Reactor Neutrinos in a
Gadolinium-Loaded Super-Kamiokande

Alexander Goldsack
Oriel College
University of Oxford

A thesis submitted for the degree ofDoctor of Philosophy
Hilary Term, 2022

“Be curious on your journey.”- Bells, Outer Wilds

Acknowledgements
I am first of all thankful to Oxford University and Kavli IPMU for providing aDPhil program that is perfectly matched to what I wanted out of a graduate degree.
I’m very glad I have been given the opportunity to work in such a welcoming
collaboration so I would also like to thank everyone in Super-K who has helped
me in the last few years, especially within the LowE group.
I found nothing but support from my wonderfully-patient partner Sam in mydecision to choose a degree that took me to the other side of the world for two
years. After returning right at the height of the COVID-19 pandemic, she went
above and beyond to ease my non-academic burdens as best as she could while I
slowly became an anxious, thesis-writing lump and for that I am eternally grateful.
For all his support getting me to this point, I cannot thank my dad enough. I
hold somewhat of a grudge, however, given that the countless hours opening myeyes to the wonders of the universe, be it through documentaries, fostering mylove for science fiction or simply lying in the back garden looking at the stars haveresulted in an obsession with science that means that I was crazy enough to attempt
a doctorate. He let me live in his house when coming back from Japan, however,paying rent with KFC, so maybe I shouldn’t be so harsh.
I am thankful to all the Kamioka staff for welcoming me to Japan, especially
Masa Ishikura for helping me get settled and deal with everything where my broken
Japanese failed me. I am also thankful to Lluis Marti for giving me frequent excuses
to go to Shogun Burger and for being an all round good friend to me while inToyama. I’d also like to thank him, Michael Smy and Scott Locke for their patience
with my frequent LowE/WIT questions.
For the many hours-long discussions about physics, living in Japan, and life ingeneral, as well as being an overall great friend, I would very much like to thank
Laurence Cook. I think Starbucks would also like to thank him too, given thatmost of those discussions occurred over coffee and frappuccinos.
Many thanks to Hannah, Matthieu, Raf and especially Ryan Randolph Riches
for the weekly insanity that was our D&D sessions. Special thanks to Ryan forbeing such a good friend, as well as introducing me to most of the people in Japan
who I came to call my friends, including Jean Shin and Josh Mueda.

My sanity in early 2020 would not have fared well without the many hours
playing Civilisation with Ellie Jones and Aidan Reynolds. Thanks to them both, aswell as Amy Hughes and Rory Evans for welcoming me into the D&D group.
For all things Python, I thank my long term coding guru Ryan Cross, who
never liked me in the first place, a fact he reminds me of frequently. I also thankhim, Cameron, Chris and Dec for helping me unwind in the evenings by making
me stress about my poor performance in WoW.
Finally, I would very much like to thank my supervisors, Professors Dave Wark
and Mark Vagins, for the endless advice and anecdotes and for generally being in
my corner in many ways during my time as a student.

Abstract
In July of 2020, Super-Kamiokande (SK), a 50 kt water Cherenkov detector, enteredits new phase: SK-Gd [1]. In this phase, the detector’s once-ultrapure water wasdoped with 0.02% gadolinium sulphate octahydrate by mass, increased to 0.06%
in July 2022. This provides far greater sensitivity to neutron captures, thereby
increasing the detection efficiency of electron antineutrinos interacting via inverse
beta decay. One such source of these neutrinos is the numerous fission products
in nuclear reactor cores. To date, only one reactor neutrino interaction has been
identified in a large scale water Cherenkov detector [2], in part due to their energy
spectrum extending less than 10 MeV above the Cherenkov threshold of positronsin water. A search has been performed for reactor neutrinos in data obtained by
SK’s Wideband Intelligent Trigger (WIT) system from December 2020 to October
2021, using a boosted decision tree-based selection method. The search intended
to identify an increase in event rate consistent with that expected due to therestart of 9 Japanese reactor cores between December of 2020 and October of 2021.
Apparent issues with the WIT data between March and August of 2021 motivatedthe comparison of the rates measured in the data before and after this period.
Though the measured rate up to March 2021 of (1.6 ± 0.2) d−1 was consistent withpredictions, the rate measured between August and October 2021 was found to be(8.8 ± 0.4) d−1 , far in excess of the predicted rate of 3.7 d−1 . While not inconsistent
with the expected total interaction rate of 9.75 d−1 , an unreasonably large signal
efficiency would be required for this increase to be solely explained by reactor
restarts. One suspected cause of this increase is the persistence of issues with the
WIT data from March 2021, continuing after August, when the data was previously
thought to be once again stable. As such, this work cannot conclusively say thatreactor neutrinos have been identified in SK; however, the Monte Carlo studies
presented in this thesis indicate that the experiment has this capability.

Contents
List of Figures

viii

List of Tables

xiv

1

Introduction

1

2

Neutrinos
2.1 History and Oscillation . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Mass Ordering and The MSW Effect . . . . . . . . . . . . . . . . .
2.3 Neutrino Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Cosmic Neutrino Background . . . . . . . . . . . . . . . . .
2.3.2 Solar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Atmospheric . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Supernovae and Pre-Supernova Stars . . . . . . . . . . . . .
2.3.6 Geo-neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Cosmogenic . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.8 Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Inverse Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
5
9
11
11
12
12
14
16
20
21
22
22

3

Super-Kamiokande
3.1 Detector Structure . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Detection Principle . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Electronics and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Data Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 BONSAI Low Energy Event Reconstruction . . . . . . . . . . . . .
3.6 The Wide-Band Intelligent Trigger (WIT) . . . . . . . . . . . . . .
3.7 Monte-Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26
27
32
34
36
37
41
53

4

A Gadolinium Loaded Super-K
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Water Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 EGADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56
56
57
59

vi

Contents
4.4
4.5

vii
Deployment and Validation . . . . . . . . . . . . . . . . . . . . . .
WIT Coincidence Trigger . . . . . . . . . . . . . . . . . . . . . . . .

61
63

5

Reactor Neutrinos
5.1 Nuclear Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Nuclear Power in Japan . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Neutrino Production . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Reactor Neutrino Experiments . . . . . . . . . . . . . . . . . . . . .
5.5 Monitoring Nuclear Reactors . . . . . . . . . . . . . . . . . . . . . .
5.6 SK-Gd and Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . .
5.7 Simulating Reactor Neutrinos: SKReact . . . . . . . . . . . . . . .

72
72
79
82
85
89
91
93

6

Restart Detection
100
6.1 Introduction and Objective . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Sources of Background . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.3 Cut Optimisation with SPLASH . . . . . . . . . . . . . . . . . . . . 108
6.4 BDT Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.5 Background Prediction and Data Availability . . . . . . . . . . . . . 127
6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7

Conclusion

144

Appendices
A Japanese and South Korean Nuclear Reactors

148

B Coefficients for Antineutrino Emission Spectra of Reactor Fuels 151
C Fuel Contribution Fractions

153

References

155

List of Figures
2.1
2.2

2.3

2.4

2.5
3.1
3.2

3.3
3.4

3.5

3.6

The proton-proton chain and CNO cycle, modified from [17]. . . . .
A diagram of the accelerator neutrino beam production process,including magnetic horns for focusing the desired pions and rejecting
the oppositely charged pions to produce a neutrino or antineutrino
beam. Adapted from [23]. . . . . . . . . . . . . . . . . . . . . . . .
The luminosity (top left) and average energy (bottom left) of νe ,
ν̄e and νx (all other flavours) with time from core “bounce” dueto neutron degeneracy pressure, and the energy spectrum of ν̄e atdifferent times from this bounce (right) [36]. . . . . . . . . . . . . .
The spectra of geo-neutrinos produced in the decays 2.26 ( 238U chain,solid black), 2.27 ( 232Th chain, dash-dotted red) and 2.28 ( 40K chain,dashed blue) [45]. The solid vertical line indicates the inverse beta
decay interaction threshold of 1.806 MeV. . . . . . . . . . . . . . .
The cross section for inverse beta decay on free protons, calculatedusing Strumia and Vissani’s parameterisation given in [58]. . . . .
A cross section of the SK detector (partially filled with water). . . .
Photograph of the structure which supports the PMTs and separates
the ID and OD. The fibreglass rear of the ID PMT cases can be seen
within the structure. Taken during the 2018 tank open work. . . . .
Photographs of the SK inner detector taken during the 2018 tankopen work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A photograph from the bottom of the SK OD looking up, showing
how Tyvek is used to optically isolate the OD from the ID andencourage reflection within the OD. The Hamamatsu R1408 PMTs
and wavelength-shifting light collection plates can also be seen. Taken
during the 2018 tank open work. . . . . . . . . . . . . . . . . . . . .
The formation of a Cherenkov ring in a medium of refractive index
n by a charged particle of velocity v > c/n. The particle is either
created or given energy by a neutrino interaction at A and stops
producing Cherenkov radiation at B. . . . . . . . . . . . . . . . . .
A sharp muon-like Cherenkov ring event (a) compared to a fuzzier
electron-like ring (b) for two T2K events in SK [24]. . . . . . . . . .
viii

13

14

18

21
24
28

29
29

30

33
34

List of Figures

ix

3.7

The Super-Kamiokande data acquisition (DAQ) system, in placesince SK-IV except for the WIT PCs which were added in 2015. . .
3.8 STORE Goodness for simulated events and raw WIT data (BG).
Events below the black line (in the hatched region) are rejected in
WIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9 Radial position for simulated events and raw WIT data (BG) thatpass the preceding stages of WIT, reconstructed by Clus-Fit. Events
above the black line (in the hatched region) are rejected in WIT. . .
3.10 Height of simulated events and raw WIT data (BG) that pass thepreceding stages of WIT, reconstructed by Clus-Fit. Events outsideof the two black lines (in the hatched region) are rejected in WIT. .
3.11 Radial position for simulated events and raw WIT data (BG) thatpass the preceding stages of WIT, reconstructed by BONSAI. The
disconnect in the BG distribution at the trigger threshold is a
symptom of the WIT process applying FV cuts to some events,
and is not physical. Events above the black line (in the hatchedregion) are rejected in WIT. . . . . . . . . . . . . . . . . . . . . . .
3.12 Height of simulated events and raw WIT data (BG) that pass thepreceding stages of WIT, reconstructed by BONSAI. The disconnect
in the BG distribution at the trigger threshold is a symptom of the
WIT process applying FV cuts to some events, and is not physical.
Events outside of the two black lines (in the hatched region) arerejected in WIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 BONSAI goodness of simulated events and raw WIT data (BG) thatpass the preceding stages of WIT. Events below the black line (inthe hatched region) are rejected by WIT. . . . . . . . . . . . . . . .
3.14 N18 of simulated events and raw WIT data (BG) that pass thepreceding stages of WIT. Events below the black line (in the hatchedregion) are rejected by WIT. . . . . . . . . . . . . . . . . . . . . . .
4.1
4.2
4.3

Schematic of the SK-Gd water systems [1]. . . . . . . . . . . . . . .
The EGADS hall. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The conductivity of water samples taken at a range of heights
throughout the SK ID over the course of first Gd loading, in 2020.
The sampling system encountered issues between the 23rd and 29thof July. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 An example of neutron capture times and the resultant fit for 30
mins of AmBe calibration data with the source placed in the centreof the detector. Measurements were carried out for a range of source
placements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

45

46

47

48

49

50

51
58
60

62

64

List of Figuresx

4.5

The logic of the WIT coincidence trigger, including the trigger
identification numbering scheme. . . . . . . . . . . . . . . . . . . . 66
4.6 The distance between prompt and delayed event vertices for simulated
gadolinium and hydrogen capture, reconstructed by online BONSAI,
compared to the distance between sequential events in a sample of
WIT data considered to be background.Gadolinium concentration istaken to be that after first loading (0.02% by mass). . . . . . . . . . 67
4.7 The time difference between prompt and delayed events for simulated
gadolinium and hydrogen capture, reconstructed by online BONSAI,
compared to the time between sequential events in a sample of WIT
data considered to be background. Gadolinium concentration is taken
to be that after first loading (0.02% by mass). . . . . . . . . . . . . 68
4.8 WIT detection efficiencies when relaxing the hit threshold (and therefore STORE goodness threshold) for all events, and for coincident
pairs only. Sequential events in WIT data (BG) are compared tosimulated reactor IBD pairs. . . . . . . . . . . . . . . . . . . . . . . 69
4.9 WIT detection efficiencies when relaxing the N18 threshold for all
events, and for coincident pairs only. Sequential events in WIT data
(BG) are compared to simulated reactor IBD pairs. . . . . . . . . . 70
4.10 WIT detection efficiencies when relaxing the BONSAI goodness
threshold for all events, and for coincident pairs only. Sequential
events in WIT data (BG) are compared to simulated reactor IBD pairs. 71
5.1

5.2

5.3

The simulated electron-antineutrino spectra with associated errors
produced by individual fuels in a 3423 MW core of the Ohi 3 PWR
reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
exp
Ratio Ra,HM
of measured and expected IBD yields for a selection ofreactor experiments as a function of reactor-detector distance L for
the Huber-Mueller model of reactor antineutrino spectra, taken from[94]. The horizontal green band shows the average ratio R̄HM and
its uncertainty, indicating a 2.5σ deviation from the expected. . . .
Left: Allowed parameter regions (at 1σ, 90%, 2σ, 99%, 3σ confidence
limit for 2 degrees of freedom) for fixed θ13 = 8.6° from the analysis
of KamLAND data (solid green contours with the best fit marked bya green star) and from the combined analysis of solar data for the
GS98 model (full regions with the best fit marked by black star) andthe AGSS09 model (dashed void contours with the best fit marked
by a white dot). The orange contours are the results of a global
analysis for the GS98 model using the previous SK4 neutrino data.
Right: ∆χ2 dependence on ∆m221 for the same four analyses after
marginalizing over θ12 . Taken from NuFit 5.1 (2021) [96]. . . . . . .

85

89

90

List of Figures
5.4
5.5
5.6

5.7
5.8
5.9
6.1
6.2

6.3
6.4

6.5

6.6

6.7

6.8

The simulated neutrino emission spectrum on production s−1 fromthe Ohi-3 pressurised water reactor (PWR) core. . . . . . . . . . . .
The simulated 2018 reactor spectrum after oscillation s−1 at SK,
with the Ohi-3 pressurised water reactor (PWR) core highlighted. .
The Gaussian fit (solid lines) of BONSAI reconstructed energy for
simulated positrons of energies from 1 to 10 MeV, area normalised
to the efficiency of detection. Dotted lines at true energy given forreference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The process for converting interacted spectrum to reconstructed
spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The interacted and smeared spectrum over the course of 2018, with
the Ohi-3 core highlighted, simulated by SKReact. . . . . . . . . . .
The SKReact GUI. . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

94
96

97
98
99
99

The length of the data files in the WIT pair data, calculated using
the hardware trigger counter differences in each file. . . . . . . . . . 102
The length of the data files in the WIT pair data, calculated using
the hardware trigger counter differences in each file, removing files oflength greater than 87.38 s. . . . . . . . . . . . . . . . . . . . . . . . 102
The size of the data files in the WIT pair data, removing files oflength greater than 87.38 s. . . . . . . . . . . . . . . . . . . . . . . . 103
The simulated reactor neutrino interaction rate from late 2020 tolate 2021, with the ramp up simulated using sigmoid functions. A
ramp up of 62 days is used in this analysis. . . . . . . . . . . . . . . 105
Vertex z as reconstructed by BONSAI for 2021 reactor spectrum
prompt positrons, and delayed neutron captures corresponding to
0.02% Gd concentration, both simulated (MC). BG is raw pre-reactor
restart WIT data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Vertex r as reconstructed by BONSAI for 2021 reactor spectrum
prompt positrons, and delayed neutron captures corresponding to
0.02% Gd concentration, both simulated (MC). BG is raw pre-reactor
restart WIT data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
BONSAI reconstructed energy for 2021 reactor spectrum prompt
positrons, and delayed neutron captures corresponding to 0.02% Gd
concentration, both simulated (MC). BG is raw pre-reactor restart
WIT data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
OVAQ goodness variable for simulated 2021 reactor spectrum prompt,and delays corresponding to 0.02% Gd concentration (MC). BG is
raw pre-reactor restart WIT data. . . . . . . . . . . . . . . . . . . . 114

List of Figures
6.9

xii

EffWall for simulated 2021 reactor spectrum prompt, and delays
corresponding to 0.02% Gd concentration (MC). BG is raw prereactor restart WIT data. . . . . . . . . . . . . . . . . . . . . . . . 115
6.10 BONSAI reconstructed distance between simulated 2021 reactor spectrum prompt, and delays corresponding to 0.02% Gd concentration(MC). BG is raw pre-reactor restart WIT data. . . . . . . . . . . . 115
6.11 Simulated neutron capture times corresponding to 0.02% Gd concentration (MC). BG is time between prompt and delayed events in
raw pre-reactor restart WIT data, identified by the WIT coincidence
trigger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.12 The input variable importance for a BDT trained on the 2019 reactor
spectrum, including the β isotropy parameters. . . . . . . . . . . . . 123
6.13 The input variable importance for a BDT trained on the simulated
2021 reactor spectrum, the BDT which formed the final reactor
sample selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.14 The final tree in the ensemble BDT used in this analysis. . . . . . . 125
6.15 The BDT score for 10 k reactor MC events and two weeks of SK-Gd
WIT data (BG). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.16 The BDT score for 10 k reactor MC events and two weeks of SK-Gd
WIT data (BG), with a >0.2 BDT score cut. . . . . . . . . . . . . . 127
6.17 The BDT score for 10 k reactor MC events and two weeks of SK-Gd
WIT data (BG), with a >0.95 BDT score cut. . . . . . . . . . . . . 128
6.18 A comparison of all BDT variables for a 24h run in the pre (85766)
and post (86102) datasets. . . . . . . . . . . . . . . . . . . . . . . . 131
6.19 A comparison of the BDT score between events in a 24h run in thepre (run 85766) and post (run 86102) datasets. . . . . . . . . . . . . 132
6.20 The predicted BG and reactor rate over the entire dataset, binned
weekly, with no file quality requirements. Errors are statistical only. 133
6.21 The predicted BG and reactor rate over the entire dataset, weekly
binned, with file quality requirements. Errors are statistical only. . . 135
6.22 The pair rate in the pre and post periods, compared to the expected
BG and reactor rates. The red line represents the reactor rate with
100% efficiency. Errors are statistical only. . . . . . . . . . . . . . . 136
6.23 The pair rate in the pre and post periods, weekly binned, comparedto the expected BG and reactor rates, with the livetime calculatedusing assumed 100% run lengths. The red line represents the reactor
rate with 100% efficiency. Errors are statistical only. . . . . . . . . . 137
6.24 The required signal (MC) efficiency in the pre period needed to
explain the observed pair rate increase for a range of BG rate increases
and relative signal efficiency increases. . . . . . . . . . . . . . . . . 138

List of Figuresxiii

6.25 The required signal (MC) efficiency in the pre period needed to
explain the observed pair rate increase for a range of BG rate increases
where the MC efficiency increases as a factor of the BG increase. . . 139
6.26 The difference between the known run length and run length derived
from the sum of all calculated file lengths. . . . . . . . . . . . . . . 140
6.27 The pair rate in the pre and post periods, weekly binned, compared tothe expected BG and reactor rates, with the livetime calculated using
the file lengths as opposed to assumed 100% livetime run lengths.
Errors are statistical only. . . . . . . . . . . . . . . . . . . . . . . . 141
6.28 The pair rate across the whole WIT pair dataset, without quality
cuts which would remove the pre→post intermediary data. Livetimes
are calculated using the summed file lengths. Errors are statistical
only. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.29 The pair rate across the whole WIT pair dataset, without quality
cuts which would remove the pre→post intermediary data. Livetimes
are calculated using the run lengths. Errors are statistical only. . . 143

List of Tables
3.1
3.2

The data-taking phases of SK. . . . . . . . . . . . . . . . . . . . . .
Hit-counter trigger thresholds and their approximate trigger rates in
SK as of September 2021. The range of hits for the triggers do not
overlap; for example, the SLE trigger only activates for events with
34-46 hits in the trigger window. The OD trigger is not independently
monitored and is only considered when an ID trigger is activated. .

Operable commercial nuclear power plant designs throughout theworld [73]. The column “GWe” refers to the total electrical power
capacity, measured in GW. . . . . . . . . . . . . . . . . . . . . . . .
5.2 Nuclear power reactors currently operating in Japan and South Korea,
ordered by (Pth )/(RSK )2 where Pth is thermal power output capacityof the reactor and RSK is the distance from the core to the SK
detector [75]. An asterisk by a plant’s name denotes a South Korean
plant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Japanese reactor core restarts during the SK-Gd phase, ordered bydate of restart. The expected increase in IBD events in the SK ID
due to the restart is included, as well as the expected pre-restartrate, calculated from SKReact as detailed in section 5.7. . . . . . .

38

42

5.1

6.1
6.2

77

81

92

Criteria of radioactive impurities in Gd2 (SO4 )3 · 8 H2 O powder andthe physics goals driving the requirements [1]. . . . . . . . . . . . . 106
The predicted pre/post results based on pre offline data and post
online. An asterisk denotes a predicted value. . . . . . . . . . . . . 135

A.1 All nuclear reactors in Japan and South Korea, ordered by (Pth )/(RSK )2
where Pth is thermal power output capacity of the reactor and RSK
is the distance from the core to the SK detector [75]. An asterisk by
a plant’s name denotes a South Korean plant. A status of pendingrefers to plants that have applied for a restart and are pending
approval from either the local government or the NRA. . . . . . . . 148
B.1 Coefficients αpk of the Mueller et al. fifth-order polynomial parameterisation of antineutrino flux from elements k = 235 U, 238 U, 239 Pu
and 241 Pu. In the column δαpk the 1σ error on αpk are given [78]. . 151
xiv

List of Tables
C.1

xv

U, 238 U, 239 Pu, and 241 Pu fission (fi ) or power (pi ) fractions for arange of reactor designs, compiled by [101]. . . . . . . . . . . . . . . 154
235

List of Abbreviations
AAS Atomic absorption spectrometer
ABWR Advanced boiling water reactor
AFT After (trigger)
AGR Advanced gas-cooled reactor
ANN Artificial neural network
ATM Analogue timing module
BDT Boosted Decision Tree
BG Background
BNO Baksan Neutrino Observatory
BONSAI Branch Optimisation Navigating Successive Annealing Iterations
BooNE Booster Neutrino Experiment
BOREX Boron Solar Neutrino Experiment
BSM Beyond the Standard Model (of particle physics)
BWR Boiling water reactor
CνB Cosmic Neutrino Background
CC Charged current (interaction)
CCSN Core collapse supernova
CL Confidence limit
CMB Cosmic microwave background
CNN Convolutional neural network
CP Charge-parity (operator)xvi

List of Tables

xvii

CP-1 Chicago Pile-1 (reactor)
DAQ Data acquisition
DC Double Chooz
DirKS Directional KS (test)
DOF Degrees of freedom
DSNB Diffuse supernova neutrino background
DT Deuterium-tritium (neutron generator)
DUNE Deep Underground Neutrino Experiment
EGADS Evaluating Gadolinium’s Action on Detector Systems
FBR Fast breeder reactor
FIFO First-in-first-out
FNR Fast neutron reactor
FOM Figure of merit
FPGA Field programmable gate array
FV Fiducial volume
GADZOOKS! Gadolinium Antineutrino Detector Zealously Outperforming Old
Kamiokande, Super!
GCR Gas cooled reactor
GdLS Gadolinium doped liquid scintillator
GEANT-3 Geometry and Tracking
GRB Gamma ray burst
GUI Graphical user interface
GUT Grand Unified Theory
GZK Greisen-Zatsepin-Kuzmin (neutrinos)
HE High energy (trigger)List of Tables
HEU Highly enriched uranium
HK Hyper-Kamiokande
HM Huber-Mueller (model)
HPGe High-purity germanium
HV High voltage
IAEA International Atomic Energy Agency
IBD Inverse beta decay
ICRR Institute for Cosmic Ray Research
ID Inner detector
IH Inverted hierarchy (neutrino mass)
ILL Institute Laue-Langevin
IMB Irvine–Michigan–Brookhaven (experiment)
INGRID Interactive Neutrino GRIDIO Inverted ordering (neutrino mass)
IPMU Kavli Institute for the Physics and Mathematics of the Universe
JUNO Jiangmen Underground Neutrino Observatory
K2K KEK-to-Kamioka
KamiokaNDE Kamioka Nucleon Decay Experiment
KamLAND Kamioka Liquid Scintillator Antineutrino Detector
KamLAND-Zen Kamioka
KEK The High Energy Accelerator Research Organization
KS Kolmogorov-Smirnov (test)
LArTPC Liquid argon time projection chamber
LE Low energy (trigger)
LEU Low-enriched uranium

xviii

List of Tables

xix

LF Load factor
LINAC Linear accelerator
LMC Large Magellanic Cloud
LS Liquid scintillator
LSND Liquid Scintillator Neutrino Detector
LWGR Light water graphite-moderated reactor
M⊙ Mass of the Sun
MC Monte Carlo
ML Machine learning
MSG Multiple Scattering Goodness
MSW Mikheyev-Smirnov-Wolfenstein (effect).
MW Mega watt (unit)
NC Neutral current (interaction)
ND280 Near Detector at 280 m
NH Normal hierarchy (neutrino mass)
NO Normal ordering (neutrino mass)
NOvA NuMI Off-axis νe Appearance
NPT Treaty on the Non-Proliferation of Nuclear Weapons
NRA Nuclear Regulation Authority
NuMI Neutrinos at the Main Injector
OD Outer detector
OVAQ One-dimensional Variable of Vertex and Angular Reconstruction Quality
pe Photo-electrons (unit)
PHWR Pressurised heavy water reactor
PMNS Pontecorvo-Maki-Nakagawa-Sakata (matrix)

List of Tables

xx

PMT Photo-multiplier tube
PRIS Power Reactor Information System
PWR Pressurised water reactor
QAC Charge to analogue converter
QBEE QTC-based electronics with ethernet
QTC Quantum tunelling composite
RAA Reactor antineutrino anomaly
RENO Reactor Experiment for Neutrino Oscillation
SBN Short-Baseline Neutrino (program)
SHE Super high energy (trigger)
SK Super-Kamiokande
SKG4 SK Geant4 (MC software)
SLE Super low energy (trigger)
SM Standard Model (of particle physics)
SN Supernova
SNO Sudbury Neutrino Observatory
SPLASH Super-K Python Library of Analysis Software and something beginningwith HSRN Supernova relic neutrinos
SSM Standard solar model
STEREO Sterile Reactor Neutrino Oscillations
STORE Simultaneous Trigger and Online Reconstruction
T2K Tokai-to-Kamioka
TAC Time to analogue converter
TOC Total organic carbon reduction

List of Tables
TOF Time of flight
TPC Time projection chamber
UCI University of California, Irvine
UDEAL Underground Device Evaluating Attenuation Length
UF Ultra filtration
UHECR Ultra high energy cosmic rays
UV Ultraviolet
WatChMaL Water Cherenkov Machine Learning
WATCHMAN Water Cherenkov Monitor for Antineutrinos
WC Water Cherenkov
WIT Wide-band Intelligent Trigger

xxi

1

Introduction

Now is an exciting time for the Super-Kamiokande (SK) experiment and the worldof neutrino physics research in general. While the field is gearing up for an eraof extraordinary-scale, high-precision experiments with the approaching HyperKamiokande and DUNE experiments, SK, the 50 kt water Cherenkov detector
now in its 26th year of operation, has expanded the neutrino horizon in an
altogether different direction.
In the summer of 2020, SK entered its SK-Gd phase where its once ultrapure
water was doped with 0.02% gadolinium sulphate octahydrate by mass, providing aneutron capture target with ∼ 100, 000× the cross section of pure water, and one
which releases a signal that SK can detect with almost 100% accuracy. Neutrons
are produced in a range of processes in SK, but of particular interest is the inverse
beta decay reaction, where an electron antineutrino interacts with a proton to
produce a positron and a neutron.
Though the primary motivation for the SK-Gd project is to detect the spectrumof neutrinos produced by distant supernovae, this thesis explores its capabilities todetect electron antineutrinos produced with great intensity in the cores of terrestrial
nuclear reactors nearly 200 km from the detector. Such a search has never been
performed in SK due to the difficulty in detecting these low energy neutrinos of afew MeV, and to date only one reactor neutrino event has ever been identified in11. Introduction

2

a water Cherenkov detector, during the SNO+ experiment’s pure water phase [2].
The vastly increased sensitivity to neutron capture and therefore inverse beta decay
makes the detection of reactor neutrinos possible for the first time in SK.
An ideal stage is also set for this analysis in terms of nuclear reactor activity.
Following the 2011 Tohoku earthquake and subsequent meltdown of three coresof the Fukushima Daiichi plant, Japan has been operating at a fraction of its
nuclear power capacity as reactors have undergone the long process of conforming toincreased safety standards and seeking approval from local governments to approvetheir restarts. 2021 saw a number of these restarts, most notably some selectreactors of the Takahama, Ohi and Mihama plants, all less than 200 km from SK.
There are two main motivations for this search, the first is that of a purely
academic nature. In the world of reactor neutrino experiments, most detectors are
situated up to ∼1 km from their reactor complex of interest and only one sought
to measure the oscillation probability from a range of plants at a longer distance:
the Kamioka Liquid Scintillator Antineutrino Detector (KamLAND) experiment,
situated in the same mine as Super-Kamiokande. KamLAND provides the only
non-solar probe of ∆m221 and therefore the only measurement using antineutrinos
as opposed to neutrinos, a measurement that somewhat disagrees with the global
average. Prior to an update to the day/night asymmetry results from SK in
2020, there was a 2σ difference between the combined SK and SNO results and
KamLAND’s measurement, however this difference has now been reduced to around1.4σ [3]. While this holds little statistical significance, it remains that KamLAND
is the only experiment to probe the ∼200 km baseline reactor neutrino realm. A
repetition of this measurement with SK would therefore affirm that this difference
is indeed put to rest.
The second motivation for detecting reactor neutrinos at SK is the coveted
opportunity to provide a real-world application of particle physics. This is due
to its potential to support nuclear non-proliferation. Proving that a neutrino
detector can monitor the activity of a nuclear reactor at a significant standoff

1. Introduction

3

distance provides a new tool in the world’s arsenal in the effort to police theillegal production of nuclear weapons.
Given the unprecedented nature of this search, this thesis describes the various
new tools and analysis approaches produced in an attempt to detect reactor neutrinos
for the first time in SK. Chapter 2 provides a historical and theoretical introduction
to neutrinos. Chapter 3 then details the SK detector and its approach to detecting
these elusive particles. This chapter also introduces a crucial utility of the reactor
neutrino search: the Wideband Intelligent Trigger (WIT) system. The major
evolution of SK into the SK-Gd phase is described in chapter 4, including the
introduction of a coincidence trigger into WIT in support of this search whichseeks to improve the efficiency of detecting IBD pairs with little impact on the
WIT data stream. Nuclear reactors and their neutrino production is described inchapter 5 and here the SKReact software is detailed. This is a reactor neutrino
simulator developed to support all analyses concerning reactor neutrinos in SK. The
multivariate approach taken to attempt to isolate a sample of reactor neutrinos fromthe vast swathes of WIT data is presented in chapter 6, utilising the newly-developed
SPLASH framework, firstly through traditional methods and then through theuse of boosted decision trees. The results of the search are also presented here,
as is a discussion of the consistency of the detected rates with those expected
at the start and end of 2021.

2

Neutrinos
Contents
2.1
2.2
2.3

History and Oscillation . . . . . . . . . . . . . . . . . . .
Mass Ordering and The MSW Effect . . . . . . . . . .
Neutrino Sources . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Cosmic Neutrino Background . . . . . . . . . . . . . . .
2.3.2 Solar . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Atmospheric . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Accelerators . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Supernovae and Pre-Supernova Stars . . . . . . . . . . .
2.3.6 Geo-neutrinos . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Cosmogenic . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.8 Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Inverse Beta Decay . . . . . . . . . . . . . . . . . . . . .

5
9
11
11
12
12
14
16
20
21
22
22

Neutrinos (ν) are spin- 12 , electromagnetically neutral fermions of non-zero but
small mass. They interact via the weak force as one of three leptonic “flavours”(νe , νµ and ντ ) corresponding to the three charged leptons. The Standard Model(SM) of particle physics predicts that in a given weak interaction vertex, a neutrino
can only interact with a neutrino or charged lepton of the same flavour; however,they exhibit a property not predicted by the Standard Model, where their flavour
and mass eigenstates are mixed. This allows them to oscillate between different
flavours as they propagate. A flavour eigenstate different to that at the time of4

2. Neutrinos

5

production can therefore be observed at some distance from the source. They
have a significantly lower mass than any other massive particle. Model-dependent
cosmological measurements constrain the neutrino mass to <0.17 eV [4], whilemeasurements of beta decay in tritium set a limit of 1.1 MeV [5]. Their totalinteraction cross section is far smaller than any other particle in the Standard
Model. Neutrino experiments therefore often focus on maximising the integrated
flux of neutrinos through their detector volumes, be it through proximity to theirsource or in constructing the largest-volume particle detectors in the world.

2.1

History and Oscillation

In 1930 Woflgang Pauli postulated that a weakly-interacting, neutrally charged
particle could account for the missing energy observed in β − decay [6]. This missing
energy was evident in the continuous energy spectrum of the outgoing electron andhad no clear explanation at the time. It wasn’t until 1956 that Clyde L. Cowan
and Frederick Reines confirmed its existence by detecting electron antineutrinos
produced in a nuclear reactor [7]. The neutrinos interacted via the interaction
ν̄e + p → e+ + n(2.1)

known as inverse beta decay (IBD), detailed in section 2.4, with protons intanks of cadmium chloride-doped water, producing a positron and a neutron. The
positrons would annihilate, producing a pair of gammas in tanks of liquid scintillator
sandwiching the water tanks. Photo-multiplier tubes (PMTs) would detect thislight, identifying the positron. To confirm the PMT signal was from a positron
produced in IBD, the neutron must also be detected in coincidence, motivating thecadmium-chloride doping of the water; cadmium has a large neutron capture crosssection. The neutron would capture on the cadmium, producing another gamma up
to 17 microseconds after the pair annihilation which would also be detected by the
PMTs in the scintillator. The identification of this IBD signal at a rate proportional
to the power output of the reactor confirmed the existence of neutrinos.

2. Neutrinos

6

Headed by Raymond Davis Jr. in the 1960s, the Homestake experiment sought
to measure the flux of neutrinos emitted by fusion reactions in the Sun by counting
argon atoms produced in the reaction
νe + 37Cl → 37Ar + e− .

(2.2)

John N. Bahcall provided a theoretical value from the standard solar model(SSM), but the experiment only measured a flux of around a third of Bahcall’s
calculation [8]. This gave rise to the so-called solar neutrino problem, which saw
Bahcall’s calculations and Davis’ experimental methods come under scrutiny overthe following years to try and explain the discrepancy.
At the time, neutrinos were thought to be massless, but one potential explanation
for the flux deficit was that if neutrinos had mass, they could “oscillate” between
flavours as they propagate. The idea of neutrino oscillation analogous to kaon
oscillation was proposed by Bruno Pontecorvo in 1957 [9], with the formal theoreticalneutrino mixing framework being developed by Ziro Maki, Masami Nakagawa and
Shoichi Sakata in 1962 [10].
In this framework, the neutrino flavour eigenstates νe,µ,τ are mixed with themass eigenstates ν1,2,3 via the “Pontecorvo-Maki-Nakagawa-Sakata” (PMNS) matrix UP M N S like








νe
ν1




 νµ  = UP M N S ×  ν2  .
ντ
ν3

(2.3)

The PMNS matrix itself is defined as

Ue1 Ue2 Ue3

UP M N S =  Uµ1 Uµ2 Uµ3  ,Uτ 1 Uτ 2 Uτ 3

(2.4)

though it is often parameterised as a combination of three rotation matrices,
one for each rotation in phase between eigenstates. In this form it is given byc12 c13s12 c13s13 e−iδCP

iδ
iδCP
c12 c23 − s12 s23 s13 e
s23 c13 
UP M N S =  −s12 c23 − c12 s23 s13 e
 (2.5)iδ
iδCPs12 s23 − c12 c23 s13 e−c12 s23 − s12 c23 s13 e
c23 c13

2. Neutrinos

7

where sij = sin θij , cij = cos θij and θij is the mixing angle between states iand j. δCP is the CP violating phase, determining the difference in oscillation
between neutrinos and antineutrinos. δCP has potentially grand implications on theformation of the universe and the matter-antimatter asymmetry problem in somemodels, and is the focus of investigation for many large scale neutrino experiments.
Equation 2.5 assumes Dirac neutrinos, where the neutrino and antineutrino havedifferent lepton numbers; however, it is possible that they are Majorana particles
which would mean that neutrinos are their own antiparticle. In this case, two
extra phases α1,2 must be included to fully describe this parameterisation of the
PMNS matrix; however, this property of the neutrino has not been confirmed andso this thesis will exclusively consider Dirac neutrinos.
The evolution of a neutrino mass eigenstate from x, t = 0 to x = x, t = t is givenby|ν(x, t)⟩ = e−iϕ |ν(0, 0)⟩(2.6)

where ϕ = Et − px is the phase of the state with energy and momentum E and
p. It can be shown that for ϕ = Et + P x, the difference ∆ϕ = ϕ1 − ϕ2 for twoneutrino flavour states after propagating some distance x = L is given by
∆ϕ ≈

∆m2 L
2E

(2.7)

where ∆m2 = m21 − m22 .
The probability of a neutrino with energy E initially of flavour α being detected
as flavour β at some distance L from the source is given by
Pα→β (L, E) = | ⟨νβ |να ⟩ |2 .

(2.8)

If a two neutrino universe is considered and δCP is assumed to be 0 for simplicity(though recent results hint towards a maximal value of δCP [11]), using equations
2.6 and 2.7 and a two-flavour version of the PMNS matrix, this can be rewritten as

2. Neutrinos

8Pα→β (L, E) = sin (2θ) sin
2

2

∆m2 L
2E

!

α ̸= β(2.9)

where θ is the mixing angle between the two mass states. The trigonometricdependence of probability with distance is the reason this phenomenon is dubbed
neutrino “oscillation”.
The Super-Kamiokande (SK) experiment and the Sudbury Neutrino Observatory(SNO) provided the crucial evidence required to confirm neutrino oscillation.
The “smoking gun” evidence for neutrino oscillation was SK’s discovery thatthe flux of atmospheric neutrinos demonstrated a zenith-angular dependence.
These neutrinos are produced when primary cosmic rays interact with the upper
atmosphere, detailed in 2.3.3, producing a mix of muon and electron neutrinos andantineutrinos at a ratio of (νµ + ν̄µ )/(νe + ν̄e ) ≈ 2. In the absence of oscillation,
this flux ratio should be isotropic at SK as these interactions occur approximately
evenly around the Earth, and the neutrinos will have negligible interaction with
the Earth itself. Instead, there was a significant difference in the flux of up-going
muon neutrinos (created on the far side of the Earth travelling up through the
Earth to SK) compared to down-going [12]. This measurement is consistent with
the idea that the up-going neutrinos oscillated away to other flavours, while thedown-going neutrinos created in the atmosphere above the detector primarily remain
as muon-type due to their shorter propagation length.
To definitively confirm that the neutrinos had oscillated away, the flux of allneutrino flavours must be shown to be consistent with Bahcall’s predictions. SK isonly sensitive to νe and νµ , but SNO used heavy water ( 2H2 O) as its target material,
permitting the neutral current (NC) interaction with deuterium 2H
να + 2H → p + n + να ,(2.10)

which is sensitive to all flavours of neutrino. If solar neutrinos were indeed
oscillating to different flavours by the time they reached Earth, SNO would still beable to make a complete measurement of the solar neutrino flux in this interaction

2. Neutrinos

9channel. SNO’s measurement was consistent with Bahcall’s prediction for the total
flux produced by the solar 8 B fusion chain [13].
SNO’s verification of the total solar neutrino flux and SK’s measurement of thezenith angle dependency of atmospheric neutrino flux confirmed the existence ofneutrino oscillation. The 2015 Nobel Prize in Physics was jointly awarded to Arthur
B. McDonald of SNO and Takaaki Kajita of SK for this discovery.

2.2

Mass Ordering and The MSW Effect

The oscillation probability Pα→β (equation 2.9) introduces a problem when trying
to obtain a complete measurement of all of the oscillation parameters. As the ∆m2term is contained within a sin2 function, measurement of Pα→β alone is insufficient todetermine its sign. Expanding to three flavours and therefore three mass eigenstates
results in further degeneracy in the form of three ∆m2 terms, introducing theneutrino mass hierarchy problem. In vacuum oscillation as derived above, only thedifferences in magnitude of the mass states can be measured and not the sign ofthese differences, nor their absolute masses. It is therefore unclear which of thethree mass states is the heaviest and which is the lightest.
This problem has been partially solved thanks to the modification of theoscillation probability when traversing matter. While all flavour eigenstates undergocoherent forward scattering off of electrons in matter, the electron flavour eigenstate
can do this via the charged current interaction channel, unavailable to the muonand tau flavour eigenstates. This modifies the potential experienced by the electron
eigenstate exclusively, resulting in an effective potential difference between Ve andVa for the νe and νa (other flavour) eigenstates given by
V = Ve − Va =√2Gf ne(2.11)

where GF is the Fermi coupling constant and ne is the number density ofelectrons in the medium [14]. This modifies the Hamiltonian of the system as H0 →Hm = H0 + V leading to a change in the eigenstates ν1 and ν2 and their eigenvalues:2. Neutrinos

10(2.12)

ν1 , ν2 → ν1m , ν2m
m21 m22,→ H1m , H2m
2E 2E(2.13)

where ν1m and ν2m are the neutrino eigenstates in the presence of matter, withrespective Hamiltonians H1m and H2m .
The equation of motion for a two-neutrino state of νe and νa in matter istherefore given byd νe∆m2 − cos 2θ sin 2θ
i=+sin 2θ cos 2θ
dx νa
4E
!

"

!

0
0 − V2

V
2

!#

νe
νa

!

(2.14)

which has clear dependence on the sign of ∆m2 . Given the high electron
density in the Sun, solar neutrinos experiencing this effect have been utilised todetermine the sign of ∆m212 , concluding that m2 > m1 . The sign of ∆m231 is yet
to be measured and determining whether neutrinos exhibit a normal hierarchy(NH, m3 > m2 > m1 ) or inverted (IH, m2 > m1 > m3 ) is a key physics goal ofsome modern experiments. These experiments primarily study electron neutrino
appearance in beam or atmospheric neutrino samples that experience matter effects
as they propagate through the Earth; however, this measurement is relatively
difficult given the vastly lower electron density and propagation length whencompared to the solar analysis.
In matter, the flavour states of a two-flavour νe and νa state can be expressedin terms of the mass eigenstates and a single modified mixing angle θm like so:|νe ⟩ = cos θm |ν1m ⟩ + sin θm |ν2m ⟩(2.15)|νa ⟩ = cos θm |ν2m ⟩ − sin θm |ν1m ⟩ .

(2.16)

θm can be expressed assin2 2θm =sin2 2θR(2.17)

2. Neutrinos

11

where R is the resonance factor, given by2EV
R ≡ cos 2θ −
∆m2


2

+ sin2 2θ.

(2.18)For ne → 0 as in vacuum, V → 0 as there is no longer a modified potential dueto the presence of electrons. In this case, R → 1 and θm → θ, recovering vacuum
oscillation. In the limit of very high electron density, V → ∞ and sin2 2θm → 0,suppressing any oscillation effects whatsoever.
As θm = θm (ne ), a resonance can occur. The condition for this resonance is givenby
2EV = ∆m2 cos 2θ.

(2.19)

If the electron density changes slowly enough, such as for a solar neutrino exiting
the Sun, the resonance condition can be satisfied, which maximises equation 2.17
and maximises oscillation. This resonance with adiabatically changing electron
density is known as the Mikheyev-Smirnov-Wolfenstein (MSW) effect and is clearlyobserved in solar neutrinos [15].

2.3

Neutrino Sources

There exists an abundance of neutrino sources due to the relative ease of theirproduction; neutrinos are exceptionally light and are therefore produced in a large
variety of weak interactions involving charged leptons. The nature of the largest
contributing sources of neutrinos at Earth are detailed here.

2.3.1

Cosmic Neutrino Background

Neutrinos were created in abundance in the high energies of the very early universe.
These neutrinos decoupled from matter around one second after the Big Bangand, thanks to their weak interaction, are expected to permeate the universe
today, forming the Cosmic Neutrino Background (CνB). The density of the CνB is
predicted through Big Bang cosmology to be extremely high, at about 336 cm−3 [16];2. Neutrinos

12

however, they are of a particularly low energy given their age, with a temperatureof ∼1.95 K, and so CνB have yet to be detected. Their flux is dependent on theirenergy which is in turn dependent on the neutrino’s absolute mass. This is not yet
known to a degree where it can be determined whether CνB neutrinos are relativistic,
but if they are, they would be the largest neutrino flux contributor at Earth.

2.3.2

Solar

The greatest contribution to the measured flux of neutrinos at Earth is due tonuclear interactions in the Sun. There are a number of fusion reaction chains which
produce electron neutrinos, the primary contributor being the proton-proton chain.
This begins with the fusion of two protons to form deuterium in the reaction
p + p → 2H + e+ + νe .

(2.20)The resulting deuterium then typically fuses with another proton in the interaction
H + p → 3He + γ.

2

(2.21)The helium-3 from this reaction can then interact via one of four branches,
detailed in figure 2.1, which also demonstrates an alternative production of helium-3
via the so-called “pep” reaction.
Solar neutrinos are of great interest due to their well understood production
and well known and large distance from their source. They have been studied
extensively in SK, detailed in [18][19][20] and [21].

2.3.3

Atmospheric

The Earth’s upper atmosphere is constantly being bombarded by high energy
particles known as (primary) cosmic rays produced throughout the universe froma wide range of sources. The cosmic ray flux is dominated by protons. Whenthese protons interact with the Earth’s upper atmosphere, they produce pions. The
charged pions then decay, primarily via the interactions

2. Neutrinos

13

pp chain
pep-

ppp+p

2 H + e ++99.6%

p + e– + pe

2H + p7 Be +

3 He + p

7 Be +e–

7 Li +

7 Li + p

2 4 He7 Be +
8 B-

8B

13 C + e + +

CNO-

e

13 C + p

14 N + γ

14 N + p

15 O + γ

e

15 O

0.13%
e

13 N + γ

17 O + p

14 N + 4 Heγ

99.87%

pp-II

hep-

4 He + e + +15%
3 He + 4 He

12 C + pe

13 N

2 × 10 –5 %4 He + 2p

pp-I
7 Be-

2H +

0.4%

3 He + γ

85%
3 He + 3 He

CNO cycle

8B + γp

8 Be* + e + +8 Be* + p

2 4 He15 N + e + +e

15 N + p

4 He + 12 C

99.96%

0.04%

e

17 F

17 O + e + +e16 O + p

17 F + γ

15 N + p

16 O + γ

pp-III

Figure 2.1: The proton-proton chain and CNO cycle, modified from [17].

π + → µ+ + νµ(2.22)

π − → µ− + ν̄µ(2.23)

while the neutral pions undergo electromagnetic showering. The muons fromthe charged pions then also decay, predominantly via the channelsµ+ → e+ + νe + ν̄µ(2.24)µ− → e− + ν̄e + νµ(2.25)

resulting in a ratio of (νµ + ν̄µ )/(νe + ν̄e ) ≈ 2, with some minor contribution
from higher order processes. Atmospheric neutrinos are of particular interest as
their flux and energy spectrum can be well constrained through the measurementof their accompanying muon flux. They also provide a variable baseline fromproduction to detection, dependent on zenith angle. This was instrumental in the
discovery of neutrino oscillation; SK observed a strong zenith angle dependency
on the flux of muon neutrinos [12].

2. Neutrinos
Near Detector

14
Beam Dump

Neutrinos

TargetDecay Volume

Pions (Deselected)
Pions (Selected)

Muons

Magnetic Horns

Protons

Be MainamlineAccelerator

Figure 2.2: A diagram of the accelerator neutrino beam production process, including
magnetic horns for focusing the desired pions and rejecting the oppositely charged pions
to produce a neutrino or antineutrino beam. Adapted from [23].

2.3.4

Accelerators

While neutrinos themselves cannot be electromagnetically accelerated, the sameprocess which produces atmospheric neutrinos can also be used to create a beam ofneutrinos in an accelerator. Protons can be accelerated into a proton-rich target in
the direction of a neutrino detector, which produces pions and, subsequently, a beamof neutrinos. There are many benefits to this approach, and SK detects accelerator
neutrinos as part of the T2K (Tokai-to-Kamioka) experiment. T2K is in many
ways an evolution of the K2K (KEK-to-Kamioka) experiment which directed aneutrino beam from the KEK (The High Energy Accelerator Research Organization)
laboratory in Tsukuba, Japan, towards SK. It was the first long-baseline accelerator
neutrino experiment, measuring muon neutrino disappearance and paving the way
for future accelerator neutrino experiments [22].
Firstly, the beam can be chosen to be primarily composed of either neutrinos
or antineutrinos, with some contamination. Once the pions have been created,
they travel some distance before decaying. During this time, a magnetic field
can be applied to focus either π + or π − , defocusing the other. This allows thebeam composition to be switched between neutrino and antineutrino modes by
reversing the polarisation of the magnetic selection field; π + for νµ , π − for ν̄µ .
This is crucial for measuring the δCP parameter, as the oscillation probability ofneutrino and antineutrino beams can be directly compared with with relatively wellunderstood initial fluxes. A diagram of the neutrino beam production process
is shown in figure 2.2.

2. Neutrinos

15

Another advantage of creating a beam of neutrinos is the ability to fine-tune
their energy spectrum. As well as modifying the energy of the incident protons
themselves, the kinematics of the decay of the selected pions can be utilised. Alongthe beam axis, the kinematics of the pions’ decay results in a broad neutrino energy
spectrum. Moving off-axis to the beamline, however, results in a tighter energy
spectrum at the expense of reduced flux and average energy. The advantage of atighter energy spectrum is that the oscillation maxima for neutrinos in the beam inthat direction will be similarly tightly spread, given the L/E dependency. Beamexperiments can therefore use the off axis angle and baseline from beam source todetector to tune the oscillation maxima to be tightly peaked around the positionof their detector, reducing systematic uncertainties. This technique is employedby the T2K (2.5°, Ē = 0.6 GeV, L = 295 km) [24] and NOvA (0.8°, Ē = 2.0 GeV,
L = 810 km) [25] experiments. Some experiments, such as K2K and the upcoming
DUNE experiment [26], opt instead for an on-axis approach, favouring the higher
flux and average energy over a tighter energy spectrum.
To constrain the systematic uncertainties in the beam’s properties as well as tomeasure interaction cross sections, supplementary detectors are often deployed close
to the beam source. These are typically small scale detectors situated a fractionof the distance from the beamline compared to the primary detector. They are
therefore often referred to as near detectors. Primary detectors of experiments are
sometimes referred to as far detectors in contrast and are typically significantly
larger than the near detectors to account for the loss of flux with distance. Near
detectors can either utilise a similar detection technique as the far detector suchas in the NOvA experiment, or standalone detector designs, such as T2K’s ND280
and INGRID detectors.
Accelerator-based beam experiments are at the forefront of the measurementof the δCP phase. T2K currently provide the tightest constraint on this important
oscillation parameter, favouring maximum CP violation at a confidence level ofapproximately 3σ [11]. Two major next-generation experiments seek to definitively
measure δCP : Hyper-Kamiokande, a 258 kt evolution of the Super-Kamiokande2. Neutrinos

16

detector utilising an upgraded version of the beam used in T2K [27]; and DUNE, alarge-scale liquid argon time projection chamber (LArTPC) based in the UnitedStates. DUNE will utilise an upgraded version of the high-power NuMI beam
produced at Fermilab, Chicago [26], used in the MINERvA [28], MINOS [29]and NOvA [25] experiments.

2.3.5

Supernovae and Pre-Supernova Stars

By far the most instantaneously intense but fleeting source of neutrinos aresupernovae (SNe), specifically core-collapse SNe (CCSNe). As a massive ( ≳ 8 M⊙ )star reaches the end of its life, its core of higher-mass materials can collapse under
its own immense gravitational pressure, triggering a supernova.
As hydrogen is exhausted in a massive star, its core condenses, increasing thetemperature to a point where more massive elements can be fused, balancing thegravitational potential energy with the outward pressure due to fusion. The coreitself remains stable due to electron degeneracy pressure. This is the outward
pressure which emerges due to Pauli’s exclusion principle, causing electrons to resist
occupying non-degenerate states in extremely high density materials.
As the supply of lighter elements is exhausted, equilibrium is maintained throughthe fusion of the heaviest fusible nuclei such as carbon, neon, oxygen and eventuallysilicon for sufficiently massive stars. Silicon fusion is the final stage of a massive
star’s evolution, as silicon fuses to iron. Iron does not undergo fusion due to it
being the inflection point of nucleon binding energy per nucleon: the point at which
fusion becomes an energy sink rather than a source. Once a star begins its carbon
burning phase, the high temperature is offset primarily by neutrino cooling, more
so with neon and oxygen, peaking with silicon. Neutrino cooling is the process
where neutrinos produced through pair production, plasmon decay and neutrino
Bremsstrahlung take energy away from the high-temperature stellar core. This is an
exceptionally short phase in the star’s evolution when considering the timescale ofits ∼ 107 years-long life up to this point, from ∼ 1000 y for the carbon burning phasedown to a few days for silicon burning. As the star begins to fuse silicon, neutrino

2. Neutrinos

17

production increases to a level that may be detectable by neutrino experiments on
Earth, which can be used as an early warning signal of a CCSN.
A pre-SN alarm was recently introduced into SK which estimates that a preSN silicon-burning star could be detected by a gadolinium-dope SK, detailed inchapter 4, up to 600 pc away with a false alarm rate of 1 per century [30][31].
KamLAND, a liquid-scintillator neutrino detector based in the same mine as SK,
has an implementation of a pre-SN alarm [32].
As the star continues to fuse silicon, the iron core accumulates beyond the
Chandrasekhar limit of 1.44 M⊙ . This mass limit is the point at which the electron
degeneracy pressure can no longer resist gravitational collapse. At this point,
electron capture on protons in the iron core produces electron neutrinos and neutronrich nuclei. The neutrons in these nuclei can then undergo β − decay, producing
electron antineutrinos. The reduction in electrons in the core results in reduced
electron degeneracy pressure, triggering the collapse.
During this period, the core’s density is such that neutrinos cannot diffuse
outwards faster than the collapse, trapping them. If the mass of the core is morethan a few Solar masses, then neutron degeneracy is not sufficient to decelerate
the collapse and the core will directly form a black hole with no supernova [33].
Below this mass, the density of the core reaches the point where neutron degeneracypressure becomes significant and sufficient to decelerate the collapse, releasing thetrapped neutrinos over the course of tens of milliseconds and generating a shockwave
that propagates outwards into the mantle of the star. This shockwave violently
ejects the outer layers of the star, leaving only the core. The outer boundary of thisshockwave is the source of the intense light observed from a supernova; however,
the exact mechanism required to produce such luminosity is a matter of debate andlikely involves some form of absorption of the initial neutrino burst [34][35]. Thisinitial neutrino burst is the highest average energy and flux of neutrinos produced
over the course of a CCSN, shown in figure 2.3.
The super-heated core is sufficiently hot where neutrino-antineutrino pairs areformed through thermal emission at a rate greater than through electron capture2. Neutrinos

18

Figure 2.3: The luminosity (top left) and average energy (bottom left) of νe , ν̄e and νx(all other flavours) with time from core “bounce” due to neutron degeneracy pressure,and the energy spectrum of ν̄e at different times from this bounce (right) [36].

or β − decay, rapidly cooling the core over a period of ∼ 10 s, after which point
neutrino luminosity drops significantly. While the electromagnetic radiation from a
CCSN is luminous enough to outshine an entire galaxy, 99% of the total 3 × 1053
erg released by a CCSN is carried away by the neutrinos. As the core cools, theneutrino production rate falls, as does their average energy.
SNe from the Milky Way or nearby galaxies would be a plentiful source ofneutrinos. Unfortunately, given the sub-surface, electromagnetically invisible natureof a progenitor star nearing core collapse, their happening is impossible to predict.
The detection of silicon burning neutrinos is the only outward warning sign, andthese leave little time to prepare for the burst, around a day at most and justa few hours for more distant stars in the Milky Way [30][31]. They are also
infrequent. The galactic rate of CCSN is predicted to be 1.63 ± 0.46 (100 yr)−1
based on massive star counts, extragalactic SN rates and 26Al abundance, a CCSN
by-product [37]. An alternative approach models the observability of galactic
CCSN, considering visible luminosity and absorption due to interstellar dust. Thisobservability model is then combined with historical records of visible SNe to−1
predict a rate of 4.6+7.4[38].
−2.7 (100 yr)

2. Neutrinos

19

A total of 25 neutrinos produced by CCSNe have been identified to date. All
were from SN1987A on February 23, 1987, the only nearby CCSN since the discoveryof the neutrino. Kamiokande-II detected 12 [39], the Irvine-Michigan-Brookhavenexperiment (IMB) 8 [40] and the Baksan Neutrino Observatory (BNO) 5 [41].
SN1987A occurred approximately 51.4 kpc from Earth, outside of the Milky Way in
the Large Magellanic Cloud (LMC), a nearby satellite galaxy. Given the significant
progress made in neutrino detection technologies since SN1987A and prevalenceof detectors of various technologies around the world, a nearby CCSN in or near
the Milky Way would result in a significant increase in SN neutrinos detected.
SK alone expects between 2,000 and 3,000 events in its 22.5 kt fiducial volume
for an SN burst at 10 kpc using the minimum flux predicted by the Nakazato SN
burst model [42]. For many modern neutrino detectors, an important aspect of
their operation is maximising livetime, i.e. the time the detector is online andcapable of detecting a CCSN.
While detecting the burst from a nearby CCSN with modern detectors would
greatly advance our understanding of the core collapse mechanism, an alternative
approach is to probe neutrinos produced in supernovae far beyond the local cluster.
These are known as supernova relic neutrinos (SRN) given the far older pointof emission compared to local CCSN. Galactic supernovae are rare; however, it
follows that the wider a net you cast the greater the rate of CCSN, with the
payoff of a severely reduced flux for more distant supernovae. This integrated flux
forms the diffuse supernova neutrino background (DSNB) with the current upper
limit set by SK at 2.7 cm−2 s−1 for neutrino energies greater than 17.3 MeV [43].
This is many orders of magnitude lower than the flux expected from a galactic
CCSN, but has the advantage of being constant and acting as a probe into allsupernovae within the observable universe. Measuring the DSNB is the one of
the main motivations for the SK-Gd project [44].

2. Neutrinos

2.3.6

20

Geo-neutrinos

Geo-neutrinos are produced when nuclides in the Earth’s interior undergo β − decay.
These decays are also responsible for a significant portion of the heat radiatedby the Earth’s interior, at a rate proportional to the rate of neutrino production.
Measuring the production of geo-neutrinos would therefore indicate the contributionof radioactive decay to the ∼ 46 TW terrestrial surface heat flux, providing valuable
information for various studies into the Earth’s interior [45].
The majority of the heat produced by radioactive decay in the Earth’s interior
are from the elements 238U, 323Th and 40K in the decay schemes:

U → 206Pb + 8α + 8e− + 6ν̄e + 51.7 MeV(2.26)

Th → 208Pb + 6α + 4e− + 4ν̄e + 42.7 MeV(2.27)

K → 40Ca + e− + ν̄e + 1.31 MeV(2.28)

238
232

40

with energy spectra shown in figure 2.4.
At low energies, inverse beta decay is the dominant interaction mode for electron
antineutrinos, with a threshold of 1.806 MeV. Figure 2.4 shows that this excludes
the majority of the 238U and 232Th spectra and the entirety of the 40K spectrum
from detection via inverse beta decay. To add to the difficulty of geo-neutrino
detection, a nuclear power reactor will dominate the flux of electron antineutrinos
close to the IBD threshold unless a detector is sufficiently far away from sucha plant. This significantly increases the difficulty of identifying geo-neutrinos indetectors situated in Western Europe, the eastern United States, India and East
Asia (particularly Japan, South Korea and the east coast of China) due to thehigh density of nuclear power plants in these regions. Despite this, the leading
measurements of the geo-neutrino flux are jointly provided by the KamLAND(Kamioka Observatory, Japan) and Borexino (Gran Sasso, Italy) experiments [46].
The large scale scintillator experiment JUNO aims to improve upon this during
periods where its nearby reactors, its principle interest, are offline [47].

2. Neutrinos

21

Figure 2.4: The spectra of geo-neutrinos produced in the decays 2.26 ( 238U chain, solid
black), 2.27 ( 232Th chain, dash-dotted red) and 2.28 ( 40K chain, dashed blue) [45]. The
solid vertical line indicates the inverse beta decay interaction threshold of 1.806 MeV.

2.3.7

Cosmogenic

By far the highest energy neutrinos observed on Earth are those produced byparticles accelerated by undetermined astrophysical objects. The first evidence
for these most likely extragalactic neutrinos was found at the IceCube neutrino
observatory, which also holds the best constraint on their flux [48]. IceCube isa PMT-string based detector that uses a cubic kilometer of Antarctic ice as its
interaction medium, aiming to identify Cherenkov radiation produced by TeVPeV-scale neutrinos, though a subarray of the detector, DeepCore, is sensitive to+143neutrinos ≳10 GeV. IceCube detected neutrinos of energy 1.041+0.132−0.144 and 1.141−133

PeV in 2011 and 2012 respectively [49], as well as the highest energy neutrino everrecorded (later in 2012), with an energy of 2.004+236−262 [50].
PeV scale neutrinos are predicted to be produced when ultra-high energy cosmic
rays (UHECR), typically protons, collide with CMB photons, dubbed GreisenZatsepin-Kuzmin (GZK) neutrinos. There are a number of suggested sources of2. Neutrinos

22

UHECRs. Gamma ray bursts (GRBs) are one potential source. GRBs are shortlived high-luminosity electromagnetic events, predominantly due to supernovae, butalso due to the merger of binary neutron stars. Low-luminosity GRBs may provide
mild enough radiation fields with a sufficient energy budget to produce UHECRs;
however, there is debate as to if their energies truly are sufficient [51]. Relativistic
SNe are also postulated to accelerate particles to UHECR territories.
Blazars are another potential source of UHECRs. These are active galactic nuclei
with powerful jets that may have sufficiently strong magnetic fields to accelerate
UHECRs. Such powerful jets may also be produced when a star passes close to asupermassive black hole, where the star becomes tidally disrupted, tearing it apart[52]. Pulsars are another source of strong magnetic fields [53], as are galaxies witha high star-formation rate inducing strong magnetic superwinds [54].
A multimessenger collaboration identified that the direction of a high-energy
neutrino event detected by IceCube was consistent with a blazar [55], confirmingthat blazars are a source of high-energy astrophysical neutrinos.

2.3.8

Reactor

Nuclear reactors are potent sources of terrestrial neutrinos, producing large numbersof electron antineutrinos when fission fragments undergo β − decay. Reactor neutrinos
are discussed in greater detail in chapter 5.

2.4

Inverse Beta Decay

Electron antineutrinos of a few MeV total energy primarily interact with water
via inverse beta decay. This reaction has the formν̄e + p → e+ + n
with the Feynman-like diagram(2.29)

2. Neutrinos

23
e+

νe

W

p

n

Due to the difference in mass between the reactants and products, an energy
threshold of 1.806 MeV is imposed for this reaction. The positron’s low mass relative
to the neutron results in it carrying most of the incident neutrino’s energy, offset
by the nucleon mass difference ∆ = mn − mp = 1.293 MeV. Up to 15 MeV the
angular distribution of the positron is nearly isotropic, and only slightly forwardgoing at higher energies, meaning for the purposes of most low energy analyses,
the incident neutrino’s direction cannot be determined from the positron. Some
directionality is retained in the neutron’s recoil as demonstrated by the CHOOZ
reactor neutrino experiment; however, the recoil distance was measured to be
only (1.7 ± 0.4) cm [56]. Reconstructing the incident neutrino’s direction fromthe neutron is therefore a difficult task only possible for experiments with finevertex reconstruction resolution and high statistics, Double Chooz, for example[57]. This method is not commonly utilised.
The cross section for IBD on free protons increases with energy. Strumia andVissani provide a parameterisation of this cross section given by:
σIBD ≈ 10−43 cm2 pe Ee Eνa(2.30)

a = −0.07056 + 0.02018 ln Eν − 0.001953 ln3 Eν

(2.31)

where

and Ee = Eν − ∆ [58]. The cross section below 10 MeV calculated using thisparameterisation is shown in figure 2.5.

2. Neutrinos

7

24

1e 42

6

IBD [cm2]

5
4
3
2
1
0
2

4

6
E [MeV]8

10

Figure 2.5: The cross section for inverse beta decay on free protons, calculated using
Strumia and Vissani’s parameterisation given in [58].

While the positron is of primary interest given it indicates the incident neutrinoenergy, the neutron can be used to tag an IBD event in cases where the positron
cannot easily be identified. In the absence of a hadronic calorimeter, a neutron
can be identified when it is captured by a nucleus, typically referred to as neutron
capture. A short time after production, the neutron thermalises and is quickly
captured by atomic nuclei. The time difference between the IBD interaction and theneutron capture varies depending on the material in which the neutron is produced;
an abundance of nuclei with a relatively high neutron capture cross section will
decrease the capture time. This time difference leads to the neutron capture often
being referred to as the “delayed” event to the positron’s “prompt”.
When a neutron captures on a proton as with capture on hydrogen in water, a2.22 MeV photon is produced due to the change in binding energy. While this is
typically of lower energy than the prompt positron, the identification of two events

2. Neutrinos

25

in temporal and spatial coincidence can help in removing background that is not
typically tightly coincident. This is difficult in practice, however, if the vertex of
the neutron capture cannot be well reconstructed, or background events mimic aneutron capture signal. This motivates the use of materials that produce a more
distinct signal following neutron capture. One such material is gadolinium, as usedin the SK-Gd upgrade detailed in chapter 4 [44].

3Super-Kamiokande
Contents
3.1
3.2
3.3
3.4
3.5
3.6
3.7

Detector Structure . . . . . . . . . . . . . . . . . . . . .
Detection Principle . . . . . . . . . . . . . . . . . . . . .
Electronics and DAQ . . . . . . . . . . . . . . . . . . . .
Data Periods . . . . . . . . . . . . . . . . . . . . . . . . .
BONSAI Low Energy Event Reconstruction . . . . . .
The Wide-Band Intelligent Trigger (WIT) . . . . . . .
Monte-Carlo . . . . . . . . . . . . . . . . . . . . . . . . .

27
32
34
36
37
41
53

The Super-Kamiokande (SK) detector is a large-scale water Cherenkov (WC)detector located in Gifu prefecture, Japan, primarily operated by the Institute of
Cosmic Ray Research (ICRR) of the University of Tokyo. It is an evolution of the
Kamioka Nucleon Decay Experiment (KamiokaNDE, often stylised as Kamiokande)
which began data taking in 1983 and was decommissioned in 1997 following its
Kamiokande-III phase. The primary aim of Kamiokande was to detect proton
decay, a theorised process which could provide evidence for a Grand Unified Theory(GUT) of the weak, strong and electromagnetic forces. As neutrinos became agreater focus of the particle physics community towards the end of the 20th century,
it became clear that Kamiokande also served as a particularly effective neutrino
detector. Super-Kamiokande was therefore proposed: a much larger detector

26

3. Super-Kamiokande

27

of similar design with a primary aim of confirming or denying the existence ofneutrino oscillation. A powerful detector in its own right, SK is also used as the far
detector in the highly successful T2K long baseline neutrino oscillation experiment,
detecting neutrinos produced in a beam some 295 km away in the village of Tokai,
Ibaraki prefecture. It was also used similarly as part of the K2K experiment, thefirst long-baseline accelerator neutrino experiment, detecting neutrinos produced
at KEK in Tsukuba. SK began taking data in April 1996 and will continue tooperate at least until its successor, Hyper-Kamiokande (HK), is operational, whichis expected to be sometime in 2027.

3.1

Detector Structure

The detector is situated in a mine operated by the Kamioka Mining Company
under Mt. Ikeno which straddles the Gifu-Toyama prefectural boundary, though
SK itself is entirely contained within Gifu prefecture. In any given direction, there
is at least a kilometre of rock, helping to reduce the flux of atmospheric muons
passing through SK to ∼ 10−5 × the flux at the Earth’s surface. A schematic ofthe detector’s layout can be seen in figure 3.1.
SK consists of 50 kt of gadolinium-doped ultrapure water contained in a 39 m
diameter stainless-steel cylindrical tank of height 42 m. Concrete fills the space
between the outside of the tank and the rock, apart from above, where a large,
accessible dome houses the high voltage (HV) and data acquisition (DAQ) systems
for the detector. Ports for access to the detector are also found on the top of thetank. Some ports are light tight for insertion of calibration materials or samplingsystems, and some act as human access ports for the rare occasions where directaccess to the detector is needed. Within the tank is a 55 cm thick stainless-steel
structure which supports the detector’s many PMTs, as seen in figure 3.2. This
structure separates the 32 kt of the so-called inner detector (ID) from the outerdetector (OD) and its outer side leaves 2.2 m of room between it and the wall of thetank. Modular sub-structures are bolted together to form the support structure,with each module holding a 4 × 3 set of ID PMTs.

3. Super-Kamiokande

LINAC

28

Electronics Huts

Outer Detector
Tyvek
20 cm PMTs
Inner Detector

50 cm PMTs
Blacksheet

Outer Detector
4x3 Modules
Cable Bundles
Stainless Steel
Tank

Outer Detector+ Supports

Figure 3.1: A cross section of the SK detector (partially filled with water).

The inner detector contains 11,129 Hamamatsu R3600-05 50 cm diameter PMTs
on both the walls and endcaps of the ID, and are used to detect light from neutrino
interactions. The quantum efficiency of these PMTs peaks at 21% at 360-400 nm,
and the collection efficiency for photoelectrons at the first dynode is > 70% [59]. The
ID has approximately 40% photo cathode coverage. A black plastic sheet is mounted
around each of these PMTs to prevent light from crossing the ID/OD barrier. A
subset of the ID volume, > 2 m from the PMT plane in most analyses (22.5 kt ofwater), is known as the fiducial volume (FV). Events whose interaction vertex isreconstructed outside the FV are rejected in an attempt to remove events due toradioactive decay that originate close to the PMTs or from the PMT glass itself.

3. Super-Kamiokande

29

Figure 3.2: Photograph of the structure which supports the PMTs and separates the
ID and OD. The fibreglass rear of the ID PMT cases can be seen within the structure.
Taken during the 2018 tank open work.

(a) View from the main accesshatch on top of the tank.

(b) Just above the floor of the ID, with a Hamamatsu
R3600-05 PMT in the foreground.

Figure 3.3: Photographs of the SK inner detector taken during the 2018 tank open
work.

Photographs of the inner detector, showing the PMT arrays, can be seen in figure 3.3.
In the OD, 1,885 outward-facing R1408 20 cm diameter PMTs are mounted evenly
around the structure. Each PMT is coupled to a 50 × 50 cm acrylic wavelength
shifting plate designed to act as a light guide, improving the light collection forthese smaller, more sparsely arranged PMTs. Light collection is further improvedby sheets of Tyvek (an opaque paper-like material manufactured by DuPont) which

3. Super-Kamiokande

30

Figure 3.4: A photograph from the bottom of the SK OD looking up, showing how
Tyvek is used to optically isolate the OD from the ID and encourage reflection within the
OD. The Hamamatsu R1408 PMTs and wavelength-shifting light collection plates canalso be seen. Taken during the 2018 tank open work.

covers the outer side of the structure. This Tyvek is white on the outward-facing
side, encouraging light reflection and subsequently improving the light detection
efficiency of the OD PMTs. On the inward-facing side, the Tyvek is black to makethe material opaque and to absorb any light which penetrates the ID black sheet.
The Tyvek is hung on the structure in such a way that strives for optical isolationof the ID from the OD as can be seen in figure 3.4.
Tyvek is also hung on the inner wall of the tank to further encourage lightreflection, also seen in figure 3.4. This tyvek lacks a black backing as there is noneed for it to be fully opaque and must be relatively lightweight. These sheets
are hung from the very top of the tank on the wall and are only connected atthe very bottom, so being lightweight eases installation and prevents them fromripping under their own weight.
The purpose of the OD is to filter out events that originate outside of theinner detector; a neutrino interaction in the ID should have no signal in the OD,

3. Super-Kamiokande31

as all charged particles are produced at the interaction vertex. Despite the rockoverburden, cosmic muons can still reach SK, at a flux of about 6×10−8 cm−2 s−1 sr−1 ,resulting in an event rate of about 2 Hz [59]. The OD is essential in removing
these events, as well as any other events where charged particles may find theirway into the ID from outside the tank, such as those produced in radioactive
decay in the walls surrounding the detector.
Also found in the OD are 26 sets of large “compensation coils” attached to theinner walls of the tank, both horizontally and vertically. These carry a carefully
controlled current to induce a magnetic field opposite to the Earth’s geomagnetic
field, counteracting it to provide a neutral field in the detector volume. The
geomagnetic field, while relatively weak, affects the trajectory of particles in
the PMTs, reducing their collection efficiency [60]. These compensation coils
reduce this effect.
The cables feeding power to the PMTs and carrying photo-current informationfrom them are gathered in large bundles climbing up the outside of the structure.
These cable bundles exit the tank through light-tight ports and are routed to one
of four huts placed on top of the tank, which contain the HV systems and DAQ
modules. To simplify the tuning of the voltage being sent to the PMTs, all cables
are approximately the same length from the PMTs to the HV modules, requiring alarge number of cable trays on the top of the tank to contain the excess length.
Just outside the dome above the tank, in one of the hallways leading away fromthe detector, is the LINAC. This is an ultra-low intensity, low energy (∼ few MeV)
electron LINAC which can be piped into one of 3 calibration ports on the top of
the tank, all on the LINAC half of the hall. There are a range of different beam
pipe lengths that can be inserted into the port, allowing for injection at different
heights in the detector. LINAC calibration usually occurs around once a year, withextra calibration campaigns when it is deemed necessary, usually if the detector
status has undergone some change while running.

3. Super-Kamiokande

32

In the SK coordinate system, the origin is at the centre of the detector, withpositive z being vertically upwards. x increases positively from the LINAC side ofthe detector to the entrance of the SK hall on the opposite side of the dome.

3.2

Detection Principle

SK relies on the principle that charged particles travelling faster than the phasevelocity of light in a medium emit electromagnetic radiation. This is known as
Cherenkov radiation and is primarily produced in the ultraviolet spectrum, but
its distribution extends into the visible.
As the light is produced by a moving source travelling faster than its fixed
speed of c/n, where n is the refractive index of the medium, it takes the form ofa cone. This cone’s opening half-angle θ is given by:cos θ =

1
nβ

(3.1)

as shown in figure 3.5.
Given that the opening angle of the Cherenkov cone is dependent on the particle’s
velocity, this angle can be reconstructed using the projected ring image detectedby SK’s PMTs and the energy of the particle can be inferred. This then gives anindication of the energy of the incident neutrino, depending on the kinematics of
the interaction. Electrons and positrons below 10 MeV only travel a few cm inwater before they either lose enough energy through scattering to drop below theCherenkov threshold or are captured by an atom. Given that SK’s reconstruction
resolution is ∼1 m, such events can therefore be treated as a single interaction vertex.
The amount of Cherenkov light produced by a particle decreases as its energy
approaches that of the Cherenkov threshold: the point at which a particle’s velocity
is equal to the local phase velocity of light. For electrons and positrons in pure water,
this translates to a total energy of 0.767 MeV or 0.257 MeV kinetic. For electronsand positrons in SK with total energy less than 10 MeV above the Cherenkov
threshold, there are not enough PMTs hit by light to reliably reconstruct the3. Super-Kamiokande

33

𝛾
𝜈l

l

A

B

𝜃
𝜃

𝛾

ct/n
A

𝜃
𝜃

Detector
Wall

vt

B

𝛾

Figure 3.5: The formation of a Cherenkov ring in a medium of refractive index n by acharged particle of velocity v > c/n. The particle is either created or given energy by aneutrino interaction at A and stops producing Cherenkov radiation at B.

Cherenkov cone and infer the particle’s energy using its angle. Instead, the numberof PMTs hit by light is used to reconstruct the energy, as the energy dependenceof Cherenkov emission is theoretically well known. The photo-coverage of thedetector (40%) and individual PMT quantum and collection efficiencies are factored
into this reconstruction. The approach to low energy reconstruction is discussed
in further detail in section 3.5.
While SK’s low energy analyses are limited to electron or positron detection,
muon neutrino interactions are of particular interest in the energy regime above
the muon’s Cherenkov threshold of around 160 MeV. Indeed, this is crucial inSK’s role in the T2K experiment, which produces primarily muon-type neutrinos.
It is important to isolate the muon and electron-like events from one another to3. Super-Kamiokande

34

Figure 3.6: A sharp muon-like Cherenkov ring event (a) compared to a fuzzier electronlike ring (b) for two T2K events in SK [24].

determine the flavour of the incident neutrino.
To differentiate between the two lepton flavours, the sharpness of the Cherenkov
ring patterns is evaluated. Given its relatively low mass, an electron will scatter
multiple times before it stops producing Cherenkov radiation, its direction changing
with each interaction. This effectively results in a large number of rings overlaying
onto one another, each with slightly different direction, leading to a blurred ringwith many PMT hits straying from the ring that corresponds to the average
direction of the electron. This is in contrast to the heavier muon whose paths are
typically straight with minimal scattering, producing a sharp ring. This differencein sharpness can be seen visually in figure 3.6.

3.3

Electronics and DAQ

SK’s ID PMTs require a high voltage across them to work efficiently, ranging from
1.7 kV to 2 kV. This is provided by HV systems located in the electronics huts on
top of the SK tank, supplied along the same cable that also carries the signal to
the DAQ systems in the same huts. Each PMT must have its HV tuned uniquely,
and to simplify this task all PMTs have approximately equal length cables of 70 m.
Up until August 2008, the PMT signals were processed by custom-built modules
called analogue timing modules (ATMs) comprised of charge-to-analogue (QAC)3. Super-Kamiokande

35

Figure 3.7: The Super-Kamiokande data acquisition (DAQ) system, in place since
SK-IV except for the WIT PCs which were added in 2015.

and time-to-analogue converters (TAC). For each PMT there were two pairs of
QAC/TAC that would allow for the readout of multiple sequential hits in thecase where a PMT would be hit by light in quick succession. These modules were
replaced with quantum tunelling composite (QTC)-based electronics with ethernet
QBEE. The QBEE modules provide a significant upgrade to the charge and time
resolution of the ATMs, improving to beyond the intrinsic resolution of the PMTs
themselves [60]. There are 550 QBEEs, each with 24 input channels.
The hit data is stored in first-in-first-out (FIFO) memory by field programmablegate arrays (FPGAs) on the QBEE boards and passed along to the 20 front-end
computers. These computers time-order the hit data as 20 ms blocks, with 1 ms
overlap to cover events that would otherwise straddle two blocks.
As the vast majority of data generated by the SK detector is not due to neutrino
interactions, online triggers are required to curate the data sent to long term storage.
In the ATM era, this triggering was handled by hardware, only sending data to thefront-end computers if the number of PMT hits in a 200 ns window exceeds a certain
threshold. With the QBEEs a trigger is issued at a rate of 60 kHz, mimicking theATM’s true hardware trigger, and the front-end computers deal with triggering
through software. A schematic of the SK DAQ system is given in figure 3.7 which
also shows the Wide-band Intelligent Trigger (WIT) computers. These were added
in 2015 and are further detailed in section 3.6.

3. Super-Kamiokande

3.4

36

Data Periods

To date, there are 7 distinct data-taking periods of SK, named SK-I through to SKVII, generally separated by periods where the detector is shut down for a significant
amount of time, typically for general maintenance or upgrades. The transitions
between SK-V and SK-VI, and SK-VI and SK-VII had no detector downtime between
them as they signalled the point where gadolinium had finished being added tothe detector water, which occurred during while the detector was operational (seechapter 4). SK-VI represents the first stage of what is often collectively referred toas SK-Gd given the significant change from ultrapure to Gd-loaded water. These 7
periods are split into “runs” of data-taking which allows for easier segmentationand selection of offline data. These runs are capped at 24 h but may be shorter if
a run was stopped due to some change in the detector. This most often happens
when calibration data is being taken, in which case runs are marked as “test” runs
which can be easily ignored during offline analyses not concerning calibration.
First data was taken in April of 1996, beginning the SK-I period, ending inJuly 2001 with the tank being drained for general maintenance and inspection. In
November of 2001, part-way through refilling the tank to start the SK-II period,
around 7,000 PMTs were suddenly destroyed. This was likely due to the implosionof a single PMT whose glass was weakened, triggering a cascade of implosions
throughout the water-filled volume of the detector. Those outside of the waterremained intact. The tank was again drained and the remaining functional PMTs,∼47% of the total in SK-I, were redistributed evenly throughout the detector,
resulting in around 19% photo-coverage. The PMTs were also fitted with a casing.
This casing is made of two parts: a fibreglass section covering the opaque rearof the PMT, and a transparent acrylic dome in front. These sections are bolted
together and are designed to mitigate the pressure waves created were a PMT
to implode, preventing a cascade. The acrylic front does not significantly affectthe photo-collection of the PMT.
SK-II began in October 2002 with reduced photo-coverage, running until October
2005. SK-III restored the original photo-coverage with the purchase of new PMTs,

3. Super-Kamiokande

37

running from August 2006 to August 2008. SK-IV brought in upgrades to the DAQ
systems, replacing the ATM boards with new QBEEs, running from September 2008
to May of 2018, the longest data taking period for SK so far. Although much of
the work on the gadolinium processing and water systems were made during SK-IV,
there remained a significant amount of work to prepare the detector for Gd loading
between SK-IV and SK-V. As well as the changes to the water systems inaccessible
during data taking, the structure of the detector had to be meticulously cleaned in
preparation for the first time SK would run without exclusively pure water in its tank.
The upgrades in preparation for SK-Gd were complete, and the tank filledwith ultrapure water in January 2019, beginning the SK-V data taking period. A
short shutdown in February 2020 included using remotely controlled underwater
drones to make minor changes to the water inlet pipes at the base of the innerdetector. Drones were employed to avoid the slow process of draining and refilling
the tank for relatively minor modifications.
Following delays due to the COVID-19 pandemic, the planned date of Gd loading
was pushed back from March 2020 to July 14th. Loading was completed on August17, 2020, marking the beginning of the SK-Gd (SK-VI) phase of the experiment.
Further gadolinium loading began on June 1st, 2022, acting as an interim phase
before the final loading up to the ultimate target concentration. This loading wascompleted on July 5th, 2022 and signalled the start of the SK-VII phase which
continues as of the writing of this thesis.
A summary of the phases of SK is given in table 3.1.

3.5

BONSAI Low Energy Event Reconstruction

A low energy event in SK will generally produce around 6 photoelectrons per MeV
above Cherenkov threshold [61]. It takes photons up to 220 ns to traverse thedetector, which defines a coincidence window in which PMT hits could have comefrom the same light production vertex. The dark noise rate of individual PMTs
in SK (when a PMT registers a hit in the absence of light) is around 5 kHz so inthis window around 12 PMTs would register dark noise hits on average. For events

3. Super-Kamiokande
Phase
SK-I
SK-II
SK-III
SK-IV
SK-V
SK-VI
SK-VII

38

Start Date
April, 1996

End Date
July, 2001

Notes
First data taking, neutrino oscillation discovery.
October, 2002
October, 2005 Reduced photo-coverage (PMT
implosion cascade).
August, 2006
August, 2008
Restored photo-coverage.
September, 2008 May, 2018
Upgraded DAQ systems, longest
phase to date.
January, 2019
August, 2020
Ready for Gd loading.
August, 2020
July, 2022
First phase of SK-Gd, 0.02% concentration.
In
progress Increased Gd concentration ofJuly, 2022
as of August, 0.06%.
2022
Table 3.1: The data-taking phases of SK.

above 10 MeV, the number of true hits (> 60 pe) would dominate in this timeframe; however, for lower energy events the dark noise hits become comparable
in number to the true hits from the particle, skewing reconstruction. This lower
energy regime is also home to significant radioactive background, primarily from the
PMT glass and fibreglass casings. Developed in response to the severely decreased
photo-coverage during the SK-II period, BONSAI (Branch Optimisation Navigating
Successive Annealing Iterations) offers superior reconstruction quality of low energy
events below 10 MeV (and especially below 5 MeV) over previous techniques andis crucial in reducing this radioactive background.
BONSAI defines a likelihood L for a given vertex based on timing residualsof all PMT hits following time of flight (TOF) subtraction. For a TOF-correctedvertex hypothesis (⃗x, t0 ) with PMT hit times ti , each with a TOF tTi OF from theemission vertex, the likelihood is given by:L(⃗x, t0 ) =

NX
hits

log(P (ti − tTi OF − t0 ))

(3.2)

i=1

where P is the probability distribution function of the PMT photoelectron signal
timing. The Cherenkov photon hits will be coincident to within a few ns given their3. Super-Kamiokande

39

3 ns timing resolution. This likelihood is therefore a strong discriminator for noncoincident hits due to dark noise hits that are essentially randomly distributed within
the event window. The best fit vertex would therefore have the maximum likelihood.
While the likelihood could be calculated for every possible vertex, with someresolution, this would be an incredibly computationally intensive process. Instead,
BONSAI initially considers four-hit combinations of PMTs. For every combination,
the hit vertices are used to solve for an emission vertex, considering TOF fromemission to PMT hit. These test vertices serve as starting points for the main
vertex search algorithm. In this search, BONSAI employs simulated annealing. In
nature, annealing is the process of heating and cooling a material, producing larger
crystals if cooled sufficiently slowly, reducing defects in the material. Simulated
annealing is used in search algorithms to find a global maximum when local maxima
are extreme enough for traditional algorithms to misidentify them as global. It isanalogous to the natural process in that the system’s “temperature” begins high,with more aggressive search patterns, and is slowly decreased to zero, at which
point the algorithm completes its search and “freezes”.
In BONSAI’s case, the temperature of the system is the range of likelihoods
that vertices must fall within to remain active, defined by a tuneable percentageof the difference between the best and worst fits. From the starting vertices, thelikelihood is calculated for a set of twelve neighbouring vertices. These points aredefined by the area vectors of a dodecahedron z-aligned with the reconstructed
direction of the origin vertex. An optimal thirteenth point is also determined from
3D quadratic interpolation of the other twelve. All vertices that fall within therange of likelihoods of the origin remain active, and form a new “branch”. This
process is repeated along each branch, successively reducing the active likelihood
range. If the vertex around which new vertices are calculated itself has a likelihood
within the current allowed range, a new set of 12+1 vertices are evaluated in the
successive iteration, this time within a reduced radius around the origin vertex.
This process fine-tunes the location of vertices with a strong likelihood, resulting
in a high-precision fitted vertex once the system freezes.

3. Super-Kamiokande

40

This process means a small fraction of the volume of the detector is explored,significantly reducing the number of computationally expensive likelihood calculations. It also results in a fine-tuned vertex not necessarily linked to the original
grid of vertices tested in the case of a brute-force grid search.
In addition to the likelihood, a goodness criterion is evaluated for the final
vertex ⃗v , given byg(⃗v ) =NXhitswi e−0.5((ti −|⃗xi −⃗v|/c)/σ)

2

(3.3)

i=1

where wi are Gaussian hit weights based on the resolution of the hit time
residuals (60 ns), ti are the PMT hit times, ⃗xi the PMT hit locations and σ is theeffective timing resolution for Cherenkov events (5 ns) [61]. This acts as a powerfultest of the timing residual coincidence and is used in many analyses.
The direction is fit using a weighted average of all PMT hit vectors from the fitted
vertex. Each hit is weighted by its likelihood multiplied by the Gaussian functionof the hit time residual. This method also produces cos θC for the Cherenkov cone
half angle θC . While this is used in high energy analyses to determine the energy ofthe particle, as mentioned in section 3.2, for low energy events it is more accurate
to simply count the effective number of PMT hits with some considerations. Thisis also known as the effective number of hits, denoted Nef f . The calculation of
Nef f considers the TOF, number of active PMTs, dark noise rate and various
other factors, described in [20]. A fourth-order polynomial function is used toconvert Nef f to energy, obtained from MC simulations and tuned and validated
using LINAC and deuterium-tritium (DT) calibration.
Though not strictly a part of the BONSAI reconstruction, two variables, known
as OVAQ and effWall, are often used as a quality metric for events, calculatedusing BONSAI information. OVAQ is defined as
OVAQ = g 2 − DirKS2(3.4)

3. Super-Kamiokande

41

where g is the BONSAI goodness (equation 3.3) and DirKS is a directional KS
test of the PMT hit pattern. OVAQ was found to be a powerful general-purpose
measure of event reconstruction quality and is used in many low energy analyses.
The second variable, effWall, is defined as the distance from the vertex to thewall of the tank, along the negative of the reconstructed event direction. Given
that a large amount of the low energy backgrounds in SK originate in the wallsof the ID, especially from the PMT glass, cuts on effWall can significantly reduce
background rates. The distance along the positive event direction (toWall) as wellas the closest distance from the vertex to the wall (fromWall) are also used in
SK analyses, though less so than effWall.

3.6

The Wide-Band Intelligent Trigger (WIT)

Prior to 2015, the main triggering in SK was handled by hit-counters. The numberof PMT hits in a 200 ns window is checked against a number of thresholds, issuinga trigger corresponding to the highest threshold it passes. There is also an OD
trigger, flagging an event if the number of OD PMT hits exceeds a threshold, used
to remove events entering from outside the ID. There are four levels of trigger
thresholds, detailed in table 3.2. Events passing these thresholds trigger the DAQ
to save a 40 µs time window of hits centred on the 200 ns trigger window, or 1.3 µs
in the case of the super low energy (SLE) trigger, given the high data rate in thisregime. In the case of a super high energy (SHE) trigger with no OD trigger, anafter (AFT) trigger is also issued. This saves all hits in a 500 µs window after the
initial trigger window, with the aim to save neutron captures and other secondary
particles such as those produced in spallation.
The abundance of background in the low energy regime is reflected in the high
SLE trigger rate. 34 PMT hits corresponds approximately to an energy thresholdof 3.7 MeV, assuming 12 hits due to dark noise. The SLE trigger is effectively thelowest a simple hit-counter threshold can be set without overloading SK’s DAQ
systems and quickly filling up long term storage.

3. Super-Kamiokande
Name
Super Low Energy
Low Energy
High Energy
Super High Energy
Outer Detector

42
Abbreviation
SLE
LE
HE
SHE
OD

NHits Threshold
Rate
34≈15 kHz47∼40 Hz50∼10 Hz52≈60 Hz22
Unknown

Table 3.2: Hit-counter trigger thresholds and their approximate trigger rates in SK as of
September 2021. The range of hits for the triggers do not overlap; for example, the SLE
trigger only activates for events with 34-46 hits in the trigger window. The OD trigger is
not independently monitored and is only considered when an ID trigger is activated.

To lower the energy threshold further, the nature of the background contributing
to the trigger rate must be considered.

At low energies, the background isoverwhelmingly due to dark noise, as well as radioactive decay in the glass andfibreglass casings of the PMTs. The radioactive decay events typically reconstructclose to the PMT plane as a result, which motivates the SK fiducial volume
boundary being set 2 m from the PMTs. If the vertex of an event can be quickly
reconstructed online, a fiducial volume requirement can be applied to events before
being sent to long term storage. The quality of the event and its reconstruction
can also factor into this decision.
The Wide-band Intelligent Trigger was introduced to the SK triggering systems
in 2015, aiming to take a more nuanced approach to online triggering in supportof pushing the energy threshold of SK as low as possible [62]. WIT reconstructs
events in stages of increasing granularity and by extension processing time. This
gives the ability to reject events at each stage based on their reconstruction vertex
and quality, minimising processing power being wasted on events that are of low
quality or that were likely produced outside of the fiducial volume.
Despite its intelligent nature, the vast majority of the data that WIT collects isdark noise and radioactive decay events, simply as a symptom of operating so close
to the Cherenkov threshold. Regardless, it is an extremely powerful system as it
independently triggers on these low energy events without being overwhelmed, in
contrast to the hit-counter triggers which must rely on after-triggers to higher energy
events, with reduced efficiency. There is also an advantage to the large amount of

3. Super-Kamiokande

43background in WIT: unprocessed WIT data can be collectively treated as backgroundfor the purposes of optimisation of sample selections and tracking background rates.
For a given window of data in WIT, the total event rate is many orders of magnitude
higher than the rate of neutrino interactions in WIT’s energy range, providing alarge collective background sample. This is described in more detail in chapter 6.
There are 6 key stages to WIT:
1. Pre-Trigger
Akin to the existing hit counters, a pre-trigger rejects events with less than acertain number of hits in a 230 ns window, corresponding to the longest time
for light to traverse the SK tank with an extra 10 ns to give some leeway. This
number is not fixed, but is a certain threshold of hits above a dynamicallycalculated dark noise rate. The dark noise rate is typically around 12 in
SK-Gd, and the threshold above dark noise is currently set to 12. In SK-IV
the threshold was set to 11; however, an increase in trigger rate following
the 2018 tank open motivated a higher threshold. Although this trigger rate
began to decline, it again increased following Gd loading, and so the threshold
will likely remain at 12 for the foreseeable future.
2. Simultaneous Trigger and Online Reconstruction (STORE) Goodness
The first stage of BONSAI is then used to generate a set of test vertices.
These are calculated using combinations of four PMT hits, detailed in section
3.5. For each vertex, the TOF-corrected coincidence of PMT hits in a 5 ns
window is calculated, given by

STORE goodness =

NX
hits
i

∆ti
exp 0.5
5 ns

!2

(3.5)

where ∆ti is the TOF-corrected hit time for the ith PMT. ∆ti is calculated
simply by∆ti = ti −|ve − vi |− tecgroup(3.6)

3. Super-Kamiokande

44

for uncorrected hit time ti , hit vertex vi and emission time and vertex te andve . Given the powerful timing resolution1 of the SK PMTs of ∼3 ns [63], thisserves as a strong discriminator to identify events with a large number ofcoincident hits, indicating a true event.
The highest STORE goodness for all test vertices is selected. If this goodness
is below 0.6 × the pre-trigger threshold, the event is discarded. Additionally,
if the goodness exceeds 1 × the pre-trigger threshold the event is deemed tohave particularly coincident hits, relaxing some later trigger requirements.
Figure 3.8 shows how the distribution of STORE goodness for background
events is shifted downwards when compared to reactor positrons and Gd
captures, with a sharper fall-off at higher values. Hydrogen capture events
also have a higher distribution than the background; however, far less so than
Gd capture.

Compared to the vast majority of PMTs in use worldwide, the timing resolution of the PMT
design used in SK is relatively poor. This is due to the large size of the photocathode surface
necessitating a longer travel time for the photoelectrons from the point of emission to the dynode.
This travel time is significant; however, when considering the travel time of light throughout thedetector, it is comparatively small.
1

3. Super-Kamiokande

45

100

Gd Capture
H Capturee + from Reactor e
BG

10 1
10 2
10 3
10 4
10 5
5

10

15
20
STORE Goodness

25

30

Figure 3.8: STORE Goodness for simulated events and raw WIT data (BG). Events
below the black line (in the hatched region) are rejected in WIT.

3. Clus-Fit Fiducial Volume
A vertex is reconstructed using the Clus-Fit fast fitter algorithm. This fitter
defines clusters of PMTs which may contribute to the event, constrained by
the 5 ns window of STORE and merges the largest clusters to form a set of
PMTs from which the vertex is reconstructed in a process similar to BONSAI.
An initial fiducial cut is then applied to this event, unless STORE flagged theevent as having highly coincident hits. Given the relative low fidelity of theClus-Fit vertex, events must be at least 1 m from the PMT wall, in contrast
to the typical 2 m cut in most SK analyses. It is possible an event may fail toreconstruct using Clus-Fit due to a lack of good PMT hit clusters. In thiscase, if STORE flagged the event as having highly coincident hits this step isskipped, otherwise the event is discarded. Figures 3.9 and 3.10 show the large

3. Super-Kamiokande

46

number of events that reconstruct through Clus-Fit close to the PMT wall,removed with this cut.

0.0040

Gd Capture
H Capturee + from Reactor e
BG

0.00350.00300.00250.00200.00150.00100.00050.0000

0

250

500

750 1000 1250
r [cm] (Clus-Fit)

1500

1750

Figure 3.9: Radial position for simulated events and raw WIT data (BG) that pass thepreceding stages of WIT, reconstructed by Clus-Fit. Events above the black line (in thehatched region) are rejected in WIT.

3. Super-Kamiokande

47

Gd Capture
H Capturee + from Reactor e
BG

0.000400.000350.000300.000250.000200.000150.000100.00005
0.00000

2000

1500

1000

500
0
500
h [cm] (Clus-Fit)

1000

1500

2000

Figure 3.10: Height of simulated events and raw WIT data (BG) that pass the preceding
stages of WIT, reconstructed by Clus-Fit. Events outside of the two black lines (in thehatched region) are rejected in WIT.

4. BONSAI Fiducial Volume
A lightweight version of the BONSAI fit with faster annealing is then performed, using the test vertices generated as part of the STORE step as thestarting points. This fit considers all PMT hits from 0.4 µs before to 1 µs
after the Clus-Fit fitted vertex. Given the higher quality of fit in this step,
the full fiducial cut is applied, removing events which reconstruct within 2 mof the PMT plane. Figures 3.11 and 3.12 show how a significant number of
events which pass the Clus-Fit fiducial volume cut reconstruct within 1 m of
the PMT wall with the more accurate BONSAI reconstruction.

3. Super-Kamiokande

48

Gd Capture
H Capturee + from Reactor e
BG

0.00100.00080.00060.00040.00020.0000

0

250

500
750
1000 1250
r [cm] (Online BONSAI)

1500

1750

Figure 3.11: Radial position for simulated events and raw WIT data (BG) that pass
the preceding stages of WIT, reconstructed by BONSAI. The disconnect in the BG
distribution at the trigger threshold is a symptom of the WIT process applying FV cuts
to some events, and is not physical. Events above the black line (in the hatched region)are rejected in WIT.

3. Super-Kamiokande

49

Gd Capture
H Capturee + from Reactor e
BG

0.00040.00030.00020.00010.0000

1500

1000

500
0
500
h [cm] (Online BONSAI)

1000

1500

Figure 3.12: Height of simulated events and raw WIT data (BG) that pass the preceding
stages of WIT, reconstructed by BONSAI. The disconnect in the BG distribution at thetrigger threshold is a symptom of the WIT process applying FV cuts to some events, andis not physical. Events outside of the two black lines (in the hatched region) are rejected
in WIT.

5. BONSAI Goodness
In response to the high trigger rate of SK-V an additional cut was introduced
which removes events with a BONSAI goodness below some threshold. This isan evaluation of the timing residuals of PMT hits following TOF-correction,
discussed in more detail in section 3.5. This threshold was set to 0.3 in early
SK-V, shown in Figure 3.13 to be a relatively loose cut, removing the tail ofthe BG distribution.

3. Super-Kamiokande

50

Gd Capture
H Capturee + from Reactor e
BG

6
5
4
3
2
1
0

0.1

0.2

0.3

0.4
0.5
0.6
BONSAI Goodness (Online)

0.7

0.8

Figure 3.13: BONSAI goodness of simulated events and raw WIT data (BG) that pass
the preceding stages of WIT. Events below the black line (in the hatched region) arerejected by WIT.

6. N18
Finally, the number of hits in an 18 ns window around the BONSAI vertex iscounted, acting as a final hit coincidence metric. Despite its simplicity, N18 is
a powerful discriminator, with the majority of BG events having a particularly
low N18, as seen in figure 3.14. The N18 threshold is currently set at 9.

3. Super-Kamiokande

51

Gd Capture
H Capturee + from Reactor e
BG

0.30
0.25
0.20
0.15
0.10
0.05
0.00

0

10

20

N18

30

40

50

Figure 3.14: N18 of simulated events and raw WIT data (BG) that pass the preceding
stages of WIT. Events below the black line (in the hatched region) are rejected by WIT.

Given its computationally intensive nature compared to the other SK triggers,
WIT requires dedicated hardware, independent of the primary SK DAQ dataflow.
WIT consists of ten computers. Eight are from the original WIT installation, eachconsisting of two 2.7 GHz Intel Xeon E5-2680 CPUs (8 physical cores, 16 hyperthreaded). Seven of these machines have 62 GB of DDRIII RAM and are tasked
with running the main WIT execution; they are worker machines processing thereconstruction and triggering described above. The eighth machine has 256 GB of
RAM. This is the organiser machine, tasked with receiving the data from the other
WIT machines and organising the events in time order. Two additional worker
machines were installed after WIT’s initial deployment, each with two 2.6 GHzIntel Xeon Gold 6132 CPUs (14 physical cores, 28 hyper-threaded) with 125 GB of
DDRIII RAM. New WIT machines are expected to be installed sometime in 2022.

3. Super-Kamiokande

52

The organiser is the main bottleneck of the WIT data flow. Data does not arriveat the WIT machines in time order, instead arriving in data blocks as described in
section 3.3. While the events within a given block will be time-ordered, the blocks
themselves will be processed across the main WIT worker machines asynchronously.
This is the reason for the larger memory allocation to the organiser machine. Alldata must be collected by this machine, organised, then transferred to long term
storage. If the organisation takes too long, the machine’s memory will become fulland the WIT worker machines must hold onto their data until space is available. Ifthey themselves run out of memory, the main DAQ is instructed to stop sending
data to WIT until the system can recover. In rare cases, the automatic processes
dictating the flow of data may not catch such a backlog, resulting in memory
overflow errors and the crashing of the WIT machines.
To prevent such issues, the various trigger values are tuned to produce a data
rate a little below the maximum the organiser can handle. This means in thecase of an increased event rate, WIT will still be able to continue as normal or,in extreme cases, temporarily keep data on the worker machines until the rate
decreases and the organiser recovers.
The WIT machines hook into the SN watch system, which would read out all
events from SK in the case of a supernova. Data is directly handed to SN watch,with no triggering, in a data stream shared with WIT. This gives WIT access to SK’s
raw data before any kind of reduction is applied. The drawback of this approach isthat, in the case of a supernova, data is no longer sent to WIT as priority is given
to the SN system. There are efforts, however, to instead maintain the data flow to
WIT during an SN neutrino burst in an effort to improve the efficiency of detecting
neutron captures and other low energy events during the burst.
Once data has been saved by WIT and transferred to the SK computing cluster,
the complete BONSAI reconstruction is run on each event, providing more accurately
reconstructed event information with which to apply a first reduction to the data.
Given the large number of events passing through WIT, even with the online cuts,
the first reduction process is crucial to retain a manageable amount of data. In

3. Super-Kamiokande

53

the typical WIT first reduction, some minor, energy-dependent cuts are applied,
namely on OVAQ and effWall which removes the majority of all events fromthe data. Since March 2020, WIT can identify pairs of temporally and spatiallycoincident events in the online data (discussed in section 4.5) and apply relaxed
trigger requirements in these cases. Such events have specific trigger ID numbers
and so in parallel to the main WIT first reduction, coincident pairs are fullyreconstructed and saved regardless of their event quality. These do not make up
a significant portion of the raw data, and so it is reasonable from a storage space
perspective to retain all pairs of events.

3.7

Monte-Carlo

The vast majority of analyses in SK take a Monte Carlo (MC) approach topredicting detector response. This process involves simulating the intricacies ofparticle interactions in the materials throughout SK as well as their Cherenkov light
production. The PMT responses and their dark noise signals must also be simulated.
SK’s standard MC production is primarily handled by the SKDetSim detector
simulation software. This is built on the GEANT-3 particle simulation platform[64], an extensive suite of FORTRAN-based MC libraries. The long operational
history of SK has allowed for a large amount of development and validation of
SKDetSim, crucial to understanding the detector’s response in support of a wide
range of analyses. GEANT-3 has been superseded by Geant4 (now stylised without
all-caps), primarily built in C++ [65]. A new version of SKDetSim called SKG4
which utilises this is in limited use, motivated by GEANT-3’s inability to accurately
simulate neutron capture on gadolinium [66], a requirement of the SK-Gd phase of
the experiment (chapter 4). Analyses not utilising SKG4 typically model neutron
capture externally, and the produced gamma cascade vertex information is used
as input to SKDetSim. SKG4 is still in its early adoption phase, and so all MC
production in this work was handled by SKDetSim.
The dark noise rate of the PMTs in SK is frequently measured and SKDetSim
is updated to account for this; however, correctly modelling the pattern of dark

3. Super-Kamiokande

54

noise “hits” throughout the detector is of particular importance at energies wherethese dominate over true hits of Cherenkov light. To minimise inaccuracies in thereconstruction quality of events due to this effect, MC production for WIT studies
involves injecting simulated events into real data. The events are simulated using
SKDetSim, but with the dark noise rate of the PMTs set to zero. This results inevents with exclusively true hits. A modified version of the standard WIT dataprocessor takes these events and overlays them onto raw data taken after the DAQ
but before WIT processes the file. The program then processes the file essentially as
if it were a real data file, which means that MC events will not be saved naturally ifthey do not pass WIT’s requirements. To track the MC which was injected into thefile, an additional process forces the reconstruction of all of the injected MC events,
no matter the event quality, using the true timing as the centre of the event window.
This often results in MC events being duplicated in the final file: one version
which was forced to save with the event window centred on the true event time,and another which was saved naturally if WIT deemed it a good event based on its
trigger values. The former version of the event should be avoided in most cases,
as it will generally have superior reconstruction quality to the latter given thatthe starting point of the reconstruction is at the correct time vertex. These events
are trivial to remove as they are saved with a unique trigger identification number
which indicates that they are MC events forced to save.
The issue comes when identifying the MC events which saved naturally, as there
is no clear identifier separating them from events which WIT naturally identified in
the data file. Such events cannot necessarily be tagged as MC on reconstruction, as
the concept of what deems whether it truly is an MC event is somewhat abstract.
The data file used for MC injection will contain numerous events that WIT
deems an eligible event. When injecting a large number of MC events into a data
file, there is a chance that such an event would overlap with an injected MC event.
In these cases, the MC event itself may not pass the WIT thresholds; however, it
may contribute a small number of hits to the event from the file which may or may
not factor into the reconstruction. The simple presence of MC hits in an event is

3. Super-Kamiokande

55

therefore not a good indicator of an MC event that naturally saved. If instead the
MC would’ve produced a good event in isolation, the overlap with another event
can skew the reconstruction to produce a vertex not indicative of the injected event.
Practically, the vast majority of events do not experience an overlap with eventsin the real data; however, such events must be avoided so as to not skew the sample
selections, especially as events which overlap will inherently produce more hits andwill likely form a higher quality event. To identify the MC events in the file, thereconstructed time of events is compared to that of the nearest simulated event
time, stored in the file for all events produced in SKDetSim. Events from thedata file will be randomly distributed in time, so only a small number will fallclose to the true emission vertex. The reconstructed vertex of MC events, however,will be temporally close in the case of at least reasonably accurate reconstruction.
Events greater than 150 ns from the MC vertex are therefore rejected, resulting
in an MC sample with > 99% purity.

4

A Gadolinium Loaded Super-K
Contents
4.1
4.2
4.3
4.4
4.5

4.1

Motivation . . . . . . . . . . . . . . . . . . . . . . . . . .
Water Systems . . . . . . . . . . . . . . . . . . . . . . . .
EGADS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deployment and Validation . . . . . . . . . . . . . . . .
WIT Coincidence Trigger . . . . . . . . . . . . . . . . .

56
57
59
61
63

Motivation

As discussed in section 2.4, inverse beta decay is the dominant interaction channel
for electron antineutrinos of a few MeV, producing a positron and a neutron. These
neutrinos originate from numerous neutrino sources of interest to Super-Kamiokande.
Given the high amount of background in this energy regime, IBD searches in SK
typically require the detection of a delayed neutron capture in coincidence witha prompt positron event. In SK’s pure water phase, the neutron would capture
on a hydrogen atom after ∼200 µs, producing a 2.2 MeV photon. Such a photon
goes on to scatter atomic electrons that in turn produce Cherenkov light. Given
the low energy, very few PMTs detect light in these events; on average, only 7 willregister a hit. Neutron capture events are therefore usually lost to the main SK

56

4. A Gadolinium Loaded Super-K

57

trigger system, and so either the WIT or 500 µs after trigger systems (see section
3.6) are employed in neutron capture searches. According to Monte Carlo studies,
WIT is approximately 17% efficient at detecting fiducial 2.2 MeV photons.
To greatly improve the detectability of neutron captures in SK, in 2003 Beacom
and Vagins proposed GADZOOKS! (Gadolinium Antineutrino Detector Zealously
Outperforming Old Kamiokande, Super!), an upgrade to Super-Kamiokande throughthe doping of its water with 0.2% gadolinium trichloride by mass [44]. Natural
gadolinium’s neutron capture cross section is 48,800 b, ∼ 100, 000× larger than thatof free protons. At the proposed concentration, this results in a mean capture timeof ∼30 µs, 10× shorter than in pure water. Additionally, when a neutron captures
on gadolinium it releases an 8 MeV gamma cascade. These cascades result in around
23 PMT hits, a far more distinct signal in comparison to hydrogen capture and
one which WIT is approximately 100% efficient at triggering on.
A long process of research and development supported this project, including
the move away from gadolinium chloride hexahydrate to using gadolinium sulphateoctahydrate1 Gd2 (SO4 )3 · 8 H2 O, thanks to its lower reactivity while retaining easy
dissolution and Cherenkov light transparency. GADZOOKS! was realised as the SKGd phase with two planned stages: a first deployment 0.02% gadolinium sulphateby mass, ensuring approximately half of all neutrons are captured by gadolinium,
before later increasing to the GADZOOKS! proposed loading of 0.2% with a ∼90%
Gd neutron capture rate. The first phase successfully completed its deployment
in July of 2020 [1] and loading for an interim phase where the concentration wasincreased to 0.06% finished in July of 2022.

4.2

Water Systems

In its pure water phase, SK’s water systems strived to remove any and all impurities
from the water, resulting in exceptional water purity. If the water were doped withgadolinium sulphate in this configuration, it would quickly be removed by these
Gadolinium sulphate or more simply gadolinium is often used to refer to the full molecularform as a short hand.
14. A Gadolinium Loaded Super-K

58

systems which continuously circulate and purify the water. A challenge is therefore
presented: retain the level of water purity and hence transparency of SK’s purewater phases without removing the gadolinium sulphate. This required developmentof new, bespoke water systems specific to the SK-Gd phase, first to dissolve andpre-treat the Gd2 (SO4 )3 · 8 H2 O and then to continuously circulate and purify thegadolinium-loaded water. A schematic of these systems is shown in figure 4.1.
Gd2 (SO4)3 8H2O

Dissolving system
Weighing hopper
Circle feeder

UV

Solution tank Dissolving Solvent tank
tank

2400L

0.2 m

2400L

Shear blender

1 m
1 m Dissolving system bypass line
A-Ex C-Ex TOC
Resin Resin

Pretreatment system

Returnwater ﬁlter

Main return line

1st buﬀer tank

2400L

4600L

C-Ex A-ExUVResinResin
1 m

Pump

2nd buﬀer tank Temp. control

UF

Supply HE
pump

4600L

2400L

TOC HETOC HE C-Ex A-Ex 1 m UVResin Resinunit AUF

Temp. control
unit BMD
SK tankHEbottomRe-circulation system

Returnpumps

Figure 4.1: Schematic of the SK-Gd water systems [1].

First, a measured amount of Gd2 (SO4 )3 · 8 H2 O powder is fed into a buffer tank
via a circle feeder where it is dissolved in water taken directly from the SK water’srecirculation feed. The solution is then transferred to the pretreatment system,
responsible for removing all substances from the water other than gadolinium andsulphate ions. Pretreatment begins with a passive 1 µm filter before irradiation
with ultraviolet light designed to remove any organic impurities by oxidising carbon

4. A Gadolinium Loaded Super-K

59

and other compounds. The light is delivered using a total organic carbon reduction(TOC) lamp. To remove inorganic, ionised impurities, the specially prepared
AMBERJET™1020 [67] and AMBERJET™4400 [68] ion exchange resins remove
positive and negatively charged impurities respectively. These resins are specificallydesigned to retain the gadolinium sulphate. The solution is then sent througha 1 µm filter, further UV sterilisation and finally a 0.2 µm filter, all designed toremove bacterial contamination.
The pretreatment system is only used during initial Gd loading; however, therecirculation system which continuously cycles and treats the water largely mirrors
pretreatment with some modifications. The final, 0.2 µm filter is replaced by aset of ultra filtration (UF) modules and a heat exchanger is included to carefully
control the temperature of the water. The water is kept at 12°, primarily tolimit bacterial growth that may reduce the water purity and dirty the detector
components. Additionally, a membrane degasifier is included, primarily to remove
dissolved radon gas from the water. The recirculation system is duplicated, with
two lines running in parallel supporting a flow rate of 60 m3 h−1 through each line.
This allows for maintenance on one line while the system continues to treat thewater, albeit at a lower flow rate. Any water which is rejected by the recirculation
system is returned to a buffer tank upstream so it can be reprocessed.

4.3

EGADS

Before full-scale deployment for SK-Gd, the unique water treatment systems weredeveloped and tested first in small scale at the University of California, Irvine (UCI),
before scaling up to a test bed known as EGADS (Evaluating Gadolinium’s Action
on Detector Systems) [69]. Shown in figure 4.2, EGADS is a 200 t detector utilising
the same components and construction techniques as SK, serving primarily as atest platform for SK-Gd, based in the Kamioka mine. Though lacking an OD, it
otherwise acts as a scale version of SK, instrumented with 240 PMTs, 224 of which
are the 50 cm Hamamatsu R3600-05 design used in SK’s ID. The remaining 16 areof various designs that will potentially be used in Hyper-Kamiokande.

4. A Gadolinium Loaded Super-K

60

Figure 4.2: The EGADS hall.

As well as serving as a proof of the water systems’ capabilities, EGADS also
addressed two main challenges regarding Gd loading.
First, SK’s size introduces particular importance in retaining the Cherenkov
light transparency; a significant loss of light attenuation length would affect all
analyses utilising SK. To monitor this, the UDEAL (Underground Device Evaluating
Attenuation Length) system was deployed to measure the light attenuation length
in water from EGADS for a range of wavelengths. UDEAL showed that, outsideof short reductions when first loading gadolinium, the light attenuation length
remained within the range of SK-III and SK-IV values.
Another challenge with Gd loading arises with a property of gadolinium inthat it promotes rusting in untreated metals. SK’s tank and structure are bothconstructed of stainless steel which should resist this; however, understanding theeffect of gadolinium-doped water on its numerous other submerged components
as well as long term exposure to stainless steel is crucial. EGADS sought out tobe as close an analogue of SK as possible, even down to its stainless steel bolts.

4. A Gadolinium Loaded Super-K

61

Gadolinium was first loaded into EGADS in 2014 and after two and a half yearsof running in SK-Gd conditions with full Gd loading, the tank was emptied andthe inner structure was inspected. No deterioration was found.

4.4

Deployment and Validation

To house the extensive SK-Gd water systems, a new cavern named Hall G was
excavated in the Kamioka mine in close proximity to the SK experimental hall.
The existing water systems were also modified to accommodate the new water
treatment process.
In 2018, the SK tank was opened for maintenance for the first time in 12 years.
This maintenance largely consisted of: cleaning the structure and tank of SK of any
rust and debris; replacing dead PMTs in both the ID and OD; replacing the Tyvek
sheets in the OD; fixing any leaks from the tank; and installing upgrades to thewater system. SK is a powerful supernova neutrino burst detector and as such any
downtime such as this maintenance is minimised to maximise the chance of catchinga galactic supernova. To ensure a speedy maintenance period, the cleaning of thestructure and Tyvek and PMT replacement was largely a joint effort of SK and
T2K collaborators. Maintenance of the tank and support structure was primarily
carried out by employees of the Mitsui Engineering and Shipbuilding company. It
is crucial that, when gadolinium-loaded, SK’s water must not leak from the tankinto the surrounding environment. Following the 2018 maintenance, measurements
indicated no detectable leak, with a limit of < 15 kgd−1 .
After refilling, a minor modification of the ID inlet pipes was required to preventa convection pattern forming, disturbing the water in the tank. These pipes arefound at the bottom of the ID and required the fitment of a diffuser. In lieu ofthe long process of draining the majority of the tank to fit the diffusers by hand, aremotely operated underwater drone was employed, provided by the Mitsui company.
The drone had a diffuser attached to its underside and was manoeuvred above
the inlet pipes and gently lowered. Once the diffuser was seated, the drone would
separate from the diffuser. Now lighter, the drone would float to the surface of4. A Gadolinium Loaded Super-K

62

Figure 4.3: The conductivity of water samples taken at a range of heights throughout
the SK ID over the course of first Gd loading, in 2020. The sampling system encounteredissues between the 23rd and 29th of July.

the water where it would be recovered and fitted with another diffuser to repeat
the process. A second drone was provided by the Canadian national laboratory
TRIUMF to help guide the drone and monitor the drone’s tether. This operation
was the first use of drones to carry out maintenance in SK and prevented a long
downtime that would be needed to drain the tank.
Initially planned for March 2020, the COVID-19 pandemic delayed the first
Gd loading to July 14th, 2020 at 10:29. Gd-loaded water was pumped to thebottom of the tank at a rate of 60 th−1 . To monitor the rise of the Gd-water front,
water was sampled each day at a range of heights throughout the detector andthe conductivity was measured. Ultrapure water has low conductivity, but thepresence of the charged ions of gadolinium sulphate significantly increases this,so the conductivity of the samples can be used to differentiate between pure andGd-loaded water. As shown in figure 4.3, a clear Gd front was observed duringloading, advancing at a rate of approximately 1.5 md−1 , as expected. Gd loading
concluded on the 17th of August, 2020 with no major issues.
Both during and after the loading, the concentration of Gd2 (SO4 )3 · 8 H2 O

4. A Gadolinium Loaded Super-K

63

was accurately measured with an atomic absorption spectrometer (AAS) using
water sampled at various positions throughout the tank, alongside the conductivity
measurements. Once loaded, the average Gd2 (SO4 )3 · 8 H2 O concentration was
found to be (271 ± 4) ppm, corresponding to an ionic gadolinium concentration of(114 ± 2) ppm, with uniformity throughout the tank. This confirmed the desired
homogeneity and concentration of the Gd loading.
To further verify the presence of gadolinium sulphate at the expected concentration, the neutron capture time was measured using an Americium-Beryllium(AmBe) source embedded in a bismuth germanate (BGO) crystal. AmBe produces
a 4.4 MeV gamma and a neutron when it decays. The gamma scintillates in the
BGO crystal and the resulting scintillation light can be used to fix the neutron’semission time and tag the decay event. Neutron capture times were measured in
November of 2020 using AmBe in various positions throughout the detector, an
example of which is shown in figure 4.4. Fitting provides a neutron capture time of(115 ± 1) µs which corresponds to a gadolinium ion concentration of (111 ± 2) ppm,
in agreement with the AAS measurements.
More gadolinium was loaded into SK’s water in the summer of 2022, from June
1st to July 5th to increase the gadolinium concentration up to 0.06% by mass,acting as an interim phase before loading to the full targeted concentration of 0.2%.
No date is currently set for this final Gd loading.
A wide range of analyses utilising neutron capture are now underway at SK
with vastly improved sensitivity. Though the main motivation for SK-Gd was tomeasure the DSNB, many other analyses benefit from the gadolinium loading. In
particular, the identification of reactor neutrinos for the first time in SK would bea momentous achievement only made possible through gadolinium loading.

4.5

WIT Coincidence Trigger

In searches for relatively low rate events like reactor neutrino interactions, efficiency
must be maximised where possible. While the events that fail WIT’s requirements
are inherently of a lower reconstruction quality, it is crucial in an IBD searchNumber of events [/5µ s]

4. A Gadolinium Loaded Super-K

900

64

Fit Function

800! " = $% ∗ ' − )*$ −

+
,. .

700

∗ )*$ −+
+ $0$'

Fit Results:
p0: 946.0 ± 13.4
p1: 119.9 ± 2.69
P2: 38.4 ± 3.0

600
500
400
300
200
100

3

0
0

100

200

300

400

500
Time [µ s]´10Figure 4.4: An example of neutron capture times and the resultant fit for 30 mins of
AmBe calibration data with the source placed in the centre of the detector. Measurements
were carried out for a range of source placements.

that both the positron and neutron capture are identified to correctly tag theinteraction. In SK-Gd the efficiency of tagging neutron captures has significantly
improved and to fully capitalise on this WIT must ensure that even low quality
positron events are saved.
WIT’s original configuration considered events in isolation. A relaxation of
trigger requirements would therefore apply to all events that reach WIT. In theparticularly low-energy, high-background regime close to the Cherenkov threshold,this results in a significant increase in background rate. WIT’s trigger thresholds
are effectively set at a point where minor fluctuations in rates can be handled, butloosening these cut criteria quickly reaches a point where WIT, or more specifically
the WIT organiser, cannot keep up with the data rate.
The dominant sources of background in WIT produce events which are randomly
time-distributed with no expectation of there being any spatial coincidence between
successive events. Coincidence requirements on spatial and temporal distance4. A Gadolinium Loaded Super-K

65

between events therefore act as a powerful discriminator between signal andbackground. Given the frequency of background events in WIT there will still besignificant impurities; however, a coincidence requirement within the WIT system
would allow an increased efficiency of IBD pair detection with a significantly lower
total rate increase compared to reducing the standard trigger thresholds.
To realise this, I modified the logic of WIT’s main trigger process to impose acoincidence cut on all successive events. Events are processed largely the same as inits original configuration; however, events must initially pass a relaxed set of trigger
requirements before being temporarily saved in a buffer. These requirements are
merely lowered thresholds of the same event variables as in the usual WIT process.
The event is tagged with a trigger ID number which represents the highest trigger
threshold it passed: 0 for relaxed, 1 for the usual trigger requirements or 2 for ahigh-level STORE goodness, described in section 3.6.
The next event is then processed, and its vertex is compared to that of theevent in the buffer. If the events pass the preset positional (∆r) and temporal (∆t)
coincidence thresholds, the event in the buffer is saved to file regardless of its trigger
ID and the new event takes its place, flagged as being a coincident event.
The event now stored in the buffer will be saved regardless of its coincidencewith the subsequent event; however, it must still be temporarily stored in memory
to check the next event’s coincidence. Given the trigger rate of WIT, it is entirely
possible that for three successive events, any two may form an IBD pair with thethird being background. It is therefore important to check the coincidence of all
events, even if the buffered event is already in coincidence with its previous event.
Practically, this means that all events are evaluated for coincidence with the buffered
event before replacing it, regardless of the outcome of the coincidence check.
If the incoming and buffered events are not in coincidence, the buffered event
will only be saved if it is flagged with a trigger ID of 1 or 2, i.e. it successfully
passed the normal WIT trigger requirements.
As well as the advantage of increased online pair efficiency, the coincidence
trigger also simplifies the identification of coincidence pairs in the offline data,

4. A Gadolinium Loaded Super-K

New Eventpassespre-trigger

Pass relaxed
trigger?

66

No

Send current
event tobufferSkip

Yes

In coincidencewith buffered
event?

No

Buffered event
passed normal
trigger?

Delete buffered
event

Yes

Yes

Buffered event
flagged as prompt?

No

No

Yes
For buffered
event

Set trigid to[0/1/2]0 for
rlx/nrm/hi.

Set trigid to[0/1/2]1 for
rlx/nrm/hi.

Set trigid to[1/2] fornrm/hi.

Add [32/64]
if [prompt/
delayed]Save buffered
event to file.

Figure 4.5: The logic of the WIT coincidence trigger, including the trigger identification
numbering scheme.

as coincident pairs can be tagged in WIT itself. For events which are first in
their coincidence pairs, 32 is added on to their existing trigger ID and saved withthe event. These prompt events therefore have a trigger ID of 32, 33 or 34 ifthey passed the most stringent out of the relaxed, normal or high levels of trigger
respectively. Delayed events have 64 added to their trigger ID, regardless of if
subsequent events are in coincidence with them. The logic for this trigger ID
scheme and the coincidence trigger as a whole is shown in figure 4.5. Additionally,a unique identifier of the event’s partner is saved. Pair events can therefore beeasily selected in the data through their trigger ID and then matched up with theirpartner through the identifier stored in the event.

4. A Gadolinium Loaded Super-K

67

Gd Pair
H PairSequential BG

0.005
0.004
0.003
0.002
0.001
0.000

0

500

1000 1500 2000 2500 3000 3500 4000
r [cm]

Figure 4.6: The distance between prompt and delayed event vertices for simulated
gadolinium and hydrogen capture, reconstructed by online BONSAI, compared tothe distance between sequential events in a sample of WIT data considered to be
background.Gadolinium concentration is taken to be that after first loading (0.02%
by mass).

With the relaxed thresholds set to that of the normal, the processing time of WIT
with the added coincidence trigger logic was measured to be less than 1% longer ofthat of the original WIT configuration, within typical fluctuations in processing time.
The coincidence requirements for two sequential events are currently set to be∆r < 5 m and ∆t < 512 µs. The ∆r requirement was based on an existing spallationrelated neutron cloud analysis using WIT data, and removes a significant amountof background pairs as seen in figure 4.6 when compared to MC reactor IBD pairs.
The ∆t requirement is minimal, requiring that two events must be within
30 hardware triggers of one another. It can be gathered from figure 4.7 that
this is a less powerful discriminator than the ∆r cut, and was chosen initially toretain as many hydrogen capture events as possible. Especially with an increased

4. A Gadolinium Loaded Super-K

68

Gd Pair
H PairSequential BG

10 2
10 3
10 4
10 5
10 6
0

100

200

300
t [ s]

400

500

600

Figure 4.7: The time difference between prompt and delayed events for simulated
gadolinium and hydrogen capture, reconstructed by online BONSAI, compared to thetime between sequential events in a sample of WIT data considered to be background.
Gadolinium concentration is taken to be that after first loading (0.02% by mass).

Gd concentration following future loading, there is scope to impose a tighter
temporal coincidence requirement.
The WIT organiser is the main bottleneck of the WIT system, with a morethan-linear processing time dependence on the number of events. The main impactof the coincidence trigger on processing time can therefore be measured simply
in the produced data rate. To be effective, the coincidence trigger must allow asignificant increase in IBD rate without significantly increasing the background rate.
Figures 4.8 and 4.9 show that imposing coincidence requirements of ∆t < 512 µs and∆r < 5 m results in no significant increase in background efficiency when relaxing
the STORE goodness and N18 trigger thresholds, while significantly increasing theefficiency for simulated reactor pairs for both gadolinium and hydrogen capture.
Here, the background efficiency is evaluated using sequential events in real WIT

Sequential BG Eff

H Pair Eff

Gd Pair Eff

4. A Gadolinium Loaded Super-K

69

No coincidence cut
With coincidence cut

0.45
0.40
0.35
0.12
0.10
0.08
0.03
0.02
9.0

9.5

10.0
10.5
11.0
11.5
Hit Threshold (STORE Goodness/0.6)

12.0

Figure 4.8: WIT detection efficiencies when relaxing the hit threshold (and therefore
STORE goodness threshold) for all events, and for coincident pairs only. Sequential events
in WIT data (BG) are compared to simulated reactor IBD pairs.

data, i.e. the efficiency of the nth and (n + 1)th events passing the cuts when
paired. The BONSAI goodness threshold of > 0.3 could be considered a relatively
minor cut, so figure 4.10 takes the standard trigger requirement to be a tighter,but still minor, 0.35 to more clearly demonstrate the effect of the coincidence
requirement on background. Especially when combined, these relaxed trigger
thresholds can provide a significant increase in IBD pair detection efficiency withminimal increase in background trigger rates.
The coincidence trigger came online in March of 2020, ahead of Gd loading.
Given the high trigger rate following the 2018 tank open when compared to SK-IV
levels, the trigger thresholds for coincident pairs were initially set to the same as
the normal thresholds, to verify that the coincidence trigger did not interfere withany part of the WIT data stream. In this configuration, events in coincidence would

4. A Gadolinium Loaded Super-K

70

No coincidence cut
With coincidence cut

0.350

H Pair Eff

0.345
0.09

Sequential BG Eff

Gd Pair Eff

0.355

0.08
0.06
0.04
0.02

0.08

6.0

6.5

7.0

7.5
N18

8.0

8.5

9.0

Figure 4.9: WIT detection efficiencies when relaxing the N18 threshold for all events,and for coincident pairs only. Sequential events in WIT data (BG) are compared tosimulated reactor IBD pairs.

still be identified as pairs, but would have to pass the usual WIT requirements.
During Gd loading, the trigger rate increased and in response the normal trigger
values were tightened: the hit threshold was increased from 11 to 12 (therefore
increasing the STORE cut by 0.6), the minimum N18 requirement was increased
from 9 to 10, and a BONSAI goodness requirement of > 0.3 was imposed. The
hit threshold and N18 requirement was also increased for coincident pairs, but
the BONSAI goodness requirement was not introduced. This configuration meant
the coincidence trigger was saving extra events in addition to the normal trigger
scheme; paired events would not need to meet any BONSAI goodness requirement.
No issues were found while WIT ran in this configuration and the extra eventswere seemingly saved correctly.
The trigger rate has effectively stabilised for the SK-Gd period. N18 was4. A Gadolinium Loaded Super-K

Sequential BG Eff

H Pair Eff

Gd Pair Eff

0.348

71

No coincidence cut
With coincidence cut

0.346
0.344
0.342
0.078
0.077
0.076
0.014
0.013
0.20

0.22

0.24

0.26 0.28 0.30
BONSAI Goodness

0.32

0.34

Figure 4.10: WIT detection efficiencies when relaxing the BONSAI goodness thresholdfor all events, and for coincident pairs only. Sequential events in WIT data (BG) arecompared to simulated reactor IBD pairs.

therefore reduced to 9, though the hit threshold was left at 12. There is scope
to reduce the relaxed trigger requirements further, based on the potential gains
shown in figures 4.8, 4.9 and 4.10, especially with the future expansion of the WIT
machines. However, in the interest of simplifying ongoing analyses it is generally
preferable to minimise disruption in the available data, so this has not yet been
fully explored. The reactor analysis specifically assumes the tightest online trigger
thresholds in the period to provide a stable background rate and avoid the need toconsider different signal efficiencies for different periods in the data. As such, WIT
continues to operate such that paired events need not pass a BONSAI goodness
threshold but must otherwise meet the same requirements as singles.

5

Reactor Neutrinos
Contents
5.1
5.2
5.3
5.4
5.5
5.6
5.7

5.1

Nuclear Reactors . . . . . . . . . . . . . . . . . . . . . . .
Nuclear Power in Japan . . . . . . . . . . . . . . . . . .
Neutrino Production . . . . . . . . . . . . . . . . . . . .
Reactor Neutrino Experiments . . . . . . . . . . . . . .
Monitoring Nuclear Reactors . . . . . . . . . . . . . . .
SK-Gd and Reactor Neutrinos . . . . . . . . . . . . . .
Simulating Reactor Neutrinos: SKReact . . . . . . . .

72
79
82
85
89
91
93

Nuclear Reactors

In 1938, expanding on work by Enrico Fermi and his colleagues [70], the teamof Otto Hahn, Fritz Strassman, Lise Meitner and Otto Robert Frisch discoveredthat bombarding uranium with neutrons resulted in the splitting of atomic nuclei[71]. This process was dubbed nuclear fission in reference to binary fission, thename at the time for the splitting of living cells. Fission was observed to produce alarge amount of energy, both through electromagnetic radiation and in the kinetic
energy of the products. This energy stems from the difference in binding energy
between the reactants and products. Following the discovery that more than one
neutron is produced in fission, Leó Szilárd theorised that these could induce further

72

5. Reactor Neutrinos

73

fission, triggering a chain reaction that may yield a vast amount of energy. Given
the advent of World War II, Szilárd advocated for restricting the publication ofthese findings in the interest of preventing development of weapons utilising thischain reaction by foreign powers. He and Fermi then proposed the constructionof a nuclear reactor, using natural uranium as fuel and graphite as a neutron
moderator. The graphite would slow the neutrons to thermal energies, increasing
the cross section of their capture on the uranium, thereby increasing the rate at
which they would induce fission.
Fermi and Szilárd’s proposal was approved and on 2 December 1942, Chicago
Pile-1 (CP-1) became the world’s first artificial, self-sustaining nuclear reactor[72]. It consisted of a wooden frame supporting piles of graphite blocks, assembled
by Fermi and his team. The uranium was fashioned into round-ended rods andembedded in alternating layers of graphite blocks. CP-1 made use of control rods
composed of cadmium, a strong neutron absorber, attached to wooden strips that
could be dropped into the pile to halt the chain reaction. Given the low power CP-1
produced, there was no radiation shielding and the pile was not actively cooled.
The work on CP-1 was absorbed into the newly-formed Manhattan Project,
the Allied efforts to develop nuclear weapons during the Second World War. The
Manhattan Project subsequently produced a range of nuclear reactors with theprimary aim of producing plutonium to be used in nuclear weapons. After thewar, the reactor technologies developed were shared worldwide in the interest of
promoting the use of nuclear power. The first non-research reactor was installed
into the USS Nautilus submarine in January of 1954 followed in June by the first
civil nuclear power plant, the Obninsk-1 reactor in the Soviet Union. The firstcommercial plant reached criticality in 1956 in the United Kingdom.
The fuel typically used in modern nuclear reactors has a much higher 235U
concentration than that used in CP-1. CP-1 used natural uranium, comprisedof 0.7% 235U and over 99.2% 238U.

U is non-fissile in that slow (thermal)

238

neutrons do not induce fission. Under neutron bombardment, however, 238U canproduce 239Pu in the reaction

5. Reactor Neutrinos

U + n → 239U → 239 Np + e− + ν̄e → 239Pu + e− + ν̄e .

238

74

(5.1)

Though 239Pu is fissile, it is a relatively slow process to convert the 238U to 239Pu.
U is therefore the dominant source of fission in natural uranium. A process

235

known as enrichment increases the percentage of 235U by separating the isotopes
in gaseous form in a centrifuge. For use in power reactors, low-enriched uranium(LEU) is sufficient, with about 3–5% 235U, though the definition of LEU extends
to 20% enrichment. Highly enriched uranium (HEU) composed of > 20% 235U
is used in nuclear weapons; however, weapons-grade uranium is typically used inthese applications, with a 235U concentration of > 85%.
Though commercial reactors all use steam-driven turbines to generate electricity,
the method of extraction of this steam varies as well as the general reactor design.
These designs differ in many ways, crucially in the materials used as their coolant
and neutron moderator. There are 443 operable commercial nuclear power plants
in the world [73], each taking one of six forms:• Pressurised water reactor (PWR)
The most common design, PWRs were originally designed for use on submarines and are still used in this capacity. PWRs contain their enricheduranium fuel and control rods within a pressurised vessel full of ordinarywater. The water acts as both the neutron moderator and coolant. The
pressure is kept at a level such that the water heated by fission does notform steam in the main vessel but instead is pumped to an external vessel.
Here the heat is exchanged between the reactor water and an external watersupply without cross contamination. The heated water is allowed to boil tosteam which is used to drive a turbine, generating electricity, before beingcondensed and pumped back into the steam vessel. The reactor water is alsothen pumped back into the reactor vessel for re-heating. An inherent safety
feature emerges in that any failure in the pressure vessel would release thewater as steam, thereby depriving the reactor of its neutron mediator, reducing

5. Reactor Neutrinos

75

the fission rate. Another advantage to this design is that the reactor water is
kept in a closed loop, separate from the water used to drive the steam turbine.
As the reactor water is contaminated with radionuclides, it is preferable tokeep this separate to the water used in power generation, removing the needfor radiation shielding of the generators and easing maintenance.
• Boiling water reactor (BWR)
BWRs remove the secondary vessel and hence separate water loop from PWRs
and instead allow the reactor water to form steam in the top of the main
reactor vessel where it is extracted for power generation, condensation andrecirculation. Though this is a simpler design, the reduced neutron moderationin the reactor vessel results in an overall lower efficiency. Additionally, thesteam turbine must be shielded to prevent damage from the radioactively
contaminated water and maintenance requires radiological protection. An
upgraded design of BWRs known as the advanced boiling water reactor(ABWR) improves many aspects of the design while retaining the core
operating principle and is now in limited use globally. The first ABWR
to reach criticality was unit 6 of the Kashiwazaki-Kariwa plant in Japan in
1995 [74].
• Pressurised heavy water reactor (PHWR)
PHWRs operate under the same principle as a PWR, but use natural uranium
as their fuel. This small fissile fraction warrants heavy water to act as a more
efficient moderator to effectively sustain the chain reaction. Given the low
fissile fuel density, more frequent replacement of the fuel rods is required. Fuelrods are placed in separate horizontal pressure tubes through which the heavy
water flows, in contrast to the large pressure vessel in PWRs. This allows forthe replacement of individual rods without disrupting the operation of thereactor as a whole. Though the energy produced per unit fuel is lower, there
are great cost savings made through skipping the enrichment process.

5. Reactor Neutrinos

76• Advanced gas-cooled reactor (AGR)
These reactors do not use water in their design outside of the steam generators.
Graphite is used as a neutron moderator and carbon dioxide as the coolant.
The reactor is contained within a steel and concrete pressure vessel, into which
the steam heat exchangers penetrate. A development of older gas cooled
reactors (GCRs), specifically the British Magnox reactor designed primarily togenerate weapons-grade plutonium, AGRs offer the option of online refuelling,similar to PHWRs. This reactor design forms the majority of nuclear reactors
deployed in the UK.
• Light water graphite-moderated reactor (LWGR)
As the name suggests, graphite is used as a neutron moderator in LWGRs.
Ordinary water is the coolant and, like in BWRs, is allowed to boil in thevertical pressure tubes surrounding the fuel rods. This design presents a riskin that a positive feedback loop can occur. If the core temperature rises,
more water boils to steam in the vessel. Given the graphite acts as a neutron
moderator, this simply reduces the neutron absorption from the water without
reducing the neutron moderation, increasing the rate of fission. The No. 4
reactor at the Chernobyl Nuclear Power Plant used the Soviet RBMK designof an LWGR and, through a series of missteps, initiated such a loop. A
further flaw in the RBMK design, specifically the graphite tips of the control
rods, meant that initiating an emergency shutdown significantly increased thefission rate, which led to the meltdown at Chernobyl. The design flaws wereaddressed and a number of RBMK reactors have since been in operation forover thirty years with no serious incidents.
• Fast neutron reactor (FNR)
FNRs do not use a moderator and rely on fission induced by fast neutrons.
These high-energy (∼1 MeV) neutrons are sufficiently energetic to induce fission in the non-fissile 238U. 239Pu produces three neutrons in its most common
fission reaction, compared to two or three for 235U. This neutron yield is5. Reactor Neutrinos

77

sufficient to sustain a chain reaction if the fuel is sufficiently enriched, offsetting
the reduced neutron capture cross section of fast neutrons. Additionally, theextra neutrons can be used to breed 239Pu in 238U blanketing the reactor core.
The result is a reactor which can make efficient use of 238U and therefore
increase the energy output per unit fuel compared to other designs, withthe added advantage of greatly reducing the long-lived radioactive isotopes
in spent fuel. A typical coolant in such a design is liquid metal. This has
the advantage of superior heat transfer over water and carbon dioxide gas,
as well as a far higher boiling point. The disadvantage is that liquid metal
is typically more toxic and reactive than water, requiring more robust andtherefore expensive cooling systems. If an FNR produces more 239Pu thanthey consume, they are referred to as a fast breeder reactor (FBR).
The breakdown of reactor types and their commercial usage worldwide as of
September 2021 is given in table 5.1.
Type
PWR

Main Countries Number
USA, France,
304
Japan, Russia,
China, S. Korea
BWR USA,62
Japan,
SwedenPHWR Canada, India
49

GWe
289.1

Fuel
Coolant Moderator
Enriched Water Water
UO2

63.1

AGR

UK

14

7.7

LWGR

Russia

12

8.4

FNR

Russia2

1.4

Enriched
UO2
NaturalUO2NaturalU,enriched
UO2
Enriched
UO2
UO2 ,
PuO2

24.5

Water

Water

Heavy
water
CO2

Heavy
Water
Graphite

Water

Graphite

Liquid None
SodiumTable 5.1: Operable commercial nuclear power plant designs throughout the world [73].
The column “GWe” refers to the total electrical power capacity, measured in GW.

Nuclear power far surpasses the fuel efficiency provided by fossil fuels andis often cited as a viable alternative to gas, coal and oil stations in the face of5. Reactor Neutrinos

78

climate change. Despite this, a small number of high-profile incidents, especially
the Chernobyl disaster, as well as the association with nuclear weapons has resulted
in an often negative public perception of nuclear power. One common criticism
of nuclear power is in regard to its spent fuels. Though nuclear power produces aminute amount of greenhouse gases in comparison to fossil fuels, spent fuel rodspresent environmental risks of their own.
After the immediate halting of fission in a reactor, the flow of coolant must
continue due to decay heat in the fuel. This is the significant heat produced byradioactive decay of short-lived isotopes, amounting to 6–7% of the core’s total heatproduced during fission. While this quickly decreases, spent fuel rods must still be
stored with some form of cooling once removed from the core, often for many years
kept in pools of cycling water which also acts as a shield to the radiation. This
radioactivity is the primary concern with regards to long-term storage of spent fuel.
The half life of elements producing harmful radiation can be ∼ 10, 000 y, requiring
careful, effectively permanent storage of the hazardous waste. Currently, spent fuelis disposed of in dedicated facilities, often in disused mines to minimise exposure to
the environment. FNRs seek to combat this issue of disposal by inducing fission in
the long-lived, fissionable radioactive actinides, leaving only the fission products.
These fission products (primarily strontium-90 and caesium-137) have half lives∼30 y, far reducing the length of time spent fuel poses risk due to radioactivity.
Another complaint from nuclear power critics is regarding the risk of a meltdown.
A meltdown occurs when, through loss of coolant or runaway chain reactions, thefuel rods are heated beyond their melting point. The separate fuel rods may then
combine after melting their housings, increasing the fission rate further and releasinga dangerous amount of energy. A number of meltdowns and criticality incidents haveoccurred in the history of commercial nuclear power, most notably the Chernobyl
disaster in Soviet Ukraine of 1986 and the meltdown at the Fukushima Daiichi
plant in Japan following the 2011 Tohoku earthquake. Despite these events, thescientific and statistical consensus is that the human impact of nuclear power is
one of the most beneficial of all energy sources, rivalling that of renewables like

5. Reactor Neutrinos

79

solar and wind power. Nuclear power plants are, however, particularly expensive
to build and maintain, with long construction times.

5.2

Nuclear Power in Japan

Japan was a strong adopter of nuclear power since its first reactor, Tokai 1, cameonline in July of 1966. By the year 2011, approximately 30% of Japan’s electric
power supply came from its 33 nuclear plants and Japan is home to the largest
capacity nuclear power plant in the world: Kashiwazaki-Kariwa, which also houses
the world’s first advanced boiling water reactor. Japan aimed to provide 40% of
its power through nuclear by 2017. These plans were halted, however, when themagnitude 9.1 Tohoku earthquake struck off of the east coast of Japan’s mainisland of Honshu in 2011. Though all of Japan’s nuclear plants survived the initialquake with no failures, the resulting tsunami triggered the meltdown of cores 1,
2 and 3 of the Fukushima Daiichi plant.
Fukushima’s reactor cores correctly shut down, ceasing fission, upon detecting
the earthquake. Despite this, the flow of coolant is still required due to the decay
heat of the fuel. In the absence of power generated by the reactor, emergency
diesel generators are used to power the coolant pumps. These correctly activated;
however, the tsunami was high enough to flow over the sea wall and into the power
stations, flooding the basements where the generators were located. The flooding
disabled the generators and hence the coolant pumps. Backup generator sites weresimilarly flooded. Three of the six reactor cores then overheated and underwent
a meltdown; the other three cores were offline for maintenance at the time of theearthquake. Overheating also led to hydrogen gas to form in three of the reactors,
eventually triggering a hydrogen-air explosion in each.
This incident led to a shift in public perception of nuclear power in Japan, as
well as a re-evaluation of Japanese reactor safety standards. In response, all ofJapan’s reactors were shut down and each plant is now required to implement more
stringent tsunami-related safety measures (including extended sea walls) as well as
gain local government approval before they can restart operation. Japan’s Nuclear

5. Reactor Neutrinos

80

Regulation Authority (NRA) must also approve the restart. The first to restart was
Sendai-1 in August 2015, followed in October by Sendai-2. A further 8 have sincerestarted and 15 have applied for approval. While some local governments andcommunities have resisted, Japan’s severely reduced energy production capacity
motivates the restarts, with the insurance of far more stringent safety standards.
There are a number of reactors in relatively close proximity to SK, mostprominently the Takahama, Ohi, Kashiwazaki and Mihama plants. Extending
further, there are a number of Japanese reactors at the extremities of Honshu
and beyond, as well as a number of reactors on the east coast of South Korea that are both more powerful and closer to SK than some Japanese reactors. Table 5.2 lists all active Japanese and South Korean reactors, orderedby (thermal power Pth )/(distance to SK RSK )2 to approximately demonstrate themost relevant contributions to reactor neutrino flux at SK. The full list of Japaneseand South Korean reactors is given in appendix A.1

5. Reactor Neutrinos

81

Plant

Core

Type

Mihama
Ohi

3
4
3
4
3
3
4
3
3
4
1
2
6
5
4
3
2
1
4
3
1
2
4
3
2
1
2
1
2
3
4
5
6
1
2

PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PHWR
PHWR
PHWR
PHWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR

Takahama
Ikata
Shin-Kori*
GenkaiShin-Wolsong*
Hanul*

Kori*
Shin-Kori*
Wolsong*

Sendai
Kori*
Hanbit*

PT h
[MW]
2440
3423
3423
2660
2660
2660
3983
3983
3423
3423
2825
2825
2825
2825
2825
2825
2775
2775
2912
2912
2825
2825
2061
2061
2061
2061
2660
2660
1882
2825
2825
2825
2825
2787
2787

RSK
[km]
145.6
178.8
178.8
191.4
191.4
560.3
732.0
732.0
753.7
753.7
708.9
708.9
709.0
709.0
709.1
709.2
709.3
709.4
732.5
732.6
732.0
732.0
708.6
708.7
708.8
708.9
829.8
829.8
732.7
987.0
987.0
987.0
987.0
987.0
987.0

PT h /R2SK[MW km−2 ]
0.115
0.107
0.107
0.073
0.073
0.008
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003

Table 5.2: Nuclear power reactors currently operating in Japan and South Korea, orderedby (Pth )/(RSK )2 where Pth is thermal power output capacity of the reactor and RSK isthe distance from the core to the SK detector [75]. An asterisk by a plant’s name denotes
a South Korean plant.

5. Reactor Neutrinos

5.3

82

Neutrino Production

Nuclear fission produces isotopes rich in neutrons. These fission fragments arenaturally unstable, decaying to stable isotopes via beta decay (n → p + e− + ν̄e ).
Given the high frequency of fission reactions in reactor cores, and that a single fission
reaction yields around 6 neutrinos on average, nuclear reactors are particularly
prominent sources of electron antineutrinos; the first neutrinos ever detected werefrom a nuclear reactor, in the Cowan-Reines experiment in 1956 [7].
The exact spectrum and flux of neutrinos produced by a reactor varies basedon fuel makeup and thermal power. Different fuels produce different combinationsof neutron rich isotopes following fission, each with their own neutrino emission
spectra and decay branches.
Predicting the electron antineutrino flux from nuclear reactors is non-trivial
thanks to the contribution of over 6,000 decay branches to each isotope’s production[76], and four primary isotopes which contribute to over 99.9% of the fission occurringin a reactor core: 235U, 238U, 239Pu and 241Pu. Two main approaches to quantify
these contributions exist. First is the ab initio or “summation” method, which
individually calculates and directly sums the contributing decay branches based on
their measured beta emission spectra [76]. The alternate approach is to generate
virtual decay branches to match measurements of integrated electron emission
spectra of a given isotope as a whole, dubbed the “conversion” method [77]. While
the ab initio method introduces uncertainty from measurements of rare or otherwise
not well understood decay branches as well as non-existent measurements, theconversion method’s uncertainty comes from linking nuclear charge number and theendpoint energy of the beta decay branches when generating the virtual branches.
Mueller et al. developed a parameterisation of the antineutrino spectra for thefour dominant fuels, an exponential fifth order polynomial defined as:
Sk (Eν̄ ) = exp(

6
X
p=1

αpk Eν̄p−1 )(5.2)

5. Reactor Neutrinos

83

where αpk is the pth coefficient for fuel k’s emission spectra and Eν̄ is theantineutrino energy [78]. An ab initio approach was taken for 238U, whereas the
spectra for 235U, 239Pu and 241Pu were fit using a conversion approach to the integral
beta spectra measured in the 1980s by the group of Walter Mampe at InstituteLaue-Langevin (ILL), the most recent and complete example of such measurements[79]. The fit coefficients are given in appendix B.1.
To add to the complexity of producing a total reactor spectrum, determining
the fuel makeup of a power reactor at any one time is difficult. Firstly, there are thevariations in fuel makeup for different reactor designs, resulting in a different total
spectrum. To further complicate this, fuels undergo fission at different rates resulting
in an ever-changing fuel makeup, an effect known as burnup [80]. Power reactor
operation typically involves the redistribution and replacement of fuel rods within
the reactor core over time to balance the effect of burnup, maximising the power
produced by the plant as well as ensuring spent fuel rods conform to safety standards.
While power reactor design is public information, burnup status and fueldistribution is typically a closely guarded secret due to the research and development
companies put into maximising profits from their reactors through delicatelybalancing burnup and fuel restrictions. To account for burnup, measurementsof the fuel fractions from different sampling times during the operation of a reactor
can be used, approximating an average makeup over a core’s lifetime.
Also publicly available is the monthly load factor (LF) and yearly reference
power of a reactor. The load factor of a reactor for a given period is the net electricalenergy produced in that period as a fraction (or percentage) of the electrical energy
produced were the reactor running at reference power. The reference power is notstrictly the maximum power the reactor can produce (load factors are often greaterthan one), but is the approximate maximum power the reactor aims to produce,
typically given in mega watts (MW). The International Atomic Energy Agency(IAEA) publishes yearly reports on the world’s power reactor load factors andreference power (modifications to existing reactors sometimes motivates a change ofreference power) as part of their Power Reactor Information System (PRIS) [81].

5. Reactor Neutrinos

84

The thermal power Pth of a reactor is the thermal energy released per second
from the core when operating at reference power, ignoring any inefficiencies inelectrical energy extraction. For fuel k, the total energy released per fission which
contributes to Pth is calculated by:kkk
Qk = Etot− ⟨Eν̄ ⟩k − ∆Eβγ
+ Enc

(5.3)

k
where Etot
is the total energy produced in the fission process including the beta

decay of all the unstable fission fragments, ⟨Eν̄ ⟩k is the mean total energy carriedkaway by the antineutrinos produced in these decays, ∆Eβγ
is the energy of beta

electrons and photons from fission fragments that do not contribute to the reactor’skenergy (and subsequent heat) output and Enc
is the energy released from neutron

capture (which does not induce fission) on materials within the core [82].
The contribution of fuel k to the total fission rate in a reactor running at
Pth is therefore calculated by:
Nfkiss = Pth

pk
Qk

(5.4)

where pk is the fuel’s total fission contribution fraction. Various measurementsof pk have been made for different reactor designs, the results of some have been
given in appendix C.1, including a collection of measurements for the most common
reactor types from different sampling times to account for burnup.
Using equations 5.4 and 5.2, the resulting antineutrino spectrum produced by agiven reactor of thermal power Pth running at a load factor of LF is then:S(Eν̄ ) = Pth LF

4X
pk
k=1 QkSk (Eν̄ )(5.5)

where k = 235U, 238U, 239Pu and 241Pu. The spectrum for each fuel in an example
PWR with their associated error is shown in figure 5.1.

5. Reactor Neutrinos

85

Figure 5.1: The simulated electron-antineutrino spectra with associated errors produced
by individual fuels in a 3423 MW core of the Ohi 3 PWR reactor.

5.4

Reactor Neutrino Experiments

Given their abundance and flavour-purity, reactor neutrinos are a cornerstone of
neutrino physics, especially in their historical significance in being the first neutrinos
ever identified [7]. They provide an opportunity to measure electron antineutrino
oscillation, sin2 2θ13 in particular. Three reactor experiments have been constructedprimarily to provide a high-precision measurement of this oscillation parameter,each with similar detector designs. One, RENO, is still active; however, the othertwo, Daya Bay and Double Chooz, have now stopped data taking. There is also
one large-scale next generation reactor experiment currently under constructionin China: JUNO. The details of all these experiments are as follows:• Daya Bay

5. Reactor Neutrinos

86

The Daya Bay experiment, named for its location in China, was a combinationof eight liquid scintillator detectors distributed across three locations investigating neutrinos from the Daya Bay and Ling Ao reactor complexes [83].
From August 2011 until December 2020 it monitored six reactor cores, two at
Daya Bay and four at Ling Ao, and provided the first significant measurementof θ13 in 2012 [84]. Two of its experimental complexes acted as near detectors,
each situated as close to their respective reactor cores as practically possible(360–370 m for Daya Bay, 470–500 m for Ling Ao). The third’s location wasdetermined through optimisation of oscillation sensitivity, with geological andpractical considerations, acting as a far detector ∼2 km from the reactor cores.
The detectors themselves had a target volume of gadolinium doped liquid
scintillator (GdLS) contained in a cylindrical acrylic vessel 3 m high and 3 m
in diameter. This resulted in a target mass, per individual detector, of 20 t,
40 t for each near detector complex, 80 t for the far. This GdLS vessel was
surrounded by a second, concentric vessel containing pure liquid scintillator(LS) which served to identify gammas. Finally, these volumes were surrounded
by a third cylindrical vessel made of stainless steel. PMTs were mounted
to a structure in this outer volume, filled with mineral oil for suppressing
radioactive background from the PMT glass. PMTs were exclusively mounted
on the walls of the detector, with circular reflectors employed to direct lightfrom the endcaps to the PMTs. The individual detectors were immersed
together in a large water bath surrounded by PMTs, one bath per detector
complex. This detected Cherenkov light from cosmic muons, acting as a veto.
• RENOThe only currently operating experiment in this list, RENO (Reactor Experiment for Neutrino Oscillation), based in Korea, uses a pair of GdLS detectors
acting as near and far detectors with a target mass of 16 t per detector andhas been running since August 2011 [85]. Using both a LS layer as a gamma
catcher and mineral oil layer to suppress background, RENO uses a water5. Reactor Neutrinos

87

Cherenkov outer cosmic muon veto like Daya Bay. The inner detectors are
fully instrumented with PMTs. Its detectors are 292 m and 1380 m from thesix cores of the Hanbit nuclear power plant (previously known as Yonggwang)
which has the second-largest thermal power output of any plant, second to
Kashiwazaki-Kariwa in Japan.
• Double Chooz
An evolution of the Chooz experiment, which published its results in 1993
[56], Double Chooz (DC) was a pair of GdLS detectors observing neutrinos
from the two cores of the Chooz reactor complex in France [86]. The identicalnear and far detectors were placed 400 m and 1050 m respectively from theaverage reactor core position. Like Daya Bay, DC used GdLS in its central
inner detector, albeit with a smaller target mass of 8 t per detector and with
PMTs on the endcaps of the tank in addition to the wall. It also used a LS
volume surrounding the target volume, itself surrounded with an oil volume
to reduce radioactivity. DC used plastic scintillator as an outer muon veto. It
stopped taking data in December 2017 after 6 years of data taking.
• JUNO (Under Construction)
The Jiangmen Underground Neutrino Observatory (JUNO) is a 20 kt liquid
scintillator detector currently under construction in the town of Jinji, China[87]. JUNO is of a far larger scale than existing reactor neutrino experiments,
but aims to retain the powerful energy resolution offered by liquid scintillator.
In contrast to the experiments described above, JUNO opts for a sphericaldesign and only has a central acrylic vessel of un-doped LS used as the target
material, suspended in a water bath. PMTs are mounted around the central
vessel, searching both the target volume for scintillation light and the water
bath for Cherenkov light from cosmic muons. JUNO will also make use ofan extra plastic scintillator tracking detector mounted above the main tank,which will further support the cosmic muon veto. Placed 43 km from the
Yangjiang and Taishin nuclear power plants, the detector is at a far longer

5. Reactor Neutrinos

88baseline than other reactor experiments. This is because JUNO’s approach
to measuring the mass ordering requires measurements of both θ12 and θ13 ,which is possible at a 43 km baseline.
As well as their usefulness in measuring sin2 2θ13 , in recent years reactor neutrinos
have garnered further interest due to the reactor antineutrino anomaly (RAA) [88].
This is a discrepancy between the expected and detected IBD rates in reactor
experiments, where the global average measures a deficit. In contrast, an excess
of events was observed in the Liquid Scintillator Neutrino Detector (LSND) [89]and MiniBooNE [90] experiments. Shown in 5.2, recent reevaluations of the flux
model have largely resolved the global deficit, reducing the difference to 2.5σ for the
Huber-Mueller model of reactor antineutrino spectra, and lower for other models.
Though the flux anomaly is largely resolved, it originally prompted the suggestionthat one or more additional neutrino states could be responsible for the difference.
These so-called sterile neutrino states would interact only via gravity, explaining
their as-yet lack of discovery, and would provide a disappearance channel, leading toa deficit in the flux. A single sterile state would not be able to explain both the global
deficit and the LSND and MiniBooNE excess simultaneously. In addition to searches
by existing reactor experiments, experiments such as STEREO (Sterile Reactor
Neutrino Oscillations) [91], MicroBooNE [92] and the Short-Baseline Neutrino(SBN) program at Fermilab [93] have been established with the primary goal of
searching for sterile neutrinos.
Another important reactor experiment is the KamLAND [95]. KamLAND
was a 1 kt LS detector situated in the cavern once occupied by the KamiokaNDE
experiment in the Kamioka mine, in close proximity to SK. The LS was containedin a 13m diameter balloon made of transparent film, in contrast to the acrylic
vessels of modern LS experiments. The balloon was surrounded by oil, instrumented
with PMTs and at the time of deployment was the largest target mass of any
LS experiment.
While reactor experiments are typically placed as close as possible to reactor
cores to maximise both neutrino flux and sensitivity to θ13 -driven oscillations, theDaya Bay
Double Chooz
GosgenILL
Krasnoyarsk
Nucifer

Palo Verde
RENO
Rovno88

Rovno91
SRP
STEREO

0.90

1.00

1.10

Bugey−3
Bugey−4
Chooz

89

0.70

0.80

exp
HM
R aexp,HM = σf,a σ f,a

1.20

5. Reactor Neutrinos

R HM = 0.936 +0.024−0.023
10 2

10

L

10 3

[m]

exp
Figure 5.2: Ratio Ra,HM
of measured and expected IBD yields for a selection of reactor
experiments as a function of reactor-detector distance L for the Huber-Mueller modelof reactor antineutrino spectra, taken from [94]. The horizontal green band shows theaverage ratio R̄HM and its uncertainty, indicating a 2.5σ deviation from the expected.

KamLAND detector was uniquely placed with an average baseline of 180 km to its
reactors of interest. This baseline allowed it to perform oscillation measurements
previously limited to those of solar neutrino experiments, measuring the θ12 mixing
angle.

KamLAND provided the first evidence of neutrino oscillation from aterrestrial neutrino source and the first non-solar probe of θ12 and ∆m221 . Thiswas particularly important as there arose tension between solar and KamLAND
measurements of sin2 θ12 and ∆m221 , shown in figure 5.3. This measurement has notbeen repeated by another experiment and KamLAND has now been repurposed
as KamLAND-Zen, a neutrinoless double beta decay search.

5.5

Monitoring Nuclear Reactors

Due to their involvement in the production of nuclear weapons, the interest in reactor
neutrinos is not limited to the academic. 239Pu, created in nuclear reactors throughthe process described in equation 5.1, is a desirable fuel for nuclear weapons due to its
high probability of induced fission but low rate of spontaneous fission. 240Pu on theother hand is undesirable in nuclear weapons due to its tendency to emit neutrons
which could induce unwanted chain reactions prior to a weapon’s deployment. 240Pu

5. Reactor Neutrinos

90

NuFIT 5.1 (2021)
14

12
2

12

GS98 (NuFIT 4.1)
GS98
AGSS09
KamLAND

sin θ13 = 0.0222
10

eV ]

10

2

2

8
★

∆χ

∆m21 [10

−5

2

8

6

6

★

4
4
2

2
0
0.2

0
0.25

0.3
2

sin θ12

0.35

0.4

2

4

6

8

10

2
−5
2
∆m21 [10 eV ]Figure 5.3: Left: Allowed parameter regions (at 1σ, 90%, 2σ, 99%, 3σ confidence limit
for 2 degrees of freedom) for fixed θ13 = 8.6° from the analysis of KamLAND data (solid
green contours with the best fit marked by a green star) and from the combined analysis
of solar data for the GS98 model (full regions with the best fit marked by black star) andthe AGSS09 model (dashed void contours with the best fit marked by a white dot). Theorange contours are the results of a global analysis for the GS98 model using the previous
SK4 neutrino data. Right: ∆χ2 dependence on ∆m221 for the same four analyses after
marginalizing over θ12 . Taken from NuFit 5.1 (2021) [96].

is created when 239Pu absorbs a neutron, and so to produce weapons-grade plutonium
of 3-7% 240Pu concentration a reactor must run long enough to produce 239Pu fromits 238U fuel, but not so long that the fuel is significantly contaminated with 240Pu.
This typically happens on the timescale of a few days and results in a significantly
different operating signature than that of power reactors that generally refuel once
every 18-24 months and spend approximately 2 months ramping up to full power.
In 1970, the Treaty on the Non-Proliferation of Nuclear Weapons (NPT) cameinto effect, seeking to prevent countries without nuclear weapons from attaining
them, encouraging the sharing of peaceful nuclear technology and promoting global
nuclear disarmament [97]. Only a select few “nuclear-weapon states” are allowed
access to nuclear weapons, and non-nuclear-weapon states are forbidden fromproducing nuclear weapons or weapons-grade fuel. Additionally, in January 2022,

5. Reactor Neutrinos

91

the five 1970-era nuclear weapon states released a joint statement emphasising theimportance of nuclear non-proliferation and disarmament [98].
To ensure non-nuclear-weapon states aren’t breaching the NPT by producing
weapons-grade plutonium in their plants, their activity must be publicly available
to the IAEA, and frequent inspections must be permitted. If a state is secretly
producing 239Pu, however, it is difficult to detect. Almost all the products offission can be shielded and if the reactor is in a remote location, disconnected fromthe power grid, there is no obvious external signature of its operation. Only theneutrinos cannot be shielded. It is therefore possible to monitor the flux of neutrinos
to in turn monitor the fission rate of a reactor and use this to identify a refuelpattern inconsistent with power reactors. The majority of detector technologies
in use today do not have the target material to provide an interaction rate great
enough that such flux variations are detectable. The primary aim of the proposed
Water Cherenkov Monitor for Antineutrinos (WATCHMAN) experiment is to provethat this approach to nuclear reactor monitoring is possible [99].

5.6

SK-Gd and Reactor Neutrinos

To date, only a single reactor neutrino interaction has been identified in a water
Cherenkov detector, by the SNO+ experiment during its pure water phase [2].
Reactor neutrinos are very difficult to identify in a water Cherenkov detector due tothe small amount of light produced at low energies a few MeV above the Cherenkov
threshold. Despite this, the scalability of WC detectors can provide larger target
materials than any other detector technology. With the vastly improved neutron
sensitivity provided by gadolinium doping, SK is in a strong position to detect
reactor neutrinos. The current situation in Japan in regard to its nuclear power
stations also puts SK in a unique position where it may be the first experiment
to detect the restart of a nuclear power plant at long range.
Since the completed loading of gadolinium into SK, there have been a totalof nine Japanese reactor core restarts, listed in table 5.3. Cores 6 and 7 of the5. Reactor Neutrinos
Core
Base Rate
Sendai-1
Genkai-3
Sendai-2
Ohi-4
Takahama-3
Genkai-4
Takahama-4
Mihama-3
Ohi-3

92
Restart Date[YYYY/MM/DD]
2020/11/17
2020/11/21
2020/12/22
2021/01/15
2021/03/07
2021/03/17
2021/04/12
2021/06/23
2021/07/03

Interaction Rate
[/d]
1.82
0.06
0.09
0.06
1.71
1.13
0.09
1.13
1.94
1.71

Total Rate
[/d]
1.82
1.88
1.97
2.03
3.74
4.87
4.96
6.10
8.04
9.75

Table 5.3: Japanese reactor core restarts during the SK-Gd phase, ordered by date ofrestart. The expected increase in IBD events in the SK ID due to the restart is included,
as well as the expected pre-restart rate, calculated from SKReact as detailed in section
5.7.

Kashiwazaki-Kariwa plant were slated for restart in late 2020; however, a security
breach on the reactor premises has indefinitely delayed this.
The Ohi, Takahama and Mihama cores especially provided a significant increasein the reactor neutrino flux over the course of 2021. If an increase in IBD rate is
detected to be consistent with the predicted increase in flux due to these restarts,
it can be confidently said that SK-Gd has identified reactor neutrinos.
Detection of reactor neutrinos in SK-Gd has two primary motivations. First is
the impact on non-proliferation of nuclear weaponry. While the activity of individual
reactor cores would be lost due to a combination of the closeness in restart times
and the long ramp up of power reactors, this would be the first detection of achange in reactor power output at long range, more than a few kilometres. Thisis the first step towards proving the effectiveness of large-scale, Gd-doped WC
detectors as long range reactor monitors.
The second motivation is to measure θ13 . KamLAND is the only reactor
experiment which performed an oscillation analysis with a baseline of ∼180 km.
This was the only non-solar probe of θ13 and the results did not wholly agree withthe solar fit. While beyond the scope of this work, if SK-Gd can identify reactor

5. Reactor Neutrinos

93

neutrinos then this tension could be investigated further by performing a second
measurement of θ13 using reactors at long range.

5.7

Simulating Reactor Neutrinos: SKReact

Unlike many sources of neutrinos (neutrino beams, a nearby supernova burst or theSun, for example) which can be approximated as an almost point-like source, there
are many individual sources of reactor neutrinos. Therefore, when considering anexperiment like Super-Kamiokande where no one reactor is close enough for its flux
to dominate, a mix of many baselines, reactor types and reactor operations must
be considered when calculating the oscillated spectrum, in addition to converting
this into what would be seen in the data.
To tackle the task of understanding what the reactor neutrino spectrum would
look like in SK, I developed the SKReact software. The aim of this software is
to simulate the production, oscillation, interaction and reconstruction of reactor
neutrinos produced in all known power reactors worldwide, using the information
provided by the PRIS (dating back to 2003), to support analyses involving reactor
neutrinos in SK.
Interest in reactor neutrinos is not unique to a dedicated reactor analysis as
the reactor neutrino spectrum overlaps with other interesting sources of electron
antineutrinos that primarily interact via IBD, such as supernova relic neutrinos(SRN), geo-neutrinos and pre-supernova neutrinos. The relatively large flux ofreactor neutrinos therefore acts as a significant background to these analyses,
and so SKReact was designed with accessibility for other researchers in mind.
Barna and Dye’s “Web Application for Modelling Global Antineutrinos” [45] served
as both inspiration and a form of validation for SKReact, and Baldoncini et al.
provided the condensed information from the PRIS [100], as well as a reference
throughout its development [101].
First, the produced spectrum (s−1 ) is calculated for every reactor listed in the
PRIS, using equation 5.5, assuming an LF of 100% and using the pk /Qk fractions
applicable to each reactor type as listed in appendix C.1. The spectrum of the Ohi-3

5. Reactor Neutrinos

94

Figure 5.4: The simulated neutrino emission spectrum on production s−1 from theOhi-3 PWR core.

pressurised water reactor (PWR) core is given as an example of this in figure 5.4. Theenergy range and number of points to generate is determined by the user (1-9 MeV,
800 points by default). This spectrum represents the neutrinos produced per second;
however, of typical interest is the spectrum expected after some exposure time.
Each spectrum is therefore scaled by the sum of monthly load factors in the period
of interest (as selected by the user from the available PRIS information) multipliedby the number of seconds in the respective month. The integral of this spectrum
provides the number of neutrinos produced by the reactor in the given period.
The survival probability after three-flavour oscillation of electron-antineutrinosof energy E at a distance of L is defined by:

P (ν̄e → ν̄e ) = 1 − sin2 (2θ12 ) cos4 (θ13 )p21
− sin2 (2θ13 )[cos2 (θ12 )p31 + sin2 (θ12 )p32 ]5. Reactor Neutrinos

95

where
∆m2ij L[m]1.267,
Eν̄ [MeV]!

pij = sin

2

(5.6)

θij are the PMNS matrix oscillation parameters and ∆m2ij is the mass squared
difference between the mass states [102]. The values of these parameters in
SKReact are the global fit values as calculated by the NuFit group, from July
2019 (the most recent at the time SKReact was created) [103]; however, the user
can redefine custom values.
The longitude and latitude of reactors in the PRIS is known, so the linear
distance L to SK can be calculated through conversion from geodesic to geocentric
coordinates, considering Earth’s bulging at the equator. It is assumed that all
reactors are at sea level as the altitude of the reactors is not necessarily known andthe reactors relevant to SK are all based by the coast for easy access to water forcooling. L is calculated for all reactors, and each point on the spectrum is thenscaled by P (L/Eν̄ ) and (4πL2 )−1 to produce the oscillated flux of reactor neutrinos
at SK. Figure 5.5 shows the resultant spectrum s−1 for 2018 reactor information.
As discussed in section 2.4, inverse beta decay is the dominant interaction
mode for electron-antineutrinos above the IBD threshold of mn + me − mp ≈ 1.806
MeV up to a few tens of MeV. SKReact uses the Strumia and Vissani IBD crosssection parameterisation to generate an interacted spectrum for all reactors. Thisis then scaled by the number of free protons (i.e. hydrogen atoms) in SK’s ID(≈ 2.14 × 1033 ) to show the interacted spectrum in SK for a given exposure. Due tothe kinematics of inverse beta decay, it is reasonable to approximate the outgoingpositron spectrum as the neutrino spectrum offset by ∆ = 1.293 MeV.
From this interacted spectrum, SKReact can generate a file with initial positronvertex information which can be used as input into SKDetSim, SK’s Geant3-based
MC detector simulation software. For historical reasons, SKDetSim takes the fileformat produced by the NUANCE interaction generator as input [104], though
NUANCE itself is no longer used.

5. Reactor Neutrinos

96

Figure 5.5: The simulated 2018 reactor spectrum after oscillation s−1 at SK, with the
Ohi-3 PWR core highlighted.

It is often useful to modify reactor information, oscillation parameters andexposure periods, especially when simulating the restart of a currently-offline
reactor. Regenerating an MC sample and passing it through the full simulation andreconstruction chain to evaluate the impact of these changes on the reconstructed
spectrum becomes cumbersome when comparing between many different simulation
parameters. To partially combat this, in addition to the true interacted spectrum,
SKReact generates a “smeared” spectrum, indicative of what the reactor neutrino
sample would look like after being reconstructed by BONSAI, discussed in 3.5. To
achieve this, 90 MC samples of 10,000 positrons of a fixed energy were generated,with each sample increasing in energy from 1 to 9 MeV. The events were randomly
distributed throughout SK’s ID with random direction.
For each sample, events which would pass WIT’s trigger requirements wereselected, and the reconstructed energy spectrum of the resulting sample was fitted

5. Reactor Neutrinos

0.006

1 MeV
2 MeV
3 MeV
4 MeV
5 MeV
6 MeV
7 MeV
8 MeV
9 MeV
10 MeV

0.005
Arbitrary Units

97

0.004
0.003
0.002
0.001
0.000
0

2

4
Positron Energy

68

Figure 5.6: The Gaussian fit (solid lines) of BONSAI reconstructed energy for simulated
positrons of energies from 1 to 10 MeV, area normalised to the efficiency of detection.
Dotted lines at true energy given for reference.

with a Gaussian. The areas of these Gaussian fits were then scaled by the inverse of
the sample size so that when a point on the interacted spectrum is multiplied by its
corresponding Gaussian, it will be both smeared by the reconstruction resolution
and effectively scaled by the efficiency of detection for that energy. Examples ofthese Gaussian fits are shown in figure 5.6 which demonstrates how BONSAI tends
to reconstruct above the true energy in the particularly low energy regime. Thisis likely because the only events that reconstruct at very low energy are when an
unusually large number of photons hit the PMTs, feigning a higher energy signal.
The Gaussian parameters are interpolated (if needed) to match the points in theinteraction spectrum, and then sampled at a user-defined number of evenly-spaced
points. These values are then put into matrix form, with each row containing
a Gaussian fit/interpolation for a corresponding energy value in the interacted
spectrum. The row vector of the interacted spectrum as a function of energy is thenmultiplied by this matrix, producing a smeared spectrum with the number of points
matching the number of sample points of the Gaussian fits. A visualisation of thisprocess is given in figure 5.7. The difference between the smeared and simulated
neutrino interaction spectrum for the 2018 can be seen in figure 5.8. The smeared5. Reactor Neutrinos

98

spectrum simulates the reconstructed energy of the positrons so it is offset by ∆to demonstrate the incident neutrino energy.

(



(

E

(

(

E



Smeared Spectrum

E

(

(

Interacted Spectrum...

Reconstruction Gaussians

Figure 5.7: The process for converting interacted spectrum to reconstructed spectrum.

One advantage of generating a smeared spectrum directly from the calculated
spectrum is that it can be used to measure oscillation parameters. By varying
the parameters to minimise the χ2 between the smeared and measured spectra,
the best fit can be found. This χ2 minimisation was implemented into SKReact
partly in preparation for an oscillation analysis, but also as a simple validation of
the smearing process by demonstrating that the measured oscillation parameters
were consistent with those used as input to the smearing process. The current
fitter crudely minimises using an iterative grid search of the fit parameter spaceand could be improved.
To increase SKReact’s accessibility, each step of the process described here isdisplayed in a graphical user interface (GUI), with the option to vary and inspectmany control parameters on the fly, shown in figure 5.9.
The exposure period selection (centre right) is accompanied by a plot of numberof interactions in SK over the available data period to better visualise reactor
activity. The spectrogram (top right) expands on this, showing the spectrum overtime for the entire data period. A list of reactors contributing to the spectrum is also
shown (top left), ordered by their integrated flux at SK over the exposure period.
This allows for inspection and modification of a selected reactor’s information(bottom left) as well as adding custom reactors.

5. Reactor Neutrinos

99

700

dN/dE [0.01 MeV^-1]

600
500
Reconstructed
Total
OHI-3

400
300
200
100
0

1

2

3

4

5

E [MeV]

6

7

8

9

Figure 5.8: The interacted and smeared spectrum over the course of 2018, with the
Ohi-3 core highlighted, simulated by SKReact.

Figure 5.9: The SKReact GUI.

SKReact has been particularly useful in the development of a reactor sample
selection and was used to calculate reactor background rates in SK’s most recent
DSNB study [43].

6Restart Detection
Contents
6.1
6.2
6.3
6.4
6.5
6.6

6.1

Introduction and Objective . . . . . . . . . . . . . . . . 100
Sources of Background . . . . . . . . . . . . . . . . . . . 105
Cut Optimisation with SPLASH . . . . . . . . . . . . . 108
BDT Selection . . . . . . . . . . . . . . . . . . . . . . . . 117
Background Prediction and Data Availability . . . . . 127
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Introduction and Objective

Following the first Gd loading of SK in 2020 there was a period of high event rates
as the detector’s water stabilised. This had recovered from the point of view of the
WIT trigger rate by the end of 2020, opening up the opportunity to study reactor
neutrinos in a Gd-loaded SK over the course of 2021. A caveat to this is that
the SK computing systems that store the data and provide an analysis platform
for SK researchers received a major upgrade in early 2022, updating its operating
system and libraries. While this upgrade was largely met with no major issues, theWIT-specific offline reconstruction and reduction program was not trivially updated.
As it must be manually initiated, it had been some time since the WIT reduction

100

6. Restart Detection

101

had been processed. As of the writing of this thesis, uncut, fully-reconstructed
WIT pair data is only available up to the 14th of October 2021.
While this would ideally provide around 10 months of data (December of 2020is considered stable enough to include), upon analysing the 2021 WIT data forevent rate stability it was discovered that between the 4th of March and the 31st of
July there is some strange behaviour exhibited. A sudden, unexplained change inthe trigger thresholds (specifically the hit counter and N18 requirements) resulted
in an increase in the event rate. WIT experts recorded no manual changes tothe WIT system at the time; however, there were issues in the power delivery
to the Kamioka mine on the same day as the change. It is not clear how theseissues could have caused a change in the compiled executables running on the WIT
computers, but it is believed that this may be the cause. While it should be possible
to retroactively counteract the changes to WIT by simply reapplying the tighter
WIT trigger requirements as cuts to the offline data, doing so results in instead adrop in the event rate for this period relative to its surrounding periods. Applying
loose quality cuts such as OVAQ or minimum energy requirements does not remove
this drop, indicating a core issue with the WIT data.
This is confirmed when the individual file lengths are inspected, as calculatedusing the range of hardware triggers in each file. WIT data is partitioned into files
which are usually cover up to 87.38 s of data as a result of the approach to processing
data blocks issued by the DAQ. While the file lengths in this unstable period are
generally matched to this cap, a relatively small number of files unexpectedly
exhibit far larger lengths when calculated from the hardware triggers, as seen in
figure 6.1, apparently not conforming to the cap. These large file lengths are notnecessarily reflected in the file sizes, especially in the cases where the file lengthis extremely large. The majority of files are 87.38 s long, as expected; however,
below this there is a large spread in the calculated file lengths as seen in figure
6.2, not generally observed in the rest of the data.
There are also a number of files of a significantly larger file size than the average,
though this is observed elsewhere in the data. If the files with an unusually long

6. Restart Detection

102

EntriesFigure 6.1: The length of the data files in the WIT pair data, calculated using the
hardware trigger counter differences in each file.

EntriesFigure 6.2: The length of the data files in the WIT pair data, calculated using the
hardware trigger counter differences in each file, removing files of length greater than
87.38 s.

calculated length are removed, what remains in this period is an average file size
over double that of before and after the period, as well as a far wider spreadof file sizes, as seen in figure 6.3.
The beginning of this period was coincident with issues with the HV systems;

6. Restart Detection

103

EntriesFigure 6.3: The size of the data files in the WIT pair data, removing files of length
greater than 87.38 s.

however, this is not necessarily suspected as the cause, given that the WIT data
seemed to return to normal following an unrelated update to the executables
deployed on the WIT machines. It is not clear what the cause of the issues is,
nor whether the data is recoverable through some form of re-processing. Due tostorage requirements the raw data has since been deleted so if the core hardware
information was somehow corrupt during or before the offline reconstruction step,
the data cannot be recovered. It is currently unclear if this issue is reflected in thedata which passed through the WIT singles data stream; however, use of this data
would require new studies into the effect of the first reduction cuts on the sample
selection discussed later in this chapter, developed before these issues were identified.
To monitor the WIT data and prevent any such issues arising again, or at least
identify them before the raw data is deleted, a number of plots of various event
variables are now generated for each run. These plots are periodically inspectedby SK collaborators within the low energy analysis group and runs that exhibit
issues are flagged as requiring closer inspection.
Despite the issues with WIT, the data allows for comparison between the event
rate at the start of 2021 with that at the end. This is a promising position to be6. Restart Detection

104

in as 2021 was a particularly active year in terms of Japanese reactor restarts. As
mentioned in section 5.6, the SK-Gd phase has seen 9 such restarts, including twocores each of the nearby Ohi and Takahama plants following long maintenanceshutdowns, as well as a core of the even-closer Mihama plant.
The restart information in table 5.3 is taken from public announcements; however,
the monthly reactor power output is only available in the annual PRIS report, whichis unpublished for 2021 data at the time of writing. From previous PRIS reportdata, it is understood that reactor cores typically take around 2 months to ramp
up to full power. The time-dependent total interaction rate I(t) can therefore
be simulated by overlaying a series of sigmoid functions which approximate therestarts, in this case the logistic function given by
f (x) =

1
1 + e−x(6.1)

which produces a sigmoid increasing from 0 to 1. If the ith reactor restart,
with restart date ti ramps up to its interaction rate contribution Ii over a periodof ∆t, I(t) is given byI(t) =

Xi

Ii
1 + eA

(6.2)

where
A=

−(t − ti − ∆t
)
2
.
S

(6.3)

S scales the width of the sigmoid, i.e. the time it takes for the sigmoid function
to increase from approximately 0 to its approximate maximum. For a pure sigmoid
f (x) (equation 6.1), this is taken to be ∆x = 10 and so S is given by ∆t/10. The∆t/2 in the exponent’s numerator offsets the ramp up to begin on the restartdate rather than being centred on it.
The continuous result of this approximation is given in figure 6.4, which can
be averaged over a given period to give a predicted rate for each bin in whatever6. Restart Detection

105

Figure 6.4: The simulated reactor neutrino interaction rate from late 2020 to late 2021,
with the ramp up simulated using sigmoid functions. A ramp up of 62 days is used inthis analysis.

scheme the data is presented in. A ramp up time of 62 days is used for this analysis,
matching that of previous restarts reported in the PRIS.
Given the issues with the WIT data, two data periods are defined: the “pre”
period (i.e. pre-2021 reactor restarts), beginning on the 1st of December 2020 andending on the 4th of March 2021; and the “post” period, from the 31st of July to
the 14th of October 2021. The aim of this work is to identify a significant increasein event rate in the post period when compared to the pre, consistent with thereactor neutrino interaction rate increase. With this in mind, no full reduction wasapplied to data beyond June 2021 during the development of a sample selection,
so as to avoid biasing the selection to detect this feature.

6.2

Sources of Background

The main backgrounds to an IBD search on an energy scale close to the Cherenkov
threshold search are radioactive decays, and dark noise hits registering as an event,both of which may happen in coincidence with other background events. For
radioactive decays, the main contributor in the low energy regime is radon which6. Restart Detection
Chain
U

238

Th

232

U

235

Isotope
Criterion [mBq/kg]
238
U
<5
226
<0.5
Ra
232
Th
<0.05
228
<0.05
Ra
235
U
<30
227
227
<30
Ac/ Th106
Physics target
SRN
Solar
Solar
Solar
Solar
Solar

Table 6.1: Criteria of radioactive impurities in Gd2 (SO4 )3 · 8 H2 O powder and the physics
goals driving the requirements [1].

emanates from the walls of the detector, particularly from the PMT glass. Radonis carefully controlled and well understood in SK, and the fiducial volume cuts
exist primarily to reduce this background [105].
In preparation for SK-Gd, extensive studies were performed to quantify theradioactive contamination of the gadolinium that would be introduced into thedetector. This was an iterative process: receiving samples of powder from suppliers,
measuring their radioactivity with high-purity germanium (HPGe) detectors, andfeeding back to the suppliers to identify a source of gadolinium sulphate which
conformed to a stringent set of criteria. The broad requirement for the cleanlinessof the gadolinium powder was that radioactive background rates for SK low energy
analyses should less than double. These criteria are given in table 6.1.
Neutrons are also produced in the process 18O(α, n) 21Ne* , and its equivalent withO, triggered by αs emitted by 235U. Spontaneous fission of 235U is another source17of neutrons. These neutrons may be misidentified in coincidence as an IBD pair.
As discussed in section 3.6, the dark noise in SK can be simulated in MonteCarlo, but for particularly low energy events where the number of dark noise hits iscomparable to those from signal, it is preferable to use real data. This is also true
when considering background events entirely composed of dark noise hits. The darknoise rate for the individual PMTs in SK can fluctuate, especially during changes tothe detector as with gadolinium loading. Increases to the dark noise rate increases
the flat event rate due to the larger number of hits potentially triggering the DAQ
and being saved by WIT. An increase in the flat event rate therefore increases the6. Restart Detection

107

pair rate, which can be quantified by monitoring the event rate through WIT itself,
an advantage to its data collection independent of SK’s main triggers.
In this work, backgrounds were not simulated and instead the events in prereactor restart WIT data were collectively treated as background, with a reactor
neutrino “contamination” that can be quantified using SKReact. The signal rate
for a given window of data in WIT is orders of magnitude lower than the total
event rate and so cut optimisation and training of machine learning methods
are not affected by potential reactor neutrino events. This allowed for collective
measurements of all the aforementioned sources of background as an overall rate,
including accidental coincidences of dark noise events.
The spallation rate was not explicitly quantified. Spallation is a process wherehigh energy cosmic muons produce fast neutrons, and unstable nuclei which decay.
The majority of the neutron interactions and nuclear decays occur a short time after
the muon passes through the detector, short enough compared to the cosmic muon
rate in SK that all events in some time window after the muon can be rejectedwith little dead time introduced into the data. This was not implemented in thisanalysis as the BDT selection alone (introduced in section 6.4) was found to be
sufficient in reducing the collective background rate to acceptable levels. Gains
may be made, however, by introducing a dedicated spallation cut, as the BDT
does not currently consider the time since the most recent cosmic muon event,nor an event’s proximity to the muon’s path.
There also exists irreducible background in the form of geo-neutrinos. Theseare electron antineutrinos of a few MeV; however, as discussed in section 2.3.6, theenergy of geo-neutrinos is limited to a little over 3 MeV, below the reactor neutrino
peak. At Kamioka, the integrated flux is also far lower than that of reactor neutrinos
which combines with their low energy to remove them as a concern for a reactor
search. Pre-SN neutrinos would also form an irreducible background; however, theseare only detectable in the final hours or days before a nearby supernova, an event
which has not occurred since 1987. Were a supernova to occur in the period of

6. Restart Detection

108

interest of a future reactor study, the pre-SN neutrinos would be trivially removed
by correlating their timing with the supernova burst.
Ideally, the background rate would be measured using pre-reactor restart data,
and this would act as a fixed baseline and a significant increase in flux above thisbaseline would indicate a reactor restart. While the sources of background aretheoretically stable with time, the radioactive contamination of the water anddark noise rate of the PMTs can fluctuate, and it is important to ensure any
increases above the pre-restart baseline are not due to such fluctuations. The
approach to quantifying this included is described in section 6.5, utilising the BDT
selection introduced in section 6.4.

6.3

Cut Optimisation with SPLASH

The MC sample used to develop the selection was formed by first simulating positron
events throughout the ID volume, with an energy spectrum which approximates
the predicted reactor spectrum at the end of 2021. At the time of MC generationand initial sample selection development, the 2019 PRIS report was the latestthat was available. The energy spectrum was therefore simulated to match thatof the 2019 reactors power outputs, modified so that the reactors described intable 5.3 were set to 100% load factor for the year if not already described as suchin the 2019 PRIS report. The only significant changes to the Japanese reactor
situation between 2019 and 2020 was that the Ohi and Takahama plants wereshut down. In approximating the 2021 spectrum, these plants are simulated to
be running at full power anyway, and so the 2019 spectrum serves as an equally
appropriate baseline as the 2020 spectrum.
An equal number of delayed events were simulated alongside the positron
MC sample, each uniquely matched to a positron vertex. These were equally
split between a single 2.2 MeV photon and an 8 MeV gamma cascade, simulatinghydrogen and gadolinium capture respectively. The number and energy distributionof the gammas in the Gd capture sample was pre-simulated using Geant4 by an
SK collaborator. Given that the prompt and delayed events aren’t truly generated

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together and the neutron capture isn’t itself simulated, once paired, the ∆t between
the events is generated using a random number weighted by the neutron capture time
formula (exponential decay) with a neutron capture time of 203.7 µs for hydrogencapture [106], and 30 µs for gadolinium.
A 24 h run of real WIT data was used as the background to optimise against, andthe signal rate was taken to be 9.75 d−1 , as it is predicted to be at the end of 2021.
The BG data run began on the 18th of February 2021, before any major reactor
restarts; however, there is still an expected reactor interaction rate of 1.82 d−1 due
to more distant reactors. To calculate the expected background rate for a given
cut or set of cuts, the MC and BG would be reduced in parallel. An efficiency for
the MC can then be calculated, which is then used to find the expected number ofreactor neutrino events appearing in the BG sample post-cut. This number is thensubtracted off of the number of BG events surviving the cuts and this offset BG rateis used to calculate the BG efficiency without any (expected) signal contamination.
This introduces a dependency on the reactor interaction rate prediction to the BG
efficiency; however, without this offset, the BG efficiency would be overestimated.
The development of a reactor neutrino sample selection began with the cuts
used in the SK-IV solar analysis [21]. These were chosen as a starting point as thesolar analysis is particularly mature in SK and as such the variables used within
it are well established as powerful discriminators in event identification. Thereis little information in low energy events in SK given the small number of hits
and the general simplicity of the detector and there is therefore little scope toinnovate on the established low energy cuts. The variables used in the SK-IV
solar analysis sample selection are:
• Vertex position - A fiducial volume is defined by the minimum distance fromthe PMT plane to the event vertex, 2 m in most analyses.
• Energy - BONSAI reconstructed energy of the event.

6. Restart Detection

110• OVAQ - (g 2 − DirKS2 ), where g is the BONSAI goodness and DirKS is adirectional KS test of the PMT hit pattern. A general event quality parameter
described in more detail in section 3.5.
• effWall - Distance to the detector wall in the reverse direction of the event,powerful at identifying radioactive events originating close to the PMT plane
but emanating away from it. BONSAI has reduced vertex reconstruction
accuracy along the direction of the event, so such events often reconstructwithin the fiducial volume.
• Multiple Scattering Goodness (MSG) - Measure of directionality confidence,
based on fitting multiple direction vectors assuming a 41° Cherenkov coneand evaluating their general alignment with one another.
• BONSAI Pattern Likelihood (PatLik) - A χ2 goodness of fit for angles between
pairs of hits to the expected opening angle of the Cherenkov ring.
Given the different energy regime and the addition of the pair selection, thesecuts would need to be re-optimised to the reactor neutrino MC sample, separately
for the prompt and delayed events, and the coincidence variables ∆t and ∆r, thetime and distance between the prompt and delayed vertices respectively, would
need to be added and optimised. The initial values of the cuts taken from the solar
analysis were treated purely as a starting point to optimise from. To facilitate
this, I developed the SPLASH framework.
SPLASH arose from the lack of a column-wise approach to cut-based analyses
in ROOT, the C++ analysis framework most commonly used in the field of particle
physics [107]. ROOT’s approach to analysis is geared towards looping through afile event-by-event, saving events which pass cuts to a new structure and rejecting
those which don’t. While this is a reasonable approach to applying cuts, it becomes
cumbersome to optimise an individual cut and especially a set of cuts. Such a
process would require repeatedly looping through the dataset, re-applying the cut
and evaluating its efficiencies with each iteration.

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An alternative approach instead structures the data in a table-like Dataframe ofrows and columns, with each row representing an event and the columns the event
variables. In this format, events can be selected as in a database, with a single
query returning the Dataframe which contain events which satisfy that query. To an
extent, the per-event method is utilised in the backend of the code in this approach;however, a range of optimisations ensure far more efficient data extraction. While
Dataframe structures have recently been introduced to ROOT’s libraries, they arein their infancy and are therefore less well documented and established than other
Dataframe libraries. They are also not present in the version of ROOT used in SK.
SPLASH at its core utilises pandas [108], a Python-based Dataframe libraryleveraging the NumPy [109] library’s CPython arrays to provide fast data manipulation. To minimise its dependencies, SPLASH uses the Uproot [110] library
to load ROOT files without requiring a local ROOT installation, before placing
them into a pandas Dataframe container.
This Dataframe approach allows for easy per-cut optimisation as the cut canbe repeatedly applied to the data effectively as a query, and the number of events
which pass can then be counted. MC and background samples can be separately
cut, and the number of each that survives, appropriately scaled to match real-worldrates, can be passed to a function which acts as a figure of merit (FOM) for thecut. In SPLASH, this FOM takes the form
FOM = √S
S + BG(6.4)

which, when maximised, provides the most certain measurement of S, thoughalternative FOMs can be used. In future work, it may be preferable to use FOM =√S/ BG to maximise the statistical difference between the signal S and background
BG rates, depending on the intention of the measurement. The negative of thisFOM is minimised using the SciPy [111] package’s minimize function.
Optimising the established cuts for the reactor selection did not provide asignificant signal rate above the background rate. The optimised selection criteria
are given below. For each, the distribution is given for prompt and delayed events

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from the 2021-spectrum MC pairs used in optimisation, both compared to promptand delayed events for pairs identified in WIT data. Both have passed throughthe WIT online processing (or an analogue of it, in the case of the MC). Each
distribution is given without any other cuts applied so as to better demonstrate theoverall distribution for each; the statistics of the BG distribution quickly degrades
as cuts are applied, as intended.
• Fiducial Volume
Prompt > 2 m
Delay > 2 m
The majority of the background within the fiducial volume tends to reconstructmore centrally in the detector, most likely due the approximate isotropy of darknoise. This tendency is seen in figures 6.5 and 6.6. Optimisation beyond thestandard SK FV of 2 m did not provide a significant improvement to the FOM.

PromptDelay
Cut (FOM = 28794.434917)
MC
BG

0.00050.00040.00040.00030.00030.00020.00020.00010.00010.0000

1500

1000

500
0
500
BONSAI Vertex z [cm]

1000

1500

Cut (FOM = 28813.434235)
MC
BG

0.00050.0000

1500

1000

500
0
500
BONSAI Vertex z [cm]

1000

1500

Figure 6.5: Vertex z as reconstructed by BONSAI for 2021 reactor spectrum prompt
positrons, and delayed neutron captures corresponding to 0.02% Gd concentration, both
simulated (MC). BG is raw pre-reactor restart WIT data.

6. Restart Detection

113

Prompt0.00120.00100.00080.00060.00060.00040.00040.00020.00020250

500

Cut (FOM = 28866.447468)
MC
BG

0.00100.00080.0000Delay

0.0012

Cut (FOM = 28886.955659)
MC
BG

750
1000 1250
BONSAI Vertex r [cm]

1500

1750

0.0000

0

250

500

750
1000 1250
BONSAI Vertex r [cm]

1500

1750

Figure 6.6: Vertex r as reconstructed by BONSAI for 2021 reactor spectrum prompt
positrons, and delayed neutron captures corresponding to 0.02% Gd concentration, both
simulated (MC). BG is raw pre-reactor restart WIT data.

• Energy.
Prompt > 5.2 MeV
Delay > 5.3 MeV

Shown in figure 6.7, the energy cut is the most aggressive, as it is the mostsignificant measure of the quality of an event and has generally good separation
between signal and background. This cut removes the most BG by far, leaving
only the higher quality events to be removed by the more fine quality cuts.
PromptDelay
Cut (FOM = 22540.259880)
MC
BG

1.0
0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

2

4

6
BONSAI Energy [MeV]810Cut (FOM = 28272.449779)
MC
BG

1.0

0.0

2

4

6
BONSAI Energy [MeV]8

10

Figure 6.7: BONSAI reconstructed energy for 2021 reactor spectrum prompt positrons,
and delayed neutron captures corresponding to 0.02% Gd concentration, both simulated(MC). BG is raw pre-reactor restart WIT data.

6. Restart Detection

114• OVAQ
Prompt > 0.22
Delay > 0.20

The powerful background discrimination of OVAQ can be seen in figure 6.8,
leading to another somewhat aggressive cut.
PromptDelay

Cut (FOM = 31165.186789)
MC
BG

6

6

5

5

4

4

3

3

2

2

1

1

0

0.6

0.4

0.2

0.0
OVAQ

0.2

0.4

0.6

0

Cut (FOM = 34497.720422)
MC
BG

0.6

0.4

0.2

0.0
OVAQ

0.2

0.4

0.6

Figure 6.8: OVAQ goodness variable for simulated 2021 reactor spectrum prompt, anddelays corresponding to 0.02% Gd concentration (MC). BG is raw pre-reactor restart
WIT data.

• effWall
Prompt > 4.3 m
Delay > 4.4 m

EffWall shows some separation; however, the chosen FOM results in a fairly
conservative cut, shown in 6.9.

6. Restart Detection

115

Prompt0.0006Delay
Cut (FOM = 6113.190707)
MC
BG

0.00050.00050.00040.00040.00030.00030.00020.00020.00010.00010.0000

0

1000

2000
effWall [cm]3000

Cut (FOM = 6126.327078)
MC
BG

0.00060.0000

4000

0

1000

2000
3000
effWall [cm]4000

Figure 6.9: EffWall for simulated 2021 reactor spectrum prompt, and delays corresponding to 0.02% Gd concentration (MC). BG is raw pre-reactor restart WIT data.

• ∆r < 1.52 m

The ∆r distributions shown in figure 6.10 demonstrate the power of thecoincidence requirement in a gadolinium-loaded SK as there is clear separation
between the MC and BG, a fact which the optimisation capitalises on with aparticularly harsh cut.

Pair
Cut (FOM = 32216.728588)
MC
BG

0.00350.00300.00250.00200.00150.00100.00050.0000

0

1000

2000

r [cm]

3000

4000

Figure 6.10: BONSAI reconstructed distance between simulated 2021 reactor spectrum
prompt, and delays corresponding to 0.02% Gd concentration (MC). BG is raw pre-reactor
restart WIT data.

6. Restart Detection

116• ∆t < 92 µs

Though less drastic a separation than ∆r, the different ∆t distributions for
MC and BG can be seen in figure 6.11.

Pair

1e 5

Cut (FOM = 33877.868707)
MC
BG

2.5
2.0
1.5
1.0
0.5
0.0

0

100000200000300000t [ns]

400000500000Figure 6.11: Simulated neutron capture times corresponding to 0.02% Gd concentration(MC). BG is time between prompt and delayed events in raw pre-reactor restart WIT
data, identified by the WIT coincidence trigger.

Optimisation removed the MSG cut and PatLik was removed as, upon inspection,
it was not clear that it was calculated correctly for MC and is often not calculated forvery low energy events regardless, as a clear Cherenkov ring cannot be identified. The
BONSAI energy cut was especially optimised to provide a particularly harsh rejection
in an attempt to reduce the extremely high background rate. This cut alone removes
around 53% of fiducial Gd captures to attain a background efficiency of just 0.03%.
The MC efficiency of the optimised cuts is calculated to be 1.5%, resulting in asignal rate of 0.14 d−1 , while the BG rate was reduced to 36.0 d−1 . The livetimein the data periods is not sufficient to provide a statistically significant difference
between the two due to reactor restarts for this selection. In future work, thisoptimisation could be revisited, perhaps utilising an alternative FOM to focus on
exclusively detecting a significant signal, and including a spallation cut.

6. Restart Detection

6.4

117

BDT Selection

Manual optimisation of individual, independent cuts did not provide selection criteriathat could significantly isolate reactor neutrino events. Increasing the complexityof such cuts to interweave different variables is possible, but it is a difficult andarguably unintuitive approach to such a sample selection. The application ofmachine learning (ML) techniques offers an alternative solution. Machine learning
in general seeks to improve upon traditional multivariate analyses by leveraging thepower of modern computing to generate complex models which can describe input
data, be it through discrete classification or continuous output variables. Suchcomplexity comes with the risk of over-optimising the model to match the data
used to generate it, a phenomenon known as overfitting in the ML world. This is
the primary concern when transferring from cut-based methods to ML methods;
however, it is one which can be avoided with careful consideration, especially withthe constant advancements in various ML implementations. Thanks in part to its
ability to provide powerful models that are simple to implement, with the payoffof some model dependency, ML is used throughout particle physics and indeed
the world of data analysis in general.
While cut optimisation was the original goal of SPLASH, a secondary focus wasto provide a platform for ML tools which may be used in SK. The front end of
ML libraries handling Boosted Decision Trees (BDTs), artificial neural networks(ANNs) and convolutional neural networks (CNNs), for example, are typically
written in Python. It is therefore common for particle physics analyses to either
use PyROOT, an officially-supported Python wrapper for the ROOT libraries, or
produce intermediate files which can be read by Python programs when working
with ML. Uproot has, however, more recently gained traction in this regard thanks
to its independence on ROOT itself and comparable performance to native ROOT.
SPLASH seeks to streamline the ML data preparation process, by providing thetools to load data from ROOT files and format the data ready for use in ML libraries
without being bound to a specific analysis. Some work was done to implement the6. Restart Detection

118

framework for 2D and 3D CNN-based event classification in SPLASH; however,this analysis focused on the use of BDTs.
The pre-SN alarm recently implemented in SK uses BDTs to identify an increasein IBD rates consistent with a star progressing through its silicon-burning phase
in WIT data [30]. To minimise the delay between a detectable rate increase andthe issuing of an alarm, two BDTs are used: one running on the WIT system itself,using only variables calculated during online processing to intially reduce the data;and one which performs the final selection after the initial, partially-reduced sample
has been fully reconstructed. A significant background to this alarm is the increasein rate due to reactor restarts given the similar energy regime. Though the predicted
rates would not be significant enough to explicitly identify a restart, this begins
to demonstrate the potential a BDT selection may have to identify a significant
number of reactor neutrinos and helps to motivate their use in this study.
BDTs are a method of multivariate analysis, removing the need to optimise
a number of cuts by using gradient boosting to assign a score to events. Thisscore represents the BDT’s predicted likelihood that the event is one of a numberof classes. In the case of particle physics analysis this often means classifying an
event as either signal or background. BDTs are in some ways comparable to neuralnetworks given that they take a large, labelled dataset for training and seek to modelthe data to provide a score; however, the models take significantly different forms.
While the more complex NNs can outperform BDTs in similarly complex, large
scale datasets, BDTs are frequently used in multivariate analysis thanks to theirquick implementation, minimal tuning requirements and strength in classifying lesscomplex data where the input variables for a given row (event) is relatively small.
For example, the Water Cherenkov Machine Learning (WatChMaL) group [112]developed an implementation of a ResNet CNN [113] to classify and reconstruct
events in water Cherenkov detectors (the target network architecture for the 2D
CNN formatter implemented into SPLASH). This CNN takes every single PMT
hit’s position and time as input for each event, intending to model the hit patterns.

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119

To take the same approach with a BDT would require an unfeasibly complex model
which would realistically never achieve the same accuracy as the CNN.
BDTs calculate an event’s score using an ensemble of decision trees. Trees are aseries of queries which subclassify a dataset into two or more “leaves”. The depth of atree is the maximum number of queries the dataset could be subject to, determining
the maximum number of leaves in the tree (not all branches will necessarily reachthe maximum depth). Events are assigned a per-tree score based on the importanceof the leaf to which it is assigned. These scores are not necessarily symmetrical;
being assigned to one leaf may provide a positive contribution to the tree score
while the other won’t necessarily negatively affect the event’s score significantly. An
example would be that events above a certain energy threshold have a good chanceof being signal, but being below the threshold is not necessarily a good indicationthat the event isn’t signal. The final BDT score for a given event is calculated bysumming the score assigned by every leaf of every tree in the ensemble.
The reason these decision tree ensembles are considered “boosted” is because
trees are generated iteratively, and the structure of each tree is influenced (orboosted) by the performance of the previous tree. The act of boosting defines a loss
function that acts as an objective function: the metric for how well the algorithm
predicted the class of an event. One example of such a function is the negative log
likelihood function, given, for a prediction yi of an event i of the class ŷi , byL(θ) =[yi ln(1 + e−ŷi ) + (1 − yi ) ln(1 + eŷi )]

X

(6.5)

i

where θ is the model’s parameter space.
Beginning with a single tree, the BDT makes predictions for a subset of a large
training dataset and the loss is calculated. The full tree ensemble is built one-by-one
by iterating through subsets of the training set, the performance of the latest
iteration determining the structure of the new tree. This is done through gradientdescent, where the derivative of loss decides the direction in which the parameter
space should be shifted to approach a minimum. A learning rate is defined, which
determines the extent that each iteration moves the parameter space towards the6. Restart Detection120

minimum. A lower learning rate avoids skipping over the minimum with each step,at the expense of a longer training time needed to reach the minimum.
An implementation of the XGBoost [114] BDT classifier algorithm was usedin this work’s sample selection. This algorithm is widely used in the world of
multivariate analysis thanks to its portability and optimisations, both in the logicalapproach as well as in its hardware utilisation. XGBoost takes a generalised
approach to tree ensemble optimisation to support a range of loss functions andin this work the negative log likelihood loss function was used.
In addition to the loss function, XGBoost introduces a regularisation term which
limits the complexity of the model, linearly combining the two to form the objectivefunction by which the model is judged. BDTs which do not include this term areprone to overfitting, a common issue in the world of machine learning whereby
a model becomes overly complex during training. Such a model can predict thetraining data with a high degree of accuracy, but will struggle to classify new data
which doesn’t very closely match the training dataset.
To further reduce overfitting and to optimise the trees, XGBoost removes
suboptimal leaves in a process known as pruning. After building a tree up to thepre-defined maximum depth, XGBoost then iteratively works upwards throughthe tree, evaluating whether each leaf’s performance is good enough to warrant
its existence. There are a number of other steps taken to optimise the trees andreduce overfitting in addition to this, as described in detail in [114].
The XGBoost model used in this work was trained using the same BG and MC
sample used to optimise cuts as described in section 6.3, with ∼12 k MC events and∼7 M BG events in the training set. This is a comparatively low number of MC
examples to BG and would ideally be far higher; however, the issues with the WIT
offline reconstruction in SK’s new computing system prevented the generation of alarge MC sample with the full set of offline reconstruction variables. A smaller 2021
MC sample generated prior to the upgrade was therefore used. An initial BDT using∼1 M MC events matching the 2019 reactor spectrum was trained prior to the BDT
used in this work for some initial investigations. The performance between this and6. Restart Detection

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the 2021-spectrum BDT was comparable when cross-validated with a 2021-spectrum
MC sample containing 10 k event pairs set aside for testing and so the newer BDT
was used. The same 2021-spectrum testing sample was used to validate the BDT’s
effectiveness. Using a sample independent to the training data in such a way iscommonplace in ML work as it verifies that the model is not overtrained if it canperform similarly when evaluating either dataset. If a BDT provides a classification
accuracy far higher for the training set than for an independent sample, there is achance the model is overtrained. Such a disparity was not observed in this work.
No strict conditions were placed on what variables were to be included in the
BDT and the relatively small pool of information to pull from meant that initially
all available variables from the offline reconstruction were included, both BONSAI
and ClusFit, as well as those calculated after vertex reconstruction (OVAQ, DirKS,
EffWall, MSG). PatLik was not included for the same reason it was removed fromthe traditional cut optimisation: it was not clear it was being calculated correctly
for the MC and it is often not able to be calculated for low energy events regardless.
The variables used in the traditional cut selection, given in section 6.3, composed
the majority of the input variables, though the STORE goodness and N18 online
variables used in the WIT system were included. Additionally, two more variables
not frequently used in SK low energy analysis were added: fromWall, the closest
distance between the event vertex and the PMT plane; and ClusFit goodness,the goodness of the ClusFit vertex, calculated similarly to the BONSAI goodness
described in section 3.5. These aren’t used in most analyses as they don’t offer
improved background rejection in most low energy analyses. EffWall is more effective
than FromWall in reducing the most common radioactive backgrounds, and the
BONSAI goodness is more relevant than ClusFit. When considering the input into
a BDT, however, especially when investigating events with such little information,
it is wise to include all available variables in case there is a correlation between
seemingly irrelevant properties which has not been otherwise identified.
The importance of a variable is a metric used for evaluating whether a variable
contributes significantly to a tree’s decision. It is calculated for a single decision

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tree by summing the classification performance of all splits in the tree which
depend on the variable. This score is then averaged across all the trees in theensemble. The XGBoost algorithm is sufficiently efficient that trimming which
variables are included for the sake of performance was generally not required, though
the BONSAI and Clus-Fit DirKS variables were removed due to being significantly
less important in initial testing on the 2021 sample. OVAQ (which depends on
the BONSAI DirKS value) is still included.
The BDT used in the pre-SN alarm sample selection includes a set of PMT
hit isotropy parameters [31]. These are based on the Legendre polynomials of theangular separation between PMT hits, denoted β1−6 for each order of the polynomial.
A BDT was trained including these variables (using and evaluated on 2019 reactor
spectrum MC); however, all but the first order variable was found to have the lowest
weight of all the inputs, not counting DirKS, as shown in the feature importanceplot in 6.12. Given that these β variables are computationally intensive to calculate
and must be manually added after full offline reconstruction, they were deemed
unnecessary and were omitted from the final BDT.
The BDT ensemble was capped at 10 k trees of maximum depth 10. With alearning rate of 0.01, this took approximately 9 hours to train on the SK computing
system. The feature importance for this model is given in figure 6.13, and the final
tree in the generated ensemble is shown in figure 6.14.
The uncut distribution of the BDT score for MC and two weeks of pre-reactor
WIT data is shown in figure 6.15. The vast majority of the background is easily
identifiable as such thanks to the particularly low quality of the events, resulting inalmost all of these events being assigned a score close to 0. MC events aren’t as easily
identified; however, only a small portion of events are clearly wrongly categorised,
likely given the small amount of information in particularly low quality events.
SPLASH was again used to optimise the BDT score cut. Given the effectivenessof the BDT in comparison to the traditional cuts, two weeks of SK-Gd data wasused as the BG sample rather than just 24 h. This data, with a >0.2 BDT cut toremove the obvious BG events, is shown in figure 6.16. From this distribution itFigure 6.12: The input variable importance for a BDT trained on the 2019 reactor spectrum, including the β isotropy parameters.

6. Restart Detection
123Figure 6.13: The input variable importance for a BDT trained on the simulated 2021 reactor spectrum, the BDT which formed the final
reactor sample selection.

6. Restart Detection124leaf=-0.0178146847

leaf=-0.0193498079

leaf=-0.0195717216

no, missing

no, missing

leaf=-0.0142513365

yes

leaf=-0

yes

no, missing

leaf=-0.0175906066

yes
leaf=-0

no, missing

bsvertex(4)(2)_delay<1023.9566

yesno, missing
bsr_delay<837.010986

bsvertex(4)(2)_delay<-889.469299

yes

leaf=-0.0083950609

yes
leaf=-0

no, missing

bsvertex(4)(2)_delay<729.928711

yes

STORE.sgoodness_prompt<9.82117081

no, missing

yesleaf=-0

yes

yes

leaf=0.00745945936

no, missing

leaf=-0

no, missing

yesdr<139.654053

leaf=-0

yes

yes

leaf=-0.00910891127

yes

leaf=-0

no, missing

effwall_prompt<1388.9906

no, missing

leaf=0.00514429063

no, missing

dr<55.6984024

no, missing

fromwall_prompt<186.129517

no, missing

leaf=-0.00312499981

leaf=-0.0098089166

no, missing

effwall_prompt<455.723755

yeseffwall_prompt<605.037354

leaf=-0.0186015666

dr<55.6984024
yes

leaf=-0.0199785382

no, missing

no, missing

dr<139.654053

no, missing

STORE.sgoodness_prompt<13.7537155

Figure 6.14: The final tree in the ensemble BDT used in this analysis.

leaf=-0.00444444455

no, missing

bsvertex(4)(2)_delay<892.979126

yes

STORE.sgoodness_prompt<11.9108477

yes

no, missing

effwall_prompt<704.225708

yes

STORE.sgoodness_prompt<10.583828

effwall_prompt<2344.97925

dr<184.585678
yes

6. Restart Detection
125

6. Restart Detection

126

Figure 6.15: The BDT score for 10 k reactor MC events and two weeks of SK-Gd WIT
data (BG).

can be seen there is no obvious cut off, as there are a number of events still present
with scores close to 1, shown in more detail in the BDT score > 0.95 plot in 6.17.
It is unclear what the source of these high-score events are; however, they arelikely accidental coincidences where the individual event qualities are unusuallyhigh and as such no specific non-BDT cuts would trivially remove them.
Optimisation resulted in a BDT score requirement of >0.991, producing an
MC efficiency of 10.3% which translates to a signal rate of 0.97 d−1 by the end of
2021. In some cases, such a high and precise BDT cut would be indicative of an
overtrained BDT; however in this case it is purely due to the extremely large BG
rate compared to MC, requiring a very tight cut to remove a significant amount of
BG. An alternative approach would be to apply some minor quality cuts on the event
variables before the BDT is trained, to remove the vast majority of the BG firstand only leave the questionable events. This would still result in basically the same

6. Restart Detection

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Figure 6.16: The BDT score for 10 k reactor MC events and two weeks of SK-Gd WIT
data (BG), with a >0.2 BDT score cut.

issue, albeit with a less precise BDT score threshold. This approach wasn’t taken
so as to simplify the final sample selection somewhat, as the initial cuts would haveto be taken into account when calculating efficiencies as well as the BDT cut itself.

6.5

Background Prediction and Data Availability

An attempt was made to predict the background rate as a function of time in the
post-restart period, without (fully) unblinding the data. Before the data undergoes
full reduction ready for analysis, a softer set of cuts was applied, known as the“online” cuts, named as such as they originally mimicked the WIT online thresholds,
but later saw the inclusion of a soft BDT score cut of >0.5. The full >0.991 BDT
cut is therefore referred to as the offline cut. The intention of the online cuts is toprovide a dataset which does not reveal a significant number of reactor events while6. Restart Detection

128

Figure 6.17: The BDT score for 10 k reactor MC events and two weeks of SK-Gd WIT
data (BG), with a >0.95 BDT score cut.

providing a metric for the activity of the background which will influence the final
dataset. The assumption is that if there is an increase in the rate of events passing
a >0.5 BDT cut, the final BDT selection will likely see a similar increase.
To predict the background rate in each dataset, a subset of the pre data has
both the online and offline cuts applied. The ratio of offline to online events is theneffectively an online→offline efficiency. This is used to scale the number of eventsin a data period which pass the pre-selection (the online rate) to predict the final
background rates. This allows for more direct background stability measurements,
beyond using the pre dataset to predict the rates in the post.
One side effect of this approach is that the data will inherently fit the predicted
rates particularly well, as the two are somewhat coupled. Therefore, strict conclusions can not be drawn from the agreement between measured and predicted rates
using this approach until the correlation can be somehow quantified. This does not6. Restart Detection129

affect the comparison between data points, however, as is the case in detecting an
increase in rates due to reactor restarts. Were it the case that SK’s pair rates werestable over time, the subset of data used to calculate the background efficiency could
instead be used to simply estimate a flat background rate; however, the dynamic
background calculation acts as a probe of the stability of the pair rate in SK.
The online pair rate scaling method was applied to the entire post dataset, which
revealed a concern in that the post had significantly higher background rates whencompared to the pre; the online rate approximately doubled in the post period. This
is not trivially explained, as there are few sources of time-dependant backgroundin SK beyond the increase in activity introduced during Gd loading, which hadstabilised by 2021. A soft >0.2 BDT score cut was applied to two 24 h runs in the
pre and post periods and the BDT variable distributions were compared to shedsome light on the nature of these extra events. Though little can be drawn fromsuch a small sample size, there are some variables which demonstrate a shift in
distribution from the pre run (85766) to the post (86102) as shown in 6.18. There
are also a far larger number of events in the post (428) compared to the pre (161),
more so than predicted by the online pair rate scaling. χ2 was therefore calculated byscaling the pre data, taken to be the expected, to match that of the post, which wastreated as the observed. This is not an exhaustive statistical test given the sample
sizes but does indicate which distributions demonstrate a more significant shift.
While not statistically significant, the downward shift in ∆t could be indicativeof an increase in the dark rate driving the flat event rate up and reducing the time
between accidental coincidence events. This would cause a shift upwards in ∆r asthese events won’t necessarily be spatially correlated, a shift which is observed butthat is, again, most probably not statistically significant. An increase in dark rate
may also explain, for example, the increase in events with a lower STORE goodness,
as low-quality events would then have more hits and therefore coincidence hits,
feigning a higher quality event by this metric. Given the small sample size, it isdifficult to confirm that this is indeed the cause. Regardless, the result is a noticeable
shift in BDT score is shown in figure 6.19. There is not enough data in a single

6. Restart Detection

130

run to determine whether the assumption of a constant online→offline backgroundefficiency holds, and to determine this would result in necessarily unblinding thedata somewhat, introducing bias in the BG efficiency calculations.
Prompt8Delay
2 = 20.7

p = 0.00424
85766
86102

7
6

7

Delay
2 = 31.3

p = 5.43e-05
85766
86102

5

3
2

2

1
4

6
BONSAI Energy

8

0

4

6
BONSAI Energy

Prompt

8

6

8

5
4

10

20

6

4

4

3

2

2

15
20
STORE Goodness

25

Prompt0

7

2 = 22.9

p = 0.0018
85766
86102

6

0

10

20

30
N18

40

Delay

7

2 = 14.8
p = 0.0219
85766
86102

6
5
4

2

1
10

15
20
STORE Goodness

25

1

0

1000

Delay

2000 3000
effWall

4000

0

1000

Prompt5

2 = 8.4

p = 0.299
85766
86102

Delay
5

2 = 45.5

p = 3.78e-08
85766
86102
4

4

2000 3000
effWall

4

3

3

2

2

1

1

2 = 9.13

p = 0.166
85766
86102

3
3
2

2

1
0

1
0.4

0.5
0.6
BONSAI Goodness

0.7

0

50

3

5

4

50

2

1

1

40

2 = 4.45
p = 0.616
85766
86102

5

5

3

30
N18

Prompt2 = 107
p = 1.34e-19
85766
86102

7

3

10

0

1

Delay
2 = 165
p = 1.71e-31
85766
86102

7

2

1

1

0

6

4

3

3

2

2 = 70.6
p = 1.11e-12
85766
86102

7

5

4

4

3

5

Prompt654

6

p = 8.44e-09
85766
86102

8

6

5

0

2 = 48.7

0.4

0.5
0.6
BONSAI Goodness

0.7

0

0.0

0.2
OVAQ

0.4

0

0.0

0.2
OVAQ

0.4

4000

6. Restart Detection

131

Prompt6Delay

2 = 61.9
p = 6.43e-11
85766
5
86102

Prompt2 = 28.8
p = 6.57e-05
85766
86102

5
4

4

3

3

Delay

5

2 = 45.5
p = 3.78e-08
85766
86102
4

5

3

3

4

2

2

2

2

1

1

1

1

0

0.4

0

0.5 0.6 0.7 0.8
Clus-Fit Goodness

0.4

PromptDelay

2 = 24.1

7 p = 2.86e-05
85766
86102
6

5

5

4

4

3

3

2

2

1

1
0

500
1000
BONSAI Vertex r

1500

0

0

1500

p = 0.0531
85766
86102

2 = 34

6
5
4

3

3

2

2

1

1

5

3

3

2

2

2

1

1

1

3

1000
0
1000
BONSAI Vertex z

0

0

500

1000
fromWall

0

1500

0

500

1000
fromWall1500

2 = 30p = 0.000211
85766
86102

4

1000
0
1000
BONSAI Vertex z

50.4

2 = 25.5
p = 0.000617
85766
86102

7

4

0

0.2
MSG

Delay
2 = 15.3

6

500
1000
BONSAI Vertex r

0.0

Prompt7

5 p = 4.11e-05
85766
86102
4

p = 2.5e-09
85766
86102

0

0

0.4

Delay
2 = 56.3

4

0.2
MSG

5

Prompt50.0

8

2 = 32.8

7 p = 0.00111
85766
86102
6

0

0

0.5 0.6 0.7 0.8
Clus-Fit Goodness

2 = 9.13
p = 0.166
85766
86102

0

0

100

200

r

300

400

500

2 = 18.3
p = 0.0105
85766
86102

4
3
2
1
0

0

10000

20000

30000

40000
t

50000

60000

70000

80000

Figure 6.18: A comparison of all BDT variables for a 24h run in the pre (85766) andpost (86102) datasets.

6. Restart Detection132
2 = 1868

p = 9.9e-37
85766
86102

7
6
5
4
3
2
1
0

0.2

0.3

0.4

0.5

0.6
BDT Score

0.7

0.8

0.9

1.0

Figure 6.19: A comparison of the BDT score between events in a 24h run in the pre(run 85766) and post (run 86102) datasets.

In this case, it would be useful to view the online rates with more temporal
granularity to determine if it was a sudden or gradual increase in the rate, andif the increase is coincident with some detector-related activities. The issue with
the WIT data between the pre and post periods inherently prohibits this. The
weekly-binned data up to June of 2021 in figure 6.20 shows that the selected
data exceeds what is expected based on the online data rates, as well as being
inconsistent week-on-week, confirming this data’s unsuitability.
A number of files in the entire dataset showed signs of failed reconstruction orsome form of corruption which may cause some of the more erratic online rates,
especially those seen in the post period. The following requirements were imposed
to ensure these erroneous files were removed:
1. N online pairs < 50 and file length < 1000 s.
While the typical file length cap is 87.38 s, a number of files were calculated tohave a longer length, which was sometimes reflected in the number of events

6. Restart Detection

133

Figure 6.20: The predicted BG and reactor rate over the entire dataset, binned weekly,
with no file quality requirements. Errors are statistical only.

they contained. Such files may therefore have an accurate file length andevent rate and should be retained.
2. N offline pairs < 20.
Similar to the previous cut, but ensuring a reasonable number of offline pairs.
3. File size > 1 MB.
WIT file sizes are typically between 40–60 MB; however, a number of smaller
files seemed to have a strangely large number of online events.
4. File length > 100 s for files of size > 70 MB.
Ensures that files which are larger in size are so because they cover a longer
period of data. This is the most impactful requirement, removing a large
portion of the intermediate period between the pre and post data where there
appears to be issues with the file length calculations and/or hardware trigger
counters.
Additionally, runs are removed if their total file size is more than halved following
these cuts. This is a relatively loose requirement given that a number of otherwise
good-quality runs are skewed by a single, extremely large file, and the majority

6. Restart Detection

134

of runs lose only 1–2 % of their total file size, if any at all. This requirement,
coupled with requirement 4 in the list above, removes the entirety of the datain the pre-post intermediate period.
Given the relative immaturity of SK-Gd, a number of calibration efforts were
undertaken over the course of 2021, including calibration campaigns around a week
in length in both the pre and post periods. The runs where calibration is active
must be discarded. Ideally the runs in between calibration runs would produce
viable data, when work is completed for the day and normal data taking resumes
overnight before calibration continues the next day. Inspecting the online pair rate
in such runs revealed a significant increase in events not localised to the calibration
ports, likely due to activity in the PMTs thanks to HV restarting or as a by-productof opening the tank to insert sources. Each entire calibration period, including
a day following, is therefore discarded in this work.
As well as removing these calibration periods, two weeks of data is set aside in
the pre period to calculate the background efficiency. Given the low rates involved
with this analysis, it is important to properly understand the expected backgroundrate. Two weeks of data straddling the 2021 new year was used to calculate thebackground efficiency. This subset was selected specifically to give the most accurate
prediction in the rest of the pre dataset. The separate two weeks of data used to
optimise the BDT cut wasn’t removed, as it doesn’t bias the BG rate calculations
and merely provides a general distribution to optimise against. The 24h run ofdata used as BG in the BDT training was excluded, however.
The trimmed-down rates are shown weekly-binned in figure 6.21, showing good
agreement between the prediction and the data in the pre period and an increased
and still somewhat erratic set of rates in the post.
Between figures 6.20 and 6.21, there is reason to believe the WIT issue itself
is the cause of the increased rates. Despite the file length issues being resolved at
the start of the post period and the overall improvement of the file quality, theerratic, high online event rate seems to persist. This is discussed in more detailin the context of the unblinded data in section 6.6.

6. Restart Detection

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Figure 6.21: The predicted BG and reactor rate over the entire dataset, weekly binned,
with file quality requirements. Errors are statistical only.

Livetime
[d]
Pre
35.6
Post
51.8

Total Rate
[/d]
1.6
3.7*

Total Events

BG Events

Frac. Err.

58
189*

50*
140*

0.13
0.073*

Table 6.2: The predicted pre/post results based on pre offline data and post online. An
asterisk denotes a predicted value.

With 100% livetime, the pre/post approach would provide 93 and 75 days of datain each dataset respectively; however, the trimming described above significantly
reduces this. The true total livetimes, calculated using the known run lengths, are35.6 d for the pre period and 51.8 d for the post. While the post period can be
expanded once the offline processing systems have been recovered, there is little
scope to expand the pre period, limiting the statistical strength of any conclusionthat could be gained from this analysis. Section 6.6 discusses an alternative approach
to livetime calculations, using the files themselves, which may retain more data
otherwise lost by removing whole runs. Despite this, between background efficiency
calculations, high data rates in 2020, and the abundance of calibration periods, thepre period will always be somewhat limited in its livetime. The expected pre/post
results using the reduced livetimes are given in table 6.2.

6. Restart Detection

6.6

136

Results

In the absence of a more in-depth systematic error evaluation, all errors shown inthese results are statistical only, calculated assuming Poissonian statistics using√
σ = N for N counts in each bin. The comparison between the rates measured
in the pre and post periods is given in figure 6.22, showing an increase in the rate
between the two periods far in excess of what is predicted. The measured rate in
the post period is (8.8 ± 0.4) d−1 while the predicted is 3.7 d−1 .

Figure 6.22: The pair rate in the pre and post periods, compared to the expected BG
and reactor rates. The red line represents the reactor rate with 100% efficiency. Errors
are statistical only.

Figure 6.23 shows that the weekly-binned rates match the pattern of the predictedbackground, albeit with a large offset. The implication of this is that the core
principle of tracking the background pattern through the online pair rate is somewhat
accurate, but another effect is causing the online→offline background efficiency
to dramatically increase between the two periods. A potential explanation is6. Restart Detection

137

Figure 6.23: The pair rate in the pre and post periods, weekly binned, compared tothe expected BG and reactor rates, with the livetime calculated using assumed 100%run lengths. The red line represents the reactor rate with 100% efficiency. Errors are
statistical only.

that the signal efficiency derived from MC is underestimated, meaning what isclassified as BG in fact may contain signal events and the increase in rate would
be greater than predicted.
The data in figure 6.23 is plotted alongside the predicted reactor interaction
rate, without any efficiency scaling. While the majority of the data points are
below this line, some lie above, implying that this increase is unlikely to be solely
driven by an increase in reactor rate.
Figure 6.24 shows the required signal efficiency in the pre period against theincrease in BG rate for the increase to be consistent with the expected reactor
neutrino rate. If the BG remained constant (1 on the x-axis), and the signal
efficiency similarly did not change between the pre and post periods (orange line),
then the signal efficiency would have to be an unreasonable 93% to explain theincrease. The predicted efficiency is 10.3% and, given that approximately half ofall events exhibit neutron capture on hydrogen with around 17% WIT efficiency,
an efficiency beyond 50% is generally unreasonable.
Figure 6.24 also shows these required efficiency curves for a range of relative
increases in the MC efficiency between the two periods. This increase would more

6. Restart Detection

138

Figure 6.24: The required signal (MC) efficiency in the pre period needed to explain theobserved pair rate increase for a range of BG rate increases and relative signal efficiency
increases.

likely be somewhat coupled to the change in BG rate, however, and so figure 6.25
displays these curves where the efficiency of the signal increases as a factor of the
BG. If this was driven by an change in dark rate, for example, the inflated numberof hits in the trigger window would boost the likelihood that an IBD pair would
pass the cuts, as well as accidental coincidences.
Another indication that this increase is not due to the reactors is that the weekon-week data points aren’t entirely consistent with one another, and it is expectedthat the reactor rate would remain approximately constant once the cores had
reached full power, as expected in this period. It is also expected, however, that there
are no time-dependant sources of background in SK. The detector itself remained
stable through each of these periods, with no major changes in its water supply or
gadolinium concentration. If the number of events is expected to remain constantwithin each period, suspicion may then fall on the livetime used to calculate the rate.
To calculate the rates given in figures 6.22 and 6.23, the total number of events
is counted and divided by the sum of the length of all runs used in the dataset. This

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Figure 6.25: The required signal (MC) efficiency in the pre period needed to explain
the observed pair rate increase for a range of BG rate increases where the MC efficiency
increases as a factor of the BG increase.

assumes that each run has 100% livetime, and the number and file size differences
before and after the quality cuts described in 6.5 typically reflect this. These cuts
may remove more viable data than is assumed, however, resulting in a disconnect
between the calculated and true livetimes.
The livetime can be alternatively calculated using the files themselves. While
WIT data doesn’t inherently contain a description of how long a period it covers,
the length of a file can be calculated using the difference in hardware triggers in
the data. This approach does not provide a fully accurate livetime, as the data in
the fully reconstructed file does not necessarily contain the first and last events of
the raw file produced by WIT. The file length calculated using this procedure will
therefore be underestimated by an amount equal to the sum of the time between
the true start of the file and the first event present, and between the last eventand the true end of the file. This varies depending on the event rate; however, thedifference is not insignificant. The difference between the run length and summed
length of all files in a run is given in figure 6.26. This shows that, in general, the6. Restart Detection

140

two rarely agree, especially during the pre/post intermediary period. It is therefore
difficult to quantify to what extent the file length-based calculations underestimate
the length of a run, and to determine which method is more accurate.

Figure 6.26: The difference between the known run length and run length derived fromthe sum of all calculated file lengths.

Regardless, the weekly-binned rates calculated using this alternative livetime
calculation are given in figure 6.27. Using this livetime calculation, a far more stablebackground rate is predicted, potentially indicating that the file length calculations
are more accurate than one would assume from figure 6.26. The average backgroundrate is predicted to be far higher than when calculated using the uncut run lengths.
This could confirm the theory that inaccurate run-based livetime calculations are
the cause of the varying background rates, as an overprediction of livetime would
lead to an underprediction of the background rates. If that were the case, figure 6.27
indicates insufficient background rejection by the BDT selection to demonstrate areactor-driven increase, which is unsurprising given that the BDT cut was optimisedusing a BG rate calculated using the run-based livetime approach.
Though the more-stable background implies the alternative livetime calculation
may be preferable, this approach needs more in-depth validation, and shows signs
that it may not be entirely accurate.

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141

Figure 6.27: The pair rate in the pre and post periods, weekly binned, compared tothe expected BG and reactor rates, with the livetime calculated using the file lengths as
opposed to assumed 100% livetime run lengths. Errors are statistical only.

Firstly, the difference between the true file length and the calculated filelength should be cross-checked through comparing raw WIT data with the fullyreconstructed pair data to determine the true significance of the missing start andend periods. If the deficiency is large enough to explain the disagreement shown infigure 6.26, then an offset or scaling can be applied to account for this. If instead
the missing time is insufficient, the file length calculations may be untrustworthy,
as it is unlikely that such a large portion of WIT data would have been lost. Thereexists an alternative approach to calculating the length of a file which uses hardware
trigger meta-information saved for each file; however, this method has not been
fully explored given that some files appear to be missing this information.
Secondly, the unstable period between the pre and post periods appears to be
driven at least in part by issues with the saved hardware trigger counter which would
be used to make this calculation. Until this issue is diagnosed and confirmed to
not affect the rest of the data, it is preferable to avoid making livetime calculations
using this information. Indeed, the higher offline rate observed in the post period
may be due to this issue itself causing a shift in the file length calculations, though
this would most likely be reflected in the background rate predictions.

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Regardless of which way the livetime is calculated, the measured rates in thepost period far exceed the predicted, and the reason for this is unclear and cannot
be easily identified without clear analysis of the pre-post transition period. Whilethe issues with this data prohibit a continuous pair rate measurement linking thetwo datasets, some initial investigations are possible.
If the quality cut removing files of spurious file length is removed (item 4 in thequality cuts listed in section 6.5), the majority of the intermediate data remains
available. While this data was specifically avoided due to issues with the hardware
triggers, figure 6.28 shows that the rates calculated using the file length method
suddenly increase immediately following the pre period, as expected; however,there appears to be no obvious disconnect between the intermediate and post
data periods. This would imply that the issue that motivated the rejection of theintermediate period is somehow still affecting the post data and is not exclusively
related to the file length calculations.

Figure 6.28: The pair rate across the whole WIT pair dataset, without quality cuts
which would remove the pre→post intermediary data. Livetimes are calculated using thesummed file lengths. Errors are statistical only.

Calculating livetime using the run length, shown in figure 6.29, similarly showsno obvious disconnect and arguably demonstrates more erratic week-on-week rates in6. Restart Detection

143

the post period compared to the intermediate, possibly indicative of the inaccuracy of
the run-based livetime calculations in this period where frequent calibration occurred.

Figure 6.29: The pair rate across the whole WIT pair dataset, without quality cuts
which would remove the pre→post intermediary data. Livetimes are calculated using the
run lengths. Errors are statistical only.

Given that the data largely agrees with the predicted rates in the pre period
when using either livetime calculations but are far in excess beyond this dataset, the
WIT issues must be addressed, if possible, before any strict conclusion can be drawn.
If this data is permanently corrupted, a future analysis could, instead of detecting
a new restart, monitor the monthly rate for a decrease in the pair rate coincident
with the refuelling of a reactor. Such an analysis would require either the cooperationof nuclear plant operators or corroboration of identified potential restarts with thosereported in the PRIS report when available. This would arguably act as a moreconvincing proof of the detection of reactor neutrinos, given the truly blind search
for a refuelling. It would also more realistically simulate the real-world motivation
for this analysis, where the activity of a single reactor core must be monitored
against a reactor background for unannounced shutdowns.

7Conclusion

Thanks to gadolinium loading, SK’s sensitivity to neutron capture, and therefore
inverse beta decay interactions, has increased significantly. For the first time in its
long-running history, the detector is in a position where it may be able to detecta significant number of reactor neutrinos. This is compounded with the uniqueposition the Japanese nuclear power sector is currently in, where a number ofreactors, offline in some cases for over a decade, have recently seen restarts. Thereis a window of WIT data available from December of 2020, when the detector hadstabilised following gadolinium loading, up to October of 2021, the latest data that
had been fully reconstructed before an upgrade to the SK computing systems broke
the processing software. In this window, a number of restarts took place which
increased the expected reactor interaction rate from 1.82 d−1 to 9.75 d−1 . Many
steps were taken in support of this unprecedented search in SK.
A coincidence trigger has been added to WIT, the system responsible for saving
the crucial ultra-low energy events of the focus of this search. This modification
relaxes the trigger requirements for events in temporal and spatial coincidence, aswith IBD positron/neutron pairs, and tags these coincident events with a unique
identifier. This tagging simplifies the offline identification of paired events andallows pairs to skip the first offline reduction step typically applied to WIT data.

144

7. Conclusion

145

To simulate the reactor neutrino spectrum at SK, the SKReact software wascreated. Based on [101], this provides a tuneable, SK-specific reactor neutrino
simulation package, including an estimation of the effect of reconstruction on theenergy spectrum. SKReact was used to generate the spectrum used as input toSK’s Monte Carlo software to produce the sample used to develop the reactor
neutrino selection.
The sample selection itself was supported by the newly-developed SPLASH
framework, a cut optimisation and machine learning-based analysis platform for use
with WIT and general SK data. SPLASH was used to develop an optimised cut-based
analysis; however, this was shown to provide insufficient background rejection toprovide a significantly detectable rate increase over the course of 2021 due to reactors.
A boosted decision tree was then developed using the XGBoost algorithm,
trained on 2021-spectrum MC events and real WIT data from the pre-reactor
restart period which was collectively treated as background. Though trained ona limited MC dataset, the BDT selection was optimised and shown to provide asignificant signal above the expected background rate based on pre-reactor restart
event rates in WIT. The expected signal efficiency was calculated to be 10.3%, witha predicted background rate of less than one event per day.
Inspection of the data quality throughout this 2020/2021 dataset revealed that,between March and August of 2021, the WIT data appeared to have erratic data
rates with inconsistent data file properties. As such, two periods were defined,
the “pre” and “post” periods signalling the data before and after this intermediate
period, and the intention of this study was to detect a significant increase inrate between the two periods.
The background rate in each period was predicted by first applying a soft “online”
BDT cut to a two-week period straddling the 2021 new year. Events which pass thispre-selection are referred to as online events. The efficiency of online background
events passing the full “offline” BDT cut was then measured. Finally, the number of
online events in the pre and post periods were scaled by this efficiency. This revealed
a significant increase in the background rate, as indicated by the increase in the7. Conclusion

146

online pair rate. Inspection of a run of pre and post data indicated there were some
shifts in the BDT input variables which may be indicative of an increase in darkrate, though the small sample size was insufficient to draw any clear conclusions.
Once unblinded, the data in the post period was found to be far in excessof the predicted rate which itself significantly exceeded both the measured andpredicted rates in the pre period. Though not inconsistent with an increase due toreactor neutrinos, the signal efficiency would have to have been underestimated to
explain the increase; what is defined as “background” would then instead containa significant number of signal events. Further inspection of the pre and post
datasets as well as the intermediary period signalled that the increase may be due
to persistent, as-yet undiagnosed issues with the WIT data.
Before any conclusion can be drawn, the issues with the WIT data must be
addressed and the confidence in the MC efficiency and therefore BG composition
further investigated. Based on the Monte-Carlo studies in this thesis, SK has
the capability to detect a significant increase in reactor neutrino rate due to areactor restart once these issues are addressed. An alternate analysis perhaps
aiming to identify a decrease in rate due to a reactor refuelling may be a sufficiently
convincing signal to confirm the identification of reactor neutrinos in SK. The
work in this thesis has laid all the necessary groundwork, from data acquisition
to the final analysis, to support such a search.

Appendices

147

A

Japanese and South Korean Nuclear
Reactors
Table A.1: All nuclear reactors in Japan and South Korea, ordered by (Pth )/(RSK )2
where Pth is thermal power output capacity of the reactor and RSK is the distance fromthe core to the SK detector [75]. An asterisk by a plant’s name denotes a South Korean
plant. A status of pending refers to plants that have applied for a restart and are pending
approval from either the local government or the NRA.

Plant

Core

Type

Shika

2
1
2
7
6
5
4
3
2
1
3
1
2
4
3
5
4
3

BWR
BWR
PWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
PWR
PWR
PWR
PWR
PWR
BWR
PWR
PWR

TsurugaKashiwazaki-Kariwa

MihamaOhi

HamaokaTakahama

PT h
[MW]
3926
1593
3411
3926
3926
3293
3293
3293
3293
3293
2440
3423
3423
3423
3423
3926
2660
2660

148

RSK
[km]
87.5
87.5
138.8
159.9
159.9
160.0
160.0
160.1
160.1
160.1
145.6
178.7
178.7
178.8
178.8
214.4
191.4
191.4

PT h /R2SK
Status−2[MW km ]0.513
Pending
0.208
Offline0.177
Pending
0.154
Pending
0.153
Pending
0.129
Offline0.129
Offline0.129
Offline0.128
Offline0.128
Offline0.115
Online0.107
Offline0.107
Offline0.107
Online0.107
Online0.085
Offline0.073
Online0.073
OnlineA. Japanese and South Korean Nuclear Reactors
HamaokaMihamaTakahama
Tsuruga
HamaokaMihamaTokai
Hamaoka
Fukushima-Daini

Fukushima-Daiichi

ShimaneOnagawa
Fukushima-Daiichi
ShimaneOnagawa
Ikata
Higashidori (Tohoku)
Shin-Kori*
GenkaiShin-Wolsong*
Hanul*

Kori*
Shin-Kori*
Ikata

3
4
2
2
1
1
2
1
2
1
1
2
3
4
6
2
3
5
4
2
2
3
1
1
1
3
1
4
3
3
4
1
2
6
5
4
3
2
1
4
3
1
2
2
1

BWR
BWR
PWR
PWR
PWR
BWR
BWR
PWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
BWR
PWR
BWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR

3293
3293
1456
2440
2440
1070
2436
1031
3293
1593
3293
3293
3293
3293
3293
2381
2381
2381
2381
2436
2436
2436
1380
1380
1593
2660
3293
3983
3983
3423
3423
2825
2825
2825
2825
2825
2825
2775
2775
2912
2912
2825
2825
1650
1650

149
214.3
214.3
145.7
191.4
191.5
138.9
214.6
145.6
295.8
214.6
345.1
345.1
345.2
345.3
349.2
349.1
349.2
349.2
349.2
400.6
430.6
430.6
349.0
400.7
430.6
560.3
636.1
732.0
732.0
753.7
753.7
708.9
708.9
709.0
709.0
709.1
709.2
709.3
709.4
732.5
732.6
732.0
732.0
560.4
560.5

0.072
0.072
0.069
0.067
0.067
0.055
0.053
0.049
0.038
0.035
0.028
0.028
0.028
0.028
0.027
0.02
0.02
0.02
0.02
0.015
0.013
0.013
0.011
0.009
0.009
0.008
0.008
0.007
0.007
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.005
0.005
0.005
0.005
0.005
0.005

Pending
Pending
OfflinePending
Pending
OfflineOfflineOfflinePending
OfflineOfflineOfflineOfflineOfflineOfflineOfflineOfflineOfflineOfflinePending
Pending
OfflineOfflineOfflineOfflineOnlinePending
OnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOnlineOfflineOfflineA. Japanese and South Korean Nuclear Reactors
Tomari
Wolsong*

Sendai
Kori*
Genkai
Hanbit*Tomari

3
4
3
2
1
2
1
2
1
1
2
3
4
5
6
1
2
1
2

PWR
PHWR
PHWR
PHWR
PHWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR
PWR

2660
2061
2061
2061
2061
2660
2660
1882
1729
1650
1650
2825
2825
2825
2825
2787
2787
1650
1650

150
783.1
708.6
708.7
708.8
708.9
829.8
829.8
732.7
732.7
753.6
753.7
987.0
987.0
987.0
987.0
987.0
987.0
783.3
783.4

0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.004
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003

Pending
OnlineOnlineOnlineOnlineOnlineOnlineOnlineOfflineOfflineOfflineOnlineOnlineOnlineOnlineOnlineOnlinePending
PendingB

Coefficients for Antineutrino Emission
Spectra of Reactor Fuels

Table B.1: Coefficients αpk of the Mueller et al. fifth-order polynomial parameterisationof antineutrino flux from elements k = 235 U, 238 U, 239 Pu and 241 Pu. In the column δαpk
the 1σ error on αpk are given [78].

k = 235 U
p
αpk
δαpk
1
3.217
4.09(-2)-3.1112.34(-2)
2
3
1.395
4.88(-3)
4 -3.690(-1) 6.08(-4)
5 4.445(-2) 7.77(-5)
6 -2.053(-3) 6.79(-6)

Correlation Matrix ρkpp′
1
2
3
4
5
6
1.00 -0.86 0.60 0.07 -0.17 -0.14-0.86 1.00 -0.84 0.12 0.25 0.01
0.60 -0.84 1.00 -0.56 -0.19 0.24
0.07 0.12 -0.56 1.00 -0.42 -0.14-0.17 0.25 -0.19 -0.42 1.00 -0.77-0.14 0.01 0.24 -0.14 -0.77 1.00

k = 238 U
αpk
δαpk
p
1 4.833(-1) 1.24(-1)
2 1.927(-1) 5.86(-2)
3 -1.283(-1) 1.11(-2)
4 -6.762(-3) 1.92(-3)
5 2.233(-3) 2.84(-4)
6 -1.536(-4) 2.86(-5)

Correlation Matrix ρkpp′
1
2
3
4
5
1.00 -0.86 0.20 0.30 0.08
-0.86 1.00 -0.58 -0.21 0.04
0.20 -0.58 1.00 -0.48 -0.17
0.30 -0.21 -0.48 1.00 -0.36
0.08 0.04 -0.17 -0.36 1.00
-0.27 0.23 0.20 -0.20 -0.77

151

6
-0.27
0.23
0.20
-0.20
-0.77
1.00

B. Coefficients for Antineutrino Emission Spectra of Reactor Fuels
k = 239 Pu
αpk
δαpk
p
1
6.413
4.57(-2)-7.4322.85(-2)
2
3
3.535
6.44(-3)
4 -8.820(-1) 9.11(-4)
5 1.025(-1) 1.38(-4)
6 -4.550(-3) 1.29(-5)

Correlation Matrix ρkpp′
1
2
3
4
5
6
1.00 -0.86 0.60 0.10 -0.17 -0.13-0.86 1.00 -0.84 0.08 0.25 -0.01
0.60 -0.84 1.00 -0.54 -0.20 0.26
0.10 0.08 -0.54 1.00 -0.45 -0.08-0.17 0.25 -0.20 -0.45 1.00 -0.79-0.13 -0.01 0.26 -0.08 -0.79 1.00

k = 241 Pu
p
αpk
δαpk
1
3.251
4.37(-2)-3.2042.60(-2)
2
1.428
5.66(-3)
3
4 -3.675(-1) 7.49(-4)
5 4.254(-2) 1.02(-4)
6 -1.896(-3) 9.03(-6)

Correlation Matrix ρkpp′
2
3
4
5
6
0.87 -0.60 -0.08 0.17 0.13
1.00 -0.84 0.11 0.25 -0.00-0.84 1.00 -0.56 -0.19 0.26
0.11 -0.56 1.00 -0.43 -0.11
0.25 -0.19 -0.43 1.00 -0.78
0.00 0.26 -0.11 -0.78 1.00

1
1.00
0.87
-0.60
-0.08
0.17
0.13

152

C

Fuel Contribution Fractions

153

C. Fuel Contribution Fractions

Core
Type

Frac

154

U

U

Pu

Pu

235

238

239

241

0.538
0.614
0.620
0.584
0.543
0.607
0.603
0.606
0.557
0.606
0.488

0.078
0.074
0.074
0.068
0.070
0.074
0.076
0.074
0.076
0.074
0.087

0.328
0.274
0.274
0.298
0.329
0.277
0.276
0.277
0.313
0.274
0.359

0.056
0.038
0.042
0.050
0.058
0.042
0.045
0.043
0.054
0.046
0.067

0.580
0.544
0.577
0.590

0.074
0.075
0.074
0.070

0.292
0.318
0.292
0.290

0.054
0.063
0.057
0.050

[117]

0.570

0.078

0.295

0.057

[119]

0.568

0.078

0.297

0.057

[120]

0.563

0.079

0.301

0.057

[121]

0.070
0.070
0.070
0.080

0.240
0.310
0.370
0.300

0.040
0.060
0.080
0.060

[122]

pi

0.650
0.560
0.480
0.560

[123]

MOX

pi

0.000

0.081

0.708

0.212

[123]

PHWR

pi

0.543

0.411

0.022

0.024

[124]

PWR
BWR
LWGR
GCR

fi

[115]

[116]

[118]

Table C.1: 235 U, 238 U, 239 Pu, and 241 Pu fission (fi ) or power (pi ) fractions for a rangeof reactor designs, compiled by [101].

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