanic neutrino observatory
project HANOHANO [142] , which removes the crustal geoneutrinos as well as the reactor
neutrino backgrounds simply by the distance, was proposed in 2011, but abandoned later
due to the diﬃculty in construction and operation. One alternative solution is to observe
the direction of geoneutrinos, thus to perform a tomographic analysis on the componentsof geoneutrinos. However, the direction information of the incident neutrino in the IBD
interaction is carried by the neutron, which is negligible compared to the mass of neutron.
Several projects have been pushing forward the detection by loading lithium into liquid
scintillator [143,144] , but so far none of them has ever succeeded on an event by event basis.
Another possible method is to detect the geoneutrinos via elastic scattering on electrons.
This channel has smaller cross section compared to IBD, but the direction information iscarried by the outgoing electron, which can be detected via for example Cherenkov photon.
For this method, the main problem is the low energy of geoneutrinos, which results inthe multi-scattering of the electron. Two diﬀerent approaches have been employed. The
first is to reduce the multi-scattering by changing the detection material into gas, withlower density thus lower multi-scattering. This requires the detector to be a segmented
TPC [145] . The other approach is pattern identification based, which does not require heavy
modification on the detector designation of typical liquid scintillation detectors [146] . We
are looking forward to all of those projects.

160

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Acknowlegement

Acknowlegement
First, I would like to express my gratitude to my supervisor Prof. Shaomin Chen. He
introduced me to field of neutrino physics and the collaboration of Super-Kamiokande.
He has always been supportive and understanding during the entire course of my graduate
study. Without his valuable comments and detailed suggestions, I would have accomplished much less.
I am grateful to Masayuki Nakahata-san, the spokesperson for the SK collaboration,
who inspired me with his physics insight. I would like to acknowledge Michael Smy
and Takeuchi-san. From the numerous email exchanges and comments, I acquired amuch deeper understanding of LOWE group analysis. I also wish to thank Moriyamasan, Mine-san, and Luis Labarga for their advisorship when I started my analysis in SK
from calibration group. I benefitted significantly from discussions with Motoyasu Ikedasan, Yasuhiro Nakajima-san, Yoshinari Hayato-san, Yusuke Koshio-san, and Lluis Marti.
There are more names to list, and I would like to thank all the collaborators at SK and all
the staﬀs at the Kamioka Observatory.
Many thanks go to the professors and collegues at the High Energy Physics Centerat Tsinghua University. The guidance and supervision from Prof. Zhe Wang and otherteachers showed me the essences to perform a physics analysis independently. I appreciate
Dr. Hanyu Wei, Dr. Xiangpan Ji, Dr. Logan Lebanowski, and many collegues for ouracademic discussions as well as our friendship.
Besides, I would like to acknowledge Ondrej Sramek, Yufei Xi, and William F.
McDonough for leading me into the field of geoneutrinos. Thanks to Prof. Ling-Fong
Li for the chance to systemize my knowledge, and thanks to Benda Xu for the help andinspiration during my stay at Kamioka Observatory.
My friends and family have been supporting me during the long journey. Owing to
the easy atmosphere they created, I was able to concentrate on my interest and fulfill mygoal. I enjoyed their company so much.

169