Neutrino Physics in Present andFuture Kamioka Water-Čerenkov
Detectors with Neutron Tagging

Pablo Fernández Menéndez

A Dissertation Presented to the Faculty of Sciencesof University Autonomous of Madrid in Candidacy for the Degreeof Doctor of Philosophy

Recommended for Acceptance by the
Department of Theoretical Physics
PhD supervisor: Professor Luis Labarga

February 2017

Partially supported by
H2020-MSCA-RISE-2014-GA641540, SKPLUS – Marie Curie Actions

Abstract (English)
This thesis is focused on the upgrade of the Super-Kamiokande detector, consistingin the addition of a salt of gadolinium into the water of the detector to enable a very
high efficient capability to detect the neutrons produced in the detector: the SuperKGd project (former GADZOOKS!). This feature will improve largely the scientificpower of SK because the neutron production is related to the matter-antimattercharacter of the interacting neutrino; charged current interacting neutrinos tend to
produce less neutrons than their analogous antineutrinos. It also provides a newand powerful selection criterion for proton decay searches due to the fact that in a
proton decay, should it exist, basically no neutrons are produced in the final state.
In addition to these anticipated benefits, in this work other features are exploredfinding out new improvements due to neutron-tagging in various physics analyses.
For the realisation of SuperK-Gd, an exhaustive R&D program has been carried out.
It pivoted on the EGADS prototype and included many studies of different nature
to ensure the feasibility and performance of Gd-doped water-Čerenkov detectors.
This thesis covers works on EGADS, construction, calibration and monitoring, Gdneutron tagging implementation, capability and impact on the neutrino physics ona wide variety of physics phenomena within a broad energy range and from different
origins, including detectability of Diffuse Supernova Neutrino Background (DSNB),
supernova burst neutrinos, pre-supernova neutrinos (from Si-burning phase), reactor antineutrinos and solar neutrinos, and also neutrino oscillation parameters using
atmospheric and long baseline neutrinos. Since in the not-too-distant future experimental neutrino physics will need to build even larger detectors to address theremaining or new arisen unknown properties of neutrinos, this thesis also studies their
sensitivities for atmospheric and long baseline neutrinos for the Hyper-KamiokandeIIproject with neutron-tagging.
In order to proof the relevance of neutron-tagging in large water-Čerenkov detectors and confirm the studies with actual data, a complete and global analysis of SK
atmospheric neutrino data is performed including the previously developed neutrontagging tools applied to the 4th phase of Super-Kamiokande, which is already capableof detecting a low, but already useable, fraction of the neutrons produced throughhydrogen-neutron captures. It provides the most updated oscillation analysis on theatmospheric oscillation parameters of Super-Kamiokande (Note: results are preliminary).

IIIResumen (Spanish)
Esta tésis se concentra en la mejora del detector Super-Kamiokande, ésta consisteen la adición de una sal de gadolinio con el fin de conseguir una alta capacidad paradetectar los neutrones producidos en el detector: el proyecto SuperK-Gd (previamente GADZOOKS!). Esta nueva capacidad mejorará enormemente la produccióncientı́fica de SK porque la producción de neutrones está ı́ntimamente relacionada conel carácter materia-antimateria del neutrino al interaccionar; los neutrinos que interaccionan mediante corrientes continuas tienden a producir más neutrones que losantineutrinos. También aporta un nuevo y eficaz criterio de selección en la búsquedade decaimientos del protón, debido a que, si existen, estos no deberı́an producir apenas neutrones en el estado final. Además de estos ya anticipados beneficios, en este
trabajo, otras caracterı́sticas son investigadas, descubriendo nuevas mejoras que ladetección de neutrones ofrece al análisis de varios fenómenos fı́sicos.
Para la consecución de SuperK-Gd, se ha desarrollado un exhaustivo programa de
I+D. Éste se centra en el prototipo EGADS e incluye varios estudios de diferente
naturaleza para asegurar el buen funcionamiento de los detectores agua-Čerenkov
dopados con gadolinio.
Esta tésis cubre los trabajos realizados en EGADS, construcción, calibración y monitorización, ası́ como la implementación, capacidad e impacto de la detección de neutrones mediante gadolinio en una amplia variedad de procesos fı́sicos de diferentes
orı́genes y en un gran rango de energı́as, incluyendo la detectabilidad del Fondo Difuso de Neutrinos de Supernova (DSNB en inglés), ası́ como neutrinos procedentes
de supernovas, neutrinos de pre-supernovas (fase de quemado de Si), neutrinos dereactores y neutrinos solares, pero también, el impacto en el análisis de oscilaciones
de neutrinos atmosféricos y de neutrinos de aceleradores. Ya que el no tan lejanoIVfuturo de la fı́sica experimental de neutrinos necesitará la construcción de detectores
mayores para abordar las incógnitas en las propiedades de los neutrinos, en esta tésis,
también se realizan estudios de sensitividad para neutrinos atmosféricos y de aceleradores para el proyecto Hyper-Kamiokande con capacidad para detectar neutrones.
Para comprobar la relevancia de la detección de neutrones en grandes detectoresde agua-Čerenkov y confirmar los estudios hechos con datos reales, se realiza un
análisis global de oscilaciones de neutrinos atmosféricos incluyendo las herramientas
desarrolladas con la detección de neutrones en la cuarta fase de Super-Kamiokande,
el cual ya posee la capacidad de detectar una pequeña, pero considerable, fracciónde los neutrones producidos al ser capturados por el hidrógeno. Este análisis ofrece
los resultados más actuales para los parámetros de oscilación usando los datos deneutrinos atmosféricos de SK (Nota: los resultados son preliminares).

V

Resume (Asturian)
Esta tesis concéntrse na meyora del deteutor Super-Kamiokande, ésta consisten’adición duna sal de gadoliniu a fin d’algamar un’alta capacidá pa deteutar losneutrones producı́os nel deteutor: el proyeutu SuperK-Gd (enantes GADZOOKS!).
Esta nueva capacidá meyorará enormemente la produción cientı́fica de SK porque losneutrones tan muy lligaos al calter materia-antmateria del neutrino qu’interaicionen;
los neutrinos qu’interaicionen mediante corrientes cargáes amuesen una mayor
prudución de neutrones que los antineutrinos. Tamién purre un nuevu ya eficaz
criteriu pa la seleición na búsuqueda del decayimientu del protón, debı́u a que, si
esiste, esti nun purducirı́a apenes neutrones nel estáu final. Amás d’estes ventayes
ya sabı́os, nesti trabayu, investı́guense otres carauterı́stiques, escubriendo nueves
meyores que la deteución de neutrones ofréz al análisi d’otros fenómenos fı́sicos.
Pal llogru de SuperK-Gd, espoxigose un exhaustivu programa de I+D. Ésti céntrase
nel protutipu EGADS y axunta varios estudius pa asegurar el desenvolvimientu delos deteutores agua-Čerenkov dopaos con gadoliniu.
Esta tésis cubre los trabayos fechos n’EGADS, construción, calibración y monitorización, asina como la capacidá ya l’impautu de la deteución de neutrones colgadoliniu nun’amplia variedá de procesos fı́sicus de dellos orı́xes y nun gran rango
d’enerxı́es, incluyendo la deteutabilidá del Fondiu Difusu de Neutrinos de Supernova(DSNB en inglés), asina como neutrinos procedentes de supernoves, pre-supernoves(fase del quemáu de Si), neutrinos de reatores y neutrinos solares, pero tamién,estúdiase l’impautu nes camudaciones de neutrinos atmosféricos y d’aceleraores.
Debı́u a qu’el non tan lloñe futuru de la fı́sica esperimental de neutrinos pasa pola
construción de mayores deteutores, nesta tésis, tamién algámense estudios de sensitividá pa neutrinos atmosféricos y de aceleraores pal proyeutu Hyper-KamiokandeVIcon capacidá pa deteutar neutrones.
Pa ver la relevancia de la deteución de neutrones en deteutores de agua-Čerenkov ycaltener los estudios con datos reales, faise un análisis global de les camudaciones
de neutrinos atmosféricos incluyendo toes les ferramientes feches con la deteuciónde neutrinos na cuarta fase de Super-Kamiokande, la cual ya tien la capacidá dedeteutar una pequena, pero importante, fración de los neutrones pruducı́os nel deteutor al traviés de la so captura col hidróxenu. Esti análisis ofrez los resultaos más
actuales pa los parámetros de oscillación usando los datos de neutrinos atmosféricosde SK (Nota: los resultaos son preliminares).

VII

Acknowledgements
In the realisation of this thesis, several people have been certainly important andcrucial. First, I would like to thank my advisor Luis Labarga and the Kamioka Observatory director and spokesperson of the Super-Kamiokande experiment, Masayuki
Nakahata, who introduced me to the Super Kamiokande collaboration and accepted
my participation in the SuperK-Gd project since I was an undergraduate back in
2011. Also, from the very early days of my research professors Mark Vagins, Yusuke
Koshio and Michael Smy have helped me a lot in improving my skills and knowledge
in physics and its communication.
Once properly adapted to the SK collaboration, and since the beginning of my
PhD members of all the Super-Kamiokande and Hyper-Kamiokande collaborations
have, in greater or lower level, allowed me to learn a lot of fundamental physics. I
would like to emphasise the knowledge acquired from Lluis Martı́, Sekiya-san, Ikedasan, Yokozawa-san, Mori-san, Nakano-san, Yano-san, Yang Zhang, Takeuchi-san,Shiozawa-san, Ed Kerns, Chris Walter, Roger Wendell, Zepeng Li, Chris Kachulis,José Palomino, Hirota-san, Mine-san, Moriyama-san, Bill Kropp and Jeff Griskevich.
With a very special mention to Roger Wendell, a great person from whom I haveacquired a huge amount of knowledge, and without his dedication and patience animportant part of this work would not have been possible.
I am very thankful for the continuous support of my family, Manuel, Celestina andEncarna, which have been crucial not only to complete this job, but also to my personal development, helping me in every aspect of my life and coping with me and myhead. A part from these living people, I specially remember Argentina and Mario.
The first one was very important in my childhood and, most probably, without her
endless efforts I could not be where I am. The latter is, who I think, the major

VIIIcontributor of my tireless attitude for finding things out and for my love for mathematics and physics.
My friends have also contributed to this work with continuous support and interest.
I cannot avoid mentioning Adrián, Antonio, Carlos, César, Eddy, Fer, Jose and Juan.
And of course, my mind-mate Irene, who is the person most understands me andcares for me. She has been crucial producing uncomfortable, but incredibly enriching
discussions about almost everything and from who I have learnt countless things. I
thank all of them for accepting this disturbed mind of mine, that, I know, is notalways easy to deal with.

IX

Pa Mario, pa Irene y pa’quellos que-yos puea prestar.

Pensa uomo, pensa.

X

Contents
Abstract/Resumn/Resume . . . . . . . . . . . . . . . . . . . . . . . . . . .

IIAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII
1 Preface

1

2 Neutrinos

7

2.1

2.2

2.3

2.4

Main Neutrino Sources . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.1.1

Atmospheric Neutrinos. . . . . . . . . . . . . . . . . . . . .

9

2.1.2

Accelerator Neutrinos. . . . . . . . . . . . . . . . . . . . . .

11

2.1.3

Solar Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.1.4

Reactor Neutrinos. . . . . . . . . . . . . . . . . . . . . . . .

14

Supernova Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.2.1

Supernova Burst . . . . . . . . . . . . . . . . . . . . . . . . .

15

2.2.2

Diffuse Supernova Neutrino Background . . . . . . . . . . . .

18

Neutrino Mass and Neutrino Oscillations . . . . . . . . . . . . . . . .

19

2.3.1

Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . .

20

2.3.2

Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . .

24

2.3.3

Experimental Status . . . . . . . . . . . . . . . . . . . . . . .

32

Neutrino-Nucleus Interactions . . . . . . . . . . . . . . . . . . . . . .

33

XI

CONTENTS

3 The Super-Kamiokande Detector

43

3.1

Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.2

Čerenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3.3

Detector Description . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

3.3.1

Water Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.3.2

Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.4

Water and Air Purification Systems . . . . . . . . . . . . . . . . . . .

51

3.5

SK-IV Electronics and Data Acquisition . . . . . . . . . . . . . . . .

53

3.6

Calibration of the Detector . . . . . . . . . . . . . . . . . . . . . . . .

55

4 The SuperK-Gd Project

57

4.1

Gadolinium-Neutron Tagging . . . . . . . . . . . . . . . . . . . . . .

58

4.2

Gadolinium Addition to Super-Kamiokande . . . . . . . . . . . . . .

61

4.3

Main Physics Outcomes . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.3.1

Low Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

4.3.2

High Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

EGADS R&D Program and Experiment . . . . . . . . . . . . . . . .

66

4.4.1

Detector Description . . . . . . . . . . . . . . . . . . . . . . .

66

4.4.2

Water Purification System . . . . . . . . . . . . . . . . . . . .

67

4.4.3

Data Acquisition System . . . . . . . . . . . . . . . . . . . . .

68

4.4.4

PMT Pre-Calibration . . . . . . . . . . . . . . . . . . . . . . .

69

4.4.5

Detector Construction and Instrumentation . . . . . . . . . .

71

4.4.6

Monitoring and Main Results of the EGADS Program

72

4.4

. . . .

5 On Relevant Items for SuperK-Gd Physics

79

5.1

Neutron Production in Neutrino-Nucleus Interactions . . . . . . . . .

80

5.2

Gd-Neutron Tagging Reconstruction . . . . . . . . . . . . . . . . . .

83

XII

CONTENTS

5.2.1

Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . .

83

5.2.2

Neutron Tagging Algorithm . . . . . . . . . . . . . . . . . . .

88

5.2.2.1

First Candidate Selection . . . . . . . . . . . . . . .

89

5.2.2.2

Gd-Neutron Capture Selection Likelihood . . . . . .

91

5.2.3

Overall Gd-Neutron Tagging Efficiency . . . . . . . . . . . . . 104

5.3

Classification of Charged Current and Neutral Current Interactions . 106

5.4

Neutrino-Antineutrino Separation

5.5

Neutron-Corrected Reconstructed Neutrino Energy . . . . . . . . . . 115

5.6Radioactive Contamination
5.6.1. . . . . . . . . . . . . . . . . . . 110. . . . . . . . . . . . . . . . . . . . . . . 117

Measurement of Radioactive Contamination in Materials with
HPGe Germanium Detectors: Gadolinium Sulphate . . . . . . 120

5.6.2

238

5.6.3

Radioactivity-Induced Neutron Production . . . . . . . . . . . 125

5.6.4

β-Rays from Radioactivity . . . . . . . . . . . . . . . . . . . . 128

U Spontaneous Fission . . . . . . . . . . . . . . . . . . . . . 123

6 SuperK-Gd Physics Potential

131

6.1

Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.2

Diffuse Supernova Neutrino Background . . . . . . . . . . . . . . . . 135

6.3

Silicon Burning Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.4

Supernova Burst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.5

Solar Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.6

Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.6.1

Monte Carlo Simulation, Event Classification and Reconstruction in Super-Kamiokande . . . . . . . . . . . . . . . . . . . . 143
6.6.1.1

Atmospheric Neutrino Simulation . . . . . . . . . . . 144

6.6.1.2

Atmospheric Data Reduction . . . . . . . . . . . . . 150

XIII

CONTENTS

6.6.1.3
6.6.2

Atmospheric Event Reconstruction . . . . . . . . . . 153

Neutral Current and Charged Current Separation for Fully
Contained Samples . . . . . . . . . . . . . . . . . . . . . . . . 159

6.6.3

Neutrino and Antineutrino Separation for Fully Contained
Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.6.4

6.6.3.1

SubGeV and MultiGeV e-like . . . . . . . . . . . . . 165

6.6.3.2

SubGeV and MultiGeV µ-like . . . . . . . . . . . . . 168

6.6.3.3

MultiRing CC νe -like . . . . . . . . . . . . . . . . . . 171

6.6.3.4

MultiRing µ-like . . . . . . . . . . . . . . . . . . . . 174

Neutron-Corrected Reconstructed Neutrino Energy for Fully
Contained Samples . . . . . . . . . . . . . . . . . . . . . . . . 177

6.6.5

6.7

Oscillation Analysis Sensitivity . . . . . . . . . . . . . . . . . 187
6.6.5.1

Analysis Method . . . . . . . . . . . . . . . . . . . . 187

6.6.5.2

Oscillation Sensitivity Study . . . . . . . . . . . . . . 189

Long-Baseline Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.7.1

The T2K experiment . . . . . . . . . . . . . . . . . . . . . . . 195

6.7.2

Monte Carlo Simulation and Gd-neutron Tagging . . . . . . . 197

6.7.3

T2K Neutrino Event Selection . . . . . . . . . . . . . . . . . . 198

6.7.4

Neutrino-Antineutrino Separation . . . . . . . . . . . . . . . . 198
6.7.4.1

e-like Neutrino Sample . . . . . . . . . . . . . . . . . 199

6.7.4.2µ-like Neutrino Sample . . . . . . . . . . . . . . . . . 201

6.7.5

Neutron-Corrected Reconstructed Neutrino Energy . . . . . . 203

6.7.6

Oscillation Analysis . . . . . . . . . . . . . . . . . . . . . . . . 207
6.7.6.1

6.8

Oscillation Sensitivity Study . . . . . . . . . . . . . . 208

The Next Generation: Physics Potential of Gd-Doping in HyperKamiokande . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

XIV

CONTENTS

6.8.1

Detector Description . . . . . . . . . . . . . . . . . . . . . . . 211

6.8.2

Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . . . 214
6.8.2.1

6.8.3

Oscillation Sensitivity Study . . . . . . . . . . . . . . 215

Long Baseline Neutrinos . . . . . . . . . . . . . . . . . . . . . 219
6.8.3.1

Oscillation Sensitivity Study . . . . . . . . . . . . . . 220

7 Neutron-Tagging with Hydrogen in Super-Kamiokande IV: Global
Atmospheric Neutrino Oscillation Analysis with SK
7.1

Hydrogen-Neutron Tagging . . . . . . . . . . . . . . . . . . . . . . . . 224
7.1.1

7.2

223

H-Neutron Tagging Analysis . . . . . . . . . . . . . . . . . . . 225
7.1.1.1

First Candidate Selection . . . . . . . . . . . . . . . 225

7.1.1.2

H-Neutron Capture Selection . . . . . . . . . . . . . 226

Including Neutron-Tagging Information in SK Atmospheric Neutrino
Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.2.1

Neutral Current and Charged Current Separation for Fully
Contained Samples . . . . . . . . . . . . . . . . . . . . . . . . 229

7.2.2

Neutrino and Antineutrino Separation for Fully Contained
Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

7.2.3

7.2.2.1

SubGeV and MultiGeV e-like . . . . . . . . . . . . . 236

7.2.2.2

SubGeV and MultiGeV µ-like . . . . . . . . . . . . . 240

7.2.2.3

MultiRing CC νe -like . . . . . . . . . . . . . . . . . . 244

7.2.2.4

MultiRing µ-like . . . . . . . . . . . . . . . . . . . . 250

Neutron-Corrected Reconstructed Neutrino Energy for Fully
Contained Samples . . . . . . . . . . . . . . . . . . . . . . . . 257

7.3

Oscillation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.3.1

Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . 261

XV

CONTENTS

7.3.1.1

Neutrino Flux Errors . . . . . . . . . . . . . . . . . . 262

7.3.1.2

Neutrino Interaction Errors . . . . . . . . . . . . . . 266

7.3.1.3

Event Reduction Errors . . . . . . . . . . . . . . . . 268

7.3.1.4

Event Reconstrucion Errors . . . . . . . . . . . . . . 269

7.3.1.5

Fully Contained Event Selection Errors . . . . . . . . 270

7.3.1.6

Neutron Energy Corrections for Fully Contained Events280

7.3.2

Oscillation Sensitivity Study . . . . . . . . . . . . . . . . . . . 281

7.3.3

Data Fit Results . . . . . . . . . . . . . . . . . . . . . . . . . 286

8 Conclusions (English)

293

9 Conclusiones (Spanish)297

A Evaluation of Systematic Errors in the Neutrino Oscillation Analyses with SuperK-Gd

301

A.1 Fully Contained Event Selection Errors . . . . . . . . . . . . . . . . . 301
A.2 Neutron Energy Corrections for Fully Contained Events . . . . . . . . 308
B Evaluation of Systematic Errors in the Neutrino Oscillation Analyses with Hyper-Kamiokande

311

B.1 Fully Contained Event Selection Errors . . . . . . . . . . . . . . . . . 311
B.2 Neutron Energy Corrections for Fully Contained Events . . . . . . . . 318
C Neutron-Corrected Energy for Fully Contained Events in SuperKamiokande with H-Neutron Tagging

321

D Systematic Errors at Best Fit Point in the Global Atmospheric Neutrino Oscillation Analysis with H-neutron Tagging in SK

XVI

327

CONTENTS

Bibliography

329

XVII

1. Preface
Neutrinos are the only particles showing deviation from the Standard Model ofFundamental Interactions (SM) [Weinberg67, Glashow70]. It states that they aremassless but they are not. This was discovered by the Super-Kamiokande (SK) experiment in 1998 from the observation of a deficit in the atmospheric neutrino data,
correlated to the distance of their production point [Fukuda98a]. Those oscillations
come from changes from one neutrino flavour to another during their flight to SK,
implying that their mass eigenstates are different to their flavour eigenstates.

There are many natural and human-made neutrino sources. Some are known as
our Sun (and most probably the rest of the stars), supernovae, cosmic rays interacting with the atmosphere, nuclear reactors, neutrino accelerators and radioactive
decays of unstable isotopes, and some others are only conjectured like black holes[Halzen95], dark matter [Choi15] and gamma ray bursts [Vietri98]. In addition,
there is the widely accepted cosmic neutrino background generated after the very
first second from the Big Bang [Faessler16]. This diversity in origin also determines
their characteristics, such as flavour or energy, providing information about a broad
range of physics phenomena and properties.

1

CHAPTER 1. PREFACE

Although neutrinos are the most abundant of the known massive particles in our
universe, adding up to 0.3% of its total mass, they are extremely hard to detect due
to their tiny interaction cross sections, only through nuclear weak force. For thatreason, in order to detect them and study their properties, huge experiments withvery large amount of active matter and very low background are needed. One of themost successful technology employed in neutrino experiments is the so called waterČerenkov. They measure the radiation emitted by charged particles traveling in thewater (for instance those originated in a neutrino interaction) with momentum larger
than their Čerenkov threshold. This is the case of all the ongoing and projected
experiments treated in this thesis.

Large water-Čerenkov detectors have provided numerous and crucial discoveries
and results for neutrino physics. These kind of experiments, and specially SuperKamiokande, are responsible of the major discoveries in neutrinos physics up to date.
The precursor of SK, the KamiokaNDE experiment, first detected supernova neutrinos from SN1987a [Hirata87], and Super-Kamiokande is responsible for the discoveryof neutrino oscillations using atmospheric neutrinos, it solved the solar neutrino
problem by measuring with high precision solar neutrinos [Fukuda98b, Fukuda99a],
providing also the first indication of the day-night asymmetry of solar neutrinos due
to terrestrial effects [Renshaw14]. Furthermore, Super-Kamiokande has been the far
detector of the K2K neutrino beam [Ahn03, Ahn06], confirming the atmosphericoscillation parameters and, currently, it is the T2K far detector providing the world’s
most stringent bounds for the CP violating phase [Abe15a]. Super-Kamiokande isalso a leader in the measurement of the supernova relic neutrinos (DSNB), having
the best limits to its flux [Bays12, Zhang14]. In addition and besides neutrino
physics, SK has also the best limits for a numerous variety of exotic nucleon decays,2

such as proton decay [Miura16] or neutron-antineutron oscillations [Abe15b], bothpredicted by Grand Unified Theories (GUT) beyond the Standard Model (SM) of
particles.

The core of this work is focused on the near future upgrade of the SuperKamiokande detector consisting in the addition of a salt of gadolinium into thewater of the detector to enable a very high efficient capability to detect the neutrons produced in the detector. This upgrade is called SuperK-Gd, (previously
GADZOOKS!) [Vagins04]. This feature will largely improve the detection power ofSK because the neutron production is related to the matter-antimatter character ofthe interacting neutrino: charged current interacting neutrinos tend to produce lessneutrons than their analogous antineutrinos. It also provides a new and powerfulselection criterion for proton decay searches due to the fact that proton decays,
if exist, are accompanied by almost no neutrons in the final states. In addition
to these anticipated benefits, this work explores other features and finds out new
improvements from neutron-tagging to various physics analyses.
This work covers Gd-neutron tagging implementation, capability and impact on theneutrino physics, comprising a wide variety of physics phenomena within a broad
energy range and from different origins. It presents detectability studies for Diffuse
Supernova Neutrino Background (DSNB), supernova burst neutrinos, pre-supernova
neutrinos (from Si-burning phase), reactor antineutrinos and solar neutrinos, andalso sensitivity studies to neutrino oscillation parameters using atmospheric andlong baseline neutrinos.
For the realisation of SuperK-Gd, an exhaustive R&D program and feasibility studies have been done, being the most important the EGADS program. The EGADS
prototype for SuperK-Gd is a scaled down SK detector where most of the technology

3CHAPTER 1. PREFACE

needed for the addition of Gd to a water-Čerenkov detector was developed. In
parallel to the R&D at EGADS, another studies have been performed to assure thefeasibility of Gd-doped water-Čerenkov detectors and their performance.
For the not-too-distant future of neutrino physics in water-Čerenkov detectors evenlarger detectors will be needed to be built to address the remaining unknown properties of neutrinos. This this thesis also presents a sensitivity study for atmosphericand long baseline neutrinos for the Hyper-Kamiokande project with neutron-tagging.
In order to proof the relevance of neutron-tagging in large water-Čerenkov detectors
with actual data and confirm the studies carried out, a complete and global analysis
of SK atmospheric neutrino data is performed including the previously developed
neutron-tagging tools applied to SK’s fourth phase which is capable of detecting
a low fraction of the neutrons produced through hydrogen-neutron captures. This
provides the most updated and with the most stringent limits on the atmosphericoscillation parameters of SK (Note: results are preliminary).
In Chapter 2, an overview of neutrino physics is given, from its theoretical prediction
to the current state of neutrino physics experiments, containing an explanation of
how each neutrino source can be used to solved different neutrino physics and how
they are connected with some of the most fundamental problems in physics. This
Chapter also includes a description of the neutrino-nucleus interactions, which areof great importance for water-Čerenkov detectors.
In Chapter 3, a brief description of the Super-Kamiokande experiment is presented,
which will be used as detector framework for the rest of the work involving SuperKGd and Hyper-K.
Chapter 4 deals with the projected and approved upgrade of SK by dissolving agadolinium salt into its water to enhanced the detection of the final state neutronsof the interactions occurring in the detector. Along this Chapter, the Gd-neutron4

tagging technique will be fully described, as well as the main R&D program towards
the realisation of SuperK-Gd.
In Chapter 5 the neutron production mechanisms from neutrino physics is reviewed
and, then, the Gd-tagged neutron reconstruction is developed, as well as various
tools which use neutrons as base, such the neutrino-antineutrino separation, theneutral and charged current interactions discrimination and the neutrino energy corrections with neutrons. Finally, an important issue, as the study of the radioactive
contamination added with the Gd salt is explained.
Chapter 6 uses all the items explained in the previous Chapter to perform studiesof the physics potential of SuperK-Gd and also the extension to the next generation
detector, Hyper-Kamiokande.
In Chapter 7, the Gd-neutron tagging tools are applied to SK-IV data with Hneutron tagging and a global atmospheric oscillation analysis is performed withall SK data. Finally, the current status and future prospects of neutrino physics,
the most important results and the conclusions extracted from them are shown in
Chapter 8.

Based mainly on the results of this doctoral work, the author has presented thefollowing conferences, posters and documents:• Oral presentation, Identifying ν with Super-Kamiokande: GADZOOKS!, status
and some of its current challenges at International Meeting of Fundamental
Physics, Santander, Spain.

• Poster, Identifying ν with Super-Kamiokande: GADZOOKS!, status and remaining issues at INVISIBLES13 workshop, Durham, United Kingdom

5

CHAPTER 1. PREFACE• Oral presentation and proceedings, Status of GADZOOKS!: Neutron-tagging
in Super-Kamiokande at International Conference of High Energy Physics(ICHEP14), Valencia, Spain.
• Poster and proceedings, GADZOOKS!: status and physics potential at International Cosmic Ray Conference (ICRC15), The Hague, The Netherlands.
• Poster and proceedings, Gd-doping and the impact on SuperK and T2K at
Neutrino16, London, United Kingdom.
• Oral presentation, Gd-doping and the impact on SuperK and T2K at Next Generation Nucleon Decay and Neutrino Experiments (NNN16), Beijing, China.
• GADZOOKS! proposal: document presented to SK and T2K collaborations
reviewing the feasibility and impact of SuperK-Gd.

6

2. Neutrinos

Neutrinos are, currently, the most unknown particles in the SM, therefore, the physics
related to them, involve many fields and there are various independent experiments
dedicated to measure their properties, such as their masses or their oscillation parameters. Neutrinos are crucial in theoretical models beyond the Standard Model[Bilenky15, Ringwald16] and may be key to solve the flavour problem [King04b] orused as motivation to a hidden symmetry in quark sector to explain the strong CP
problem [Cao15]. Another peculiarity of neutrinos is that they lack of right-handed
partners and are neutrally charged (electric and colour) being a reasonable candidate
to be a Majorana particle [Majorana28].
In addition, they are important also in cosmology because their number of species
determine the element abundances and could be they key to understand the matterantimatter asymmetry of our universe [Chen16].
This thesis and this chapter will be focused on the study of astrophysical neutrinos
and atmospheric and long baseline neutrino oscillation parameters. Nevertheless, abrief introduction and description of the whole neutrino physics picture is presented.

7

CHAPTER 2. NEUTRINOS

2.1

Main Neutrino Sources

There are various neutrino sources, booth natural and artificial. The formers have thebenefit that usually produce neutrinos in large quantities and help us understanding
the subjacent physics process which may, in some cases, be very complex. On theother hand, artificial sources produce fewer neutrinos but with a much better known
properties, such as energy, direction, flavour and travelled distance.

Figure 2.1: Spectrum of all neutrino sources except accelerator neutrinos. CνB (Cosmological Neutrino Background with T=1.9 K after the Big Bang), solar neutrinos, neutrinos from SN1987A burst (few seconds), reactor neutrinos, terrestrial neutrinos, atmospheric neutrinos, the so-called GZK (Greisen-Zatsepin-Kuzmin) neutrinos and AGN (Active Galactic Nuclei) neutrinos [Spiering12].

The upcoming paragraphs will be describing the main neutrino sources that willbe treated along this thesis, looking at the main characteristics of the neutrinos
produced and arguing their physics potential.

82.1. MAIN NEUTRINO SOURCES

2.1.1

Atmospheric Neutrinos

Atmospheric neutrinos are produced in the interaction of cosmic rays with the
Earth’s atmosphere [Honda15]. Cosmic rays are made up of high energy particles
arriving at the Earth from many places in the Universe, these particles are, mainly,
protons, ∼5% are Helium nuclei and the remaining fraction are heavier nuclei.

Figure 2.2: Schematic diagram of neutrino production from cosmic rays interacting withthe atmosphere.

These particles interact with the Earth’s atmosphere and produce π and K mesons,which are unstable and decay into other particles, being neutrinos a significant fraction of them. In Equation (2.1), the decays with the largest branching ratios (BR)9

CHAPTER 2. NEUTRINOS

are shown.
K + → µ+ + νµ → e+ + νe + ν µ + νµ (BR = 63.6%)
K − → µ− + ν µ → e− + ν e + νµ + ν µ
K + → π+ + π0

(BR = 20.7%)

K + → π− + π0
K + → π+ + π+ + π−

(BR = 5.6%)(2.1)

K + → π− + π− + π+
K + → π 0 + e + + νe

(BR = 5.1%)

K + → π 0 + e− + ν e
π + → µ+ + νµ → e+ + νe + ν µ + νµ(BR ∼ 100%)

π − → µ − + ν µ → e − + ν e + νµ + ν µ
The neutrino energy spectrum strongly depends on that of the primary cosmic-ray
flux, which decreases with energy, at, approximately, a rate of E −2.7 , for energies
larger than 1 GeV.
The neutrino production can be, naively, obtained from the previous interactions,
(−)

(−)

noting that there are about twice as many ν µ than ν e . Additionally, neutrinos areproduced homogeneously in all the Earth’s atmosphere, causing the up-going anddown-going neutrino fluxes to be almost the same if oscillations are not taken into
account. The actual and detailed computation of atmospheric neutrinos is a very
difficult task because of the different compositions of the atmosphere depending on
the location, the variety of production mechanisms, the wide energy range and also
due to the effect on the cosmic rays of the solar activity [Richard15] and the Earth’s
magnetic field.

102.1. MAIN NEUTRINO SOURCES

2.1.2

Accelerator Neutrinos

These are human-made neutrino sources, usually obtained by accelerating protons in
a synchrotron and, then, made collide with a target to produced large quantities ofmesons, mainly π and κ [Kopp07], rather analogous to the production of atmospheric
neutrinos. Of the mesons produced those with the same charge are selected through aseries of magnets and will mostly decay into muon neutrinos or muon antineutrinos,
depending on the operation mode of the accelerator, ν or ν mode. The resulting
neutrinos are sent to the near and far detectors in which, some of these neutrinos
will be detected almost unmistakably due to their well known energy and direction.
This kind of facilities provides neutrinos with much better determined characteristics
than those coming from other sources. This makes possible neutrino oscillation
analyses more efficient, achieving high sensitivities with much lower statistics.

2.1.3

Solar Neutrinos

The Standard Solar Model is a very successful theory developed, mainly, by John
Bahcall [Bahcall64, Bahcall92] which models the evolution, activity and processes
inside the Sun. The basic assumptions for the model are that it is in hydrostatic
equilibrium implying that the sun evolves with a local balance between pressure andgravity, the energy in the sun is transferred via radiation, convection, conduction
and neutrino losses (being the first two the most important ones), the energy is
only produced from thermonuclear reactions and that the initial condition was ahomogeneous sun.
During stellar evolution, hydrogen is burnt into helium in the hot and dense core,
there are two mechanisms for this conversion, the pp chain and CNO cycle, being
the former the dominant process in the sun and the one that produces Hep and 8 B

11

CHAPTER 2. NEUTRINOS

neutrinos, those detected by Super-Kamiokande [Fukuda99b, Fukuda99a].
Using this theory, the solar neutrino flux was calculated to be proved by the Homesteak experiment in the 1960’s by Ray Davis [Davis Jr68], where it was found to beapproximately 1/3 of the predicted flux.

Figure 2.3: Scheme of the solar neutrino production due to the nuclear interactions in theSun.

Despite the robustness of the solar model and the quality on the experimental side,
it was thought that something should be wrong in one or both of them. This was
known as the solar neutrino problem, which was understood as soon as neutrino
oscillations entered the game. Neutrino oscillations in the sun must be done taking
into account the matter effects of the sun, in which, the electron density is hugein the core (Ne,core =150 g/cm3 ) and decreases towards the surface. Neutrinos arethought to travel through the sun adiabatically, originated νe in the core of the12

2.1. MAIN NEUTRINO SOURCES

sun will emerge from the surface having oscillated to ν̃2 , the second neutrino mass
eigenstate with sun matter effects. Neutrinos will travel in this state until the hit
the Earth where there could be an enhancement of the νe as they travel throughthe Earth, this leads to a slightly larger νe flux during the night as compared withdaytime, know as the solar neutrino day-night effect.
The MSW effect, [Mikheyev85], for certain values of the mass squared splitting,the energy dependence of the νe survival probability can lead to a distortion of theobserved energy spectrum. For the current mass squared splitting and mixing angle
preferred values by solar neutrino data, the MSW resonance in the Sun will occur at∼3 MeV. This, highly distorting the observed solar neutrino spectrum by inducing
an upturn when going from high to low energies. The observation of this upturn inthe solar neutrino energy spectrum, would be a direct signature of MSW type solar
neutrino oscillations.

Figure 2.4: Solar neutrino spectrum.

SK’s latest flux measurement for 8 B neutrinos is Φ8 B (SK) = (2.345 ± 0.014 ±0.036) · 106 cm−2 s−1 [Abe16b].

13

CHAPTER 2. NEUTRINOS

2.1.4

Reactor Neutrinos

Nuclear reactors generate energy by the fission of heavy nuclei, usually 235 U, thesefragments have way too many neutrons, and are unstable, decaying through a seriesof α and β-decays into stable nuclei with a lower ratio of neutrons to protons[Declais94].
In β-decays, many ν e are produced. Their energy spectrum can be calculated fromthe estimate of the number of neutrinos produced per fission, the power output,
and taking into account all the additional fissionable isotopes produced from theprimary fissions, such as 239 Pu, 241 Pu or 238 U.

This last term is the most difficult term tocompute and which carries most of the sizeable
error of the computation. This is currently
compensated with the installation of a neardetector as in the case of accelerator neutrinos, where, without neutrino oscillations, thereactor antineutrino energy spectrum can bebetter measured, canceling out most of thesystematic errors.

2.2

Figure 2.5: Neutrino energy spectrum from the different isotopes
used as fuel in nuclear reactors.

Supernova Neutrinos

Supernovae are one of the most energetic events occurring in our universe and which
produce an enormous amount of neutrinos. Since just one or two of these explosions
happen in a hundred years, and close enough to detect their neutrinos, they are14

2.2. SUPERNOVA NEUTRINOS

treated separately from the previous section concerning the most common neutrino
sources. Neutrinos coming from this phenomenon are of great importance from aphysical viewpoint and play a key role in the development of this work.

2.2.1

Supernova Burst

Supernovae are explosions occurring at the end of life of a massive star. They areusually categorised depending on the abundances of certain spectral lines.

In terms of neutrinos, the most interestingsupernovae are those whose mass is more thaneight solar masses and their core collapses
produce large quantities of neutrinos of all
kinds, i.e. TypeIb, TypeIc and TypeII. During a core-collapse explosion, around 99% of
the gravitational binding energy liberated iscarried away by neutrinos, leaving afterwards

Figure 2.6: Diagram of the dynamics of matter and neutrinos during
Supernova core-collapse.

a neutron star or a black hole [Burrows13].
The evolution of such stars begins with the burning of hydrogen, turning it into
helium as seen in Figure 2.3, for the solar case. Once it runs out of most hydrogenin the core, the star collapses increasing the core’s density, and allowing the helium
fusion into carbon. This process continues with heavier elements making the star
being separated in layers of different elements.

15

CHAPTER 2. NEUTRINOS

Figure 2.7: Scheme of the supernova types depending on the former star.

The last stage, before the core-collapse, is the Si-burning phase, also known as the
pre-supernova phase. This phase occurs in the final days of a massive star before
the core-collapse. It starts when the central temperature exceeds 3 · 109 K. This
stage includes a complex combination of photo-disintegration and α-capture reactions, playing a key role in the future supernova explosion. During the Si burning
phase ∼1% of the total energy of core-collapse are emitted through pre-supernova
neutrinos. Antineutrinos from Si burning stage have an average energy of 1.85 MeV,
much less than the typical 10 to 20 MeV of supernova neutrinos.
Once the silicon in the core is exhausted, the star begins to collapse again, andthis time no nuclear fusion will compensate the gravitational force only the electron
degeneracy. The matter is then accelerated towards the centre, increasing density
and temperature rapidly, making electrons and protons to be quickly converted into
neutrinos and neutrons, which diminishes the electron degeneracy. This causes thecollapse to occur quicker and quicker. This process is called neutronisation burst andneutrinos created during this stage are inside the core, which reaches densities large

16

2.2. SUPERNOVA NEUTRINOS

enough to slow, or, even trap, the neutrinos from escaping during a few milliseconds.
Depending on the theoretical model and mass of the star, the neutrino emission andthe last details of the star’s life may vary, but, in general, most of the gravitationalenergy of the star is released in the form of neutrinos with same abundance in all
flavours. These neutrinos and antineutrinos evolve very differently due to the charged
leptons associated, such that the muon and tau neutrinos interact only via NC interactions, as seen in Figure 2.12. This makes that hEν i < hEν i < hE(−) i ≈ hE(−) i.
ν µ

ν τ

Figure 2.8: νe (solid line), ν e (dashed line) and the rest of neutrino types (dotted line)
spectra from a core-collapse supernova produced by a fifteen solar mass star. In the righthand plot, the upper lines are the luminosity (L) and the lower lines are the mean energy(hi).

After exploding, the majority of the light elements and the outer layers are dispersed, leaving a hugely dense neutron core. Of these stars, those beginning withless than twenty solar masses, are left as neutron stars, whereas for those in between
twenty and fifty solar masses, a black hole is produced after the supernova explosion.
For stars above fifty solar masses, the collapse causes directly a black hole with nosupernova explosion [Totani98a].

17

CHAPTER 2. NEUTRINOS

2.2.2

Diffuse Supernova Neutrino BackgroundThe basics of the core-collapse model were checked with the unique, up to date,nearby supernova explosion seen by neutrino detectors. This is the famous SN1987a,
occurred in the Large Magellanic Cloud, close to our Milky Way, around 50 kpc
away. About three hours before the photons from the supernova explosion arrived
to the optical telescopes, twenty four neutrinos were detected in KamiokaNDE (8)[Hirata87], IMB (11) [Velde88] and Baksan (5) [Alexeyev88], a huge signal comparedwith the solar neutrino one.
The SN1987a measurement meant a much better knowledge of the neutrino flux,
spectrum and time profile, which was crucial for a more accurate prediction of the
Diffuse Supernova Neutrino Background (DSNB) [Beacom10]. The DSNB is theoverall neutrino flux of all supernovae that happened in the history of our universe.
The DSNB flux is calculated as the convolution of core-collapse supernova rate andthe neutrino emission per supernova, accounting for the different redshifts of supernovae. Equation (2.2) shows the expression for its calculation.
dΦDSN B
=c
dEν

Z ∞
0


 dt
RSN (z)(1 + z)φ Eν (1 + z)
dz
dz

(2.2)

Where RSN is the the core-collapse supernova rate at redshift z, φ is the neutrinopdt −1
emission per supernova, | dz
| = H0 (1 + z) ΩΛ + Ωm (1 + z)3 , which depends on
the Hubble constant H0 , is the cosmic matter density Ωm and the cosmologicalconstant ΩΛ . The neutrino spectrum and the neutrino rate per supernova are themost uncertain inputs in this calculation, making the first measurement of theseneutrinos essential to understand key processes during supernovae.
On the other hand, the supernova rate is well known and proportional to the star18

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONS

formation rate (RSF ), which is a function of the star mass. The supernova calculation
rate follows Equation (2.3).
R 50
8
RSN (z) = RSF R 100
0.1

ψ(M )dM

M ψ(M )dM≈

RSF (z)
143Msun(2.3)

Where ψ is the initial mass distribution of the stars and M is the mass of the star.
Figure 2.9 shows the expected fluxes and spectra for a series of theoretical models
for different effective temperatures.

Figure 2.9: Predicted DSNB ν e spectrum for different models and showing the three main
backgrounds for this measurement and the energy region where they apply.

2.3

Neutrino Mass and Neutrino Oscillations

In this section, the current understanding of the neutrinos as particles of the Standard
Model is reviewed briefly and divided into two parts: the neutrino mass and particle
characteristics, and the neutrino oscillations, in Sections 2.3.1 and 2.3.2 respectively.

19

CHAPTER 2. NEUTRINOS

At the end, in Section 2.3.3, the latest results from different experiments of thedifferent parameters and properties are reviewed.

2.3.1

Neutrino Masses

The existence of neutrinos was first theoretically proposed by W. Pauli as explanation for the broad spectrum of e in β-decays [Pauli30, Fermi08], turning the one
body decay problem, which violates energy conservation, into to a two body decay
which does not. This was confirmed experimentally by C. Cowan and F. Reines in1956 with the discovery of the electron neutrino [Cowan56].

Figure 2.10: Particle and force content of the Standard Model.

Years latter the corresponding muon and tau neutrinos were proposed and discovered[Danby62, Kodama01], leaving the picture of three generations of neutrinos, each ofthem associated to a charged lepton.
Neutrinos are until today the lightest massive particle known Standard Model (SM)20

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONS

contains. They are fermions with nor electric neither colour charge, being able forthem to interact only throw the gravitational and the nuclear weak forces. Due tothe smallness of their masses, just the latter is relevant and reachable by current
experiments.
Neutrinos have spin one half (Sν = 1/2) and weak hypercharge -1 (YW = −1). In
the Standard Model gauge group, SU(3)C ×SU(2)L ×U(1)Y ,they are embedded in theleft-handed lepton doublet of SU(2)L , along with their charged partner, and from asinglet of SU(3)C . The langrangian corresponding to this part of the SM is as shownin Equation (2.4).

/
LSM = iν L DνL + (h.c.) = ν L i∂/ +


e
e
/
/
B−
W νL + (h.c.)2 cos θW
2 sin θW

(2.4)

Where νL is the chiral left-handed, flavour (e, µ, τ ) neutrino field.
Neutrinos have been proven to be non-massless throw their oscillations from one
flavour to another, impossible for massless neutrinos.
The fact that neutrinos have mass, makes necessary to extend the SM with a mechanism to provide neutrinos with mass. There are basically, two different ways torealise the scenario of three massive neutrinos: the existence of a right-handed neutrino or assuming that neutrinos are Majorana particles. Here, both of them are
explained separately in order to be as clear as possible since more elaborated models
can be found in the literature, for instance in [King04a].
The most straightforward attempt is the addition of a right-handed neutrino (νR )for each generation, such that neutrinos acquire mass in a similar way to the rest of
the fermions of the SM, through the Higgs mechanism. This right-handed neutrino
would be a singlet of SU(2)L and of SU(3)C with YW = 0. Therefore, it would

21

CHAPTER 2. NEUTRINOS

only interact through gravity or through some other new force. The Dirac massterm obtained then for neutrinos after the SU(2)L ×U(1)Y is spontaneously broken
symmetry and the Higgs field acquires a vacuum expectation value.
yν v
LDiracν,mass = − √ νL νR + (h.c.)
2

(2.5)

Where yν is the neutrino Yukawa coupling and v the v.e.v. of the Higgs field.
This leads to the following expression for the neutrino masses of each generation.
yν v
mD
ν = √
2

(2.6)

The inclusion of the right-handed neutrinos and the Yukawa couplings Yν open thepossibility of mixing in the lepton sector as well as in the quark sector. The lepton
unitary mixing matrix UP M N S is the product of the left-handed unitary matrices
diagonalising charged lepton and the neutrino Yukawa couplings. This matrix has(3−1)2 = 4 degrees of freedom, corresponding the 3 to the three neutrino generations[Pontecorvo57, Maki62].


−iδ



c13 c12c13 s12s13 e iδ
UP M N S = c23 c12 − s23 s13 s12 eiδ
s23 c13 −c23 s12 − s23 s13 c12 e



iδ
iδ
s23 s12 − c23 s13 c12 e−s23 c12 − c23 s13 s12 e
c23 c13(2.7)

Where cij = cos θij and sij = sin θij .
Despite this approach looks very reasonable, there exists one problem concerning
the neutrino Yukawa couplings. They are orders of magnitude smaller than those forthe other charged fermions of the same generation. This suggest that there may besomething else that makes the neutrino masses so small without having to deal withsuch small Yukawa couplings.

22

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONSAn alternative to the addition of right-handed neutrinos to the SM, is to assume
neutrinos as Majorana particles, that is they are its own antiparticle. Neutrinos are
the only particles in the SM allowed to be Majorana because of their neutral charges.
This allows to have another possible mass term, in addition to the Dirac mass term,
the Majorana mass term.
1ajoranaLM= νLT M CνL + (h.c.)ν,mass2(2.8)

Where C is the charge conjugation operator and M is the Majorana mass matrix. The
matrix M can be diagonalised by a unitary transformation UM , obtaining Mdiag =T
UM
M UM . Therefore, for Majorana neutrinos, one also has a lepton mixing matrix

UP M N S+M aj. , shown in Equation (2.9). This results in a mixing matrix with 3 − 1
more degrees of freedom, the Majorana extra phases (α1 , α2 ).


0 
1 0



iα
UP M N S+M aj. = UP M N S · 0 e 1 0 


iα2
0 0 e

(2.9)

The Majorana phases cancel out for any observable in neutrino oscillations and,
therefore, neutrino oscillation experiment only see the parameters of the UP M N S
matrix.
The fact that no new particles are required makes this mechanism appealing, but
the mass term breaks explicitly the SU(2)L and, as the Dirac mass term, fails to
explain the smallness of the neutrino masses. Because both of these methods are
not fully satisfactory, a third mechanism involving the previous one is proposed invarious versions, that is the seesaw mechanism. The simplest case is the Type I
seesaw mechanism, where three heavy right-handed Majorana neutrinos (one for23

CHAPTER 2. NEUTRINOS

each generation) are added to the particle content.

seesawLInu,mass= −mD νL νR +MN T
ν CνR + (h.c.)
2 R(2.10)

Rearranging the neutrino fields, one gets the following mass matrix,

 0 mD 
M =

mD MN

(2.11)

This means that neutrinos are a mixture of Dirac and Majorana particles, but themost interesting scenario is that where mD  MN and giving naturally the lefthanded small masses assuming right-handed neutrinos have large masses, near GUT
scale. In this case, the right-handed neutrinos have mass ∼ MN and the left-handed
neutrinos mν .
mν = −

m2D
MN(2.12)All versions of this mechanism work in a similar way, assuming the existence of avery large particle which is responsible for the smallness of left-handed neutrinos.
This method is very interesting also because it relates the neutrino physics to the
GUT scale.

2.3.2

Neutrino Oscillations

In this section, the formalism of neutrino oscillations is explained in vacuum and in
matter.
As we have seen in the previous section, neutrinos are transformed by a non-diagonal
lepton mixing matrix U . This idea was first proposed by Gribov and Pontecorvo in[Gribov69]. Following this reasoning, flavour neutrino eigenstates |νl i (l = e, µ, τ )24

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONStransform to the neutrino mass eigenstates |νi i (i = 1, 2, 3).

|νl i =X

(UPliM N S )∗ |νi i(2.13)l

This mixing matrix has only four degrees of freedom which correspond to the threeneutrino mixing angles and the CP phase. This can be parametrised as the productof three-dimensional rotations in the following manner.

UP M N S = U23 (θ23 )Iδ U13 (θ13 )Iδ† U12 (θ12 )(2.14)The neutrino propagation through vacuum is governed by the Schrödinger equation
with no potentials acting on the neutrino mass eigenstates.

id|νl i= H0l |νl i ⇒ |νi (t)i = e−iEi t |νi (0)idt

(2.15)

Where H0l is the neutrino dynamics Hamiltonian and Ei its eigenstate of |νi i.
As seen before, the mass of the neutrino will be much smaller than its total energy,
being able to approximate its energy by doing a first order Taylor expansion.
!
q m4 
2
4
mi
mi
m2i
2
2
Ei = p + mi ≈ p 1 + 2 + O 4=p++ O 3i2pp2pp(2.16)

One also needs to consider that neutrinos will be generated as a neutrino flavour
eigenstate, since it will come from a weak interaction. With all this one can computethe amplitude of having a |νl i in another flavour state, |νl0 i, after some time t.

Aνl →νl0 (t) =

X
X
0j
0i
−iEi t−iEi t(UPliM N S )∗ UPl M
e
hν
(p)|ν
(p)i
=
(UPliM N S )∗ UPl M
j
i
NSe
NS
i,j

i

(2.17)

25

CHAPTER 2. NEUTRINOS

It will come clear now, in the computation of the oscillation probabilities, that neutrino masses, cannot be observed in neutrino oscillation experiments, but only thedifferences of their squares. The notation, ∆m2ij = m2i − m2j , is assumed.
The neutrino oscillation probability in vacuum from one flavour eigenstate νl to another flavour eigenstate νl0 , is given by Equation (2.18).
Pνl →νl0 (t) = |Aνl →νl0 (t)|2 =
X

l0 i
li
∗ −iEi t 2=
i UP M N S (UP M N S ) e

P

0i
l0 j
li
∗
∗ lj
−i(Ei −Ej )t
UPl M=
N S (UP M N S ) (UP M N S ) UP M N S e

i,j

X

−i
Uij
ll0 e

∆m2
ij
2p

t

(2.18)

i,j
0

0

lj
∗
li
∗ lj
li
Where the product of matrices, Uij
ll0 = UP M N S (UP M N S ) (UP M N S ) UP M N S , is defined.

Due to the smallness of the neutrino masses and in the ultra-relativistic case (like isthe case in neutrino oscillations with Eν > 1M eV ), the momentum of the neutrino
can be very well approximated by its energy and the speed of the neutrino is very
close to the speed of light.
L c
L
t
≈
=
2p
c 2E
2E

(2.19)

Where L is the distance travelled by the neutrino and E is its energy. With this,the probability can be rewritten in terms of the diagonal, real and imaginary partsin the following way.


 ∆m2 X
ij
L +2
Im(Uij
)
sin
L =
0
ll
2Ei
2Ei
i
i<j
i<j




X
X
∆m2ij L∆m2ij Lij
ij
2
+2
Im(Ull0 ) sin
δll0 − 4Re(Ull0 ) sin
4E
2E
i<j
i<j

Pνl →νl0 =X

Uiill0 + 2

X

Re(Uijll0 ) cos

 ∆m2

ij

(2.20)

26

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONSIn the case of antineutrino oscillations, there is only a difference in the definition of
their states.

|ν l i =X

UPliM N S |ν i i(2.21)l

Therefore, the oscillation probabilities are equivalent to the neutrino case but
exchanging (UPliM N S )∗ → UPliM N S . Obviously, this change only affects the imaginary
terms of the oscillation probability, responsible for the neutrino CP violation.

Figure 2.11: Neutrino oscillation probabilities assuming initial state is an electron neutrino.

All the previous is valid for vacuum neutrino oscillations, but the presence ofmatter can greatly affect the neutrino oscillation probabilities [Mikheyev85]. This
happens due to the coherent forward scattering as neutrinos interact with theconstituents of the matter both through charged-current (exchange of W ± bosons)or neutral-current (exchange of Z 0 bosons). This interactions enter as a new termin the Hamiltonian which will affect the propagation of neutrinos by Equation (2.15).

27

CHAPTER 2. NEUTRINOS

Figure 2.12: Tree-level Feynman diagrams for coherent forward scattering of neutrinos on
any fermion, x, for NC interactions (left) and on electrons for the CC scattering (right).

For the CC case only electron neutrinos and antineutrinos are affected becauseof their weak interaction with electrons. .
The Lagrangian for the neutrino CC coherent forward scattering with matter has
the following form.
GF
LCC = − √ |ν e iγ µ (1 − γ 5 )hνe ||eiγµ (1 − γ 5 )he|2

(2.22)

As electrons form part of the medium, they can be seen as a distribution of electrons
and not as single particles. Then, the electron degrees of freedom can be integrated
out and the electron number density Ne introduced.
GF Ne
LCC = − √ |ν e iγ µ (1 − γ 5 )hνe |2(2.23)

Being the resulting CC neutrino Hamiltonian,
1 0 0√
HCC = 2GF Ne 
0
0
0




0 0 0

28

(2.24)

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONS

and the total neutrino energy

E ≈p+

m2 √
+ 2GF Ne
2p

(2.25)For switching between neutrinos and antineutrinos it is enough to exchange√√
2GF Ne → − 2GF Ne .
On the other hand, in the NC case all neutrino flavours are affected equally, occurring
the interactions with any of the constituents of matter. However, in an electricallyneutral medium the NC interactions between electrons and protons cancel eachother, being the only remaining term that corresponding to the interactions withneutrons. The formalism is very similar to that of CC scattering.

1 0 0√
HN C = − 2GF Nn 
0 1 0
0 0 1(2.26)

Where Nn is the neutron density in the surrounding matter.
For standard three neutrino flavours, the phase introduced by this term can beabsorbed and will not have any effect in the neutrino oscillations.
The effective (ignoring NC term) hamiltonian needed for the computation of thestandard neutrino oscillations through matter is

Hef f = H0 + HCC = H0 +√2GF Ne diag(1, 0, 0)(2.27)

One can now proceed as in the vacuum case by defining ν̃i the matter eigenstates
which diagonalise the effective Hamiltonian Hef f , satisfying then the analogous transformation as in Equation (2.13).

29

CHAPTER 2. NEUTRINOS|νl i =

X(Ũ li )∗ |ν̃i i(2.28)

lBeing Ũ the effective lepton mixing matrix with matter effects.
One caveat before the computation is that the electron density is not constantthroughout the Earth, meaning that the transformation matrix, Ũ , is timedependent. Then, the analogous to Equation (2.15) has the following expression in
matrices terms.

id(Ũ † |ν̃i)
d|ν̃i dŨ † d|νi
= Hef f |νi ⇒ i= Ũ † H̃ef f Ũ Ũ † |νi ⇒ i= H̃ef f − iŨ
|ν̃i
dt
dt
dt
dt
(2.29)

Where ν and ν̃ are all the flavour and matter neutrino eigenstates respectively andH̃ef f is the diagonalised effective Hamiltonian with the matter potential. The final
solution to Equation (2.29) is rather difficult, being the analytic solution obtained
after several approximations.
The different Earth’s densities are usually treated as an overlay of constant density
layer, namely the mantle (ρmantle =5.5 g/cm3 ) and the core (ρcore =11.5 g/cm3 ).
Matter effects affect the neutrino mixing, being crucial for the measurement of thedifferent oscillation parameters. In fact, one of the main properties of the oscillations
in matter, is the opposite behaviour of the term depending on the mass hierarchy(sign(∆m231 )). The oscillograms in Table 2.1, show the Earth’s matter oscillation
probability difference between neutrinos and antineutrinos as defined next.

ν−ν
Γl,M
H =

X

(ν)

(ν)

Px→l,M H − Px→l,M H

x=e,µ

30



(2.30)

2.3. NEUTRINO MASS AND NEUTRINO OSCILLATIONSNormal hierarchy

Inverted hierarchy

νeνµTable 2.1: Sum in all flavours of the difference of neutrino-antineutrino oscillation probabilities as a function of energy and cosine of zenith angle, with final electronic (top) andmuonic (bottom) flavours and for both neutrino mass orderings, normal (left) and inverted(right).

Table 2.1 only shows the values for those neutrinos passing through the Earth,that is with cos θzenith < 0, in order to better focus on the importance of the matter
effects. The Earth’s matter resonance is seen at energies from 1 GeV to 10 GeV
and it is also seen clearly how the zenith angle affects that resonance, being dimmer
towards the horizontal direction and stronger when neutrinos travel through themantel and the core of the Earth. It is seen that both possible neutrino massorderings have opposite behaviour.
The mass ordering of the neutrinos is one of the main remaining uncertainties inneutrino physics. The measurement of this property is mainly based on the analysis

31

CHAPTER 2. NEUTRINOS

of the oscillation matter effects of atmospheric neutrinos passing through the Earth.

Figure 2.13: Scheme of the two possible neutrino mass hierarchies depending on the signof ∆231 . In the left for normal (third mass eigenstate is the heaviest) and right for inverted(third mass eigenstate is the lightest).

2.3.3

Experimental Status

In this section, the latest results for the neutrino properties are summarised, fromthe mass to the oscillation parameters.
The measurement of the neutrino mass is addressed by measuring the spectrum ofelectrons near the endpoint in 3 H β-decay experiments and from cosmological andastrophysical data, being the most stringent upper limits for the mass of ν e the result
from the Troitzk experiment, mν e < 2.05 eV at 95% confidence level. Gathering datafrom Planck, supernovae and Baryon Acoustic Oscillations the limit on the sum ofP
the neutrino masses is lowered, j mj < 0.23 eV at 95% confidence level.
Concerning the oscillation parameters, solar and reactor neutrinos are most sensitiveto θ12 and ∆m221 , coming the best results from KamLAND. The parameter θ13 is very32

2.4. NEUTRINO-NUCLEUS INTERACTIONS

precisely obtained from short baseline reactor experiments, such as Daya Bay, RENO
or Double Chooz, and also, from the long baseline experiments T2K and Noνa. The
latter, together with the SK atmospheric neutrino results, provide the constraints on
θ23 and ∆m232 , but not enough to determine the octant or the mass ordering. Finally,
the CP violating phase has the largest uncertainty of all oscillation parameters, andlong baseline neutrino experiments are the responsible of the best limits on its value.
The relatively large value of θ13 , enables the possibility for SK, T2K and Noνa tomeasure the three least known parameters, i.e., the octant of θ23 , the neutrino massordering and the CP phase [Patrignani16].
Parameter∆m221 (10−5 eV2 )|∆m2 | (10−3 eV2 )sin2 θ12
sin2 θ23
sin2 θ13
δCP /2Mass Ordering
NH/IH
NH
IH
NH/IH
NH
IH
NH
IH
NH
IH

Best-fit
7.37
2.50
2.46
0.297
0.437
0.569
0.02140.02181.35
1.32

3σ (2σ for δCP )range
6.93-7.97
2.37-2.63
2.33-2.60
0.250-0.354
0.379-0.616
0.383-0.637
0.0185-0.0246
0.0186-0.0248
0.92-1.99
0.83-1.99

Table 2.2: Neutrino oscillation best-fit values derived from a global fit of the current neutrino oscillation data, where ∆m2 is defined as ∆m2 = m23 − (m22 + m21 )/2.

2.4

Neutrino-Nucleus Interactions

In this section, the basic neutrino interactions occurring inside a water-Čerenkov
detector are reviewed. Each type of interaction becomes relevant for certain physicalphenomena depending on its energy range, [Formaggio12]. Therefore, the complete

33

CHAPTER 2. NEUTRINOS

understanding of the neutrino-nucleus interactions will be of great importance acrossthe development of this work.

Elastic Scattering
The first of the interactions is also the simplest of them and crucial for the detectionof low energy neutrinos, mainly solar neutrinos. In this process, an electron isscattered off by an electron via the exchange of a virtual vector boson. This type ofinteraction was the first used for the measurement of neutrinos and the confirmationof weak neutral currents [Hasert73].

Figure 2.14: Tree level Feynman diagrams for the neutral current (left) ν − e scatteringand charged current (centre and right) νe − e scattering.

ν + e− → ν + e−

(2.31)The expression of the differential cross-section for this process is the following.
dσ(ν + e− → ν + e− )G2F me Te 22
2 2 me Te=(gV + gA ) + (gV − gA ) 1 −+ (gV − gA ) 2
dTe
2π
Eν
Eν
(2.32)

34

2.4. NEUTRINO-NUCLEUS INTERACTIONS

Where GF is the Fermi coupling constant, me the electron mass, Eν the neutrinoenergy and Te the kinetic energy of the scattered electron. The axial-vector andvector couplings gA and gV can be expressed in terms of the weak angle θW (sin2 θW =0.2317) as follows.
gA = 21 ,gV = 2 sin θW + 12 for νegA = −1,
2

gV = 2 sin θW − 21

(2.33)for νµ and ντ

The recoil electrons are scattered in the forward direction as the neutrino energy
increases. The angle between the incident neutrino and the outgoing recoil electronis given by the next formula.
1 + me /Eν
cos θ = p
1 + 2me /Te(2.34)

Inverse-β Scattering
This is the simplest nuclear interaction that we can study, the antineutrino-proton
scattering, also known as inverse-β decay. This process is very important at low
energies, from its energy threshold, Eν = 1.806 MeV, up to tenths of MeV. Low
energy antineutrinos from reactors, DSNB and close enough supernova bursts aredetected through this interaction.

Figure 2.15: Tree level Feynman diagram of inverse-β decay.

35

CHAPTER 2. NEUTRINOS

The reaction takes part between an incoming antineutrino and a hydrogen nucleus.
ν e + p → e+ + n(2.35)

Its differential cross-section has the next expression.
dσ(ν e + p → e+ + n)
G2 |Vud |2 Ee pe  2
βe= F
fV (1 + βe cos θ) + 3fA2 (1 − cos θ) (2.36)
d cos θ2π
3Where fV and fA are the vector and axial-vector form factors, Ee , pe , βe and θ are
the energy, momentum, velocity and scattering angle of the outgoing positron.
The fact that the signature of this interaction produces a neutron is the central
motivating piece for the development of Gd-doped water-Čerenkov detectors. By
tagging the final state neutron, it is possible from distinguish neutrinos interacting
elastic scattering, from antineutrinos interaction inverse-β decay. This will be further
explained in Section 5.1.

Quasi-elastic Scattering

Climbing in the energy of the incoming neutrino, the available phase space for theoutcomes makes the interactions more complex and diverse.
From 100 MeV to ∼2 GeV, the quasi-elastic scattering dominates the neutrinonucleus cross-sections. This makes this process crucial for the study of long baseline
and low energy atmospheric neutrinos and, therefore, for the study of the neutrinomass ordering and the leptonic CP violating phase.
The differential neutrino cross section with respect to the momentum transferred q
has the following expression for the charged current version.

36

2.4. NEUTRINO-NUCLEUS INTERACTIONS2dσν
M 2 G2F cos θC2
2 s−u
2 (s − u)
A(q
)
+
B(q
)
=
+
C(q
)
dq 2
8πEν2
M2
M4

!
(2.37)

Where M the nucleon mass, neutron or proton respectively. GF is the Fermi constant,Eν the neutrino energy, θC the Cabibbo angle and s and u the corresponding
Mandelstam variables. The factors A, B and C are defined as follows.
!


q2 
q2
q2 
2
2
2
4− 2
|FA | −|FV,1 | − 2 |ηFV,2 | 1 +
M
M
4M 2
!
2

4q 2 ηFV,1 FV,2
m 
2
−
−
FV,1 + ηFV,2 + |FA |M2M

m2 − q 2
A(q 2 ) =4M 2

q2  
B(q ) = 2 FA FV,1 + ηFV,2
M
2

1
q2
C(q 2 ) =|ηFV,2 |2|FA |2 +|FV,1 |2 −4
4M 2

(2.38)(2.39)!
(2.40)

m is the outgoing lepton mass, η is the anomalous magnetic dipole moment, η =µp − µn , and the axial vector and vector form factors FA , FV,1 and FV,2 have the next
expressions.
FV,1 (q 2 ) = 1q 2 2
1−
4MV2

ηFV,2 (q 2 ) = 


q2
(1
+
η)
4M 2
q2
1−
4M 2

1−

1
η
2 2
q
q2
1−
1
−
4MV2
4M 2

q2
FA (q 2 ) = −1.232 1 − 2MA37(2.41)(2.42)!
(2.43)

CHAPTER 2. NEUTRINOS

Where MA and MV are the axial vector and vector masses with values of 1.12 GeV
and 0.84 GeV respectively.
For the neutral current analogous, the expression for the differential cross section
with respect to the transferred momentum is very similar to Equation (2.37).
dσν
M 2 G2F
=
dq 2
8πEν2

2
s−u
2 (s − u)A(q 2 ) + B(q 2 )
+
C(q
)
M2
M4

!
(2.44)

where the factors A, B and C are modified accordingly to the different expressionsof the axial vector and vector form factors.

Resonant Single Meson and Coherent Pion Productions
Single mesons, from neutrino interactions, are produced mainly through baryon resonances with the invariant mass of the hadronic system being less than 2.0 GeV/c2 .
The main species produced are pions, although other mesons are also produced, like
κ and η. In this interactions, neutrinos with enough energy excite a nucleon producing a baryon resonance. This quickly decays, most often to a nucleon and singlepion.

νl + N → l + N ∗(2.45))

N∗ → π + N0
Where N and N 0 correspond to neutrons or protons. The charged current interactions
for single pion production are the following.
νl + p → l − + p + π + ,ν l + p → l+ + p + π −νl + n → l − + p + π 0 ,ν l + p → l+ + n + π 0

νl + n → l− + n + π + , ν l + n → l+ + n + π −38(2.46)

2.4. NEUTRINO-NUCLEUS INTERACTIONS

These processes involve various resonances, but the most important for current
neutrino experiments are those occurring at the lowest energies, dominated by the∆(1232) resonance.
Baryonic resonances can also decay into multiple pions through other inelastic scatterings.
Additionally, neutrinos can also coherently produce single pion final states by scattering the entire nucleus (A). This produces almost no nuclear recoil and a pion
almost parallel to the direction of the interacting neutrino. The charged current
mechanisms for the coherent pion production are the next.

νl + A → l − + A + π + , ν l + A → l + + A + π −(2.47)

And analogously for the neutral current interactions, substituting the charged lepton
by its neutrino partner and charged pions by the neutral ones.
Neutrino interactions above GeV energies can also produce strange quarks, thus
kaons, in the final state. Next, the charged current processes of κ production arelisted.
νl + n → l− + κ+ + Λ0
νl + p → l− + κ+ + p
νl + n → l− + κ0 + p
νl + n → l− + κ+ + n
νl + p → l− + κ+ + Σ+νl + n → l− + κ+ + Σ0
νl + n → l− + κ0 + Σ+

39

(2.48)

CHAPTER 2. NEUTRINOS

The antineutrino and neutral current analogous have similar expressions with theappropriate electric charge balancing.

Deep Inelastic Scattering
In deep inelastic scattering, the neutrino scatters off a quark in the nucleon via the exchange
of a virtual W ± or Z boson, producing a lepton and a hadronic shower in the final state.

νl + N → l− + X, ν l + N → l+ + X (CC)νl + N → νl + X, ν l + N → ν l + X (NC)(2.49)

Figure 2.16: Tree level Feynman diagram for CC DIS muon neutrino
interaction.

Where N is the target nucleon and X represents the resulting hadronic shower. The Bjorken scaling variable is defined as follows.

y=

Ehad
−q 2
, x=
Eν
2M Eν y(2.50)The differential cross section of neutrino DIS with respect to the Bjorken variables
has the next expression.
 y2 
d2 σ ν,ν
G2F MN Eν
MN xy 222= 
F2 (x, q )± y−
xF3 (x, q 2 )2 y xF1 (x, q )+ 1−y−
dxdy
2Eν
2
2
2
π 1 − q /MW,Z(2.51)
Where MN is the nucleon mass and Fi (x, q 2 ) are the nucleon structure functions.
The ± sign corresponds to the charged or neutral current processes respectively.
As these interactions mainly take place when the neutrino energy is larger than ∼10
GeV, secondary interactions of the hadronic shower within the nuclear media are40!

2.4. NEUTRINO-NUCLEUS INTERACTIONS

important. These are very hard to model and they contribute to large multiplicitiesof hadrons in the final state.

41

3. The Super-Kamiokande Detector
In this Chapter, the SK detector is described and explained in detail since it is the
precursor and base experiment for SuperK-Gd. SK is described as a neutrino detector
itself for astrophysical, solar and atmospheric neutrinos and also as far detector of
the T2K neutrino beam.

3.1

Detector Overview

The SK detector is a cylindrical tank with 39.3 m in diameter and 41.4 m in height
and filled with 50 kton of ultrapure water. It is located under Mountain Ikenoyama,in the Kamioka mine (Gifu Prefecture, Japan), with 1000 m of rock overburden(or 2700 m water equivalent) to reduce as much as possible the cosmic ray muon
background. Although the inner detector volume is 32 kton, the fiducial volume,
used for most of the physics measurements, is 22.5 kton, 2 m away from the innerdetector wall.

43

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.1: Schematic view of SK emplacement.

The SK experiment began its data taking in April 1996 and shut down for maintenance in July 2001.This first phase of the experiment is called SK-I. During
refilling after maintenance, an accident occurred in November 2001, in which morethan half of the PMTs were destroyed due to the implosion of a PMT. After theaccident, the SK detector was rebuilt with half of the original PMT density in the
inner detector. An FRP case was also attached to each PMT this time, to prevent
chain reaction implosions. The operation was resumed in October, 2002, phasecalled SK-II. In October 2005, the experiment was completely rebuilt and resumed
data taking with the full number of PMTs in July 2006, this phase is SK-III. In
September 2008 starts the current phase, SK-IV, with upgraded front-end electronics.

44

3.2. ČERENKOV RADIATION

Phase

PeriodSK-I
SK-II
SK-III
SK-IV

Apr. 1996 - Jul. 2001
Oct. 2002 - Oct. 2005
Jul. 2006 - Sep. 2008
Sep. 2008 - Today

Number of PMTs
ID (Coverage) OD
11146 (40%) 1884
5182 (19%)
1884
11129 (40%) 1884
11129 (40%) 1884

FRP case

Electronics

no
yes
yes
yes

ATM
ATM
ATM
QBEE

Table 3.1: Super-Kamiokande phases and main features.

3.2

Čerenkov Radiation

According to special and general relativity postulates, the speed of light in vacuum cis an absolute limit on velocity [Einstein05], however, it is also true that light travels
slower through other media.
In the 19th century, Heaviside first realised that a charged particle passing througha medium at higher speed than the speed of light in that medium, should emit someelectromagnetic radiation, [Heaviside08]. He formulated part of the theory of theČerenkov radiation, predicting the angle that would be formed between the charged
particle and the emitted light, shown in Equation (3.1).
1
1=
cos θČ =
nβ
n

r
m
1−
|~p|

(3.1)

Where m and p~ are the mass and momentum of the charged particle, β is the quotient
between the speed of the charged particle and the speed of light in vacuum, and n
is the refraction index of the medium. The light emission has cylindrical symmetry
with axis the track of the particle. This makes the emitted light form a cone.
Čerenkov radiation occurs when the following is satisfied.

β≥n

45

(3.2)

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTORThis radiation was then discovered by Vavilov
and Čerenkov in 1937 while observing water
being bombarded by radiation, [Čerenkov37].
Čerenkov together with Frank and Tamm, whodeveloped the theory of the phenomenon, received the Nobel prize in 1958.
The theoretical formalism of this phenomenon
Figure 3.2: Schematic diagram ofa charged particle passing througha medium of refractive index larger
than 1 at β > n and emittingČerenkov radiation.

is obtained by solving Maxwell’s equations ofa charged current ~j,s in a polarisable medium.
The charged current is that associated withthe charged particle with charge e and β ≥ n.

~j = eδ(~r − ~v t)~v

(3.3)

And the medium will have a polarisation vector P.

P = (n2 − 1)E ⇒ D = n2 E

(3.4)

Once solved the equations, the number of photons per unit length and unit wavelength is given by the next expression.
2πα
d2 N
= 2
dxdλ
λ


1−

1
2
β n(λ)2=

2πα
sin θČ
λ2(3.5)

Where α is the fine structure constant and n(λ) is the refraction index of themedium.
In water-Čerenkov detectors the refraction index is ∼ 1.34 and the charged particles,
ideally produced after the interaction of a neutrino, are in the ultra-relativistic

46

3.3. DETECTOR DESCRIPTION
regime, β ∼ 1. Hence, the typical Čerenkov angle is ∼ 41.70 .

Figure 3.4: Medium polarisation due toa charged particle passing through it atspeed β > n.

Figure 3.3: Medium polarisation due toa charged particle passing through it atspeed β < n.

For water, the typical wavelength is of the around of 375 nm, the full spectrum isshown in Figure 3.7.

3.3

Detector Description

The Super-Kamiokande detector can be divided into two major parts, those are thetank containing the ultrapure water and the photomultiplier tubes acquiring the light
produced inside the detector. In the upcoming sections, these are described and theirmost important characteristics reviewed [Fukuda03].

47

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.5: Čerenkov radiation spectrum in water.

3.3.1

Water Tank

The SK detector is optically divided into
inner (ID) and outer (OD) detectors, being the latter used, mainly, as veto to reduce the cosmic muon background. The
inner detector is currently (SK-IV) instrumented with 11129 photomultipliertubes (PMT) of 20 inches in diameter
facing inwards, accounting for a photocoverage of 40%. The outer detector,
on the other hand, is instrumented with
1884 8-inch PMTs facing outwards thedetector.

Figure 3.6: Supporting structure of
SK PMTs.

For the optical separation,

black polyethylene terephthalate sheets(black sheets) are used behind the inner PMTs and tyvek sheets behind the outer48

3.3. DETECTOR DESCRIPTION

PMTs.
Around the inner surface of the tank, 26 sets of horizontal and vertical Helmholtz
coils are arranged to compensate for the Earth’s magnetic field, which otherwise
would affect the photoelectron trajectories between dynodes inside the PMTs.

3.3.2

Photomultipliers

The ID PMTs were developed by Hamamatsu Photonics in collaboration with
KamiokaNDE collaborators (model R3600). These PMTs are most sensitive to
predominant wavelengths in the Čerenkov spectrum, that is in the range of 300 nm
to 600 nm, as shown in Figure 3.7.

Figure 3.7: Schematic diagram of the inner structure of the 20” SK’s ID PMTs.

The photocathode of the PMTs is coated with bi-alkali (Sb-K-Cs) being its maximum quantum efficiency is 22% and optimised so it is reached at ∼390nm, as seenin Figure 3.8, very close to the water Čerenkov spectrum maximum.

49

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

Figure 3.8: Wavelength dependence of PMT photocathode quantum efficiency.

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

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

Table 3.2: Specification of SK ID PMTs.

The main characteristics of these PMTs are listed in Table 3.2.

The ID PMTs have an uniform gain of 107 at a high voltage ranging from 1500 V
to 2000 V.

50

3.4. WATER AND AIR PURIFICATION SYSTEMS

Figure 3.9: The 1 p.e. distribution in pC. In logarithmic scale in the right and in linear
scale in the left, where the solid line shows the data with normal PMT gain, the dashedline shows the data with double gain and half threshold, and the dotted line corresponds tothe linear extrapolation between them.

On the other hand, in the OD, the PMTs used are Hamamatsu R1408. Their quantum efficiency spectrum does not match so well that of the Čerenkov radiation.
Therefore, in order to acquire more photons, a wavelength shifter plate is attachedto their photocathodes. Although this worsens the time resolution, this is not aserious problem in the OD.

3.4

Water and Air Purification Systems

The understanding of the characteristics and properties of the SK water, is crucial
for all the physics measurements, as the photon propagation depends hugely on
the water quality. Therefore, the water coming from the Kamioka mine is purified
in a dedicated system, passing through several resins and filters, and continuously
recirculated at a rate of 60 ton/hour. The main purpose is to keep the light attenuation length as high as possible and to remove radioactive impurities in the water.

51

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR

The SK water system consists in: a 1 micron
filter, which removes the biggest particles,
such as dust; a heat exchanger that cools thewater up to about 130 C, in order to reduce the
PMT noise and the growth of bacteria; a cartridge polisher for removing heavy ions; UV
lamps to avoid any possible bacteria present
in the water; an ultra-filter that removes
impurities of molecular weight heavier thanFigure 3.10: Circulation scheme ofpure water in the SK tank.

100.
In addition, and for avoiding high concentra-

tions of radon, radon-free air is dissolved into the water. Then, the water passes
through vacuum and membrane degasifiers for removing as much gas as possible
from the water.

Figure 3.11: Water purification system at SK.

52

3.5. SK-IV ELECTRONICS AND DATA ACQUISITION
To monitor the water temperature, thermometers with 0.00010 C precision are placedat eight different positions in both ID and OD. Below 10 m from the bottom of thetank, water is always convecting resulting in a uniform temperature throughout thelower part of the ID. Above that region, the water temperature gradually rises,
existing a difference of 0.20 C difference between the top of the ID and the convectionzone.
As it happens in most underground facilities, the air becomes highly contaminatedwith radon (Ra), produced as the uranium (U), of the surrounding rock, decays. In
order to keep the Ra levels small for the low energy neutrino analyses, radon-free airfrom outside is continuously pumped, after passing through a filtration system, into
the SK mine.

3.5

SK-IV Electronics and Data Acquisition

In August 2008, the SK electronics and data acquisition (DAQ) systems were
upgraded. The new system has a larger charge dynamic range and can handle larger
event rates. In addition, currently, every hit is recorded and filtered with a software
trigger, enabling the implementation of more complex triggers.
The ATM (Analog-Timing-Module) system, previously existing in SK-I to SK-III,
was replaced by a QBEE system (QTC (charge-to-time)-Based Electronics with
Ethernet), which has 3 channels for the PMT signal readout.

The charge integration starts with the crossing of the discriminator threshold by the
amplified signal. This signal is then, processed through a series of steps shown in

53

CHAPTER 3. THE SUPER-KAMIOKANDE DETECTOR
Number of inputs
Speed of QTC
Number of ranges
Discriminator
Charge dynamic range
Charge resolution
Charge linearity
Timing resolution
Power consumption

24∼900 ns/cycle
3 (small, medium, large)−0.3 mV to −14 mV
0.2 pC to 25000 pC∼0.2 pC<1%0.3 ns (2 pC) and <0.2 ns (>10 pC)<1 W/channel

Table 3.3: QBEE system characteristics used in SK-IV.

Figure 3.12.

Figure 3.12: Data acquisition diagram for SK-IV.

All triggers are recorded with a 1.3 µs time lapse surrounding the event, but
depending on the type of trigger, the total event duration may vary. Furthermore,in SK-IV a new trigger was introduced, SHE, which activates, if there is no activity
in the OD, the after trigger (AFT), an additional 500 µs of data.

54

3.6. CALIBRATION OF THE DETECTOR
SK-IV triggers
OD
SLE
LE
HE

Threshold (hits/200 ns)
22
34 −→ 31

Event duration (µs)–

05/2015-0.5→1.0

SHE

47
50
70 −→ 58

-5→35
-5→35

09/2011

-5→35

AFT

SHE and no OD

35→535

Table 3.4: List of the SK-IV triggers

3.6

Calibration of the Detector

The calibration of the detector is of crucial importance for the event reconstruction
and all the physics analysis. Items like the water properties, the PMT response or theelectronics are calibrated to obtain input parameters for the Monte Carlo simulationof the detector. This way, all the physics and the detector response can be completely
simulated very accurately and, therefore, the simulation can be confidently used toanalyse the data.
The various calibration works carried out at SK deal with the high voltage, PMT
gain, quantum efficiency, charge and timing of PMTs which are compiled in [Abe14a].
Additionally, calibrations concerning the photon tracking and the energy scale arealso performed, and can be found in [Blaufuss01, Nakahata99].

55

4. The SuperK-Gd Project
The SuperK-Gd project is the proposed and approved upgrade of the SuperKamiokande detector in order to enable it to efficiently detect thermal neutrons.
The project consists in dissolving a Gd salt into SK at a concentration of 0.2%.
Once they have thermalised, the neutrons are captured by Gd, emitting a delayed 8
MeV γ cascade from its de-excitation. The detection of this cascade in coincidencewith a neutrino event, will lead to the measurement of the final state neutrons
produced in the neutrino interaction with very high confidence and efficiency (80%).
The physics of the Gd-neutron capture is explained in Section 4.1.
Across this chapter, the development of the techniques for the successful realisationof SuperK-Gd are explained in Section 4.2. Additionally, its physics potential isbriefly summarised in Section 4.3.
In the context of the development of the technology needed for the success of
the SuperK-Gd project, the main R&D program towards SuperK-Gd, EGADS, isdescribed in Section 4.4.

57

CHAPTER 4. THE SUPERK-GD PROJECT

4.1

Gadolinium-Neutron Tagging

Gadolinium has the largest neutron capture cross-section of all stable nuclei known
in nature, around 48800 barn on average,
given the natural abundances of its isotopes.
Therefore, it is a terrific candidate to achieve
the largest neutron tagging efficiency possible in water-Čerenkov detectors.
Figure 4.1, shows a schematic diagram of the

Figure 4.1: Schematic diagram of
Inverse Beta Decay (IBD) with Gdneutron tagging.

Gd-neutron capture after the inverse-β interaction of an electron antineutrino in a water-Čerenkov detector. This is the simplest
process which clearly shows the different signature in the detector between, a low
energy antineutrino and the analogous neutrino interaction.
After the neutron is produced, it is thermalised by its interactions with water in thedetector. Once it is thermal, the neutron is captured by a Gd nucleus, resulting inan excited Gd nucleus with atomic mass one unit larger. After that, the nucleus
de-excites, emitting a γ-ray cascade with total energy depending on the Gd isotope
taking part in the capture.
The Gd-neutron capture occurs following the next reaction.

n +X Gd →X+1 Gd∗ →X+1 Gd + γs

(4.1)

And Table 4.1 shows the relation between each isotope, its natural abundance,neutron capture cross section and emitted energy in the de-excitation.

58

4.1. GADOLINIUM-NEUTRON TAGGINGIsotope
152Gd
154Gd
155Gd
156Gd
157Gd
158Gd
160Gd

NaturalAbundance (%)
0.20
2.18
14.80
20.47
15.65
24.84
21.86

Cross-section(barn)
1050
85.0
60700
1.71
2540002.01
0.765

De-excitationenergy (MeV)
6.25
6.44
8.54
6.36
7.94
5.94
5.64

Table 4.1: List of gadolinium isotopes, natural abundances, neutron capture cross sections
and total energy released in the de-excitation.

The energy of the photons emitted after the neutron capture add up ∼8 MeV,
balanced by the abundances of each isotope. The photon multiplicity typicallyvaries from three to five photons, giving the Gd-neutron capture signals a very characteristic topology, very advantageous for its reconstruction, as seen in Figure 4.2.

Figure 4.2: Normalised distribution for the γ-ray multiplicity from the de-excitation ofgadolinium after neutron capture.

59

CHAPTER 4. THE SUPERK-GD PROJECT

The target solution in SuperK-Gd will be of 0.2% of gadolinium by mass. At thisconcentration, the fraction of tagged neutrons by Gd will be of 90%. This is shownin Figure 4.3.

Figure 4.3: Fraction of neutrons captured by Gd as function of its concentration.

The mean time between the neutron production and its capture is about 30 µs. The
first ∼10 µs, correspond to the neutron thermalisation time, and the posterior ∼20µs, to the Gd capture and de-excitation times. This feature makes the correlation,
between the neutrino prompt signal and the neutron capture, very efficient in termsof its detection.
The distance between the neutrino interaction, which produces a neutron, and theposition of the capture is around 2 m. This distance is mainly due to the thermalisation process in the water.

60

4.2. GADOLINIUM ADDITION TO SUPER-KAMIOKANDE

4.2

Gadolinium Addition to Super-Kamiokande

The addition of Gd into water-Čerenkov detectors is not trivial, and several considerations and studies must be done in order to assure the capability and good
performance of the detector.
First thing to be considered is in which form the gadolinium should be added.
Gadolinium is a metal and, therefore, does not dissolve in water, meaning that acompound of this element which is soluble in water has to be considered. Highlysolvable salts of Gd were chosen as candidates from the beginning of the project.
Amongst all possible salts, Gd2 (SO4 )3 and GdCl3 were taken in consideration due
to their good properties. Finally, the latter was rejected in favour of the former
because of its better light propagation and lower corrosion issues. GdCl3 absorbs
light with wavelength below 350 nm, very close to the maximum of the Čerenkov
radiation spectrum. Furthermore, GdCl3 has shown some corrosion problems insome materials of the detector, whereas the gadolinium sulphate has not shown any
corrosion problems at all.
An issue related to the SK tank becomes more relevant once Gd is poured into it,a tiny leak in the bottom of the tank, presumably caused by the SK accident in2001. This leak does not suppose any serious problem currently, but it could be an
inconvenient once the SK water is Gd-doped, since Gd is a heavy metal. Throughthis leak Gd could be transferred to the nearby river and pollute the water suppliesof the surrounding villages and towns. Although the concentration of Gd would be
extremely low and most certainly harmless to any inhabitant in the area, extreme
care is being taken to address this. Specially given the dark history of the zone with
the itai-itai disease, caused by cadmium poisoning. In order to solve this, several
sealing materials have been studied to mend the leak minimising the impact on the61CHAPTER 4. THE SUPERK-GD PROJECT

physics capabilities of the detector. From the physics point of view, this material
has not only to be resistant to water and gadolinium sulphate and attach well tothe stainless steel walls, but it must also have very low radioactive contamination.
The main upgrade for the inclusion of Gd in SK, will be the water purification system
which has to be modified to cope with Gd sulphate. For this mater, the selective
band-pass water filtration technology was specifically invented and developed at
UCI for dissolving gadolinium into Super-Kamiokande.

Figure 4.4: Selective filtration system for SuperK-Gd.

The performance of the system has already been checked at EGADS and is discussed
in Section 4.4. This system continuously recirculates the Gd-doped ultrapure water, maintaining its transparency to SK ultrapure water levels and removing most of
the unwanted impurities while simultaneously, and indefinitely, retains the desired
levels of both the gadolinium and sulphate ions. The EGADS prototype was built

624.3. MAIN PHYSICS OUTCOMES

specifically to show that gadolinium loading would be feasible in Super-Kamiokande
and, therefore, scalability was always an important design criterion. The selective
band-pass water filtration will be working together with the current water purification system of SK.
In addition to the band-pass a Gd-removal system was developed to quickly andefficiently withdraw the Gd2 (SO4 )3 once the experiment is concluded. After several
studies, the technique proposed is to make the Gd-doped water go through a cation
ion-exchange resin as the detector is drained. This method will recover all the Gdcompound avoiding the Gd to be filtered to the nearby river.
Finally, there are two important concerns for the realisation of SuperK-Gd whichhave been extensively addressed during the past years: the possible corrosion andradioactivity from gadolinium sulphate itself.
For the former, all materials present in SK or that will be in SuperK-Gd were soaked
in 0.2% Gd-doped water and then the attenuation length change was measured independently at Kamioka Observatory with a spectrophotometer and at UCI withIDEAL (Irvine Device Evaluating Attenuation Length). All the checks showed nosignificant change in the water transparency.
Radioactivity contamination is one of the most relevant and remaining issues thathas been and is being addressed in order to reduce its impact as much as possible
in the detector performance and in the low energy physics studies. A much detailed
description of the situation on this topic is treated in Section 5.6.

4.3

Main Physics Outcomes

The addition of Gd sulphate to SK to enable the highly efficient Gd-neutron tagging,has a huge impact in the detection and study of various physics phenomena. Next,

63

CHAPTER 4. THE SUPERK-GD PROJECT

the main physics improvements due to neutron tagging are briefly reviewed at both,
low and high energy regimes.

4.3.1

Low Energy

One of the main goals for this upgrade is to be able to first detect diffuse supernova
neutrino background (DSNB) antineutrinos. These are the neutrinos coming from all
the past supernova explosions in the history of the universe. This measurement will
provide very important information about core-collapse supernovae, like their meanenergy spectrum and the star formation rate of the universe. This measurement iscurrently dominated by spallation background, which will be drastically reduced withneutron tagging. The details of this measurement-to-be are treated in Section 6.2.
Similar issues happens when dealing with antineutrinos coming from nuclear reactors
in Japan and South Korea. Nowadays, this measurement is also background dominated from spallation products and solar neutrinos. Neutron tagging will enable thepossibility of performing long baseline reactor antineutrino oscillation analyses withlarge statistics, improving the current sensitivity of the solar oscillation parameters∆m221 , θ12 . This potential new measurement is described in detail in Section 6.1.
Finally, in the situation that a supernova occurs close enough, the huge amount of
neutrinos detected from it will provide much information about early stages of thecore-collapse process. Although currently, SK can distinguish supernova neutrinos
from antineutrinos thanks to their different cross-section angle dependence, with
Gd-neutron tagging this separation will be much more effective, as will be shown in
Section 6.4. Furthermore, if the supernova is less than 1 kpc away, SuperK-Gd will
be able to detect the Si burning phase of the star a few (depending on the distance)days before to the core-collapse through the monotonically increasing rate of very64

4.3. MAIN PHYSICS OUTCOMES

low energy antineutrinos during this stage. The description in greater detail is given
in Section 6.3.

4.3.2

High Energy

The advantages of Gd-neutron tagging have not been considered traditionally forhigh energy neutrino physics, but it improves the separation between neutrino andantineutrino in the range from 100 MeV to 10 GeV. High energy antineutrinos tend
to have larger neutron multiplicities in the final state as it happens for the low energy
regime. The ability to distinguish between neutrinos and antineutrinos is very usefulfor long baseline and atmospheric neutrinos and it is expected that the sensitivity
for both, the CP violating phase and the neutrino mass hierarchy are significantly
enhanced, as shown in Section 5.4.
In addition to the neutrino-antineutrino separation, the neutron multiplicity depends
on the neutrino interaction, being able to make discern, at some level, between neutral current, deep inelastic charged current and the rest of charged current interactions. This is specially important for high energy atmospheric neutrinos, where thecontamination from neutrino interacting neutral current and deep inelastic scattering becomes an issue. The classification of these events improves the sensitivity of
the atmospheric oscillation analysis to the neutrino mass hierarchy. This featured isdeveloped in Section 5.3.
Besides, at these energies, the neutron multiplicity can be used to improve the atmospheric and long baseline neutrino energy reconstructions. This is due to theinformation about the missed energy, in the production of neutral particles, thatneutrons contain. The improvement in the knowledge of the neutrino energy is very
useful for the atmospheric oscillation analysis, improving also the neutron mass hi-

65CHAPTER 4. THE SUPERK-GD PROJECT

erarchy and CP phase sensitivities. This technique is explained in Section 5.5.
Finally and in addition to neutrino physics, Gd-neutron tagging is also beneficial
for proton decay searches. It is possible to remove 83% of the atmospheric neutrino
background, by requiring the number of neutrons in the final state to be zero. This
neutron veto produces tiny detection efficiency losses, due to the fact that proton
decays rarely have any neutrons in the final state.

4.4

EGADS R&D Program and Experiment

EGADS (Evaluating Gadolinium’s Action on Detector Systems) is the main R&D
project for testing the feasibility of Gd-doped water-čerenkov detectors and focusedin the realisation of SuperK-Gd, [Magro15, Mori15]. Due to the success of its technology and its good performance, it has become the currently most sophisticatedsupernova antineutrino detector, belonging to the Multi-Messenger Astronomy Consortium.
During this section, the most important advances towards SuperK-Gd made at
EGADS are reviewed. This is done not only in terms of the hardware needed todeal with Gd-doped water, but also for items concerning the physics itself as well,such as the light propagation or the neutron capture detection. Some of the most
relevant items are the water purification system, the monitoring of the Gd concentration in the tank.

4.4.1

Detector Description

The EGADS detector is designed very similarly to Super-Kamiokande, but about 250
times smaller. The EGADS water tank contains 200 ton of ultrapure water, with
5.417 m in diameter and 4.949 m in height. It is instrumented with 240 photomulti-

66

4.4. EGADS R&D PROGRAM AND EXPERIMENT

pliers, which 227 of them are similar to those in the SK detector, 151 PMTs without
any cover, 16 PMTs with an FRP housing and the 60 remaining PMTs with FRP
and acrylic cover, achieving a 40% photocathode coverage. As in SK, black-sheets
are installed surrounding all PMTs.
For compensating the geomagnetic field, Helmholtz coils are put around the detector
in the same way as SK, achieving a tiny residual magnetic field of less than 0.1 Gauss.

Figure 4.5: Schematic drawing of the EGADS detector, including its water purification
system and water transparency measuring device.

4.4.2

Water Purification System

The EGADS water system can be divided into two parts which work jointly, thepre-treatment and the water circulation systems.
The pre-treatment system, shown in Figure 4.6,contains a 15-ton tank where thegadolinium sulphate powder is dissolved rather quick by using a stirrer, and once
it is completely dissolved, it passes through a series of microfilters of different
diameters to remove the largest dust particles, a UV lamp to kill bacteria and theresin AJ4400, specially designed to remove uranium, keeping, in its turn, all the67CHAPTER 4. THE SUPERK-GD PROJECT

dissolved Gd.

Figure 4.6: Schematic view of the 15-ton tank and the pre-treatment system.

After the pre-treatment system, the solution is 0.2% Gd concentrated and it ispumped into the main water circulation system in Figure 4.7. This system had to be
specifically design in order to match the ultrapurity requirements like the SK waterand to keep all the Gd and sulphate ions dissolved. To achieve this, the solution ischilled, to prevent the Gd2 (SO4 )3 from precipitating, and passed through microfilters
and ultrafiltration processes until it gets to the nanofilters, whose pore size is smaller
than the Gd salt ions. This leaves pure water in part of the system which is further
purified and the reunited with the previously left Gd3+ and (SO4 )2− . After this,the Gd-doped water is injected to the 200-ton tank and continuously re-circulated
through the system in order to maintain the water transparency quality.

4.4.3

Data Acquisition System

The data acquisition and electronic systems are analogous to those of SK-I to SK-III.
In fact the old SK ATM electronics from those periods. The integrated charges and68

4.4. EGADS R&D PROGRAM AND EXPERIMENT

Figure 4.7: Schematic view of the EGADS water circulation system.

the time information for each PMT are recorded and digitalised by the ATM module.
The high voltage of the PMTs is set so they have the same gain and response, in asimilar way to that described in Section 3.3.2.
Finally, in the trigger system, the signal is translated into a 200 ns width signal
called HIT SU M . If the event candidate exceeds the threshold, it is recorded andreconstructed.

4.4.4

PMT Pre-Calibration

Before the PMT installation at EGADS, the quality of 250 PMTs was checked, of
which 227 were selected to instrument EGADS. The high voltage was set in orderto obtain uniform response from all PMTs, and the 1 photoelectron (p.e.) peak anddark rate of the PMTs was reevaluated.
For all this, the following setup was used at the Kamioka mine and very similar tothat used for the PMTs that were to be installed in SK. A Xe lamp for measuring69

CHAPTER 4. THE SUPERK-GD PROJECT

Figure 4.8: Diagram of the trigger logic of the EGADS detector.

multiple p.e. was placed inside a black box, and connected through optical fibre toa scintillation ball inside a µ-metal box, together with an LED and the PMT to betested. This metal box acts as shield from the geomagnetic field.
The scintillation ball is made of acrylic and is 5 cm in diameter. It contains 15 ppm
of POPOP (1,4-bis(5-phenyloxazol-2-yl) benzene) as wavelength shifter and 200
ppm of MgO. Before arriving to the scintillation ball, the light from the Xe lamp
was passed through an ultraviolet filter and divided to the scintillation ball and toan APD (Avalanche PhotoDiode), which monitors the intensity of the source.
In addition to the scintillation ball, an LED was used for testing the PMT sensitivity
to a single photoelectron.

The high voltage was set such that the PMT gain is 1.2 · 107 . For this, seven PMTs
randomly selected from the 250 PMTs were used as reference. The output charge
data at four different high voltages around the nominal operational value is calculated

70

4.4. EGADS R&D PROGRAM AND EXPERIMENT

Figure 4.9: Diagram of the pre-calibration setup for the PMTs installed at EGADS.

by fitting the four data points using this formula y = αxβ . α and β characteristic
constants of each PMT, and y and x are the output charge and the high voltage.
The PMTs are selected based on the low dark rate at half p.e. and the high 1 p.e.
sensitivity, being this the difference between the 1 p.e. peak and the valley between
0 p.e. and 1 p.e.

4.4.5

Detector Construction and Instrumentation

The EGADS tank was built in a new cavern specifically designed for it. Its inner faces
covered by SUS304 panels. Inside the tank, everything metallic is also made out of
SUS304, such as the frames supporting the PMTs, the bolts, etc. The construction
and installation works were carried out with extreme care about the cleaning of every
surface, being every component of the detector previously cleaned with ethanol andpure water. Further, all workers were equipped with tyvek suits, masks, cap andshoes only allowed inside the detector, and the detector was continuously flushedwith fresh air preventing any dust from entering.
The PMTs were mounted on their frames outside the detector in a clean room withpositive pressure to avoid the dust, as in the detector. The FRP housings andacrylic covers were also attached in this clean room after each of the PMTs waschecked again, for the final tuning of the high voltage.

71

CHAPTER 4. THE SUPERK-GD PROJECT

Once instrumented, the EGADS detector seemed to run successfully with pure water, but when adding the gadolinium, the presence of rust was detected through alarge drop in the water transparency. After investigation, what was thought to be acomponent of stainless steel SUS304, turned out to be from other kind of stainlesssteel, producing the rust, already when the detector was filled with pure water. This
meant that the entire detector had to be thoroughly cleaned once again, and refurbished, replacing the problematic parts by ones made of SUS304. This mishap wasquickly and very efficiently solved within a month of hard work from all members of
the EAGDS group.
Lastly, the detector was ready to add gadolinium, being this time the water transparency drops as expected from the addition of the gadolinium sulphate and withvalues very close to those of SK pure water.

4.4.6

Monitoring and Main Results of the EGADS Program

In addition to some of the calibrations done at Super-Kamiokande Section 7.3.1.4
on page 270, such as Nickel calibration or auto-Xe, various other calibrations ought
to be done to prove the performance of the Gd-doped water-Čerenkov detectors.
These measurements have to do with the water transparency, the scattering andabsorption properties of the Gd-doped water, the Gd concentration in the detector
and the Gd-neutron captures themselves.
In order to monitor the transparency of the EGADS water, the UDEAL (Underground Device Evaluating Attenuation Length) device was installed nearby the
200-ton tank. UDEAL is composed by long vertical pipe of 8.6 m instrumented
with an array of seven lasers on the top, covering the main range of the Čerenkov

72

4.4. EGADS R&D PROGRAM AND EXPERIMENT

radiation spectrum (337 nm, 375 nm, 405 nm, 445 nm, 473 nm, 532 nm and 595 nm).

The attenuation length is then measured for
all these wavelengths by measuring the lightfrom the lasers after their light go throughthe column of water filling the pipe beneath.
For better accuracy in the behaviour along
the detector, the measurements are done forvarious water levels and with water from threedifferent sampling points in the detector. Thismeasurement is one of the most important in
the R&D program, because it shows the great
performance and stability of the water system,and the very little effect that the Gd salt hasin the water transparency as compared with

Figure 4.10: Schematic drawing of
the UDEAL device for measuring
the EGADS water transparency.

the usual SK values, as seen in Figure 4.11.

For the measurement of the Gd concentration and its uniformity in the detectortank, water from the three UDEAL sampling points was extracted and measured
with an Atomic Absorption Spectrometer (AAS). Figure 4.12 shows the agreementin the concentration of the three regions of the detector and with the expectedconcentration.

73

CHAPTER 4. THE SUPERK-GD PROJECT

Figure 4.11: Čerenkov light fraction remaining at 15 m of traveling through EGADS tankwater for increasing concentrations of gadolinium sulphate. The green, red, and blue lines
correspond to water from top, centre and bottom of the tank, and the pale blue line is therange of ultrapure water transparencies during SK-III and SK-IV.

Figure 4.12: Gd2 (SO4 )3 concentration in the EGADS 200-ton tank measured with an AAS
for top (red), centre (green) and bottom (blue) regions. The expected concentration isrepresented by the green horizontal lines.

To further investigate and learn more about the effect of the added gadolinium salt
in the light propagation two independent instruments measured the fraction of lightabsorbed and scattered, by the Gd-doped water. This is a new parameter that must
be introduce in the Monte Carlo simulations. Both devices were measuring Rayleighscattering, one introducing a laser injector inside the EAGDS tank, and the other74

4.4. EGADS R&D PROGRAM AND EXPERIMENT

one, called SAADI and developed at UCI, which compares the scattering of Gd withother compounds of known scattering properties. The former provides the most solid
result. The measurements were done for three different concentrations of Gd2 (SO4 )3 .
By comparing the fraction of light scattered with and without a reflector in the beamaxis, the scattering coefficient due to the Gd-doped water can be extracted. The results indicate that the amount of light loss due to Gd is mostly due to absorption
and that scattering contribution is .10%.
Finally, for checking and proving the capabilities of Gd-doped water-Čerenkov detectors, a device for mimicking an inverse β decay was used. It consists in an americium
and beryllium (AmBe) source, which is placed inside the EGADS detector. The
AmBe calibration device is made out of a core of Am and Be covered by a BGO(Bi4 Ge3 O12 ) crystal which emits scintillation light when hit by γ rays. In the coreof the AmBe source, a 4.43 MeV photon and a neutron are produced by the next
reactions.

241

Am → α +237 N p

9*Be + α →12 C ∗ + n*
12C ∗ →12 C + γ(4.43 MeV)
(4.2)

The scintillation light emulates the prompt neutrino signal and it is used as trigger
for searching the delayed neutron capture by Gd in the tank. The measurements
were done for the three different Gd concentrations as in the Rayleigh calibration.
The data show very good agreement with the Monte Carlo simulations as can be75

CHAPTER 4. THE SUPERK-GD PROJECT

seen from the distributions of the capture time and gamma cascade reconstructedenergy in Figures 4.13 and 4.14.

Figure 4.13: Data (black) and Monte Carlo (red) distributions for the time difference
between prompt and delayed Gd-neutron capture signals for data after background is subtracted data (right).

Figure 4.14: Data (black) and Monte Carlo (red) distribution for the reconstructed γ cascade energy from the Gd de-excitation after the neutron capture.

76

4.4. EGADS R&D PROGRAM AND EXPERIMENTIn addition to the on-site calibrations, the performance of the detector and status ofits components are checked every two hours remotely by all the EGADS members.
For the data quality check, a series of basic plots are verified as well. Figures 4.15
to 4.18 show some of the most characteristic distributions.

Figure 4.15: Cosmic muon rate. Number of cosmic muon candidates per fiveminutes.

Figure 4.16: Hit rate for each PMT. The
narrow peaks correspond to R&D PMTs
for Hyper-K.

Figure 4.17: Scatter plot of X and Y
coordinates of reconstructed events morethan 1 ms ago from the previous event(Tdiff cut).

Figure 4.18: Scatter plot of Z and R2
coordinates of reconstructed events morethan 1 ms ago from the previous event(Tdiff cut).

775. On Relevant Items for SuperKGd Physics

In this chapter, key aspects of Gd-neutron tagging in a water-Čerenkov detectors aredescribed, studied and developed using the SuperK-Gd project.
First, the neutron production mechanisms from neutrino interactions are reviewed in
Section 5.1. Then, in Section 5.2, and based on the previous, the detector response to
the Gd-tagged neutron signals is analysed in order to build the neutron reconstruction
algorithm, which will play the key role in the present chapter for various physics
analyses.
The neutron reconstructed information is then used to develop new tools which
will improve the atmospheric and long baseline neutrino oscillation analyses, these
are the separation between neutral and charged current interactions, the neutrinoantineutrino distinction and the neutron corrections to the reconstructed neutrinoenergy, all of them described in Sections 5.3 to 5.5 respectively.
At the end of this chapter, in Section 5.6, the radioactive contamination that the Gdsalt could bring along is studied in detail, from the measuring method to the new
backgrounds produced by itself.

79

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

5.1

Neutron Production in Neutrino-Nucleus Interactions

Since this work strongly relies on the study of the different applications of theneutron production from neutrino interactions in water-Čerenkov detectors, it isworth to have a section explaining some of the theory of the processes involved, as
well as the remaining issues in this, yet novel, topic. This, strongly depends on theneutrino energy, therefore, in this overview the low and high energy regimes will bedifferentiated.

At low energies, up to 100 MeV, only electron
antineutrinos are able to produce a charged lepton (positron) accompanied with neutrons. Thisis the inverse-β decay, seen in Section 2.4. Thisfeature provides a very simple and efficient way
of discerning antineutrinos from neutrinos at low
Figure 5.1: Feynman diagram of
Inverse Beta Decay (IBD) process.

energies, once neutrons can be tagged.

ν e + p → e+ + n(5.1)

This is the fundamental motivation for the development of neutron tagging in waterČerenkov detectors. In SuperK-Gd, this reaction has as target, the first measurementof DSNB and the antineutrinos coming from the Si burning phase of a star.
At higher energies, from 100 MeV on, the neutrino interactions are more complex
and varied, meaning that there will be various neutron production mechanisms. In

80

5.1. NEUTRON PRODUCTION IN NEUTRINO-NUCLEUS INTERACTIONS

fact, here, the neutron production not only depends on the neutrino interaction,
but also on the secondary interactions inside the nucleus. This makes the neutron
multiplicity larger than in the low energy regime and, thus, more difficult to modeland compute. Because of this, the neutrino-antineutrino differences, in terms of theneutron multiplicity, are drastically dimmed as compared to the low energy regime.
The overall neutrino cross-section at these energies can be divided into three welldefined categories for both charged and neutral current interactions. These are theelastic and quasi-elastic scatterings, the resonant and coherent meson productions
and the deep inelastic scattering. In this thesis though, and motivated by the atmospheric neutrino oscillations analysis, they will be treated in three groups CC(containing charged current quasi-elastic and meson production scatterings), CC
DIS and NC (containing all the neutral current interactions). The latter is definedin this manner, because all neutral current interactions share the lack of charged
leptons in the final state.
The CCQE scattering dominates the cross-section below 1 GeV, making its understanding crucial for accelerator neutrinos and the lower spectrum of atmospheric
neutrinos.
νl + n → l− + p, ν l + p → l+ + n(5.2)

For energies above 1 GeV CC-RES interactions dominate, mainly to the resonanceof ∆ baryons. For higher energies, CC DIS interactions dominate.

81

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.2: Charge current interaction cross sections for (a) neutrinos and (b) antineutrinos. The dashed lines are calculated quasi-elastic, dotted lines are single-meson, dash-dotted
are for deep-inelastic scatterings and dots represent the current experimental measurements.

These interaction will happen mainly on the oxygen nuclei of water. The secondaryinteractions within the nuclear media are able to knock out free nucleons from thenucleus, more specifically neutrons. Depending on the interaction, the neutrinoenergy fraction left inside the nucleus changes, and so does the neutron production
due to the secondary interactions.

Figure 5.3: Schematic diagrams involving a typical FSI process (left) and for a reaction
where a pion is produced then absorbed in the same nucleus. These explains that the large
neutron multiplicities are due to the secondary interactions inside the nucleus.

The neutrino-nucleon cross sections are modified by the transport of particles inthe surrounding nuclear medium and the binding energy of the target nucleons. The
nucleon knockout cross-section for the neutrino-nucleon interaction inside a nucleus

82

5.2. GD-NEUTRON TAGGING RECONSTRUCTION

can be calculated following Equation (5.3).
νl A→l0 N X
dσtot
=

Z

3

dr
nucleus

Z

d3 p
k·p
med
Θ(pF (r) − p) 0 0 dσtot
PPB (r, p)MN (r, p) (5.3)
3
(2π)
k ·p

This expression takes into account the Fermi momentum (pF ), the kinematics correction inside the nucleus ( kk·p
0 ·p0 ), the interaction cross-section in the nuclear media
med), de Pauli-blocking factor (PPB ), and the multiplicity of the final state with(dσtota given number of free nucleons (MN (r, p)). Basically, Equation (5.3) tells that theneutron multiplicity from secondary interactions is due to the energy fraction transferred to the nucleus, from which, some nucleons may be have enough energy toovercome their binding energy.

5.2

Gd-Neutron Tagging Reconstruction

This section describes how the neutron capture on gadolinium and its 8 MeV γ
cascade are simulated and reconstructed in the context of the SuperK-Gd experiment.

5.2.1

Monte Carlo Simulation

SKDetSim is the code in charge of simulation of the neutrino interaction productsin the SK detector. Unfortunately, with SKDetSim the gadolinium neutron capture
cannot be well simulated, because the GEANT version (GEANT3) it is based on,
differs significantly with the latest experimental data. Therefore, the Gd-neutron
capture information vectors were simulated independently from SKDetSim withGEATN4 and then, introduced into the detector’s simulator to reproduced thesignal at SuperK-Gd.
In addition to the neutron captures, Gd also has the effect of worsening the light83

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

transmission on Gd-doped water. This effect was considered to be around 15%
loss in the light left at 15 m, but more recent results show that the effect of Gd
in the light propagation will not be so severe. Actually, the light left at 15 m will
be within the SK-III and SK-IV range, as discussed in Section 4.4.6. In this work,
three scenarios are presented, two extreme and conservative cases that supposethat the 15% loss in the light left at 15 m is all due to Rayleigh scattering or only
absorption of the gadolinium. The third case considers the transparency of purewater, assuming that there is no significant transparency loss. For this, SKDetSim
was tuned to reproduce the three water transparency cases.

Figure 5.4: Number hit PMTs within 20 ns time window surrounding the Gd-neutron
capture for SK pure water (blue), and the extreme cases where the 15% loss in the light left
at 15 m due to Gd is all because of scattering (red) or absorption (black).

In Figure 5.4, it is shown how the number of hits within 20 ns surrounding theGd capture, where the differences between the three cases is most noticeable. The
distribution for the pure water peaked at larger values than those with 15% light84

5.2. GD-NEUTRON TAGGING RECONSTRUCTION

loss at 15 m.
Between the two extreme scenarios it is possible to discern different behaviours.
For the all scattering case, the number of hits tends to be larger than for the allabsorption one. This is because in the all absorption scenario, more photons areabsorbed resulting in fewer hits in the detector, whereas in the scattering case, thephotons are more dispersed. This behaviour is very similar to that of the energy
reconstruction because it relies mainly on the number of hits recorded.
These differences are propagated to the reconstructed vertex and direction. Bothextreme cases will have poorer resolution as compared to the pure water because
less light is collected by the detector. Of these two the scenarios, that with vertex
and direction poorer resolution should be the all scattering one. This is due to thefact that in this case, photons loose information of the point they are coming from,meaning that the time of flight (ToF) subtraction will leave these photons outside
the time window used by the BONSAI (Branch Optimisation Navigating Successive
Annealing Iterations) fitter, [Smy07]. This behaviour can be seen in Figure 5.5,
which shows the goodness for the vertex fit. For the fit of the direction, the effectwas not so noticeable, being the goodness of the fit (DirKS) very similar in all
three cases.

The latest measurements from UDEAL, Figure 4.11, show that such a large drop,as 15% in the water transparency, is not seen anymore. In fact, the decrease in thelight left at 15 m will not be larger than 8% with respect to current SK’s average
pure water values.

85CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.5: Goodness of BONSAI vertex fit of the Gd-neutron capture for SK pure water(blue), and the extreme scenarios where the 15% loss in the light left at 15 m due to Gd is
all because of scattering (red) or absorption (black). Larger values of the goodness represent
better reliability of the vertex reconstruction.

The last issue concerning the Monte Carlo simulation of the Gd-neutron capture
concerns the detector background. This has great importance for such low energy
signals as the 8 MeV γ cascade. Despite being a signal of 8 MeV, which is a sizeableenergy, it is shared by various photons, typically three to five, making that the meanvalue of the reconstructed energy around 4.8 MeV, close to SK’s energy threshold.

It is, therefore, important to have a reliable estimate of the detector’s background.
For that purpose it is not enough to consider the dark rate of the PMTs, but
to take into account the rest of the backgrounds present in the detector as well.
In Section 5.2.1, it is shown the fake candidates selected after running the firstcandidate selection algorithm through Monte Carlo simulated SK dark noise, of 5.7
kHz, and through SK-IV noise data. The latter consists in the hit information of
SK-IV data after removing the signal from the event. This shows that the actual865.2. GD-NEUTRON TAGGING RECONSTRUCTION

Figure 5.6: True total (pink) and reconstructed (black) energy distribution of the Gd signal
for SK water transparency.

background of SK is quite larger than that assuming the dark rate of the PMTs
in terms of the number of hits. For that reason and to better estimate the actual
background, data was taken for various periods when the T2K beam was not in
operation and no other event in SK was seen. This is called T2K dummy trigger
data.
These data were added to the full length of each simulated event as the backgroundof the detector, and in substitution of the random dark noise. This technique enables
a better description of the detector and the development of a much more reliable
Gd-neutron capture signal detection algorithm. Figure 5.9 shows the number of hits
within 20 ns time window for fake candidate selection as in Section 5.2.1, but forT2K dummy trigger data.

87

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.7: Number of hits within 20
ns time window surrounding the neutron tag candidate for the simulated darknoise with no neutron tagging.

Figure 5.8: Number of hits within 20
ns time window surrounding the neutron
tag candidate for the SK data with noneutron tagging.

Figure 5.9: Number of hits within 20 ns time window surrounding the neutron tag candidate
for the T2K dummy trigger data with no neutron tagging.

SK-IV data and T2K dummy trigger data fake candidate selection show a very similar
distribution, corroborating the validity of the usage of T2K dummy trigger data as
the background of the detector.

5.2.2

Neutron Tagging Algorithm

The algorithm for detecting the Gd-neutron captures a two-step process is used.
First, candidates are selected based on the number of hits clustered in the hit timing
distribution after the prompt signal is triggered. The second, uses different properties

885.2. GD-NEUTRON TAGGING RECONSTRUCTIONof the Gd-neutron captures to discern this from the background of the detector using
a likelihood method.

5.2.2.1

First Candidate Selection

For the first candidate selection the hits after the prompt signal of the neutrino arescanned by overlapping 1.3 µs time windows, being the first 500 ns the same of theprevious time window. The hit timing information of the event is ToF subtracted
assuming the distance from PMTs to the neutrino signal vertex, which is a goodfirst order approximation. Inside these 1.3 µs time windows, the maximum numberof events within a 50 ns and 200 ns time windows are computed.

Figure 5.10: Hit timing distribution of PMTs showing the prompt and Gd-capture delayed
signals.

Here, the mentioned ToF subtraction is crucial due to the multiple photon emissionof the gadolinium, having each of them its own direction and path to the walls of
the detector.
The criteria for the candidate selection are rather loose, but effective in identifying

89CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

the true neutron captures and keeping the fake candidate selection rather low foreach event. The requirements are chosen for the maximum number of hits in the
1.3 µs window within 50 ns (N50 ) and 200 ns (N200 ), being a candidate selected if
Equation (5.4) is satisfied.

(5.4)

N200 ≥ 20, N50 ≥ 11

These selection requirements have been optimised for the case where the water transparency of SuperK-Gd has similar values as that of SK. Although the first selection
could have been adapted to other water transparencies, the same cuts were done, sothey give an estimate of the performance of the selection for different water properties. The three water transparencies explored are those shown in Figures 5.4 and 5.5.
Table 5.1 shows the efficiencies of the first candidate selection algorithm and the fakecapture candidates per neutrino event due to the detector’s background. The lattercorrespond to the Gd-neutron tagging detector background. The length of the event
is assumed to be 535 µs corresponding to the SHE+AFT trigger, shown in Table 3.4.
Gd-neutron capture
SK water All scat. All abs.
Candidateselection

99.3%

99.0%

98.0%

SK waterBackgroundAll scat.

All abs.

2.75 event−1

2.60 event−1

2.75 event−1

Table 5.1: Efficiencies and remaining background for the first candidate selection of the Gdneutron capture signals and for the three water transparency cases considered.

Once a candidate has been selected, a new time window for the candidate is defined.
This contains the PMT hits contributing to the signal in the centre of the window.
This delayed event is treated then as a low energy signal and reconstructed with the
BONSAI fitter. Several of the variables fitted will contribute to the construction905.2. GD-NEUTRON TAGGING RECONSTRUCTIONof the likelihood distribution, explained in the next section, to further discern true
Gd-neutron captures from the detector background.

5.2.2.2

Gd-Neutron Capture Selection Likelihood

For discriminating between the actual neutron capture signal and fake first candidates from background, a likelihood function in terms of several variables is constructed. These variables take into account the detector response to the physics ofthe Gd capture. The variables for the construction of the likelihood distribution are
described next and shown for the SK water transparency case. For the other two
water scenarios these variables show little deviations, which will be shown at the endof this section in the likelihood distributions and efficiencies for all scenarios.
• N20 : The number of hits in 20 ns around the delayed signal candidate.

Figure 5.11: Number of hits within 20 ns time window surrounding the neutron tag candidate for the true Gd-neutron signal (blue) and the remaining background from the first
selection (red).

91

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

For true Gd-neutron captures the values tend to be ∼2.5 times larger than for
the fake candidates, which also show a much narrower distribution due to thebroad spectra of the Gd γ cascade.
• N bf : The the number of hits used by BONSAI, the low energy fitter.

Figure 5.12: Number of hits used by BONSAI for fitting the signal for the true Gd-neutron
signal (blue) and the remaining background from the first selection (red).

In this case, the Gd-neutron captures show a narrow distribution near 150 hits,
whereas for the background due to the randomness of the PMT hit distribution
the distribution is much wider and with smaller values.
Nef f − 2/11 · (N1300 − N200 )q, is the signal significance is2N
13 1300
based on the number of effective hits in 200 ns window with respect to the• Signal significance:

average number of hits outside that window. The effective number of hits iscomputed taking into account the poor charge resolution at these energies,
angular dependences of the PMT acceptance and that for energies below 20

925.2. GD-NEUTRON TAGGING RECONSTRUCTION

MeV, approximately 1 p.e. is produced per hit.

Nef f =

N
200
X
i=1

!
ri
Nall
(Xi + tail − dark )e λrun Gi (t)Nalive S(θi , φi )(5.5)

The 2/11 and 2/13 factors correspond to the normalisation of the 1.1 µs and1.3 µs windows so all the terms correspond to a time window of 200 ns.

Figure 5.13: Signal significance of the the candidate for the true Gd-neutron signal (blue)
and the remaining background from the first selection (red).

Being the Gd capture a stronger signal, this variable has larger values for it
than for the detector noise.
nbsr0: Another variable used by BONSAI, where nbsr0 is the radius
Nef fof the minimum sphere containing more than 20% of the event hits.

• clik = N20

For the fake candidates there are two regions, one towards zero for those events
very close to the wall for which the sphere is small and a broad region at larger
values for which the sphere needed to contain 20% is large. On the other hand,true neutron captures exhibit a much narrower distribution.

93

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.14: Distribution of the clik variable for the true Gd-neutron signal (blue) and theremaining background from the first selection (red).

• Q20 : Sum of the charge of those hit PMTs within 20 ns time window surrounding the delayed signal.

Figure 5.15: Sum of charge of hit PMTs within 20 ns window for the true Gd-neutron
signal (blue) and the remaining background from the first selection (red).

945.2. GD-NEUTRON TAGGING RECONSTRUCTION

As in the case of N bf , the true neutron capture distribution is narrower thanthat for the background, meaning that the charge is similar for all neutron
captures.
• dW all: Distance to the nearest detector wall.

Figure 5.16: Distance from candidate vertex to nearest wall for the true Gd-neutron signal(blue) and the remaining background from the first selection (red).

This variable distinguishes neutron tags from most of the background events
coming from radioactivity or PMT noise which reconstructed very close to thewalls of the detector, whereas the neutron captures happen uniformly all acrossthe detector.
p~rP M T −~rγ
22• σ(θP M T ) = hθP M T i − hθP M T i, where θP M T = arccos ~uγ · |~rP M T −~rγ | , andbeing ~uγ the reconstructed direction of the delayed signal and ~rγ − ~rP M T thevector from the reconstructed delayed candidate position to that of the hit
PMT for each of the hit PMTs.

95

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.17: RMS of the angle between the vector of delayed vertex and each hit PMT andthe reconstructed direction of the delayed signal for the true Gd-neutron signal (blue) andthe remaining background from the first selection (red).

This measures the resolution of the angle distribution between the reconstructed direction of the delayed signal and the direction from the delayedvertex to each of the PMTs. True neutron captures exhibit bigger differences
because the reconstructed direction is dominated by hit information of the mostenergetic photon, however the background usually comes from a single signalof radioactive decay or PMT noise.
• σ(tP M T ):ph|tγ − T oF |i2 − h(tγ − T oF )2 i, where ToF corresponds to the timeof flight from the reconstructed delayed vertex to each of the hit PMTs.
Here it is shown that once ToF is subtracted the time of the hit PMTs is
within 4 ns, but for the background events their differences tend to be larger.

965.2. GD-NEUTRON TAGGING RECONSTRUCTION

Figure 5.18: RMS of the distance distribution from each it PMT to the reconstructed vertex
for the true Gd-neutron signal (blue) and the remaining background from the first selection(red).

• σ(rP M T ) =ph|~rγ − ~rP M T |i2 − h(~rγ − ~rP M T )2 i, where ~rγ is the position of thereconstructed vertex of the delayed signal and ~rP M T is the position of each hit
PMT.

Figure 5.19: RMS of the time difference from each hit PMT to the time of the candidate
for the true Gd-neutron signal (blue) and the remaining background from the first selection(red).

97

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICSThis variable shows the resolution of the distances between the delayed signal
and the hit PMTs. Fake candidates have larger values on average than actual
neutron captures because the signal of the latter comes from the same point,where background events may come from noise of different PMTs and thevertex reconstruction is not so good.
• goodness: This is goodness of the BONSAI fitted vertex of the delayed signal.

Figure 5.20: Goodness of the reconstructed candidate vertex by BONSAI fitter for the true
Gd-neutron signal (blue) and the remaining background from the first selection (red).

Larger values mean better quality and reliability of the reconstruction, indicating that actual Gd-captures are better reconstructed than the background.
• dirKS2: This is goodness of the fit direction of the delayed signal.

98

5.2. GD-NEUTRON TAGGING RECONSTRUCTION

Figure 5.21: Goodness of the reconstructed candidate direction by BONSAI fitter for thetrue Gd-neutron signal (blue) and the remaining background from the first selection (red).

Larger values of this variable indicate worse direction reconstruction, confirming that also for the direction reconstruction the Gd-neutron captures performbetter than the background.
• ∆r =

p(xν − xγ )2 + (yν − yγ )2 + (zν − zγ )2 : Spatial difference in cm between

prompt and delayed signal.
For the distribution the decimal logarithm was taken to better see the behaviour and typical values. Gd-neutron captures tend to occur at order 1
m from the prompt signal, whereas the background events are randomly
distributed in the detector independently from the prompt vertex. This is themost relevant variable for the likelihood computation.

99

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.22: Decimal logarithm of the distance between prompt and delayed candidate vertices for the true Gd-neutron signal (blue) and the remaining background from the first
selection (red).

• dt = tγ − tν : Time difference in µs between prompt and delayed signal.

Figure 5.23: Time distribution of neutron capture candidates from the prompt signal forthe true Gd-neutron signal (blue) and the remaining background from the first selection(red).

100

5.2. GD-NEUTRON TAGGING RECONSTRUCTION

This quantity shows the different time distribution with respect to the neutrinosignal. It is flat distributed for fake candidates. For true Gd-neutron captures,on the other hand, the distribution is the convolution of an increasing behaviour
corresponding to the amount of neutrons thermalised until 10 µs and a decaying
exponential with mean lifetime of ∼20 µs corresponding to the Gd capture timeof the neutrons. For times larger than 100 µs it is very unlikely for the Gdneutron captures to happen.

Figure 5.24: Matrix of the linear correlation coefficients of the variables used in the identification as Gd-neutron capture of the delayed candidate signals.

Figure 5.24 shows the linear correlation coefficients of all the previous variables forthe construction of the likelihood distribution, showing that the majority of them
are completely uncorrelated. The number of hits in 20 ns window and the signal
significance are the most correlated variables because they both use the number ofhits within certain time windows. Other variables show a moderate correlation, due
to the similarities between timing and spacing of hit PMTs. These correlations werechecked not to have any worsening in the performance of the separation.
The likelihoods for the three water transparencies are shown in Figures 5.25 to 5.27.

101

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS• SK water transparency

Figure 5.25: Gd-neutron capture likelihood distribution for actual signal (blue) and detector
background (red), assuming that gadolinium sulphate does not have any effect on the watertransparency. The pink vertical line shows the selection point at 0.95.

• 15% transparency loss due to Rayleigh scattering

Figure 5.26: Gd-neutron capture likelihood distribution for actual signal (blue) and detector
background (red), assuming 15% water transparency loss due to additional Rayleigh scattering component of gadolinium sulphate. The pink vertical line shows the selection point
at 0.95.

102

5.2. GD-NEUTRON TAGGING RECONSTRUCTION• 15% transparency loss due to absorption

Figure 5.27: Gd-neutron capture likelihood distribution for actual signal (blue) and detector background (red), assuming 15% water transparency loss due to additional absorption
component of gadolinium sulphate. The pink vertical line shows the selection point at 0.95.

The cut point was chosen to be the same for all three cases like in the candidate first
selection. This point was chosen so the purity of the remaining sample of Gd-neutrontags was a higher as possible for the SK water transparency case. Table 5.2 showsthe efficiencies of selecting actual neutron tags and background events after the cut
is applied.

The method shows a great efficiency in selecting the Gd-neutron captures and withgreat confidence, given the low contamination from background events for the threecases. However, a slightly decreasing trend in the Gd-neutron captures efficiency isseen going from SK pure water to all absorption passing through all scattering.

103CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS
Gd-neutron capture
SK water All scat. All abs.
Likelihood
selection

93.3%

89.8%

BackgroundSK water All scat. All abs.

87.7%

0.009%

0.011%

0.018%

Table 5.2: Efficiencies and remaining background of the likelihood distribution for the Gdneutron tagging selection and for the three water transparency cases.

5.2.3

Overall Gd-Neutron Tagging Efficiency

The summary of both selection steps is shown next in terms of their efficiencies andthe total efficiencies for all water transparency cases.

SK water transparency
Gd-neutron capture
Candidate selection
99.3%
Likelihood selection
93.3%
Total efficiency
92.7%

Background2.72 event−1
0.009%
2.4 · 10−4 event−1

Table 5.3: Overall efficiencies and backgrounds of the Gd-neutron tagging selection methods
for the case for the SK water transparency case.

15% transparency loss due to Rayleigh scattering
Gd-neutron capture
Background
Candidate selection
99.0%
2.63 event−1
Likelihood selection
89.8%
0.011%
Total efficiency
88.9%
2.9 · 10−4 event−1
Table 5.4: Overall efficiencies and backgrounds of the Gd-neutron tagging selection methods
for the case for the 15% water transparency loss due to Rayleigh scattering.

1045.2. GD-NEUTRON TAGGING RECONSTRUCTION
15% transparency loss due to absorption
Gd-neutron capture
Background
Candidate selection
98.0%
2.72 event−1
Likelihood selection
87.7%
0.018%
Total efficiency
86.0%
4.9 · 10−4 event−1
Table 5.5: Overall efficiencies and backgrounds of the Gd-neutron tagging selection methods
for the case for the 15% water transparency loss due to absorption.

Given the latest EGADS results, only a ∼8% loss and mainly due to absorption, it issafe to know that the expected total efficiency for Gd-neutron tags will be approximately the average of the SK pure water and all absorption cases, around 89%. The
systematic error in the efficiency is taken from the difference in the efficiency of these
two extreme cases, which is of the order of 5% of the averaged efficiency. With thisassumption not only the uncertainty in the water transparency effect is considered,
but also any other error concerning the simulation, as discussed in [Mori15]
For a 0.2% concentration of gadolinium sulphate in water the total amount of neutrons captured by Gd will be 90% and the rest will be captured by hydrogen. This
gives a total neutron tagging efficiency of ∼80%±4%, this values will be taken as the
expected efficiency and associated systematic error for the physics analyses coming in
the following sections. The 5% error of the efficiency is taken as the systematic error
because the water transparency in which most of the variables rely, is the largest uncertainty in this method. This will be taken as the systematic error associated to the
Gd-neutron tagging for the atmospheric neutrino oscillation analysis in Section 6.6.

105

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

5.3

Classification of Charged Current and Neutral
Current Interactions

In this section a new method for distinguishing between neutral current (NC),charged current deep inelastic scattering (CC DIS) and the charged current (CC)electron neutrino interactions, is presented. This method is based on the neutron
multiplicity along with other properties of the neutrino interaction final state.
This feature is only considered for the MultiRing MultiGeV e-like sample of theatmospheric neutrino data. This sample contains events with more than one reconstructed ring, which the most energetic ring is e-like and visible energy greater than(−)

1.33 GeV. It is the most contaminated sample by NC and ν µ . The latter interact
mostly via CC DIS interactions, motivating the grouping of the events in the threesets of interactions. The contents of these sample is shown in Table 5.6.

Interaction mode
CC non-DIS νe
CC non-DIS ν e
CC DIS νe
CC DIS ν e
CC non-DIS νµ
CC non-DIS ν µ
CC DIS νµ
CC DIS ν µ
NC νMultiRing e-like
21.0%
7.3%
18.7%
3.4%
4.8%
1.1%
19.8%
1.8%
22.1%

Table 5.6: Relative contents of each interacting mode for the MultiRing e-like atmospheric
neutrino sample.

106

5.3. CLASSIFICATION OF CHARGED CURRENT AND NEUTRALCURRENT INTERACTIONS

For completeness, Table 5.7 shows all the variety of interactions that CC DIS and
NC englobe.

Interaction
ν + N/P → l + N/P + mesons
ν + N/P → l + N/P + mesons
ν + N → ν + N + π0
ν + N → ν + N + π0
ν + P → ν + P + π0
ν + P → ν + P + π0
ν + N → ν + P + π−
ν + N → ν + P + π−
ν + P → ν + N + π+
ν + P → ν + N + π+
ν + O16 → ν + O16 + π 0
ν + O16 → ν + O16 + π 0
ν + N/P → ν + N/P + multiπν + N/P → ν + N/P + multiπν + N → ν + N + η0
ν + N → ν + N + η0
ν + P → ν + P + η0
ν + P → ν + P + η0
ν + N → ν + Λ + κ0
ν + N → ν + Λ + κ0
ν + P → ν + Λ + κ+
ν + P → ν + Λ + κ+
ν + N/P → ν + N/P + mesons
ν + N/P → ν + N/P + mesons
ν + N/P → ν + N/P + mesons
ν + N/P → ν + N/P + mesons
ν+P →ν+P
ν+P →ν+P
ν+N →ν+N
ν+N →ν+N

Name
CC deep inelastic (JET set)

NC1π (from ∆ resonance)

NC1π
NCmultiπNC1η (from ∆ resonance)
NC1η (from ∆ resonance)
NC1κ (from ∆ resonance)
NC1κ (from ∆ resonance)
NC deep inelastic (JET set)
NC deep inelastic (JET set)

Elastic

Table 5.7: Set of CCDIS and NC interactions for atmospheric neutrinos that will be try todiscern from the rest of CC interactions.

107

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICSThis separation will become important for neutrino-antineutrino separation and theneutron correction of the reconstructed energy of the events in this sample. The last
two techniques will be developed in Sections 5.4 and 5.5 respectively.
Given the energy regime of this sample, being able to make a more pure sample ofelectron neutrinos and antineutrinos, will have an significant impact on the sensitivity to the neutrino mass ordering from the atmospheric oscillation analysis.
For this discrimination, the number of tagged neutrons is crucial because their production depends on the interaction mode and also on the secondary interactions ofmesons in the nuclear media, as discussed in Section 5.1.
The method consists in the construction of a likelihood distribution for each of theinteraction groups NC, CC DIS and CC non-DIS using a neural network method,[Hoecker07]. The variables used are described and motivated next.
• Neutron multiplicity: Neutrinos interacting via neutral current interactions
leave a larger fraction energy in the target nucleus than those interacting
charged current. This makes the typical neutron production of NC events
larger than CC ones. The CC DIS events have a intermediate behaviour, alarge part of the neutrino energy is transferred to the nucleus, although not asmuch as in the NC case because of the charged lepton produced in these interactions.The three groups of interactions have then, different typical neutron
multiplicities.
• Additional particle production: For these separations the number of rings andthe likelihood of the event to have more than one ring are used. They show
again that in NC and CCDIS events the neutrino energy is largely transferred(−)

to the nucleus producing, typically, more particles than CC ν e , similarly tothe neutron production. This means that the number of rings tends to be larger

1085.3. CLASSIFICATION OF CHARGED CURRENT AND NEUTRALCURRENT INTERACTIONS

for NC and CCDIS.
In this context, the number of electrons from muon decays and the distancefrom the prompt vertex to the furthest of them have also a significant impor(−)

tance in the separation. This becomes specially relevant for discerning ν µ(−)

from ν e as the associated charged lepton to the former are µs which will usually decays inside the detector. On the other hand, NC interactions produce(−)

more decay-e than CC ν e , but its distribution is peaked at zero, being the
(−)

(−)

distance to the furthest decay-e in between CC ν e and CCDIS ν µ because,
although more decay-e are produced none of them is coming from a µ.
Finally, the sum of particle ID likelihoods of each ring, this is used for deciding
whether the ring is e-like from µ-like. This variable shows which species, e-likeor µ-like rings, are dominant for each event. Here the differences are small but(−)

still they help the discrimination, specially for CCDIS ν µ for which it takes
larger values, i.e. more µ-like, than for the other species.

• Kinematics: Two variables having to do with the kinematics of the different
event types are defined. The pseudorapidity (η) and the energy fraction of
the most energetic ring. Both aim to distinguish NC from CC interactions
due to the more isotropic behaviour of the final products of the former, i.e.
energy is more equally distributed among all the event reconstructed rings.
The definition of pseudorapidity has been adapted from collider physics taking
by reference the total direction of the event, therefore this variable will show
how separated are all the rings between them weighted by their momenta.
nring
1 X
~u · p~jη=Evis j=1

109

(5.6)

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

where Ev is is the reconstructed visible energy of the event, ~u the direction of
the event and p~j the 3-momentum of each ring.

These variables are used in a two-step process neural network to discard first the NC
from CC DIS and CC events. Secondly muon neutrino and antineutrino interactions,which mainly CC DIS in this sample are separated from CC events. Figure 5.28
shows the procedure schematically.

Figure 5.28: Scheme of the two-step process in MultiGeV MultiRing e-like sample to separate NC interactions and νµ from CC νe events.

This method is fully developed and applied for Gd-neutron tagging and H-neutron
tagging in Sections 6.6.2 and 7.2.1. It is also developed for the Hyper-K analysis withneutron tagging in Section 6.8.

5.4

Neutrino-Antineutrino Separation

For atmospheric neutrinos, the main advantage of neutron tagging up to now was the
improvement in the distinction of neutrinos and antineutrinos. The latter tend to
produce more neutrons in the final state that the former, being the most discerning
variable for the distinction. In this section, a new method for the ν − ν separation

1105.4. NEUTRINO-ANTINEUTRINO SEPARATION

are shown and explain.
The separation is only possible for charged current interactions.

The neutrino

charged current interactions at atmospheric and long baseline energy ranges arelisted in Table 5.8.

Interaction
ν+N →l+P
ν+P →l+Nν + P → l + P + π+
ν + N → l + N + π−
ν + N → l + P + π0
ν + P → l + N + π0
ν + N → l + N + π+
ν + P → l + P + π−
ν + O16 → l + O16 + π +ν + O16 → l + O16 + π −ν + N/P → l + N/P + multiπν + N/P → l + N/P + multiπν + N → l + P + η0
ν + P → l + N + η0
ν + N → l + Λ + κ0
ν + P → l + Λ + κ0
ν + N/P → l + N/P + mesons
ν + N/P → l + N/P + mesons

Name
CCQE

CC1π (from ∆ resonance)

CC1π
CCmultiπCC1η (from ∆ resonance)
CC1κ (from ∆ resonance)
CC deep inelastic (JET set)

Table 5.8: Charged Current ν interactions showing the tendency of antineutrinos to usually
produce more neutrons than neutrinos.

Unfortunately, as explained previously, the secondary interactions with the nuclear
media produce more neutrons independently of the neutrino or antineutrino character. This makes the separation dimmer than with the inverse-β interaction of low
energy antineutrinos. For that reason, dedicated methods are preformed and optimised for the separation in each atmospheric and long baseline sample.

111

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICSThe ν − ν separation methods are developed in Sections 6.6.3, 6.7.4 and 7.2.2, foratmospheric and long baseline Gd-tagging and for atmospheric H-tagging respectively, are explained. It is also implemented for the respective analyses, atmosphericoscillation analysis with Gd-tagging in Section 6.6.5, T2K analysis with Gd-tagging
in Section 6.7.6 and atmospheric oscillation analysis with H-tagging in Section 7.3.
This separation is also implemented, although not shown explicitly, and applied in
the atmospheric and long baseline analyses at Hyper-K in Section 6.8.
Depending on the analysis and the neutrino sample, the separation will be doneby making cuts or constructing a likelihood distribution with several variables in
addition to the neutron multiplicity. These variables take into account all the differentiating features of neutrinos and antineutrinos. Next, all the variables that will be
used are described and explained.

• Number of Gd-tagged neutrons: As mentioned before, this variable is the main
motivation for the implementation of this separation. The different behaviourof neutrinos and antineutrinos comes from the primary interaction of charged
current events. At 10−1 −102 GeV energy range the charged current interactions
are dominant and they are more likely to produce a larger neutron multiplicity
in the antineutrino case.

• Number of µ decay electrons: This variable accounts for the charged pions production difference between neutrinos and antineutrinos. Due to charge balanceof the interaction, neutrinos are more likely to produce π + and antineutrinos
π − . The formers decay mostly into µ+ s and these into e+ , which are delayed
from the primary interaction and tagged as decay-e. On the other hand, the laters, are quickly absorbed by the water in the detector (mainly by 16 O), hardly

112

5.4. NEUTRINO-ANTINEUTRINO SEPARATION

ever being able to decay. This, together with the neutron multiplicity are themost discriminating variable from the neutrino and antineutrino separation.
• Time to furthest decay electron (MultiRing samples only): This shows that if
a decay-e comes from a π − or π + . If the decay happens at late times it meansthat the parent particle cannot be absorbed by water and, most likely, thiswould correspond to a π + . On the other hand if the decay is very close in timeto the primary interaction it will not have had enough time to be absorbed
even if it corresponds to a π − . Therefore, it is expected that ν have larger
times than ν.
• Distance to furthest decay electron (MultiRing samples only): This has thesame motivation as the previous variable, it simply translates time to distance.
• Sum of particle ID likelihood (MultiRing samples only): This variable takes
into account that some of the produced charged particles in the interaction will
not produce enough Cherenkov light to reconstruct a ring, but they contributeto other rings. In that sense, νs are more likely to produce charged hadrons,
meaning that these events may have mis-reconstructed rings, diluting the ringpattern.
• Number of rings (MultiRing samples only): Similar to the previous case, CCν interactions tend to produced more charged hadrons than the analogous forCC ν, and this contributes to the larger number of Cherenkov rings produced
and detected.
• Energy fraction of most energetic ring (MultiRing samples only): Variablewhich takes into account the differences in the CC cross-section between neu-113

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

trinos and antineutrinos. Neutrinos tend to have less fraction of the momentum
in its most energetic ring.
• Pseudorapidity (MultiRing samples only): It is the same variable as defined in
Equation (5.6). This variable also accounts for the different expressions of thecross-section for neutrinos and antineutrinos resulting in different angle andenergy distributions.
• Angle between neutrino beam and charged lepton scattering angle (T2K samples only): This variable is only possible for long baseline neutrinos where thedirection of the neutrino is known. The scattering angle dependence is different for neutrino and antineutrino interactions, providing additional and very
important information as compared to the atmospheric neutrino analysis.
For the case of atmospheric neutrinos, the methods can be divided into two different
strategies. In the SubGeV and single ring MultiGeV samples, simple cuts are doneon the two most relevant variables, the number of neutrons and the number of decay
electrons. On the contrary, in the MultiRing samples, the neutron multiplicities growsignificantly making even dimmer the distinction, therefore, a similar method to the
NC-CC separation is shared by these samples. It consists in the computation of alikelihood distribution via a neural network with all the variables described before.
After the NC-CC and neutrino-antineutrino separations done for the atmosphericfully contained events, the samples have the scheme shown in Figure 5.29.

114

5.5. NEUTRON-CORRECTED RECONSTRUCTED NEUTRINO ENERGY

Figure 5.29: Scheme of the new sample definition for atmospheric neutrinos based on theneutron tagging event selection.

For the T2K analysis, the neutrino-antineutrino separation is done using just the
number of neutrons and the cosine of the scattering angle. In this case, a likelihood
distribution is constructed in favour of simple cuts due to the continuous distributionof the scattering angle.

5.5

Neutron-Corrected Reconstructed Neutrino
EnergyThe neutrino energy reconstruction is very important for any water-Čerenkov neutrino detector, specially in the atmospheric oscillation analysis. Neutrino oscillation
probabilities change very rapidly with energy and different energy regions are
sensitive to particular oscillation parameters. For this reason, it is crucial to have areliable and accurate energy reconstruction.
Neutrino energy is reconstructed as the so called visible energy, and defined as thesum of the energy of each ring produced. Therefore, it does not take into accountthe energy transferred to the nucleus and transformed into neutral hadrons (π, κ,

115

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

η...) produced in the interaction.
The more energetic is the incoming neutrino the more energy fraction is lost due toneutral hadron production. These usually interact inside the nuclear media, whichtranslates into the increasing possibility of neutron production. This conclusion is
extracted directly from Equation (5.3), which shows that the neutron multiplicity
encloses information about the neutrino energy transferred to the nucleus and,
therefore, about the fraction of the neutrino energy potentially invisible to thedetector.
Figure 5.30 shows an example of the fraction of invisible energy as a function of
the neutrons tagged by gadolinium, exhibiting a clear correlation between bothquantities.

Figure 5.30: Plot showing the dependence of the quotient of the non-reconstructed energy
and the visible energy with the number of Gd-tagged neutrons for MultiRing ν e -like atmospheric neutrino Monte Carlo.

This dependency gives the opportunity for improving the reconstructed visible energy
by applying a neutron correction function to all the events in a particular sample.

116

5.6. RADIOACTIVE CONTAMINATION

The monotonically increasing behaviour is shared by all samples, but with changes in
the parameters of the fitting function, depending on the neutrino energy and flavour.
For each sample, the correction function is obtained by fitting the distribution shownin Figure 5.30 to a polynomial function. The correction is applied by using theexpression in Equation (5.7).

Gd
Erec= Evis (1 + f (Gd-neutrons))

(5.7)

Gd
Where f is the corresponding sample correction function and Erecis the correctedreconstructed neutrino energy.
This is a very novel, but certainly interesting feature. In this thesis, this techniquewill be developed for Gd-neutron tagging at Sections 6.6.4 and 6.7.5 to be implemented for the atmospheric neutrino oscillation and the T2K oscillation analyses
respectively. It has been also done for the Hyper-K analyses in Section 6.8, although
it is now explicitly shown to reduce the extension of this dissertation. In Section 7.2.3,
this method is implemented for current SK data with H-neutron tagging and applied
to the atmospheric oscillation analysis shown in Section 7.3.

5.6

Radioactive Contamination

The inclusion in SuperK-Gd of additional radioactive contamination could be potentially harmful for the future of the project. If the radioactive contamination is
too large, the capability of SuperK-Gd to discover DSNB neutrinos could be ruined
and the current low energy solar analysis of SK would be impossible. In addition, if
the radioactive contamination is huge, the signals coming from radioactive decays
could saturate the detector. Therefore, the measurement and monitoring of the117CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

radioactive contamination of new materials in SuperK-Gd is crucial.
Hence, an exhaustive campaign of radioactivity measurements has been and isbeing carried on for the pursuit of SuperK-Gd. Of all of the sources from whichradioactivity might enter the detector, the most dangerous is the Gd compound
itself. This will be diluted in the whole volume and radioactive signals could bereconstructed at any point of the detector and thus, undistinguishable from the true
low energy neutrino signals. Other sources, like the sealing materials for repairing
SK’s leak, could also contribute to the radioactive background. However, since thesematerials will be attached to the detector’s walls, it is harder for them to enter thefiducial volume and actually become a background.
The most important and potentially harmful radioactive decays that will occur, arethose from the three radioactive decay chains, shown in Figure 5.31.
The upcoming sections present the measuring method using high purity germanium
detectors (HPGe), Section 5.6.1, and the in Sections 5.6.2 to 5.6.4, the main background sources are explained as well as the latest latest techniques developed forthe removal of the most radioactive contaminants from the Gd sulphate.

118

5.6. RADIOACTIVE CONTAMINATION

Figure 5.31: From top to bottom, 238 U, 235 U and 232 Th radioactive decay chains. Blacklines between isotopes indicate α-decays, blue lines β-decays and pink writing spontaneous
fissions with their half-life. Half-life for α and β-decays is written over the lines between
isotopes. In addition, the energy and probability of the most characteristic photons areshown in red next to the corresponding isotopes.

119

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

5.6.1

Measurement of Radioactive Contamination in Materials with HPGe Germanium Detectors: Gadolinium
Sulphate

The principal method for measuring the radioactive contamination of Gd2 (SO4 )3are HPGe detectors. High precision Ge detectors are able to measure a broad range
of energies and, therefore, the majority of the characteristic photon peaks from theisotopes of the three radioactive decay chains. Based on the intensity of the peak,the detection efficiency of the detector and the time of exposure, the amount of acertain isotope can be calculated, [Vidmar09].
Several batches of the Gd compound have been bought to different companies inorder to measure and compare its radioactive contamination to choose the cleanestand purest for the detector.
The majority of the measurements have been done at Canfranc Underground Laboratory (LSC), in Spain. In addition, some complementary measurements are doneat the Kamioka Observatory and at Boulby mine.

Figure 5.32: Pictures of HPGe detectors in LSC (left) and of two of the HPGe detectors
containing a marinelli in which the sample is kept during the measurement.

120

5.6. RADIOACTIVE CONTAMINATION

For each decay chain, various energy peaks were analysed in order to obtain the
global radioactivity of each chain. The typical photons for each decay chain are
shown in Figure 5.33.

Figure 5.33: Data from the radioactivity measurement of the first Gd2 (SO4 )3 batch. Most
characteristic peaks are shown for isotopes from the three decay chains.

Next, all the measurements done are shown in Tables 5.9 and 5.10. The Gd2 (SO4 )3batches measured can be divided into two groups. Table 5.9 shows the first batches
received, which contain a sizeable and fluctuating radioactive contamination. Furthermore, the decay chains in these batches were far from equilibrium.
In Table 5.10, the group of the latest batches measured is shown, presenting a much
lower radioactive contamination. The key point for this improvement in purity was
the official approval of SuperK-Gd in 2015, and the collaboration with the providing
companies to improve their production and purification methods. The limits in theradioactive contamination shown are estimated according to [Heisel09].

121

238

U
51 ± 21< 33
292 ± 67
74 ± 28242 ± 60
22 ± 20< 76
47 ± 26
73 ± 27

238

226

Ra
8±1
2.8 ± 0.674 ± 213 ± 113 ± 2
1.3 ± 0.5
< 1.4
5±1
6±1

U

232
228

Th
28 ± 386 ± 5504 ± 6127 ± 3374 ± 6117 ± 229 ± 213 ± 1411 ± 5ThRa
11 ± 2270 ± 16
1099 ± 10
205 ± 621 ± 34.0 ± 0.72±1
14 ± 2
3±1

228

U
< 32
< 32
< 112
< 25
< 25
< 2.6
< 1.8
< 12
< 30

235

227

U

Ac
214 ± 101700 ± 202956 ± 301423 ± 21
175 ± 42231 ± 6190 ± 6
<6
< 18

235

K
29 ± 512 ± 3101 ± 1060 ± 718 ± 8
7±3
<5
3±2
8±4

40

Others
138La8±1<
683 ± 153±1
42 ± 33.5 ± 0.5
23 ± 1<1<2Lu
80 ± 821 ± 2566 ± 612 ± 18±225 ± 12.5 ± 0.6
1.6 ± 0.3
<2

176

122
U
< 76
< 37
< 139
< 20
< 59
< 25
< 13

238

238

Ra
< 1.4
< 0.8
< 2.1
< 0.64
< 0.7
< 0.6
< 0.3

226

U
Ra
2±1
< 1.1
2.8 ± 1.9
< 0.673.2 ± 1.0
< 0.7
< 0.3

228

232

Th
29 ± 22.0 ± 0.5
1.8 ± 0.9
0.5 ± 0.2< 1.4
0.9 ± 0.3
< 0.4

228

Th

U
< 1.8
< 0.6
< 2.4
< 0.7
< 1.2
< 3.1
< 0.6

235

227

U
Ac
190 ± 6
11 ± 4
< 10
< 2.3
< 4.1
< 6.1
< 1.9

235

K
<5
<3
< 14
< 1.6
< 2.7
< 2.1
< 1.8

40

Others176
La
Lu
23 ± 1 2.5 ± 0.6< 0.6 2.9 ± 0.2
< 1.9
< 1.6
< 0.3
< 0.4
< 0.2
< 0.7
< 0.5 0.4 ± 0.3< 0.3 0.4 ± 0.1
138

Table 5.10: Radioactivity contamination measurements with HPGe at Canfranc corresponding to the second group of batches.
Units are mBq per kg of Gd2 (SO4 )3 .

Chain
Sub-Chain
GSF-1412-SFM-1
GSF-1508-KJD
GSF-1512-NYC-1
GSF-1604-NYC-160303
GSF-1604-NYC-160311
GSF-1604-SHT-1
GSF-1611-SHT-003

Table 5.9: Radioactivity contamination measurements with HPGe at Canfranc corresponding to the first group of batches. Units
are mBq per kg of Gd2 (SO4 )3 .

Chain
Sub-Chain
GSF-0904-SFM-1
GSF-1008-SFM-BD
GSF-1208-BEJ-1
GSF-1302-CHS-1
GSF-1303-BEJ-1
GSF-1308-SFM-1
GSF-1412-SFM-1
GSF-1307-TAI-1
GSF-1307-TAI-2

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

5.6. RADIOACTIVE CONTAMINATION

The first group of batches, in Table 5.9, correspond to the earlier days ofdevelopment of the SuperK-Gd project. Some of them were used at EGADS, GSF1008-SFM-BD was used for the non-instrumented detector and GSF-1308-SFM-1
was added once the PMTs were installed in EGADS.
In Table 5.10, a clear trend towards cleaner gadolinium sulphate is seen. The lastmeasurements show a reduction of the radioactivity contamination of more than
three orders of magnitude as compared with those from the first group.
Finally, and for the sake of simplicity in Sections 5.6.2 to 5.6.4, Table 5.11 shows
the typical values of the radioactive contamination for the cleanest samples inTable 5.10. This radioactivity levels will be used for the background estimation in
Sections 5.6.4 and 6.2 to 6.5.

Radioactive chain
238

232

U

Th

235

U

Part of the chain
238
U
226
Ra
228
Ra
228
Th
235
U
227
Ac / 227 T h

mBq/kg
50
5
10
100
32
300

Table 5.11: Standard radioactive contamination values of the gadolinium sulphate.

5.6.2

238

U Spontaneous Fission

Spontaneous fission (SF) is the process in which a heavy nucleus splits in various
pieces, usually two with half weight of the original, plus various neutrons, [Vogt11].
Concerning the backgrounds for low energy neutrino physics, the spontaneous fission

123CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS
from 238 U is the most relevant. In this process, photons of varying energy and various neutrons may be produced. In some cases, a high energy (a few MeV) photon
and a neutron are emitted, producing the very same signature in the detector as
an inverse-β antineutrino reaction. Therefore, this is an irreducible background for
DSNB, reactor, and supernova early warning measurements.
The number of events expected from this process is estimated for the standard radioactive contamination in Table 5.11.
For the computation of this background, the following features of this spontaneous
fission are considered.
• Spontaneous fission (SF) likelihood: Only 5 · 10−7 SF occur per 238 U decay[Popeko80].
• Photon energy: This process may produce high energy γs of several MeV. The
likelihood P at this high energy regime depends on the photon energy [Sobel73].

P (E) = 0.69 · e−

E(M eV )
1.41

(5.8)

Meaning that between any given energies the amount (N) of photons in thatenergy range is the following.
Emin

Emax

N (Emin ≥ Eγ (M eV ) ≤ Emax ) = e− 1.4 − e− 1.4(5.9)

In order for the 238 U photons to have enough energy to be detected as electrons,
they need to be 0.511 MeV more energy, in order to account for the electronmass that is added in the reconstruction software of low energy events in SK.
• Neutron multiplicity: To match the inverse-β interactions, only one neutron
has to be produced, therefore, only those SFs with neutron multiplicity equal to124

5.6. RADIOACTIVE CONTAMINATION

one are relevant for this background. According to [Ethvignot05, Popeko75],
the amount of SFs emitting just a neutron is 28%. There seems to have aweak dependence with the energy of the emitted γ, but it is ignored in thiscalculation.
After all this is taken in consideration, it is possible to compute the amount of these
decays that will occur in the SK fiducial volume (SKFV) per unit time, energy range
and for the standard amount of 238 U (50 mBq/kg). It is done in Equation (5.10),
where the 80% neutron-tagging efficiency of Gd-doped SK at 0.2% concentration istaken into account from Section 5.2.
 Emin− Emax− 1.4
1.4
NSF (1γ + 1Gd-tagged n) = 21.75 e−e

1day · SKF V(5.10)

It will be used for estimating the background to the reactor antineutrinos in Section 6.1, to DSNB in Section 6.2 and to pre-supernova antineutrinos in Section 6.3.

5.6.3

Radioactivity-Induced Neutron Production

If the amount of neutrons produced due to the radioactive contamination is large,
there will be many neutron captures with no prompt signal. These could be mistaken
for neutrino signals or even saturate the detector if the contamination is too large.
To estimate this source, the number of neutrons produced by radioactivity is computed. For this, it is assumed a the radioactive contamination in Table 5.11. The
computation is done using the SOURCES-4C code, [Wilson02].
The obtained spectrum of the neutrons produced by the radioactive contaminationlevels shown in the table, split into the different contributing processes Figure 5.34.

125

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

Figure 5.34: Neutron production rates and spectrum assuming the standard radioactive
contamination of gadolinium sulphate.

The total amount of neutrons obtained is 5.084 · 10−13 neutrons/s/cm3 . The translation to neutrons/day/SKFV is calculated in Equation (5.11).

neutrons
Nrad= 988.3

neutrons
day · SKF V(5.11)

The amount of neutrons produced by the standard radioactivity levels is sizeablevalue that will, certainly, have an important impact on the low energy analyses.
As it can be seen in Figure 5.34, the main contribution to the neutron production are(α, n) reactions. However, the neutron multiplicity for this process is estimated to be
two. This fact would neglect this background for low energy solar neutrinos. Going
deeply into the (α, n) reactions in the detector, they are mediated by both isotopesof oxygen 18 O and 17 O. Equation (5.12) shows the neutron production mechanism of(α, n) on 18 O.
18O + α(Ekin ≈ 6 MeV) →22 N e∗ (Eexc ≈ 15 MeV) →→20 N e + n(Ekin ≈ 2.2 MeV) + n(Ekin ≈ 2.5 MeV)

126

(5.12)

5.6. RADIOACTIVE CONTAMINATION

Because the multiplicity of neutron coming from SF are 72% of the times larger thanone, they are considered negligible compared to the number of neutrons from (α, n)reactions. Therefore, and assuming the 80% Gd-tagging efficiency, the amount of
events with a single detected neutron is reduced as shown in Equation (5.13).

neutrons= 32% · 988.3
Nradsingle neutrons
neutrons= 316.3
day · F V
day · SKF V(5.13)

Due to the spectrum of the Gd-neutron captures, in Figure 5.35, this backgroundmay not only affect the low energy neutrino analysis, Section 6.5, but also, theanalyses involving antineutrinos . In this case, the high amount of neutrons could
produce an accidental signal between a low energy neutrino and a capture of aneutron from radioactivity. This will have the same imprint in the detector as alow energy electron antineutrino. This background will be estimated for reactor
antineutrinos, DSNB and pre-supernova antineutrinos in Sections 6.1 to 6.3.

Figure 5.35: Reconstructed energy of the 8 MeV γ cascade from the Gd-neutron capture.

127

CHAPTER 5. ON RELEVANT ITEMS FOR SUPERK-GD PHYSICS

5.6.4

β-Rays from Radioactivity

Radioactivity contamination also brings with β decays as source of background forlow energy neutrino physics. The main contributions are from the 208 Tl (Qβ = 5.00
MeV), 212 Bi (Qβ = 2.25 MeV) and 214 Bi (Qβ = 3.27 MeV) isotopes, those withhigher Qβ -value of the three radioactive chains.
This source of background, as it happens in Section 5.6.3, may be confused withthe prompt signal of a low energy neutrino or as a fake neutron-capture candidate,
if it coincides with a solar neutrino candidate. Since the corresponding backgroundestimations depend highly on the analysis, they are done specifically for each casein Sections 6.1 to 6.3 and 6.5.
The reconstructed energy spectrum for the three decays is shown in Figures 5.36
to 5.38.

Figure 5.36: Reconstructed energy spectrum of 208 Tl β-decay.

1285.6. RADIOACTIVE CONTAMINATION

Figure 5.37: Reconstructed energy spectrum of 214 Bi β-decay.

Figure 5.38: Reconstructed energy spectrum of 212 Bi β-decay.

208

Tl β-decay is the most potentially harmful one due to its large Qβ -value. Hence,for the suppression of this background source it is needed to reduced the levels of228

Ra and 228 Th from the Th decay chain.

1296. SuperK-Gd Physics Potential
In this section, all the measurements and potential searches that SuperK-Gd would
be able to performed, are addressed. This section takes into account all the advantages of the 80% efficiency neutron tagging technique using gadolinium, but also
the drawbacks that the inclusion of radioactive contamination could have in thesemeasurements. For the latter the typical values in Tables 5.9 and 5.10 are taken inorder to make the detectability predictions.

6.1

Reactor Neutrinos

The detection of reactor neutrinos is, after the DSNB and pre-supernova neutrino
searches, the most important measurements of SuperK-Gd. Nuclear reactors produce a huge amount of antineutrinos due to their nuclear reactions.
Currently, in SK these antineutrinos are masked by solar neutrinos and spallation
products, but enabling an efficient neutron tagging technique, these low energy
antineutrinos can be identified through their inverse-β decay.
Since the nuclear program of Japan is moving towards the reactivation of most of
its nuclear power plants, in this section, the full operation of all reactors will beassumed. Japanese reactors are the main producers of reactor antineutrinos arriving
to SK, but their not the only ones. South Korean reactors are close enough and131

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

ought to be taken into account. The relation of nuclear plants considered with theiroperating power and distance to the Kamioka Observatory is shown in Section 6.1
and extracted from [Murayama02].

ReactorKashiwazaki
Ohi
Takahama
Hamaoka
Tsuruga
MihamaFukushima 1
Fukushima 2
Tokai
Shimane
Ikata
GenkaiOnagawa
TomariSendaiSendaiPower (GW)
24.6
13.7
10.2
10.6
4.5
4.9
14.2
13.2
3.3
3.8
6.0
6.7
4.1
3.3
5.3
1.6

Distance (km)
160
180
191
213
139
145
344
344
295
414
561
755
430
784
824
81

Table 6.1: List of nuclear reactor power plants from which SK is able to detect antineutrinos.

The electron antineutrino oscillation probabilities can be assumed to be throughvacuum and can be approximated by the following expression.

P (ν e → ν e ) = 1 − sin2 2θ12 sin2

Lreactor
1.27∆m212
Eν

!
(6.1)

The expected spectrum is shown in Figure 6.1, from which it can be seen theoscillation peaks, assuming 3 MeV energy threshold, the most important one is that132

6.1. REACTOR NEUTRINOS

around 5 MeV and the valley from the disappearance regime at 3 MeV.

Figure 6.1: Reactor neutrino spectrum at Kamioka for true (red) and reconstructed (black)antineutrino energy.

The expected rate of reactor antineutrinos detected by SuperK-Gd is of the order of
30 events/day in the 22.5 kton fiducial volume. Several studies have been made on
the impact of this new measurement that SuperK-Gd would bring along, with highsensitivity to the solar oscillation parameters.
The main backgrounds for this measurement are products from spallation due tocosmic muons, which some of them leave the same signature as a low energy inverse
β decay, such as carbon isotopes or 16 N, [Li14].
As for the backgrounds introduced by the radioactive contamination of the gadolinium sulphate, the signals mimicking the inverse-β reaction are the 238 U spontaneous
fission and accidental coincidences of solar neutrino candidates with radioactivityinduced neutrons and β-decays.
Assuming the standard radioactive contamination levels at Table 5.11, the amount133

CHAPTER 6. SUPERK-GD PHYSICS POTENTIALof events from 238 U SF are computed following Equation (5.10), with Emin = 3 MeV(SK low energy threshold) and Emax = 10 MeV.

NSF (1γ + 1Gd-tagged n) = 2.6

1
day · SKF V(6.2)

On the other hand, the background estimation from the two possible accidental
coincidences, with neutrons and with β-decays, is calculated in Equation (6.4)
and Section 5.2.2 respectively. In these computations, it is considered that theamount of solar neutrinos in the final sample is around 200 events/day/SKFV,
according to [Abe16c], and that every event is 535 µs long (SHE+AFT, seen in
Table 3.4).
For the accidental coincidences with neutrons coming from radioactivity Equation (5.13) is considered.

neutronNaccidental= 8.0 · 10−6

1
day · SKF V(6.3)

The amount of β-decays passing the selection methods for the Gd-neutron tagging
explained in Section 5.2.2, are 20.4% for 208 Tl, 1.7% for 214 Bi and 0.2% for 212 Bi. Assuming the standard radioactivity levels, the final amount of accidental coincidences
is computed, analogously to Equation (6.4), in Section 5.2.2.

βNaccidental= 9.2 · 10−2

1
day · SKF V(6.4)

The largest contaminations come from the 238 U spontaneous fission. However, twoimportant items have to be taken into account. The first one is that the resin AJ4400,
already tested at EGADS, is able to reduce 100 times the amount of uranium present
in the Gd salt, becoming the amount of this background also reduced by a factor 100.

134

6.2. DIFFUSE SUPERNOVA NEUTRINO BACKGROUND

Furthermore, the radioactivity contamination of the latest Gd batches, in Table 5.10,
is two to three orders of magnitude smaller. This means that, for these Gd batches,
the background from radioactive contamination will be reduced by the same factor,
being negligible compared to the reactor neutrino signal.

6.2

Diffuse Supernova Neutrino BackgroundThe expected signal from supernova relic antineutrinos in SK is about 2 to 5 events
per year above 10 MeV, depending on the various theoretical models.

Figure 6.2: Expected number of events and energy spectrum for DSNB assuming different
effective neutrino temperatures (Tef f ) for 10 years of SuperK-Gd data taking.

Currently, in SK, the main backgrounds for this measurement are spallation products. This contamination is drastically reduced by Gd-neutron tagging, as DSNB

135

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

antineutrinos interact inverse-β in the detector and spallation products, beyond 10
MeV, do not produce this signature in the detector.
However, the radioactivity introduced with the Gd compound may be significant forthis measurement. The background sources are, as in all low energy antineutrino
analyses, due to 238 U spontaneous fission and accidental coincidences of neutronsand β-decays with solar neutrino candidates.
Making use of Equation (5.10), the amount of background signals from the uranium
SF is estimated in Equation (6.5).

NSF (1γ + 1Gd-tagged n) = 4.4

1
year · SKF V(6.5)

For the estimate of the amount of accidental coincidences, it assumed that ∼4 events
will pass the solar cuts per day and above 10 MeV, [Abe16c]. With the considerations,for the neutrons and βs from radioactivity, made in Section 6.1, the backgroundsignals are calculated in Equations (6.6) and (6.7).

neutronNaccidental= 2.9 · 10−3

βNaccidental= 0.3

1year · SKF V

1year · SKF V

(6.6)

(6.7)

For the DSNB measurement, as in the reactor neutrino case, the principal backgroundcomes from the 238 U SF. But again, the AJ440 resin performance for removing uranium and the lower radioactive contamination of the latest Gd batches, suggest that
this background source will become, at least, reduced by a factor 100. In addition,
the much lower radioactive contamination from the last Gd batches measured, indicate that the background from 238 U SF will be at least two orders of magnitude1366.3. SILICON BURNING STAGE

smaller than the estimate in Equation (6.5), using the standard radioactive contamination tables. In this sense, the DSNB measurement is expected to have negligible
background, crucial for the future of SuperK-Gd.

6.3

Silicon Burning Stage

This section deals with the detectability of pre-supernova neutrinos. During siliconburning phase, the luminosity is about eight orders of magnitude less than the peakof core-collapse supernovae, but while this peak lasts just a few milliseconds, theSi burning phase takes a few days. This measurement would be of enormous importance, because it helps understanding of the stellar evolution mechanisms at thisstage, few moments prior to the core-collapse. In addition, it can be used as early
warning for optical observatories to the upcoming supernova.
Given the low energy spectrum of the neutrinos from this origin, a tiny fractionof the antineutrinos could be detected through their inverse-β reaction in SK. According to [Odrzywolek07], the number of events above the inverse-β threshold that
could be detected by SuperK-Gd is 796 assuming a very close supernova, such as
Betelgeuse at 0.2 kpc away. For this study, a 3 MeV kinetic energy threshold for the
positron is considered, which would lead to ∼187 events in the 24 hours previous tothe core-collapse. Assuming the same efficiency of 11% used in the solar analysis forthis low energy positron and 80% efficiency in the neutron tagging, the amount of
events detected would be 16.4.
In this case, the main source of background are reactor antineutrinos. Backgrounds
due to Gd radioactive contamination completely negligible. The background due tothe 238 U SF is estimated in Equation (6.8).

137

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

NSF (1γ + 1Gd-tagged n) = 0.15

1day · SKF V(6.8)

For the case of the accidental coincidence backgrounds, it is enough refer to thecorresponding calculations made for the reactor antineutrinos in Equations (6.4)
and (6.4).
The significance for the pre-supernova stage measurement, assuming a star 0.2 kpc√
away, would be of 16.4/ 16.4 + 30 = 2.4σ. The actual significance for particularcase of Betelgeuse may vary because of the uncertainty in its distance to the Earth.

6.4

Supernova Burst

If a supernova happens within the Milky Way, it will produce an enormous amountof neutrinos and antineutrinos that will be detected by SK. Although, electron
neutrinos can be distinguished from electron antineutrinos via their scattering
angle differences, in SuperK-Gd this separation will be largely improved due to the
Gd-neutron tagging.

These neutrinos and antineutrinos will have energies ranging from 10 MeV up to
30 MeV and the signal will last for a few seconds, [Totani98b]. This is shown in
Figure 6.4.
This measurement, will provide much information about early stages of the corecollapse process, its spectrum and time profile, yielding to more detailed pictureof the whole core-collapse process, extracting the neutrino and antineutrino fluxes
independently.

138

6.5. SOLAR NEUTRINOS

Figure 6.3: Supernova neutrino and antineutrino total fluxes as function of the distance tothe collapsing star.

The backgrounds for this measurement are completely negligible given the hugesignal in such narrow time window, shown in Figure 6.3.

6.5

Solar Neutrinos

In order to maintain the current low energy solar analysis of SK, [Abe16c], it is
crucial to keep the low energy radioactive backgrounds as low as possible. The
new backgrounds for this analysis that SuperK-Gd will need to deal with, are thosecoming from the Gd radioactive contamination, namely, the signals from β-decays
and from the Gd-capture of neutrons.
According to [Abe16c], the amount of solar events per day in SK fiducial volume is139

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.4: Supernova neutrino and antineutrino fluxes as function of time (left) andenergy (right) for a supernova occurring 2 kpc away from the Earth.

around 200. This value will be used to quantify the size of the backgrounds next.
All the SK solar selection criteria are run over the Gd-neutron capture and 208 Tl,
214

Bi and 212 Bi spectra. The remaining fraction of this events are 40%, 0.19%, 0.01%

and < 2 · 104 %.
With this, the total amount of background signals capable of contaminating thesolar neutrino sample, due to neutron production from radioactivity, is calculated
in Equation (6.9). This estimate is based on Equation (5.13) and for the standard
radioactivity levels.
N neutron = 126.5

1
day · SKF V(6.9)

Based on the survival fraction of β-decays to the solar cuts and the standard radioactive contamination of Gd, the amount of this contamination is done in Equation (6.10).
N β = 2.6 · 105

1
day · SKF V

140(6.10)

6.5. SOLAR NEUTRINOS

Both background contributions are huge, being that related to the β-decays aroundthree orders of magnitude larger than the expected ∼200 solar neutrino candidates
per day in SK. This contribution is mainly due to the large Qβ -value of the 208 Tl
β-decay, from the 232 Th decay chain.
Nevertheless, the size of this background is drastically reduced by the cleanness
if the radioactivity levels from Table 5.10 are considered. These samples show anotable reduction of the contamination levels from the 232 Th decay chain. This fact,basically lowers each of the radioactive background from β-decays a factor 100 or
1000, depending on the gadolinium sulphate batch, as compared with the estimates
for the standard radioactivity levels shown in Equation (6.10).
Furthermore, a system for reducing this background is being developed at EGADS.
The system consists in making the dissolved gadolinium passing through a speciallydesigned resin (AJ1020Gd), which removes radium keeping the Gd2 (SO4 )3 concentration.

228

Ra is one of the longest-lived parent isotopes of 208 Tl and, therefore,

the origin of the origin of its β-decays. In Figure 6.5, a diagram of the Ra-removal
system setup at EGADS is shown.

In addition to 228 Ra, 228 Th is the other longest-lived parent isotope of the 208 Tl,
therefore, it is crucial to remove thorium from the Gd compound too. Several strategies to achieve this are under investigation, such as a special kind of filtrating paper,that can remove up to 98% of the thorium, and a PH shock to the Gd solution to
make the thorium precipitate so it could be easily removed. However, the case of the228

Th is not so severe because its half-life is 1.9 years. This means that once 228 Ra

is removed, the radioactivity background will be reduced by half after 2 years.

141

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.5: Scheme of the radium-removal system developed at EGADS.

In conclusion, although this is a serious remaining issue, the high purity of the lastGd batches and the ongoing efforts in the development of new methods and techniques to reduce it, suggest that the low energy solar neutrino analysis will also beable to be done in SuperK-Gd.

6.6

Atmospheric Neutrinos

In this section, the atmospheric neutrino analysis is developed for including Gdneutron tagging. In Section 6.6.1.2, the basic features of the atmospheric analysis in
SK are reviewed. These are the simulation of atmospheric neutrinos in Section 6.6.1.2
and the event reduction and reconstruction in Sections 6.6.1.2 and 6.6.1.3. These
will be shared by the future SuperK-Gd.
In Sections 6.6.2 to 6.6.4 the CC-NC and ν-ν separations, and the neutron-corrected
neutrino energy are implemented for the atmospheric analysis in SuperK-Gd. Lastly,in Section 6.6.5, a global atmospheric oscillation sensitivity analysis is done, including142

6.6. ATMOSPHERIC NEUTRINOS

the previous tools and comparing the obtained sensitivities to CP violating phase,
neutrino mass hierarchy and θ23 to the current SK standard analysis.

6.6.1

Monte Carlo Simulation, Event Classification and Reconstruction in Super-Kamiokande

Generating a prediction for the number of atmospheric neutrino interactions observedin Super-Kamiokande is not a simple task. Results depend heavily on detector knowledge, flux and particle interaction theoretical models, and reconstruction within thedetector. The whole process, from production, in the atmosphere, until detector
signal, is simulated and the expected output event rate distributions as function of
direction and energy.
The Monte Carlo simulation is divided in two stages, firstly the initial neutrino fluxand interaction in water is done, and the outgoing particles effects on the detector
are simulated based on the calibration data. Of these two, the one which carries
the largest uncertainties is the atmospheric flux modelling, since there are not many
input data helping to constrain their predictions.
Concerning the data management, events pass through a series of cuts in order toreduce as much as possible the background. Once these selection criteria are applied, the number of rings, the particle identification, direction, vertex position andmomentum are computed for the remaining events. In this section, the SK-IV event
reduction and reconstruction are briefly reviewed. The reader may want to refer to[Pik12, Irvine14], where this is extensively described.

143

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

6.6.1.1

Atmospheric Neutrino Simulation

Atmospheric Neutrino Flux Simulation
There are several models for the atmospheric neutrinos flux model, for this analysis
is based on the HKKM flux of 2011, overlapping with the Volkava flux for events
above 10 TeV.
The atmospheric neutrino flux is a convolution of the spectrum at the highest altitudes in atmosphere which yields to neutrino production. By using a 3-dimensional
tracking for the cosmic rays tracking, then secondary particles are produced.

Figure 6.6: Three-dimensional calculation of the neutrino flux in Honda flux.

The neutrino flux simulation also considers the geomagnetic effects and solar activity
modulation. The models are done based on high altitude experiments, such as AMS(Alpha Magnetic Spectrometer), and balloon-borne experiments.
Most of the incoming cosmic rays are hydrogen ions interacting with the higher
layers of the atmosphere, and this are deviated populating the flux towards the west
direction.

144

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.7: Atmospheric neutrino fluxes (left) averaged over all directions and neutrino
flux ratios (right) for different models, Bartol flux (dashed dark blue), Fluka (dotted green),
HKK06 flux (dashed light blue) and HKK11 (solid red).

Figure 6.8: Zenith angle distribution for neutrino flux incident on SK for two different
energies and for all neutrino species.

In addition, geomagnetic effect are also considered, which being slightly higher
at Kamioka area than the average produces an asymmetry between upward anddownward directions for low energy cosmic rays, as seen in Figure 6.8.

145

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.9: Comparison of interaction models JAM (solid lines) and DPMJET-III (dashedlines) and data from HARP (points), for π + in red and π − in blue.

The second part of the simulation, deals with the modelling of hadronic showers
induced by the cosmic rays. Two models are used here depending on the energy
region, for energies below 32 GeV the JAM model is used based on the HARP
experiment data, and for energies higher than 32 GeV the DPMJET-III model isused.

Neutrino Interaction Simulation
Neutrinos interact with nucleons and electrons in the water and the surroundingrock of the SK detector. For this simulation, the NEUT libraries are used alongwith other models, like NUANCE, for cross checks. The interactions simulated arelisted on Tables 5.7 and 5.8.
The simulation of quasi-elastic scattering (QE) by NEUT is done differently for freeand bound nucleons, corresponding to the hydrogen and oxygen nuclei respectively.

146

6.6. ATMOSPHERIC NEUTRINOS

For bound nucleons, the whole nucleus is considered, approximating it to a relativistic Fermi gas and taking into account the Pauli blocking effect for momenta larger
than the Fermi momentum, pF = 225 MeV/c.

Figure 6.10: Muon neutrino (left) and antineutrino (right) charged current quasi-elastic
cross sections compared to experimental data from various experiments.

In single meson and coherent π production interactions, the simulation is based onRein and Sehgal’s model.

Figure 6.11: Muon neutrino charged current single pion production cross section for π −(left), π 0 (centre) and π + (right) compared to experimental data from various experiments.

In addition to resonance production, neutrinos can also coherently produce
single pion final states. In this case, the neutrino coherently scatters from the147

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

entire nucleus, transferring negligible energy to the target, which produce no nuclear
recoil and a distinctly forward-scattered pion, compared to their resonance-mediatedcounterparts.

Figure 6.12: Simulation (solid line) and measurements of coherent pion production crosssections from a variety of nuclear targets and for both NC and CC.

Neutrino deep inelastic scattering has long been used to validate the Standard Modeland probe nucleon structure. Over the years, experiments have measured cross sections, electroweak parameters, coupling constants, nucleon structure functions, andscaling variables using such processes. In deep inelastic scattering, the neutrino scatters off a quark in the nucleon via the exchange of a virtual W or Z boson producing a
lepton and a hadronic system in the final state. The neutrino cross section agrees wellwith the simulation for the total cross section where the DIS interactions dominate
as seen in Figure 6.13 for high energies, ∼ 102 GeV.

148

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.13: Simulation (solid line) and measurements for inclusive total neutrino crosssection of neutrinos and antineutrinos.

Finally, nuclear effects are also considered in the simulation. They are crucial forsecondary interactions, which play a very important role in the analysis presented
in this section. These secondary interactions occur inside the nuclear media of theoxygen nuclei. This is simulated for π, κ and η interacting within the nucleus using
a cascade model.

For interactions with pions of low momentum pions (less than 500 MeV/c), theSalcedo model is used after tuning using experimental data. For momentums larger
than 500MeV/c, nucleons are treated as free particles, being able to used data from
π-12 C scattering. Similar procedure is done for other mesons, as kaons and etas.
Detector Simulation
After the neutrino interaction simulation, the produced particles are introduced into
the SK detector simulation, SKDetSim. This simulation englobes the particle tracks,
the Čerenkov photon generation and the PMT response to these photons.

149

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.14: Cross section of π − -12 C scattering with respect to the π − momentum. Solidlines are the NEUT calculation before tuning, dashed lines are NEUT calculation after
tuning, compared to the experimental points.

This simulation is based on CERN’s GEANT3 package. Photons, electrons andmuons are simulated with the default tools of GEANT3 and the hadron interactions
by using the FLUKA (energies larger than 10 GeV), HETC (energies smaller than 10
GeV), MICAP (for neutrons) and NEUT cascade model (for low momentum pions).
The particles produce Čerenkov photons, whose wavelength and group velocity iscomputed for each case depending on the refractive index and absorption and scattering properties of the SK water through which they travel.
Once this radiation gets to the PMT phototubes, its charge and timing is considered
as well as the calibration data, such as gain of PMTs and quantum efficiency.

6.6.1.2

Atmospheric Data Reduction

There are specifically selection criteria for atmospheric neutrinos. SK’s high energy
trigger fires a little more than hundred times a day, but most of these events
correspond to cosmic muons, high energy spallation events or PMT flashers. Therefore it becomes necessary to pass them through several reduction steps to reduce1506.6. ATMOSPHERIC NEUTRINOS

non-neutrino events.
There are different reduction procedures depending for each of the three event
topologies, that is Fully Contained (FC), Partially Contained (PC) and Upwardgoing Muons (UpMu).

Figure 6.15: Diagrams showing the different atmospheric neutrino event types.

FC events correspond to those neutrinos which interact in the ID and the outgoingparticles do not travel beyond the ID wall, being the produced photons capturedby the detector’s PMTs.

Furthermore, FC events are classified into SubGeV,

Evis < 1.33 GeV, MultiGeV Evis ≥ 1.33 GeV and MultiRing, if more than one ringis reconstructed. Each of these samples is divided into e-like and µ-like, dependingon the pattern of its most energetic ring. Additionally, for SubGeV events there
are two more samples, SingleRing π 0 and π0-like, which contain events with thesignature of the π 0 decay into two photons.
PC consists in those events in which the neutrino vertex is inside the ID but someof the produced particles in the interaction have enough energy to cross the ID
walls and leave a signal in the OD. These are mainly high energy muon events
since electrons transfer their energy very quickly to the surrounding water. Finally,
UpMu events are those muons which enter the detector from below, indicating that151

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

the come from a muon neutrino which has interacted with the rock beneath thedetector. These events are only upward-going because downward-going events ofthis kind could not be distinguished from cosmic muons. Furthermore, UpMu events
are split into stopping-muons, meaning the incoming µ deposits all its energy in theID, and through-going muons, which travel across the whole detector, these havethe largest energy of all events SK is able to detect.

Figure 6.16: Reconstructed energy spectrum for each sample after reduction.

152

6.6. ATMOSPHERIC NEUTRINOS

6.6.1.3

Atmospheric Event Reconstruction

Vertex and Direction Reconstruction

This reconstruction uses the timing information as in the case of low energy, but thistime in three steps. The first step is a simple fit called Point-Fit, where the vertex isestimated by assuming that all photons are emitted from a point-like source. After
subtracting the ToF, a distribution of the residual PMT hit time is constructed andthe reconstructed vertex is that which maximises distribution.
In the second step, the direction and the outer edge of the dominant ring are computed, this pair is tested by calculating the quantity G(θt ).
(θt −θC )2e− 2σ2G(θt ) =sin θtZ θtq(θ)dθ

(6.11)

0

Where θC is the critical Cherenkov opening angle, θt is the tested opening angle, σis the resolution of PMT hits around θt . The maximum G is chosen to be the firstring fit.
Next, the vertex is fitted again using only the PMT hits inside the chosen Cherenkov
ring.

This is the TDC-fit.

It computes the timing residuals, similarly to the

Point-Fit, but considering that the hits may come from any point of the track.

153

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.18: Unfolded SK detector showing a reconstructed µ-like ring.

Figure 6.17: Unfolded SK detector showing a reconstructed e-like ring.

Ring Counting
Once the initial Čerenkov ring and the vertex are determined, other ring candidates
are searched via a Hough transform method, technique used to extract a certain
shape from an image, and illustrated in Figure 6.19.

Figure 6.19: Two dimensional drawing of ring candidate searching based on the PMTs withmaximum charge in the left, and in the right, charge distribution as function of zenith andazimuthal angles in the detector, being those peaks with higher charges also the most likely
rings.

154

6.6. ATMOSPHERIC NEUTRINOS

A likelihood distribution is used to discern if the secondary ring candidate is consistent with an actual ring. This process is repeated up to a ring multiplicity offive.

Figure 6.20: Ring counting likelihood for the SubGeV events forMonte Carlo (red) and SK-IV
data (black dots).

Figure 6.21: Ring counting likelihood for the MultiGeV eventsfor Monte Carlo (red) and SKIV data (black dots).

For those events with just one ring the vertex fit is further optimised with the expected light pattern, given that the ring is either e-like or µ-like, this is the MS-Fit.

Particle ID Reconstruction
The fitted Čerenkov rings are the classified as e-like or µ-like by the Particle Identification (PID) likelihood. Electrons and γ rays produce diffuse ring patterns due tothe electromagnetic showers, whereas muons and charged pions produce rings withmuch sharper edges, as previously seen in Figures 6.17 and 6.18. In addition, thelatter ones have may have smaller Čerenkov angles if they do not achieve the ultrarelativistic regime. These differences are taken into account by the PID.
The e-like or µ-like categorisation is done by comparing the observed charge pattern

155

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

with the expected cases for electrons and muons and obtaining for which the maximum likelihood is achieved. The expected charge for a given PMT assuming thering is produced by an electron has the following form.

qiexp (e) = αe Qexp (pe , θti )16.9 m
ri

!3/2

ri

e− λ(run) f (θi ) + qiscatt(6.12)

Where αe is a normalisation factor, Qexp is the expected charge distribution for anelectron as a function of Cherenkov ring opening angle and momentum, ri is the
distance from the vertex to the ith hit PMT, λ(run) is the water attenuation length,f (θi ) the acceptance as function of incident angle and qiscatt the expected charge at
the ith PMT due to multiple scattering.
Similarly for muons one has.

qiexp (µ) =!

sin2 θxi

αµ tri sin θxi + ri dθdx

ri + qiknock e− λ(run) f (θi ) + qiscatt(6.13)

x=xi

Where αµ is a normalisation factor, x the muon track length, xi an estimate of the
track length when photons hitting the ith PMT were emitted, θt and θti the Čerenkov
angles at position x of the muon track at positions x and xi respectively, and qiknock
the expected charge deposited in the ith PMT due to electrons that were ionised by
the muon as it travelled through water.
This pattern comparison is used alone for MultiRing events and together with aČerenkov angle comparison for single ring events. For the latter, pattern distributions
are defined for electrons and muons similarly as for the charge patterns.
With all this information the PID likelihood distribution is built as follows.

PP ID =

pp−logP (µ) − −logP (e)156(6.14)

6.6. ATMOSPHERIC NEUTRINOS

The PID distributions for all fully contained samples are shown in Figures 6.22
to 6.25.

Figure 6.22: Particle identification likelihood for the SubGeV single ring eventsfor Monte Carlo (red) and SK-IV data
(black dots).

Figure 6.23: Particle identification likelihood for the SubGeV multi-ring eventsfor Monte Carlo (red) and SK-IV data
(black dots).

Figure 6.24: Particle identification likelihood for the MultiGeV single ring eventsfor Monte Carlo (red) and SK-IV data
(black dots).

Figure 6.25: Particle identification likelihood for the MultiGeV multi-ring eventsfor Monte Carlo (red) and SK-IV data
(black dots).

157

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Tau leptons from ντ may also occur in the detector, although they are extremely
difficult to detect due to its short lifetime (2.9 · 10−13 s). Despite that, SK has
developed and is improving a neural network based algorithm to try to identify these
events, [Abe13].
Neutral pions are also detected in SK by taking advantage of their characteristic
decay into γγ and their invariant mass. These events are of particular importanceas they often come from neutral current single π 0 interactions, a background sourcefor neutrino oscillations analyses.

Momentum Reconstruction
The momentum of each particle (ring) is calculated from the total charged PMTs
inside a Čerenkov cone with half opening angle of 700 . Therefore, the energy iscomputed separately for each of the reconstructed rings, and based on the expectedcharge distribution for each ring. The estimated observed charge of the ith PMTfrom the nth ring follows Equation (6.15).
exp
qi,n
obs
obs
qi,n = qi X exp
qi,mm(6.15)

exp
Being qiobs the observed charge by the ith PMT and qi,mthe expected charge of the

ith PMT from the mth ring.
The variable RT OTn is defined to correct for light attenuation, light reflection, gain
and acceptance of PMTs for each of the n rings.

158

6.6. ATMOSPHERIC NEUTRINOS

GM C
RT OTn =
α
Gdata

X

qiobs eri
λ(run)< 700

θi,n−50 ns< ti < 250 ns

cos θi−f (θi )X
θi,n

Si + Ri!
(6.16)< 700

Where, GM C and Gdata are the the relative gain PMT factors for Monte Carlo anddata, α is a normalisation factor based on the energy scale calibration, ti is thehit timing of the ith PMT after ToF is subtracted, Si is the expected charge fromscattered photons and Ri the correction for reflected photons with black sheets inthe detector.

Decay-Electrons Reconstruction
These are electrons coming from the decay of µ± , which, in its turn, may come fromthe decay of a charged pion. This muons are very likely to come from π + since π −are quickly absorbed by water. This way, decay-electron (decay-e) is also a very
useful tool to identify pion production neutrino interactions.
Decay-electrons are searched in an independent time window of 900 ns from that ofthe primary interaction. In SK-IV, the detection efficiency is 89.1%.

6.6.2

Neutral Current and Charged Current Separation for
Fully Contained Samples

In this section, the NC-CC separation described in Section 5.3 is applied forSuperK-Gd atmospheric fully contained events. This method is developed only for
the MultiRing e-like sample because, it is where neutral current and charged current
deep inelastic interactions are most present. This two-step method, first tries to159

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

separate neutral current events from the rest of the charged current ones. In thesecond step, muon neutrino events in this sample, which interact mainly throughcharged current deep inelastic scattering, are separated from the electron neutrino
ones. This has been schematically explained in Figure 5.28.
For the construction of the likelihood distribution, in both separation methods eightvariables are used. Amongst these, the neutron multiplicity is the most relevant.
The rest of the variables are the number of rings, the MultiRing likelihood, thenumber of decay-electrons, the distance to the furthest decay-electron, the sum of
all rings ID likelihood, the rapidity and the energy fraction of the most energetic
ring. All this, has been previously described in Section 5.3.
Figure 6.26 shows the distribution for neutron multiplicity and normalised to thepresent SK-IV running time, 2519.9 days, shown in Table 7.1.

160

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.26: Number of Gd-tagged neutrons for NC (orange), CCDIS νµ (violet), CC νe(green) and total atmospheric Monte Carlo (red) in the MultiRing e-like sample, normalised
to 2519.9 days.

NC interactions show a completely different distribution as compared to thecharged current ones.

It is wider and peaked around five, whereas the rest ofinteractions reach their peak at zero.
The distributions corresponding to the rest of the variables used in the constructionof the both likelihood methods are shown in Figures 7.7 to 7.13, and compared withthe actual SK-IV data.
The neural network architectures consist in one hidden layer with N + 5 neurones,
where N is the number of variables involved in the computation. In Figures 6.27
and 6.28, the neural network outputs for both steps of the selection are shown.

161

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.27: Neural network output for the NC-CC separation ffor NC (orange), CCDIS
νµ (violet), CC νe (green) and total atmospheric Monte Carlo (red) normalised to 2519.9
days (SK-IV running time). The pink vertical line shows the selection point (0.6) for the
distribution, which optimises product CC × pCC , being the NC-like sample formed by those
events at its left and the CC-like by those at its right.

Figure 6.28: Neural network output for the CCDISνµ -νe separation for NC (orange),
CCDIS νµ (violet), CC νe (green) and total atmospheric Monte Carlo (red) normalised
to 2519.9 days (SK-IV running time). The pink vertical line shows the selection point(0.55) for the distribution, which optimises product CC−e × pCC−e , being the CCDIS νµ like sample formed by those events at its left and the CC e-like by those at its right.

162

6.6. ATMOSPHERIC NEUTRINOS

In Table 6.2, the values of the relative importance for each of the variables arepresented in order to see the role of each variable in these selections, specially the
Gd-neutron multiplicity.

Variables

Relative separation power
Number of Gd-tagged neutrons
Number of rings
MultiRing likelihood
Number of decay-e
Distance to furthest decay-e
Pseudorapidity
Energy fraction
Sum of all rings PID likelihood

NC-CC separation
57.5%
0.8%
0.6%
8.7%
40.5%
3.0%
1.3%
1.5%

(−) (−)
ν µ - ν e separation

26.0%
1.3%
0.6%
27.5%
32.2%
2.9%
0.1%
1.2%

Table 6.2: Relative importance of each variable in the neural network for the NC-CC and
CCDISνµ -νe separations.

Clearly, the number of Gd-tagged neutrons has an enormous importance in theseseparations, specially for selecting NC events.
In the case of the separation of muon neutrinos from electron neutrinos, the decayelectron variables become much more important as expected. This is, precisely,
because the muon neutrinos interacting charged current (mainly CC DIS), produce
a prompt µ.
The relative contents of each selected sample is shown in Table 6.3, together withthe expected unoscillated number of events for 2519.9 days.

(−)

NC and CC DIS ν µ -like samples show large fractions of muon neutrinos and neutral
current interacting neutrinos.

163

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL
Samples(−)
CC ν e -like

57.6%
21.5%
8.2%
0.9%
11.8%
648.8

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

(−)

CCDIS ν µ -like
28.4%
3.5%
38.1%
4.2%
25.8%
388.0

NC-like
27.9%
3.9%
33.5%
4.2%
30.6%
617.7

Table 6.3: Relative contents of each species for each subsample of the MultiRing e-likesample, after the selection, and the number of entries predicted by atmospheric Monte
Carlo for 2519.9 days (SK-IV running time).
(−)

Although the remaining CC ν e -like sample is quite reduced in the number of entries,
it is also improved in terms of its purity. This fact will be helpful in its neutrinoantineutrino separation, in Section 6.6.3.3.
The method explained here, is remarkable due to the complexity and variety ofinteractions and neutrino flavours in the MultiRing e-like sample. It improves theunderstanding these events, being able to separate them into three, well-defined,groups of interactions.

6.6.3

Neutrino and Antineutrino Separation for Fully Contained Samples

In the present section, all the samples affected by the neutrino-antineutrino separation are shown in detail. The distributions and event rates are normalised to the2519.9 days of SK-IV operation.
The scheme of the samples treated here can be found in Figure 5.29.
The developments of this section will be included in the oscillation analysis studies
in Section 6.6.5.

164

6.6. ATMOSPHERIC NEUTRINOS

6.6.3.1

SubGeV and MultiGeV e-likeIn this section, the ν-ν separation is implemented for atmospheric single-ring e-likeevents. These are split into SubGeV (Evis < 1.33 GeV) and MultiGeV (Evis ≥ 1.33
GeV).
Events in these samples are divided into νe -like, νe + ν e -like and ν e -like. The separation is based on the neutron and decay-electron multiplicities as described next.

SubGeV e-like samples
Figure 6.29 shows the Gd-neutron multiplicity for this sample.

Figure 6.29: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in the
SubGeV 1Ring e-like sample, normalised to 2519.9 days (SK-IV running time).

The neutron multiplicity is typically larger for antineutrinos than for neutrinos, andthe number of decay-electrons is usually larger for neutrinos, as shown in Figure 7.17.

165

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

The cuts on the neutron and decay-electron multiplicities which define the three
regions follow the next expressions:• νe -like: Number of decay-e>0• νe + ν e -like: Number of decay-e=0 and Number of Gd-tagged neutrons=0• ν e -like: Number of decay-e=0 and Number of Gd-tagged neutrons>0
The contents an expected number of unoscillated events for 2519.9 days of exposure
are summarised in Table 6.4.

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

νe -like(dcy-e>0)
77.1%
1.7%
11.6%
3.3%
6.3%
582.9

Samplesνe + ν e -like(dcy-e=0 & neutrons=0)
85.8%
11.1%
0.3%
0.0%
2.8%
2643.8ν e -like(dcy-e=0 & neutrons>0)
51.9%
43.9%
0.3%
0.0%
3.9%
1615.2

Table 6.4: Relative contents of each species for each subsample of the SubGeV e-like sample, after the selection, and the number of entries predicted by atmospheric Monte Carlonormalised to 2519.90 days (SK-IV running time).

MultiGeV e-like samples
Events in this category follow the same logic as in the SubGeV case, being the cutsfor the sample selection the same as before:• νe -like: Number of decay-e>0• νe + ν e -like: Number of decay-e=0 and Number of Gd-tagged neutrons=0166

6.6. ATMOSPHERIC NEUTRINOS• ν e -like: Number of decay-e=0 and Number of Gd-tagged neutrons>0
The distribution of the neutron multiplicity is shown in Figure 6.30 and the distribution for the number of decay-electrons, alongside the SK-IV data, is presented in
Figure 7.19.
The contents and expected rates of the defined samples are shown in Table 6.5.

Figure 6.30: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in theMultiGeV 1Ring e-like sample, normalised to 2519.90 days (SK-IV running time).

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

νe -like(dcy-e>0)
61.4%
9.1%
11.7%
2.0%
15.7%
359.0

Samplesνe + ν e -like(dcy-e=0 & neutrons=0)
73.4%
20.1%
1.0%
0.1%
5.4%
401.1

ν e -like(dcy-e=0 & neutrons>0)
41.6%
49.8%
1.0%
0.4%
7.2%
557.8

Table 6.5: Relative contents of each species for each subsample of the MultiGeV e-likesample, after the selection, and the number of entries predicted by atmospheric Monte
Carlo normalised to 2519.90 days (SK-IV running time).

167

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

In both selection procedures, summarised in Tables 6.4 and 6.5, it is clearly seenthat the purity of the νe -like sample is very high and with low statistics. ν e -like samples contain, approximately, the same amount of neutrinos and antineutrinos, which
given the differences in their fluxes, confirms the good performance of the sample
definition. Finally, in the νe + ν e -like sample, the neutrino purity is high, but, in thiscase, mainly due to the flux dissimilarities between neutron and antineutrinos.
In addition, it is interesting to notice the worsening in the separation with increasing energy. This is because at higher energies the neutron multiplicity is larger,
which dims the differences between neutrinos and antineutrinos in terms of neutron
production.

6.6.3.2

SubGeV and MultiGeV µ-like

Although it could be tempting to subdivide these events into three categories asin the previous case. It is not done because this sample is not as important forthe oscillation analysis and because the corresponding νµ -like sample would have ahuge systematic error, ∼ 30%, induced by the uncertainty in the decay-e tagging.
Therefore, these events are simply separated into two, νµ -like and ν µ -like samples.
dims

SubGeV µ-like samples
The cuts which define the two regions in this sample are the following:Number of decay-e6=1• νµ -like:Number of decay-e=1 and Number of Gd-tagged neutrons=0• ν µ -like: Number of decay-e=1 and Number of Gd-tagged neutrons>0168

6.6. ATMOSPHERIC NEUTRINOS

The distribution for the number of Gd-tagged neutrons is shown in Figure 6.31.
The simulated decay-electron multiplicity for this sample is presented in Figure 7.21
and compared with the SK-IV data.
Table 6.6 summarises the contents of the selected samples.

Figure 6.31: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in the
SubGeV 1Ring µ-like sample, normalised to 2519.90 days (SK-IV running time).

Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

νµ -like(dcy-e6=1 or(dcy-e=1 & neutrons=0))
0.8%
0.2%
83.8%
11.5%
3.7%
4743.5

ν µ -like(dcy-e=1 & neutrons>0)
0.1%
0.0%
47.2%
49.5%
3.3%
2462.7

Table 6.6: Relative contents of each species for each subsample of the SubGeV µ-like sample, after the selection, and the number of entries predicted by atmospheric Monte Carlonormalised to 2519.90 days (SK-IV running time).

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

MultiGeV µ-like samples
For MultiGeV events, the analogous is done, being the selection criteria for the
sample separation as follows.
Number of decay-e6=1• νµ -like:Number of decay-e=1 and Number of Gd-tagged neutrons=0• ν µ -like: Number of decay-e=1 and Number of Gd-tagged neutrons>0
The distributions of the Gd-tagged neutrons and the decay-electrons are presented
in Figures 6.32 and 7.23 and normalised to the 2519.90 days of SK-IV data taking.

Figure 6.32: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in theMultiGeV 1Ring µ-like sample, normalised to 2519.90 days (SK-IV running time).

The contents for each of the resulting samples are calculated in Table 6.7.

170

6.6. ATMOSPHERIC NEUTRINOS
Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

νµ -like(dcy-e6=1 or (dcy-e=1 & neutrons=0))
0.3%
0.1%
74.9%
24.6%
0.1%
1090.0ν µ -like(dcy-e=1 & neutrons>0)
0.1%
0.0%
41.5%
58.3%
0.1%
655.5

Table 6.7: Relative contents of each species for each subsample of the MultiGeV µ-likesample, after the selection, and the number of entries predicted by atmospheric Monte
Carlo normalised to 2519.90 days (SK-IV running time).

Similarly to Section 6.6.3.1, in the e-like cases, νµ -like samples possess a very highpurity, and, in this case, with larger number of entries due to the only two sampledivision. The ν µ -like samples contain, again, similar number f neutrinos and antineutrinos.
The energy dependence of the separation method is also reproduced in these cases.
The efficiency of the selection is depleted as the neutrino energy increases.

6.6.3.3

MultiRing CC νe -like

After the NC-CC separation, explained in Section 6.6.2, is done, the remaining(−)

events in the MultiRing CC ν e -like sample are further divided into neutrino andantineutrino-like samples. This separation is performed using a neural network
method with one hidden layer and N + 5 nodes. The selection point is, then, defined
to make the separation.
In this method, the most important variable is the Gd-tagged neutron multiplicity,
whose distribution is displayed in Figure 6.33.

171

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.33: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in theMultiRing CC νe -like sample, normalised to 2519.90 days (SK-IV running time).

The rest of the variables used in the separation, for the atmospheric Monte Carloand the SK-IV dataset, are the number of decay-electrons, the distance and timeto the furthest decay-electron, the number of rings, the sum of all ring particle ID
likelihood, the rapidity and the energy fraction of the most energetic ring. They are
shown in Figures 7.25 to 7.31.
The distribution of the neural network output is shown in Figure 6.34.

In order to show the importance of the neutron multiplicity as compared with therest of the variables used, Table 6.8 shows their relative importance in the separation
procedure.

In this separation, the amount of neutrons in the final state plays a crucial role inthe separation. In importance, it is followed by the decay-electron variables, but

172

6.6. ATMOSPHERIC NEUTRINOS

MC ν information

Figure 6.34: Neural network output for the ν-ν separation in the MultiRing e-like sample,
for for true neutrinos (blue), true antineutrinos (brown), neutral current events (orange)
and total atmospheric Monte Carlo (red) normalised to 2519.90 days (SK-IV running time).
The pink vertical line shows the selection point, 0.8 for the distribution, which separates
the events into two categories, from left to right, MultiRing ν e -like and MultiRing νe -like.

Number of Gd-tagged neutrons
Number of decay-e
Distance to furthest decay-e
Number of rings
Sum of all rings PID likelihood
Pseudorapidity
Energy fraction of most energetic ring

Relative separation powerν-ν separation
77.8%
9.3%
9.2%
1.8%
1.1%
0.3%
0.4%

Table 6.8: Relative importance of each variable in the neural network for the ν-ν separationin the CCνe -like sample.

with much less separation power.
Lastly, Table 6.9 shows the contents for all four samples defined for MultiRing e-likeevents.

173

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL
Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

CC νe -like
63.1%
10.8%
12.7%
1.4%
12.0%
270.8

CC ν e -like
53.6%
29.2%
4.9%
0.6%
11.7%
378.0

(−)

CCDIS ν µ -like
28.4%
3.5%
38.1%
4.2%
25.8%
388.0

NC-like
27.9%
3.9%
33.5%
4.2%
30.6%
617.7

Table 6.9: Relative contents of each species for each subsample of the MultiRing e-likesample, after the selection, and the number of entries predicted by atmospheric Monte
Carlo normalised to 2519.90 days (SK-IV running time).

The separation is not as good as in the rest of e-like sample due to the remaining(−)

neutral current and ν µ events in the sample. Despite of that, the neutron multiplicity improves the categorisation of neutrinos and antineutrinos as seen in Table 6.8,
which will have an important effect in the mass hierarchy sensitivity, analysed in
Section 6.6.5.2.

6.6.3.4

MultiRing µ-like

As it has been done in the rest of µ-like samples, MultiRing µ-like events will beseparated in two samples. However, and in a similar fashion to the MultiRing CC(−)ν e -like samples, the selection is done based on a likelihood distribution constructedwith a neural network of one hidden layer and N + 5 neurones. The neutron multiplicity plays a very important role. The distribution for the number of Gd-tagged
neutrons is shown in Figure 6.35.

The rest of the variables entering the likelihood construction are the the number ofdecay-electrons, the distance and time to the furthest decay-electron, the number

1746.6. ATMOSPHERIC NEUTRINOS

Figure 6.35: Number of Gd-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange) and total atmospheric Monte Carlo (red) in theMultiRing CC e-like sample, normalised to 2519.90 days (SK-IV running time).

of rings, the sum of all ring particle ID likelihood, the rapidity and the energy
fraction of the most energetic ring. All of them are shown in Figures 7.34 to 7.40
for atmospheric Monte Carlo and SK-IV dataset.
The neural network output distribution is plotted in Figure 6.36 and, in Table 6.10,
the relative importance in the method for each variable is shown.
In this case, the number of decay-electrons have greater importance than neutrons.
This is because the in distribution of the latter the differences of neutrinos andantineutrinos become smaller at these high energies. Meanwhile, the decay-electrons
maintain their separation power as their origin does not depend so much on theneutrino energy and the secondary interactions.

175

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Variables

Figure 6.36: Neural network output for the ν-ν separation in the MultiRing µ-like sample,
for for true neutrinos (blue), true antineutrinos (brown), neutral current events (orange)
and total atmospheric Monte Carlo (red) normalised to 2519.90 days (SK-IV running time).
The pink vertical line shows the selection point, 0.762 for the distribution, which separates
the events into two categories, from left to right, MultiRing ν µ -like and MultiRing νµ -like.

Number of Gd-tagged neutrons
Number of decay-e
Distance to furthest decay-e
Time to furthest decay-e
Number of rings
Sum of all rings PID likelihood
Pseudorapidity
Energy fraction of most energetic ring

Relative separation powerν-ν separation
36.7%
51.9%
5.0%
4.7%
0.6%
0.1%
0.3%
0.7%

Table 6.10: Relative importance of each variable in the neural network for the ν-ν separations in the MultiRing µ-like sample.

Table 6.11 shows the contents of each sample and the expected unoscillated event
rates for 2519.90 days.

176

6.6. ATMOSPHERIC NEUTRINOS

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.

Samplesνµ -like ν µ -like
3.7%
1.8%
0.4%
0.3%
82.6%
71.1%
7.6%
23.3%
5.8%
3.5 %
167.0
584.4

Table 6.11: Relative contents of each species for each subsample of the MultiRing µ-likesample, after the selection, and the number of entries predicted by atmospheric Monte Carlonormalised to 2519.90 days (SK-IV running time).

The amount of neutrinos is much bigger than that of antineutrinos, therefore, theν µ -like sample is largely contaminated with neutrinos. On the other hand, the νµ -likesample is very pure, but with low statistics.

6.6.4

Neutron-Corrected Reconstructed Neutrino Energy
for Fully Contained Samples

The energy corrections with the neutron multiplicity, explained in Section 5.5, areapplied to all the fully contained samples of the atmospheric analysis.
The neutron correction function, f , is computed for each of these samples. For thecomputation of these functions, events with very poorly reconstructed energy are nottaken into account in order to avoid the distortion of the distribution. If these are
not removed, it would become considerably different due to a tiny fraction of events
and worsening the performance of the energy correction functions.
The averaged fraction of invisible energy ((Eν − Evis )/Evis ) for all cases, together
with the polynomial fit function, are shown in Figures 6.37 and 6.38.

Gd
Erec= Evis (1 + f (Gd − neutron))177(6.17)

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL
Gd) is computed for eachWith this and Equation (6.17) the Gd-neutron energy (Erecevent.

Figure 6.37: Gd-Neutron correction functions for each of the FC samples for atmospheric
neutrino Monte Carlo (1 of 2). Y-axis is the averaged fraction of invisible and visibleenergies and X-axis is the Gd-neutron multiplicity. The box in each plot shows the fitted
polynomial parameters and the χ2 value of the fit.

178

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.38: Gd-Neutron correction functions for each of the FC samples for atmospheric
neutrino Monte Carlo (2 of 2). Y-axis is the averaged fraction of invisible and visibleenergies and X-axis is the Gd-neutron multiplicity. The box in each plot shows the fitted
polynomial parameters and the χ2 value of the fit.

All the fit functions show a rather reasonable value for χ2 over the number of degrees
of freedom. In fact, most of the fits show values close to one, showing the good
performance of the neutron-correction functions.

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Recalling Section 6.6.3, the SubGeV and MultiGeV νe +ν e -like samples were selected
such their events have zero neutrons and, thus, there is only one point to be fitted.
1-ring π 0 and π 0 -like samples show a larger Y-axis intercept as compared with theother samples. This is because this sample is mainly populated by neutral current
events, which do not produce any prompt charged lepton, hence, being very hard toreconstruct in a water Čerenkov detector. This is very important because it meansthat neutrons may have a considerably effect in the energy reconstruction of thesesamples.
(−)

Another feature from Figures 6.37 and 6.38, is that for MultiRing NC, CCDIS ν e , νeand ν e -like samples the correction function levels up for high neutron multiplicities.
Figures 6.39 and 6.40 show the distributions of the true, visible and neutron-correctedenergies for the distributions of the different FC samples. The improvement using
the neutron correction is apparent and for all samples, being the distributions of thecorrected energy much closer to the true neutrino spectrum than the usual visibleenergy. A feature of the neutron-corrected energy are the steps seen in the SubGeV
samples, which are due to the inherited visible energy cut at Evis = 1.33 GeV.
Of special mention are the cases of the SubGeV 1-ring π 0 and π 0 -like samples andthe MultiRing samples, where the differences between visible and corrected energies
are most noticeable.
The π 0 -like samples consist, mostly, on neutral current 1π interactions, meaning that
their visible energy is reconstructed just with the photons from the π 0 decay. By
using the neutron-corrections a large fraction of the energy invisible to the detector
is recovered. This feature could have an important effect in the search for sterile
neutrinos in the neutral current disappearance channel, [Adamson11].
As for the MultiRing samples, these contain events with larger energy than thosewith a single ring, implying that their cross-section is not dominated by CCQE

180

6.6. ATMOSPHERIC NEUTRINOS

interactions and, thus, the energy fraction left in the nucleus enabling the productionof numerous secondary particles, is larger. This samples lie on the energy of the
Earth’s matter resonance, which can better detected with the corrected energy,
providing better sensitivity to the neutrino mass hierarchy.
In order to quantify the improvement in the neutrino energy reconstruction, Table 6.12 shows the variables of the corrected energy pulls ((Eν − Er ec)/Eν ) comparedto those for the visible energy. These variables characterising the energy pulls are themaximum of the distribution (mode), the mean value, the RMS and the skewness.
The mode and mean of the distribution indicate the accuracy with which the energy
is reconstructed.
The RMS in conjunction with the skewness of the distribution tell the resolution of
the energy reconstruction. Considering both parameters is key for the understandingof the effect of the energy correction. In the case of the visible energy, the energy
pulls tend to be very asymmetric with long tails for positive values. On the contrary,energy corrected pull distributions are closer to a Gaussian distribution, being theirskewness smaller. This affects the value of the RMS, being, usually, slightly larger
for the corrected energy cases, despite of having smaller tails.
In general, the neutron corrected energy improves the energy reconstruction of all
samples, which will be beneficial for the oscillation analysis done in Section 6.6.5.
However, two samples, not very relevant for the standard oscillation analysis, behave
in a different fashion to the rest of them, these are the 1ringπ 0 and π 0 -like samples.
As already noted, the correction function in these samples is much larger than for
the rest. Although the Gd-neutron-corrected spectra for these samples matches
nicely the true neutrino energy, in Figures 6.39 and 6.40, the pull distributions aremuch wider than those for the visible energy, in Figures 6.41 and 6.42.

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.39: True (green), visible (red) and corrected (blue) energy spectra of the different FC samples for atmospheric neutrino Monte Carlo (1 of 2). The distributions arenormalised to 2519.90 days (SK-IV running time).

1826.6. ATMOSPHERIC NEUTRINOS

Figure 6.40: True (green), visible (red) and corrected (blue) energy spectra of the different FC samples for atmospheric neutrino Monte Carlo (2 of 2). The distributions arenormalised to 2519.90 days (SK-IV running time).

183

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.41: Energy pulls of visible (red) and Gd-neutron-corrected (blue) energies of thedifferent FC samples for atmospheric Monte Carlo (1 of 2).

1846.6. ATMOSPHERIC NEUTRINOS

Figure 6.42: Energy pulls of visible (red) and Gd-neutron-corrected (blue) energies of thedifferent FC samples for atmospheric Monte Carlo (2 of 2).

185

186

Mode
0.548
0.198
0.233
0.233
0.233
0.863
0.898
0.178
0.058
0.058
0.058
0.093
0.478
0.408
0.233
0.163
0.478
0.338

Skewness-0.052
0.541
0.548
0.441
0.530
-0.842-0.708
0.686
0.529
0.848
0.879
0.735
-0.093
0.201
0.362
0.513
-0.214
0.036

Mode
0.020
-0.020-0.060-0.060-0.100-0.0240.060-0.0600.020-0.060-0.060-0.0600.020
0.023-0.013-0.013-0.013-0.013

Gd
Erec
Mean RMS
0.005 0.412
0.084 0.219-0.070 0.350
0.032 0.286
0.002 0.285-0.919 1.403-0.444 0.758-0.046 0.282
0.087 0.137
0.015 0.178
0.010 0.122
0.010 0.127-0.229 0.512-0.058 0.380
0.006 0.249
0.013 0.236-0.037 0.289-0.046 0.312

Skewness-0.0370.474-0.0290.321
0.359-1.224-0.665
0.048
0.491
0.420
0.573
0.548
-0.408-0.2110.075
0.106-0.084
0.107

Table 6.12: Mode, mean, RMS and skewness of the pull distributions for the visible energy and the Gd-neutron corrected energy.

Samples
SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like
SubGeV νµ -like
SubGeV ν µ -like
SubGeV 1ring-π 0 -like
SubGeV π 0 -like
MultiGeV νe -like
MultiGeV νe + ν e -like
MultiGeV ν e -like
MultiGeV νµ -like
MultiGeV ν µ -like
MultiRing NC-like
MultiRing DIS-νµ -like
MultiRing νe -like
MultiRing ν e -like
MultiRing νµ -like
MultiRing ν µ -like

Evis
Mean RMS
0.538 0.181
0.289 0.170
0.346 0.207
0.319 0.196
0.336 0.196
0.685 0.211
0.786 0.158
0.311 0.195
0.127 0.131
0.189 0.155
0.161 0.117
0.179 0.118
0.455 0.245
0.449 0.206
0.300 0.185
0.253 0.177
0.439 0.178
0.345 0.201

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

6.6. ATMOSPHERIC NEUTRINOS

In Section 6.6.5, the energy correction with neutrons is also included to theoscillation analysis, where its improvements, together with the previous ones, will
be quantified in terms of the sensitivity to the atmospheric oscillation parameters.

6.6.5

Oscillation Analysis Sensitivity

All the previous improvements are implemented in the atmospheric oscillation analysis, this will be referred as ”Gd-tag” analysis. The current official SK analysis scheme
is used for comparison purposes and will be referred as Standard analysis.
To compute the sensitivity analysis the official tools of SK were modified in order toaccommodate the new sample scheme and the corrected energy for fully contained
events.
Before the oscillation analysis is performed in Section 6.6.5.2, the analysis method
and the sample binning are described.

6.6.5.1

Analysis Method

The sensitivity is performed by the binned χ2 method, [Wendell08], where the likelihood for each of the bins is assumed to follow a Poisson distribution. Then, for nbins the likelihood is defined as follows.

L(N

exp

,N

obs

)=

exp
obs
n
Y
eNi (N exp )Ni

i

i=1

Niobs !

(6.18)

Where Nexp is the expected number of events according to the Monte Carlo simulation
at bin ith and Nobs is the observed number of events at bin ith . The χ2 is given by
the natural logarithm of the likelihood ratio where the factorial is approximated by
Stirlings’s formula.

187

CHAPTER 6. SUPERK-GD PHYSICS POTENTIALn
X
L(N exp , N obs )
Niobs
exp
2
obs
obs
χ = −2 ln
=
2
N
−
N
+
N
ln
i
i
i
L(N obs , N obs )
Niexp
i=1

!
(6.19)The effect of the systematic uncertainties is included with the pull method, being the
expected number of events allowed to vary accordingly to the size of the systematic
errors. The expected of number events is then redefined as follows.
mX
Nexp → Nexp 1 +fji j(6.20)

j=1

Where m is the number of systematic errors, j is the variation coefficient of the jthsystematic uncertainty and fij is the relative change in the event rate at bin ith due
to 1σ variation of the systematic jth .
Niexp (+1σ) − Niexp (−1σ)
jfi =2Niexp (def ault)(6.21)In addition, a term for constraining the range of the  is included in the χ2 expression.

χ2 = 2nX

Niexp 1 +

m
X

i=1

j=1

fji j



m 
X
j 
Niobs
− Niobs + Niobs ln
+
m


X
σj
exp
j=1
Ni
1+
fji j!

j=1(6.22)The best fit corresponds to the minimisation of the χ2 with respect to each of thej . In order to ensure the good behaviour of the χ2 distribution, each bin is required
to have more than seven expected entries, so the Stirling approximation is closeenough to the factorial.

188

6.6. ATMOSPHERIC NEUTRINOS

6.6.5.2

Oscillation Sensitivity Study

The true oscillation parameter used for the sensitivity study, unless otherwise stated,
are shown in Table 6.13.

Oscillation param.
∆m232
sin2 θ23∆m221
sin2 θ12
sin2 θ13
δCP

True Value
2.5·10−3 eV2 /c2
0.575
7.65·10−5 eV2 /c2
0.309
0.0219
4.19

Treatment
FittedFitted
Fixed
Fixed
Fixed
FittedTable 6.13: True oscillation parameters used for the sensitivity studies of the atmosphericoscillation analysis.

Most of the systematic errors taken are those for SK-IV, in Section 7.3.1. Only thoseerrors related to the Gd-neutron tagging tools (NC-CC separation, ν-ν separationand neutron-corrected energy) are computed specifically for the Gd-tag analysis, andcan be found in Appendix A.
The binning for the analysis is done in the cosine of the zenith angle and the Gdneutron corrected reconstructed energy. The total amount of bins for the Gd-tag
analysis is 701.
Two sensitivity studies are performed, one for each of the neutrino mass orderings.
In Figure 6.43, the χ2 distributions for sin2 θ23 and δCP are shown assuming true
normal hierarchy. In Figure 6.44 the analogous distributions are displayed for true
inverted hierarchy.

189

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.43: χ2 distributions for sin2 θ23 (top) and δCP (bottom) assuming normal mass
hierarchy and for Gd-tag analysis (violet) and current standard SK analysis (black). The
horizontal dashed lines represent the 68%, 90% and 99% confidence levels, which correspondto χ2 values of 1, 2.71 and 6.64, respectively. The dataset corresponds to that of SK-IV
presented in Table 7.1.

190

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.44: χ2 distributions for sin2 θ23 (top) and δCP (bottom) assuming inverted mass
hierarchy and for Gd-tag analysis (violet) and current standard SK analysis (black). The
horizontal dashed lines represent the 68%, 90% and 99% confidence levels, which correspondto χ2 values of 1, 2.71 and 6.64, respectively. The dataset corresponds to that of SK-IV
presented in Table 7.1.

191

CHAPTER 6. SUPERK-GD PHYSICS POTENTIALThe Gd-tag analysis improves the sensitivity to the mass hierarchy and the CP
phase significantly. These two parameters are the most sensitive to the neutrinoantineutrino separation and the reconstructed energy.

The sensitivity to theseparameters is summarised for both analyses in Table 6.14.

∆χ2 (N H − IH)
δCP fraction
over 1σStandard(true NH)
-1.62

Gd-tag(true NH)
-2.68

Standard(true IH)
0.96

Gd-tag(true IH)
1.55

22.4%

39.1%

6.0%

28.0%

Table 6.14: Mass hierarchy and δCP sensitivities, assuming as true normal and inverted
hierarchies. Comparison between standard SK analysis (black) and Gd-tag analysis (violet).

The Gd-tag analysis shows a major improvement in the sensitivity study for themass hierarchy, improving the sensitivity 1.06 units of χ2 , for the normal ordering,and 0.59 units of χ2 for the inverted one. It also improves the sensitivity to the CP
phase, improving largely the fraction of δCP over 1σ level for both hierarchies.
In order to explicitly see the improvement of the Gd sample selection as compared
to SK standard analysis, in Figure 6.45 the mass hierarchy sensitivity for each of the
fully contained samples in shown. This figure shows that, the improvement in theneutrino mass ordering, happens mainly on the MultiGeV and MultiRing samples,and for the Gd-tag analysis, an overall enhancement of the sensitivity is observed.
Additionally, the newly introduced SubGeV samples also improve their sensitivity
to the neutrino mass hierarchy.

192

6.6. ATMOSPHERIC NEUTRINOS

Figure 6.45: χ2 values for the inverted mass hierarchy rejection assuming true mass hierarchy is normal. Top plot, in violet, shows the ∆χ2 (IH − N H) for each of the defined
fully contained samples for SuperK-Gd atmospheric analysis. Bottom plot, in black, showsthe ∆χ2 (IH − N H) for each of the current fully contained samples in the official SK atmospheric analysis. The exposure assumed is 2519.90 days and the oscillation parametersassumed in Table 6.13.

193

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Further, Figure 6.46 shows the wrong mass hierarchy rejection sensitivity is done forvarious values of θ23 . The sensitivity to the mass hierarchy is seen to be improved
very significantly by Gd-tag analysis for all considered values of θ23 , becoming much
more noticeable as θ23 increases.

Figure 6.46: Wrong mass hierarchy sensitivity as function of the θ23 oscillation parameterusing atmospheric neutrinos for the Gd-neutron tagging (violet) and current SK standard
analyses (black). The analysis assumes both possible mass orderings, normal (solid lines)
and inverted (dashed), and fixed δCP = 4.19 and |∆m232 |= 0.0025 eV2 . The horizontal
dashed lines represent the 68%, 90% and 99% confidence levels, which correspond to χ2values of 1, 2.71 and 6.64, respectively. The exposure time is considered to be 2519.9 days,
the same as currently for the SK-IV dataset and shown in Table 7.1, and for the oscillation
parameters listed in Table 6.13.

6.7

Long-Baseline Neutrinos

The T2K (Tokai-to-Kamioka) experiment, [Abe11b], is a long-baseline neutrino oscillation experiment. The main goals of this experiment are, nowadays, the measure-1946.7. LONG-BASELINE NEUTRINOS

ment of the leptonic CP violating phase.
Due to the success of its measurements, in 2016 the T2K collaboration approved theextension of its running period until 20 · 1021 POT are achieved. Meaning that thesecond run of T2K will be done having SuperK-Gd as far detector and, therefore,
the T2K oscillation analyses might benefit from Gd-neutron tagging.
In this section, based on the neutron-tagging abilities of SuperK-Gd, the separation
between neutrinos and antineutrinos, presented in Section 5.4, is implemented for
T2K, Section 6.7.4, and applied to the oscillation analysis in Section 6.7.6. Furthermore, the neutron multiplicity driven energy corrections are investigated in
Section 6.7.5, although this feature will not be applied to the oscillation analysis.
Instead, a comparison between the neutron-corrected energy and the usual reconstructed energy is done.

6.7.1

The T2K experiment

T2K neutrinos are produced at the Japan Proton Accelerator Research Complex(J-PARC), 295 km away from its far detector, Super-Kamiokande.

Figure 6.47: Diagram of T2K neutrino beam produced at J-PARC and measured at ND280
and SK, near and far detectors respectively.

195

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

In this facility, protons are accelerated in a synchrotron achieving 30 GeV in themain ring. Then, the proton beam directed towards the neutrino beamline, extracting eight circulating bunches of protons. These protons are made collide with thegraphite target, resulting in the production of pions. These are focused with several
magnetic horns and let decay along a 96 m tunnel. At the end of the decay volume,a block of graphite and iron is placed for avoiding any particle, except neutrinos anda few muons with Eµ > 5 GeV, go into the neutrino beam. The final result is anearly pure beam of νµ or ν µ , depending on the neutrino beam mode.
The neutrino energy spectrum can be calculated from the beam parameters andderived from the measured muon spectrum after the beam. The neutrino beam contains some contamination from electron neutrinos, due to the production of a few
kaons, in addition to pions, when protons collide with the graphite target.
The neutrino beam is specially design so the oscillation probability of νµ to νe reaches
its maximum, making easier to measure the neutrino oscillation effects. In order tomake the energy spectrum narrower and peaked at maximal oscillation probability,
the neutrino beam is displaced 2.50 from the direction to SK, as seen in Figure 6.48.
This facility is equipped with a near detector as well, which carries cross-section,energy spectrum and flux studies of the neutrino beam. This provides great knowledge about the neutrino characteristics, decreasing the associated systematic errors.
ND280 is a compendium of various facilities, placed 280 m from J-PARC. It is formedby INGRID, a scintillation light detector made up by sixteen modules of nine ironplates and eleven tracking scintillators each and placed in front of the neutrino beam,
and ND280 placed 2.50 off-axis composed by π 0 detector and calorimeter, an electromagnetic calorimeter, a muon detector, fine grained detectors (FGD) and argon
time projection chambers (TPC).

196

6.7. LONG-BASELINE NEUTRINOS

Figure 6.48: T2K neutrino energy spectrum at Super-Kamiokande for different angles relative to the beam axis. The νµ survival probability, and νe appearance probability are shown.

6.7.2

Monte Carlo Simulation and Gd-neutron Tagging

The analysis presented in this thesis is done with external simulation tools, not
the T2K official ones. The Monte Carlo simulation used is that of atmospheric
neutrinos in SK, but weighted to match the T2K spectra, flux and direction for
all types of neutrinos. This means that the amount of neutrons detected for each
event is previously determined from the atmospheric simulator as in Section 6.6.1 on
page 143. This simulation was used in Sections 6.7.4 and 6.7.5, to determine withaccuracy the performance and behaviour of the neutrino-antineutrino separation andthe neutron-corrected energy.

197

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

6.7.3

T2K Neutrino Event Selection

The T2K reduction software categorises the beam data into three samples: FC, OD
and LE. The former includes the fully contained events. OD category correspond to
those events with outer detector activity over the threshold (15 hits). LE events arethose with energy below the FC energy threshold.
The reconstruction of T2K events is analogous to that made by SK for atmospheric
neutrinos, explained in Section 6.6.1.

6.7.4

Neutrino-Antineutrino Separation

In the case of T2K events, the neutrino-antineutrino separations are done, only, forfully contained, as for the atmospheric neutrinos.
Due to the precision required by the T2K experiment, the neutrino and antineutrino
separation is performed taking into account the different shape of the spectra. For
that, the separation is, independently, done for five different energy regions, [0.1, 0.3)
GeV, [0.3, 0.5) GeV, [0.5, 0.7) GeV, [0.7, 1.0) GeV and ≥ 1.0 GeV. Both neutrino
beam modes have sufficient similar energy spectrum for neutrinos and neutrinos
and, therefore, the likelihood distributions for their separation will be the same.
As anticipated in Section 5.4, for this analysis, a neural network was used to obtainthe likelihood distribution using just two variables, the number of neutrons in the
final state and the cosine of the charged lepton scattering angle, θscat . The neuralnetwork architecture is the analogous to that used in the previous atmospheric
neutrino section, one hidden layer with N + 5 neurones.
The number of decay-electrons is already used in T2K for sample separation and,
therefore, it is not considered in this separation method.

198

6.7. LONG-BASELINE NEUTRINOS

6.7.4.1

e-like Neutrino Sample

The distributions of the variables used in the neural network are shown in Figures 6.49 and 6.50 for the whole T2K neutrino spectrum.

Figure 6.49: Number of Gd-tagged neutrons for neutrinos (blue) and antineutrinos (red)in the e-like sample. Neutrino and antineutrino fluxes are normalised to unit.

Figure 6.50: Cosine of the scattering angle for neutrinos (blue) and antineutrinos (red) inthe e-like sample. Neutrino and antineutrino fluxes are normalised to unit.

199

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

The neural network outputs, for each of the energy regions, are shown in Figures 6.51
and 6.52.

Erec ∈ [0.1, 0.3) GeV

Erec ∈ [0.3, 0.5) GeV

Erec ∈ [0.5, 0.7) GeV

Figure 6.51: Neural network output distributions for the five energy ranges and for e-likeevents (1 of 2). Neutrino and antineutrino fluxes are normalised to unit.

Erec ∈ [0.7, 1.0) GeV

Erec ≥ 1.0 GeV

Figure 6.52: Neural network output distributions for the five energy ranges and for e-likeevents (2 of 2). Neutrino and antineutrino fluxes are normalised to unit.

Once the selection is done based on the likelihood distributions, events areclassified into neutrino or antineutrino. Table 6.15 shows the efficiency of thesesamples for correctly categorising neutrinos and antineutrinos.

The method is then, very efficient in detecting neutrinos and antineutrinos as such,
improving the already high purity of the neutrino and antineutrino beam modes.

200

6.7. LONG-BASELINE NEUTRINOS

νe -likeν e -like[0.1,0.3)GeV
78.0%
77.1%

Efficiency of samples[0.3,0.5)GeV [0.5,0.7)GeV [0.7,1.0)GeV
78.3%
76.8%
75.7%
77.0%
77.5%
76.5%

≥ 1.0GeV
72.9%
77.3%

Table 6.15: Efficiencies of each of the resulting νe and ν e -like samples in the five energy
ranges.

6.7.4.2µ-like Neutrino Sample

For µ-like events the procedure is, basically, the same as before. The corresponding
distributions for the neutron multiplicity and the cosine of the scattering angle areshown in Figures 6.53 and 6.54.

Figure 6.53: Number of Gd-tagged neutrons for neutrinos (blue) and antineutrinos (red)in the µ-like sample. Neutrino and antineutrino fluxes are normalised to unit.

201

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.54: Cosine of the scattering angle for neutrinos (blue) and antineutrinos (red) inthe µ-like sample. Neutrino and antineutrino fluxes are normalised to unit.

The obtained likelihood distributions from the neural network are in Figures 6.55
and 6.56.

Erec ∈ [0.1, 0.3) GeV

Erec ∈ [0.3, 0.5) GeV

Erec ∈ [0.5, 0.7) GeV

Figure 6.55: Neural network output distributions for the five energy ranges and for µ-likeevents (1 of 2). Neutrino and antineutrino fluxes are normalised to unit.

202

6.7. LONG-BASELINE NEUTRINOS
Erec ≥ 1.0 GeV

Erec ∈ [0.7, 1.0) GeV

Figure 6.56: Neural network output distributions for the five energy ranges and for µ-likeevents (2 of 2). Neutrino and antineutrino fluxes are normalised to unit.

The efficiencies of the method for each energy region is shown in Table 6.16.

νµ -likeν µ -like[0.1,0.3)GeV
79.7%
64.9%

Efficiency of samples[0.3,0.5)GeV [0.5,0.7)GeV [0.7,1.0)GeV
76.9%
76.1%
74.8%
73.3%
76.5%
75.8%

≥ 1.0GeV
72.0%
68.8%

Table 6.16: Efficiencies of each of the resulting νµ and ν µ -like samples in the five energy
ranges.

For µ-like events the efficiency of the separation is a smaller in general, mainly due
to the less separation power of the scattering angle, as compared with the e-like case.

6.7.5

Neutron-Corrected Reconstructed Neutrino Energy

The energy correction is also studied just for the fully contained events, where neutron tagging is available.
The neutrino energy is very well reconstructed in T2K because of the accurate knowledge in the direction of the interacting neutrino. Thus, the lepton momentum can becorrected by applying the information about the scattering angle to Equation (6.23),

203

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

where it is assumed that the interaction is a quasi-elastic scattering.

θscat
=
Erec

(Mn − V )Eµ − m2µ /2 + (Mp2 − Mn2 )/2
Mn − V − Eµ + |~pµ |cos θscat(6.23)

Although, there is very little room for improvement in the energy reconstruction, theneutron corrections to the energy are applied in order to compare their performancewith that of Equation (6.23).

Gd= Evis (1 + f (Gd-neutrons))
Erec(6.24)The neutron correction function was computed analogously to the atmospheric casefor each of the previously defined samples. This is shown in Figure 6.57.

Figure 6.57: Plot showing the dependence of the quotient of the non-reconstructed energy
and the visible energy with the number of Gd-tagged neutrons for e-like T2K neutrinos.

2046.7. LONG-BASELINE NEUTRINOSIn Figure 6.58, the different spectra of the true neutrino energy, the angle-correctedenergy and the neutron-corrected are shown. Furthermore, in order to compare theirperformance, the energy pull distributions for both corrected energies are plotted in
Figure 6.59.

Figure 6.58: T2K neutrino spectra for true, angle reconstructed and neutron reconstructedenergies assuming the beam in neutrino mode. Flux normalised to arbitrary units.

205

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.59: Neutron corrected and angle reconstructed energy pulls for the e-like sample
with the beam in neutrino mode.

In all four samples, the reconstructed energy from the neutron multiplicity exhibits
a similar performance than that obtained from the scattering angle. However, thepull distribution parameters, listed in Table 6.17, show that the neutron-correctedenergy tends to have mean values than the angle-corrected one. This is because,
although both distributions peak near zero, the neutron-corrected ones have larger
tails.
Despite of being slightly worse than the angle energy correction, the neutron corrected energy improves very significantly the energy reconstruction. This study
confirms the validity and good performance of the neutron corrections to theneutrino energy, and can be used as motivation for using them in the atmospheric206

6.7. LONG-BASELINE NEUTRINOS

neutrino analyses.

νe -likeν e -likeνµ -likeν µ -like

θscat
Erec
Mode Mean
0.014 0.031
0.027 0.086
0.007 0.035-0.009 0.097

RMS
0.256
0.208
0.240
0.207

Mode
-0.002
0.009
0.012
0.006

Gd
Erec
Mean
0.152
0.098
0.093
-0.028

RMS
0.215
0.214
0.248
0.316

Table 6.17: Parameters of the angle and neutron reconstructed neutrino energy pulls forthe neutrino mode beam.

6.7.6

Oscillation Analysis

In order to see how the neutrino and antineutrino separation affects the oscillation
analysis, sensitivity studies for the CP violation phase were done because it is theparameter most affected by the ν or ν purity of the sample.
The oscillation analysis for T2K is done using the program GLoBES (General Long
Baseline Experiment Simulator), [Huber05], with the settings for T2K.
The sensitivity studies presented here compare the standard analysis with that using
the the neutrino-antineutrino separation with Gd-neutron tagging.
In this sensitivity study, the assumed mixing parameters are, unless otherwise
stated, shown in Table 6.18. In addition, since the neutrino mass hierarchy is yet tobe known, several scenarios are explored.

The beam configuration is such that the exposure to the neutrino beam is three times
the time that the antineutrino beam is on, summing up in total 3.9 · 1021 POT. The

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL
Oscillation parm.
∆m232
sin2 θ23∆m221
sin2 θ12
sin2 θ13
δCP

Value
2.40·10−3 eV2 /c2
0.50
7.60·10−5 eV2 /c2
0.319
0.02570Treatment
FittedFittedFixed
Fixed
FittedFittedTable 6.18: True oscillation parameters used for the sensitivity studies of the atmosphericoscillation analysis.

sensitivity studies are performed with no systematic errors. The new uncertainties
associated to the ν-ν separation are considered negligible in this analysis, given thehigh purity of the neutrino beam.
The sensitivity is obtained via a χ2 method, analogous to that used for the atmospheric neutrino case and described in Section 6.6.5.1.

6.7.6.1

Oscillation Sensitivity Study

Three possible scenarios for the mass hierarchy are assumed: unknown normal
mass hierarchy, known normal mass hierarchy and known inverted hierarchy. The
sensitivity studies for these are shown in Figures 6.60 to 6.62 respectively. Thesestudies are done for the sensitivity to the CP conservation rejection.

2086.7. LONG-BASELINE NEUTRINOS

Figure 6.60: χ2 sensitivity distribution for δCP violation assuming unknown normal neutrino mass hierarchy and for the official (black) and Gd-neutron tagging (pink) analyses.
The exposure is taken to be 3.9 · 1021 POT and no systematics are considered.

Figure 6.61: χ2 sensitivity distribution for δCP violation assuming known inverted neutrinomass hierarchy and for the official (black) and Gd-neutron tagging (pink) analyses. The
exposure is taken to be 3.9 · 1021 POT and no systematics are considered.

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Figure 6.62: χ2 sensitivity distribution for δCP violation assuming known normal neutrinomass hierarchy and for the official (black) and Gd-neutron tagging (pink) analyses. The
exposure is taken to be 3.9 · 1021 POT and no systematics are considered.

There exists an slight improvement in the sensitivity to δCP by using the neutrino
and antineutrino classification in all three scenarios. This can be better seen in
Table 6.19. Here, the fraction of δCP excluded at 90% confidence level (CL) is
compared for both analyses and the three scenarios.

Unknown MH (NH)Known MH (NH)Known MH (IH)

Official analysis
δCP over 90% CL Max(χ2 )
13.9%
3.31
34.8%
4.43
34.6%
5.03

Analysis with Gd-tagging
δCP over 90% CL Max(χ2 )
16.3%
3.53
38.8%
4.84
38.2%
5.55

Table 6.19: Comparison between the official and the Gd-neutron analyses of the fraction ofδCP discarded with more than 90% CL and maximum of the χ2 distribution for the threemass hierarchy scenarios.

2106.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

6.8

The Next Generation: Physics Potential of
Gd-Doping in Hyper-Kamiokande

Hyper-Kamiokande is a next generation underground water Cherenkov, projected as
the successor of Super-Kamiokande.
The main goals of Hyper-Kamiokande (HK) are the neutrino oscillation studies fromlong-baseline (from the upgraded J-PARC beam), atmospheric and solar neutrinos,
as well as proton-decay searches. Amongst the neutrino parameters, HK aims tomeasure the neutrino mass ordering and the leptonic CP violating phase.
In addition, HK will observe an enormous number of neutrino events if a supernova
occurs nearby, providing much needed experimental results to researchers seeking tounderstand the mechanism of the explosion.
In this section, the Hyper-Kamiokande next-generation experiment is reviewed in
Section 6.8.1. Additionally, the section focuses on the improvements in the sensitivity, due to Gd-neutron tagging, for atmospheric, in Section 6.8.2.1, and long-baseline,
in Section 6.8.3, neutrinos.

6.8.1

Detector Description

Three detector configurations are still being considered for HK, in addition to theinitial proposal described in [Abe11a, Abe16a]. The latter consists in two tanks with
20% photocoverage, summing up a volume of 0.99 megatons.
On the other hand, the current three detector proposals are: three tanks with 13%
photocoverage and a volume of 774 kton, one tank with 40% photocoverage and 258
kton and two tanks with 40% photocoverage and a total volume of 526 kton (morethat 10 times larger than SK). The latter is currently the most favoured one, but

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the construction is planned in two stages. The second tank would be built aroundsix years after finishing the first one.

Figure 6.63: Schematic view for the configuration of two cylindrical tank instrumented withhigh density (40% photocoverage) PMTs.

This variety of possibilities open a bunch of possible sensitivity studies. However, in
this section, it is assumed that the volume is 258 kton.
The photocoverage is also very important for the implementation of the neutrontagging improvements. In this case, the neutron-tagging methods assume 20% PMT
coverage and the addition of Gd at 0.2% concentration, as in the case of SuperKGd. The neutron-tagging efficiency, with this assumption, is estimated to be 70%,
according to [Abe14b].
Despite of this, recent studies within the HK collaboration, indicate that hydrogen neutron tagging will also have 70% efficiency due to the photo-sensor response
improvement, seen in Figures 6.65 to 6.67. The studies presented in this section212

6.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

are, then, compatible with Gd-doped HK with 20% photocoverage, with Gd-neutron
tagging, and HK with pure water and 40% PMT coverage, with H-neutron tagging.
The ID photosensors are newly developed for HyperK (Hamamatsu R12860HQE), achieving a higher quantum efficiency (QE) and optimised box-and-line dynode. These PMTs are developed jointly with Hamamatsu and their properties arelisted in Table 6.20.
Shape
Photocathode area
Bulb material
Photocathode material
Quantum efficiency
Collection efficiency
DynodesGain
Dark rate
Transit time spread
WeightVolumePressure tolerance

Hemispherical
50 cm diameter
Borosilicate glass (∼3 mm)
Bialkali (Sb-K-Cs)
30% at λ=390 nm
95% at 107 gain
10 stage box-and-line
107 at ∼2000 V∼8 kHz at ∼107 gain and 130 C
2.7 ns for single PE
7.5 kg (without cable)
61050 cm3
9 kg/cm2 water proof

Table 6.20: Specifications of 50 cm R12860-HQE PMT by Hamamatsu.

One of the most important characteristics of these new PMTs is the enhancementof the quantum efficiency as compared to that of SK PMTs, but also charge andtiming resolutions are significantly improved as shown in Figure 6.65, Figure 6.66
and Figure 6.67.

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.64: Design of the HQE box-and-line R12860 PMT.

Figure 6.65: Measured
QE for six high-QE
R12860 (solid lines) anda normal R3600 (black
dashed line).

6.8.2

Figure 6.66:
Transittime distribution at 1p.e.
of HQE PMTs
(blue) and Super-K
PMTs (dotted line).

Figure 6.67:
Singlephotoelectron of HQE
PMTs (blue) comparedwith the Super-K PMT(dotted line).

Atmospheric Neutrinos

The simulation, reconstruction and reduction of atmospheric neutrinos is taken thesame as that for Super-Kamiokande, described in Section 6.6.1, but scaling theexposure to the HK assumed dimensions. Since the atmospheric oscillation analysis
is done for five years of exposure, just one tank of 258 kton is considered, the firststage of the HK project.

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6.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

The improvements based on neutron tagging for atmospheric neutrinos described in
Sections 5.3 to 5.5, are applied for the HK detector assuming 70% neutron tagging
efficiency. For the sake of brevity, these are not explicitly shown this time, but theresults are fairly similar to those shown in Sections 6.6.2 to 6.6.4 for the SuperK-Gd
project.

6.8.2.1

Oscillation Sensitivity Study

The sensitivity analysis method is the binned χ2 , discussed in Section 6.6.5.1.
The systematic errors used for this sensitivity study are those from the current SK
atmospheric analysis, reviewed in Section 7.3.1. The new systematic errors, due
to the CC-NC and ν-ν separations and the neutron corrections for the energy, arecomputed specifically for this analysis and shown in Appendix B.
The true neutrino oscillation parameters used for the sensitivity analysis are thesame as in Table 6.13.
The sensitivity study is shown for the sin2 θ23 and δCP oscillation parameters, andassuming normal, in Figure 6.68 and inverted Figure 6.69 mass orderings.

The 70%-analysis improves very significantly the sensitivity to the neutrino massordering and to the CP violating phase. The corresponding significance values forthese plots are summarised in Table 6.21.

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

Figure 6.68: χ2 distributions for sin2 θ23 (top) and δCP (bottom) assuming normal mass
hierarchy and for 70%-analysis (violet) and standard HK analysis (black). The horizontal
dashed lines represent the 1σ, 2σ, 3σ and 4σ confidence levels. The exposure time isconsidered to be five years of HK with one tank of 258 kton volume.

216

6.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

Figure 6.69: χ2 distributions for sin2 θ23 (top) and δCP (bottom) assuming inverted mass
hierarchy and for 70%-analysis (violet) and standard HK (black) analysis. The horizontal
dashed lines represent the 1σ, 2σ, 3σ and 4σ confidence levels. The exposure time isconsidered to be five years of HK with one tank of 258 kton volume.

217

CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL∆χ2 (N H − IH)
δCP fraction
over 1σStandard(true NH)
-4.94

70%-tag(true NH)
-11.99Standard(true IH)
3.06

70%-tag(true IH)
7.55

32.8%

55.6%

33.2%

49.9%

Table 6.21: Mass hierarchy and δCP sensitivities, assuming as true normal and inverted
hierarchies. Comparison for the 70%-analysis and standard HK analysis.

Furthermore, the wrong mass hierarchy rejection sensitivity is also improved, for all
values of θ23 , as compared to the standard analysis. This is shown in Figure 6.70.

Figure 6.70: Wrong mass hierarchy sensitivity as function of the θ23 oscillation parameterusing atmospheric neutrinos for the 70%-neutron tagging (violet) and standard analyses(black). The analysis assumes both possible mass orderings, normal (solid lines) and inverted (dashed), and fixed δCP = 4.19 and |∆m232 |= 0.0025 eV2 . The horizontal dashedlines represent the 1σ, 2σ, 3σ, 4σ and 5σ confidence levels. The exposure time is considered
to be five years of HK with one tank of 258 kton volume.

218

6.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

6.8.3

Long Baseline Neutrinos

Long baseline neutrinos to HK share most of the features describe for T2K in
Section 6.7, as the neutrino beam will be located at JPARC and the candidates for
the HK site are close to the current location of SK. The baseline, therefore, would
be of 295 km as well.
The current plan for long baseline neutrinos in HK depends not only on the far
detector layout, but also on the future upgrades of the J-PARC facility concerning
the neutrino beam. According to [Abe16a], it is planned that, by the time of theHyper-Kamiokande operation, the J-PARC neutrino beam achieves an intensity of
1.3 MW as result of various upgrades.
In addition, it is expected a considerable reduction of the systematic errors associated to this analysis. This is due to the knowledge to be acquired, in the next
years, with the current ND280 near detector of T2K. Furthermore, two new neardetectors are being considered, these are water-Čerenkov. The systematic errors
are expected to be reduced with the addition of measurements on the water targets
and not only on carbon. Namely, two proposals are made, the nuPRISM detector,[Bhadra14], and the TITUS detector, [Andreopoulos16], which is, additionally, aGd-loaded detector.
As in the case of the atmospheric analysis for HK in Section 6.8.2, here the neutrontagging improvements, developed for long baseline neutrinos in the SuperK-Gd
project in Section 6.7, are applied to the case of 70% neutron tagging efficiency.
These are not explicitly shown, but, instead, are directly implemented into theoscillation sensitivity study.

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CHAPTER 6. SUPERK-GD PHYSICS POTENTIAL

6.8.3.1

Oscillation Sensitivity Study

The oscillation analysis for long baseline neutrinos at HK, is done using the same
tools as done for the T2K analysis, using GLoBES and introducing the improvements
due to the H-neutron tagging in HK. The systematic errors considered here arethose taken in the last up to date version of the HK design, [Abe16a].
True neutrino oscillation parameters used for the sensitivity analysis are the sameas in Table 6.18.
Here, the neutrino mass ordering is considered to be know by the time this facility
is running, therefore the sensitivity studies for the CP violation are performed forboth hierarchies, but assuming they are known. The CP sensitivity plots assuming normal and inverted mass orderings are shown in Figure 6.71 and Section 6.8.3.1.

Figure 6.71: χ2 distribution for δCP assuming known inverted neutrino mass hierarchy andfor the official (black) and 70% efficiency neutron tagging (blue) analyses.

220

6.8. THE NEXT GENERATION: PHYSICS POTENTIAL OF GD-DOPING IN
HYPER-KAMIOKANDE

Figure 6.72: χ2 distribution for δCP assuming known normal neutrino mass hierarchy andfor the official (black) and 70% efficiency neutron tagging (blue) analyses.

In Table 6.22, the significance for rejecting CP conservation is summarised forboth analysis methods. The analysis done with the 70% neutron tagging neutrinoantineutrino separation, shows a slight improvement in the fraction of the δCP phase
rejected at the 5σ confidence level.

Known MH (NH)Known MH (NH)Official analysisp
δCP over 5σ Max( χ2 )
61.3%
9.10
62.1%
9.89

Analysis with H-taggingpδCP over 5σ Max( χ2 )
64.9%
9.71
65.5%
10.40

Table 6.22: Comparison between the official and the 70%-neutron tagging analyses of thefraction of δCP discarded with more than 90% CL and maximum of the χ2 distribution forboth mass hierarchy scenarios.

2217. Neutron-Tagging with Hydrogen in Super-Kamiokande IV:
Global Atmospheric Neutrino
Oscillation Analysis with SK
Currently, SK has the capability of tag neutrons through hydrogen-neutron captures.
This technique is around four times less efficient than in the proposed SuperK, Gd,i.e. ∼20%. However, it is enough for seen the relevance of the improvements, broughtby neutron tagging, in the atmospheric oscillation analysis.
Section 7.1 is focused on the review and description of the H-neutron tagging algorithm, only available in SK-IV, originally developed in [Irvine14].
In Section 7.2, all the tools developed in the context of the SuperK-Gd atmosphericanalysis, in Sections 6.6.2 to 6.6.4, are applied to the case of H-neutron tagging,H-tag analysis.
Finally, an oscillation sensitivity study, in Section 7.3.2, and the fit to the whole
SK atmospheric data using the H-tag analysis is presented in Section 7.3.3. Here,the sensitivity comparison to the atmospheric oscillation parameters is done for thewhole SK exposure, and comparing the analysis including the neutron-tagging tech-223

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK
niques in SK-IV with the current official analysis.
The total exposure time for atmospheric neutrinos in SK is summarised in Table 7.1.
SK phase
SK-I
SK-II
SK-III
SK-IV

SampleFC & PC
UpMu
FC & PC
UpMu
FC & PC
UpMu
FC & PC
UpMu

Exposure (days)
1489.199
1645.910
798.599827.744518.080635.600
2519.900
2519.900

Table 7.1: Exposure times of the different SK phases for the atmospheric neutrino dataset.

7.1

Hydrogen-Neutron Tagging

Hydrogen is present in the water molecules of SK,
behaving almost as free protons, since they are
not affected by nuclear forces. Hydrogen has aconsiderable cross-section, 0.329 ± 0.004 barns,
for the capture of thermal neutrons, which, given
the amount of H in SK, guarantees that all thermalised neutrons produced inside the tank will be
captured by hydrogen. Once hydrogen captures
a neutron, it is turned into deuterium, emitting

Figure 7.1: Schematic diagramof Inverse Beta Decay (IBD)with H-neutron capture in SK.

a 2.2 MeV photon from its de-excitation. This is similar to the gadolinium case, butwith a signal of significantly lower energy. The mean life-time of the 2.2 MeV photon
from the neutron capture is ∼200 µs, around six times larger than for Gd.

n + p → D∗ → +D + γ(2.2M eV )

224

(7.1)

7.1. HYDROGEN-NEUTRON TAGGINGOver the last years, the usage and development of neutron tagging on hydrogenis playing an increasing important role on the physics studies of SK. It was firstly
developed in [Haibing12] and the optimised in [Irvine14] for atmospheric neutrinos.
Currently, in SK, the H-neutron tagging efficiency 21.7%. This is achieved using a
two-staged reconstruction algorithm that is briefly reviewed Section 7.1.1.

7.1.1

H-Neutron Tagging Analysis

The detection of such weak signal can be done only for SK-IV due to the improvementof the electronics. As in the Gd case, the usage of several characteristics of its
signature in the detector, in addition to distance and time to prompt signal of theevent, allow to reconstruct some of these neutron captures. The selection method of
the H-neutron tagging delayed signals consists in two steps: a rough first selection
for detecting delayed candidates and likelihood, done with a neural network, todiscriminate as much detector noise as possible from the selected candidates.

7.1.1.1

First Candidate Selection

Based on the reconstructed prompt signal, the PMT hits of the event are correctedby time of flight (ToF) subtraction. Then, a 10 ns sliding window scans from 18µs after the prompt signal to the end (535 µs) of the event. This sliding window
searches a cluster of hits and requires them that the number of hits in that window,
N10 and in a 200 µs window, N200 , to satisfy Equation (7.2), removing most of the
PMT noise and the contamination from cosmic muons.

7 ≤ N10 ≤ 50, N200 ≤ 200

225

(7.2)

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK
After this selection, and comparing data with Monte Carlo, 97.8% of all neutron
captures are selected, of which, 32.7% correspond to actual H-neutron captures andthe remaining background is of 4.4 fake candidates per event. The backgroundis estimated as the candidates selected in the T2K dummy trigger data where noneutron-capture is expected, analogous to the Gd-neutron tagging in Section 5.2.2.
7.1.1.2

H-Neutron Capture Selection

In this part of the neutron tagging algorithm, a more elaborated selection criterion
is constructed to further discern between true neutron captures and miss-tagged
fake candidates. For that, sixteen different variables, concerning the physics and thedetector response to the 2.2 MeV photon, are used in a neural network to computea likelihood distribution, shown in Figure 7.2.

Figure 7.2: Neural network output of delayed signals for true H-neutron captures (green),background (blue), total Monte Carlo (red) and SK-IV atmospheric data (black dots). Vertical dashed line shows the selection point, events on the right of this line are those selected
as H-tagged neutrons.

226

7.1. HYDROGEN-NEUTRON TAGGINGIn Figure 7.3, the time distribution of the selected neutron captures is shown for
both, data and Monte Carlo. The agreement of this comparison together with similarplots for other variables proves the validity of the technique. Some of these variables
are also important for the development of the the NC-CC and ν-ν separations andthe neutron corrections to the visible energy, developed in Sections 5.3 to 5.5 andapplied to H-neutron tagging in Section 7.2. Two of these distributions are theenergy dependence of the neutron multiplicity and the averaged number of neutrons
for MultiGeV neutrinos, displayed in Figures 7.4 and 7.5.

Figure 7.3: Time distribution from prompt signal to selected neutron candidate for Monte
Carlo (red) and SK-IV atmospheric data (black dots) and its exponential fit (blue).

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CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK

Figure 7.4: Neutron-tag multiplicity as function of log10 Evis for atmospheric Monte Carlo(red) and SK-IV atmospheric data (black dots), for MultiGeV neutrinos (Evis ≥ 1.33 GeV).

Figure 7.5: Average number of neutron-tags per event as function of SK days. SK atmospheric data (black dots), fit to the data (blue line) and Monte Carlo (red line), forMultiGeV neutrinos.

228

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

7.2

Including Neutron-Tagging Information in SK
Atmospheric Neutrino Data Analysis

In this section, the implementation of the neutron-tagging improvements of Sections 6.6.2 to 6.6.4 is discussed for atmospheric neutrinos in SK using H-neutron
tagging.

7.2.1

Neutral Current and Charged Current Separation for
Fully Contained Samples

The procedure followed, will be as that done for SuperK-Gd and explained in Section 6.6.2.
The variables used by the neural network for the likelihood distribution construction
are the number of H-tagged neutrons, the number of rings, the MultiRing likelihood,the number of decay-electrons, the distance to the furthest decay-electron, the sumof all rings ID likelihood, the rapidity and the energy fraction of the most energetic
ring. All their corresponding distributions are shown in Figures 7.6 to 7.13 for theatmospheric Monte Carlo and SK-IV dataset. The description and motivation for
the usage of each of these variables is treated in Section 5.3.
These variables are used in a two-step process neural network to discard, first, theneutral current events from the rest of charged current interacting neutrinos. Then,
(−)

(−)

(−)

(−)

the ν µ are tried to be separated from the ν e in the CCDIS ν µ - ν e separation.
Both likelihood distributions are plotted in Figures 7.14 and 7.15.

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CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK

Figure 7.6: Number of H-tagged neutrons for NC (orange), CCDIS νµ (violet), CC νe(green), total atmospheric Monte Carlo (red) and SK-IV atmospheric data (black dots).

Figure 7.7: Number of decay-e for NC (orange), CCDIS νµ (violet), CC νe (green), atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset (blackdots).

230

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.8: Distance to furthest decay-e for NC (orange), CCDIS νµ (violet), CC νe (green),
atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset(black dots).

Figure 7.9: Number of rings for NC (orange), CCDIS νµ (violet), CC νe (green), atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset (blackdots).

231

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK

Figure 7.10: Multi-ring likelihood for NC (orange), CCDIS νµ (violet), CC νe (green),
atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset(black dots).

Figure 7.11: Sum of all ring particle ID likelihoods for NC (orange), CCDIS νµ (violet), CC
νe (green), atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric
dataset (black dots).

2327.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.12: Pseudorapidity (η) for NC (orange), CCDIS νµ (violet), CC νe (green), atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset (blackdots).

Figure 7.13: Energy fraction of the most energetic ring for NC (orange), CCDIS νµ (violet),CC νe (green), Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset(black dots).

233

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK

Figure 7.14: Neural network output for the NC-CC separation for NC (orange), CCDIS νµ(violet), CC νe (green), atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV
atmospheric dataset (black dots). The pink vertical line shows the selection point (0.55)
for the distribution, which optimises product CC × pCC , being the NC-like sample formedby those events at its left and the CC-like by those at its right.

Figure 7.15: Neural network output for the CCDISνµ -νe separation for NC (orange),
CCDIS νµ (violet), CC νe (green), atmospheric Monte Carlo (red) and for the 2519.90 daysof SK-IV atmospheric dataset (black dots) in the CC-like sample. The pink vertical line
shows the selection point (0.5) for the distribution, which optimises product CC−e ×pCC−e ,being the CCDIS νµ -like sample formed by those events at its left and the CC νe -like by
those at its right.

234

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSISIn Table 7.2, the values of the relative importance for each variable are listed.

Variables

Relative separation power
Number of H-tagged neutrons
Number of rings
MultiRing likelihood
Number of decay-e
Distance to furthest decay-e
Pseudorapidity
Energy fraction
Sum of all rings PID likelihood

NC-CC separation
57.5%
1.4%
1.7%
18.5%
5.1%
1.2%
0.9%
12.8%

(−) (−)
ν µ - ν e separation

49.5%
3.2%
2.1%
16.8%
6.3%
1.4%
1.0%
41.0%

Table 7.2: Relative importance of each variable in the neural network for the NC-CC and
CCDISνµ -νe separations in the MultiRing e-like sample.

It is seen that, despite the lower efficiency of the H-neutron tagging comparedto Gd-tagging, the importance of neutron tagging in the selections is the mostimportant variable, basically due to the broad neutron multiplicity distributions.
Finally, in Table 7.3, the contents after the previous selections, the expected numberof events and its comparison with the SK-IV dataset are calculated for each of thedefined samples.

The sample contents in 7.3 are rather alike for these separations, as compared with
the Gd case in Table 6.3. This is mainly due to the mentioned large neutron multiplicity of these events, meaning that the effect of the lower neutron tagging efficiency
from hydrogen, in the performance of the separations, is rather mild.

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CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK
Samples(−)

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Data

CC ν e -like
57.9%
24.3%
5.7%
0.5%
11.6%
503.9
475

(−)

CCDIS ν µ -like
36.8%
5.8%
34.5%
4.0%
18.9%
472.7
528

NC-like
28.9%
4.0%
31.9%
3.9%
32.1%
677.9
692

Table 7.3: Relative contents of each species for each subsample of the MultiRing e-likesample, after the selection, and a comparison between the number of entries predicted forthe unoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

7.2.2

Neutrino and Antineutrino Separation for Fully Contained Samples

The neutrino-antineutrino separations presented in Section 5.4 are implemented
here for the H-neutron tagging, analogously to the Gd-neutron tagging case in Section 6.6.3.

7.2.2.1

SubGeV and MultiGeV e-like

This sample is split into three event categories based on cuts on the neutron anddecay electron multiplicities. The cuts which define the three regions in this sample
are the following:• νe -like: Number of decay-e>0• νe + ν e -like: Number of decay-e=0 and Number of H-tagged neutrons=0• ν e -like: Number of decay-e=0 and Number of H-tagged neutrons>0
Next, the separation is implemented for the SubGeV and MultiGeV e-like samples.

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SubGeV e-like samples
The distributions for the H-tagged neutron multiplicity and the number of decayelectrons are shown in Figures 7.16 and 7.17 respectively.

Figure 7.16: Number of H-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the SubGeV e-like sample.

The three samples have the contents and event rates listed in Table 7.4.

Table 7.4 shows a similar trend in the sample contents than that for the Gd casein Table 6.4, although with considerable worsening of the selection efficiencies andsample purities due to the lower efficiency of the neutron tagging.

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Figure 7.17: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the SubGeV e-like sample.

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Dataνe -like(dcy-e>0)
77.1%
1.7%
11.6%
3.3%
6.3%
582.9
629

Samplesνe + ν e -like(dcy-e=0 & neutrons=0)
77.6%
19.2%
0.3%
0.0%
3.0%
3649.63961

ν e -like(dcy-e=0 & neutrons>0)
54.9%
40.6%
0.2%
0.1%
4.2%
938.8
949

Table 7.4: Relative contents of each species for each subsample of the SubGeV e-like sample, after the selection, and a comparison between the number of entries predicted for theunoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

MultiGeV e-like samples
The event selection in this sample is very similar to the SubGeV e-like one. The
neutron and decay-electron distributions are shown in Figures 7.18 and 7.19.

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7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
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Figure 7.18: Number of H-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiGeV e-like sample.

Figure 7.19: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiGeV e-like sample.

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The table contents and expected unoscillated event rates for the SK-IV period andfor the SK-IV data are shown in Table 7.5.

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Dataνe -like(dcy-e>0)
61.4%
9.1%
11.7%
2.0%
15.7%
359.0
385

Samplesνe + ν e -like(dcy-e=0 & neutrons=0)
61.4%
32.0%
0.9%
0.2%
5.4%
671.1
637

ν e -like(dcy-e=0 & neutrons>0)
42.8%
47.3%
1.1%
0.3%
8.4%
361.9
375

Table 7.5: Relative contents of each species for each subsample of the MultiGeV e-likesample, after the selection, and a comparison between the number of entries predicted forthe unoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

The contents of the samples follow the same trend as in the SubGeV e-like case andcompare in a similar fashion to those for Gd-neutron tagging in Table 6.5.

7.2.2.2

SubGeV and MultiGeV µ-like

For these samples the neutrino-antineutrino separation is also done using the numberof H-tagged neutrons and the number of decay-electrons. However, this time they
are only divided into two samples, νµ -like and ν µ -like. The cuts defining them are
the following:• νµ -like:Number of decay-e6=1
Number of decay-e=1 and Number of H-tagged neutrons=0• ν µ -like: Number of decay-e=1 and Number of H-tagged neutrons>0
The implementation of this separation is described below.

2407.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
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SubGeV µ-like samples
Figures 7.20 and 7.21 show the distributions for the H-tagged neutrons and thenumber of decay-electrons.

Figure 7.20: Number of H-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the SubGeV µ-like sample.

Figure 7.21: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the SubGeV µ-like sample.

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The contents of the resulting samples are summarised in Table 7.6.
Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Dataνµ -like(dcy-e6=1 or (dcy-e=1 & neutrons=0))
0.6%
0.2%
76.1%
19.4%
3.6%
6336.04799

ν µ -like(dcy-e=1 & neutrons>0)
0.1%
0.0%
49.8%
46.7%
3.4%
1427.61006

Table 7.6: Relative contents of each species for each subsample of the SubGeV µ-like sample, after the selection, and a comparison between the number of entries predicted by atmospheric Monte Carlo and SK-IV data.

Again, the selection worse performance due to the lesser neutron tagging efficiency
of hydrogen compared to gadolinium. This can be seen in Table 6.6.

MultiGeV µ-like samples
For this sample, the neutron and decay-electron multiplicities distributions areshown in Figures 7.22 and 7.23.

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ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.22: Number of H-tagged neutron for neutrinos (blue), antineutrinos (brown),
neutral current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90
days of SK-IV atmospheric dataset (black dots) in the MultiGeV µ-like sample.

Figure 7.23: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiGeV µ-like sample.

The contents and expected rates of the defined samples are shown in Table 7.7.

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Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Dataνµ -like(dcy-e6=1 or (dcy-e=1 & neutrons=0))
0.2%
0.1%
67.4%
32.2%
0.1%
1470.6996

ν µ -like(dcy-e=1 & neutrons>0)
0.1%
0.0%
44.3%
55.6%
0.1%
410.0
295

Table 7.7: Relative contents of each species for each subsample of the MultiGeV e-likesample, after the selection, and a comparison between the number of entries predicted forthe unoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

7.2.2.3

MultiRing CC νe -likeOnce again, here, the analogous technique as in Section 6.6.3.3, is used for the(−)

neutrino-antineutron separation of the CC ν e . A likelihood distribution for the
separation is constructed using a one hidden layer and N + 5 nodes neural network.
The variables entering the neural network computation are Gd-tagged neutron
multiplicity, the number of decay-electrons, the distance and time to the furthest
decay-electron, the number of rings, the sum of all ring particle ID likelihood, therapidity and the energy fraction of the most energetic ring. They are shown in
Figures 7.24 to 7.31.
The neural network response is shown in Figure 7.32.

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7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.24: Number of H-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing CCνe -like sample.

Figure 7.25: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing CCνe -like sample.

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Figure 7.26: Distance to furthest decay-e for neutrinos (blue), antineutrinos (brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90 daysof SK-IV atmospheric dataset (black dots) in the MultiRing CCνe -like sample.

Figure 7.27: Time to furthest decay-e for true neutrinos (blue), true antineutrinos (brown),
total atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset(black dots) in the MultiRing CCνe -like sample.

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7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
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Figure 7.28: Number of rings for true neutrinos (blue), true antineutrinos (brown), neutral
current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90 days of
SK-IV atmospheric dataset (black dots) in the MultiRing CCνe -like sample.

Figure 7.29: Sum of all ring ID likelihood for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing CCνe -like sample.

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Figure 7.30: Pseudorapidity for true neutrinos (blue), true antineutrinos (brown), neutral
current events (orange), total atmospheric Monte Carlo (red) and SK-IV atmospheric data
(black dots) in the MultiRing CCνe -like sample.

Figure 7.31: Energy fraction of the most energetic ring for true neutrinos (blue), true
antineutrinos (brown), neutral current events (orange), total atmospheric Monte Carlo(red) and for the 2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRingCCνe -like sample.

248

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.32: Neural network output for the ν-ν separation in the MultiRing CC νe -likesample, for for true neutrinos (blue), true antineutrinos (brown), neutral current events(orange), total atmospheric Monte Carlo (red) and SK-IV atmospheric data (black dots).
The pink vertical line shows the selection point, 0.8 for the distribution, which separates
the events into two categories MultiRing ν e -like (left) and MultiRing νe -like (right).

Table 7.8 shows the relative importance of each variable in the separation method.
This shows that the neutron multiplicity is still the most relevant variable in theseparation, but, because of its lower efficiency, much less than in the Gd case shown

MC ν informationin Table 6.8.

Number of H-tagged neutrons
Number of decay-e
Distance to furthest decay-e
Time to furthest decay-e
Number of rings
Sum of all rings PID likelihood
Pseudorapidity
Energy fraction of most energetic ring

Relative separation powerν-ν separation
34.1%
22.8%
9.5%
14.5%
3.6%
11.6%
3.3%
0.7%

Table 7.8: Relative importance of each variable in the neural network for the ν-ν separationin the MultiRing CCνe -like sample.

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OSCILLATION ANALYSIS WITH SK
The sample content for MultiRing e-like events, their expected event rates for theunoscillated Monte Carlo simulation and SK-IV dataset are given in Table 7.9.
Samples

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV DataCC νe -like
64.0%
12.8%
9.9%
0.8%
12.4%
147.7
153

CC ν e -like
55.3%
29.1%
4.0%
0.4%
11.3%
356.1
322

(−)

CCDIS ν µ -like
36.8%
5.8%
34.5%
4.0%
18.9%
472.7
528

NC-like
28.9%
4.0%
31.9%
3.9%
32.1%
677.9
692

Table 7.9: Relative contents of each species for each subsample of the MultiRing CCe-likesample, after the selection, and a comparison between the number of entries predicted forthe unoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

The lesser importance of H-neutron tagging as compared to Gd-neutron tagging is
confirmed in Table 7.9. This table shows the worsening in purity of the νe and ν e -likesamples, although the impoverishment is not as sizeable as in the previous samples.
This is due to the neutron multiplicity being quite large and, thus, the behaviour of
the neutron multiplicities in both cases are similar above two.
7.2.2.4

MultiRing µ-likeIn the MultiRing sample, the homologous method, already applied to Gd-neutron
tagging in Section 6.6.3.4, is implemented for the H-neutron tagging case.
The variables for the neural network computation of the ν-ν separation likelihood
are the number of H-tagged neutrons, the number of decay-electrons, the distanceand time to the furthest decay-electron, the number of rings, the sum of all ringparticle ID likelihood, the rapidity and the energy fraction of the most energetic
ring. They are shown in Figures 7.33 to 7.40.

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7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.33: Number of H-tagged neutrons for true neutrinos (blue), true antineutrinos(brown), total atmospheric Monte Carlo (red) and for the 2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

Figure 7.34: Number of µ-decay electrons for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

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Figure 7.35: Distance to to furthest decay-e for neutrinos (blue), antineutrinos (brown),
neutral current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90
days of SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

Figure 7.36: Time to to furthest decay-e for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

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7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.37: Number of rings for true neutrinos (blue), true antineutrinos (brown), neutral
current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90 days of
SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

Figure 7.38: Sum of all ring ID likelihood for true neutrinos (blue), true antineutrinos(brown), neutral current events (orange), total atmospheric Monte Carlo (red) and for the2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

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OSCILLATION ANALYSIS WITH SK

Figure 7.39: Pseudorapidity for true neutrinos (blue), true antineutrinos (brown), neutral
current events (orange), total atmospheric Monte Carlo (red) and for the 2519.90 days of
SK-IV atmospheric dataset (black dots) in the MultiRing µ-like sample.

Figure 7.40: Energy fraction of the most energetic ring for true neutrinos (blue), true
antineutrinos (brown), neutral current events (orange), total atmospheric Monte Carlo(red) and for the 2519.90 days of SK-IV atmospheric dataset (black dots) in the MultiRingµ-like sample.

254

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSISThe obtained likelihood distribution is shown in Figure 7.41.

Figure 7.41: Neural network output for the ν-ν separation in the MultiRing µ-like sample,
for for true neutrinos (blue), true antineutrinos (brown), neutral current events (orange),
total atmospheric Monte Carlo (red) and SK-IV atmospheric data (black dots). The pinkvertical line shows the selection point, 0.762 for the distribution, which separates the events
into two categories MultiRing ν µ -like (left) and MultiRing νµ -like (right).

Table 7.10 shows the relative importance of each variable considered in the separation. Here, the same behaviour is seen as in the Gd case, in Table 6.10, thedecay-electron variables have more relevance than the neutron multiplicity. In thiscase, the H-neutron tagging has less relevance in the separation as compared to the
Gd-neutron tagging.

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Variables

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK

Number of H-tagged neutrons
Number of decay-e
Distance to furthest decay-e
Time to furthest decay-e
Number of rings
Sum of all rings PID likelihood
Pseudorapidity
Energy fraction of most energetic ring

Relative separation powerν-ν separation
25.2%
43.0%
7.6%
14.0%
5.0%
3.5%
1.0%
0.7%

Table 7.10: Relative importance of each variable in the neural network for the ν-ν separation in the MultiRing µ-like sample.

The event rates and contents for unoscillated MC and SK-IV data are summarisedin Table 7.11. Again, the purity of the samples and efficiency of the separation
are slightly diminished as compared to the Gd case, in Table 6.11. However, thisworsening is very mild due to the lesser importance, than in the previous separations,of the neutron multiplicity in favour of the number of decay-electrons.

MC true νCC νe
CC ν eCC νµCC ν µNC νMC unosc.
SK-IV Data

Samplesνµ -like ν µ -like
3.7%
1.4%
0.6%
0.2%
77.2%
70.7%
12.7%
24.7%
5.8%
3.0 %
250.6
1370.0300
886

Table 7.11: Relative contents of each species for each subsample of the MultiRing µ-likesample, after the selection, and a comparison between the number of entries predicted forthe unoscillated atmospheric Monte Carlo and the 2519.90 days of SK-IV data.

2567.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

7.2.3

Neutron-Corrected Reconstructed Neutrino Energy
for Fully Contained Samples

The energy corrections with the neutron multiplicity, explained in Section 5.5, areapplied to all the, previously defined, fully contained samples of the atmosphericanalysis for the case of H-neutron tagging.
In this case, the expression for the H-neutron corrected energy is that of Equation (7.3).

H
Erec= Evis (1 + f (H − neutron))(7.3)

The correction functions as well as the performance of the energy correction, in termsof the energy pull distributions, are shown in Appendix C.
Figures 7.42 and 7.43 show the distributions of the true, visible and neutron-correctedenergies for the distributions of the different FC samples.
Comparing Figures 7.42 and 7.43 with those for Gd in Figures 6.39 and 6.40, it isseen that the neutron correction functions for the H and Gd-tagging cases are similar. This can be further seen in Table 7.12.
The lower neutron tagging efficiency is translated into steeper neutron correction
functions (Figures C.1 and C.2) than for Gd-neutrons (Figures 6.37 and 6.38). Therefore, the information about the invisible energy is similar for the H-neutron tagging
and the Gd-neutron tagging cases, although stored at different typical neutron multiplicities.

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CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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Figure 7.42: True (green), visible (red) and corrected (blue) energy spectra of the different
FC samples for atmospheric neutrino Monte Carlo (solid lines) and the SK-IV data (dots)(1 of 2).

258

7.2. INCLUDING NEUTRON-TAGGING INFORMATION IN SK
ATMOSPHERIC NEUTRINO DATA ANALYSIS

Figure 7.43: True (green), visible (red) and corrected (blue) energy spectra of the different
FC samples for atmospheric neutrino Monte Carlo (solid lines) and the SK-IV data (dots)(2 of 2).

259

260

Mode
0.548
0.223
0.313
0.223
0.268
0.863
0.898
0.178
0.043
0.088
0.088
0.133
0.493
0.358
0.223
0.133
0.493
0.313

Skewness-0.052
0.422
0.231
0.492
0.420
-0.842-0.708
0.686
0.719
0.725
0.630
0.502
-0.127
0.248
0.518
0.660
-0.2770.129

Mode-0.013-0.048-0.118-0.083-0.1180.513
0.618-0.083-0.048-0.048-0.048-0.1180.058
0.023-0.0130.023-0.013
0.058

H
Erec
Mean RMS-0.000 0.324
0.087 0.232
0.010 0.325
0.024 0.306-0.008 0.312-0.003 0.631
0.008 0.615
0.090 0.327
0.036 0.151
0.055 0.195
0.033 0.127
0.009 0.144-0.044 0.448
0.059 0.314
0.041 0.266
0.042 0.239-0.012 0.313
0.035 0.297

Skewness
0.038
0.578
0.393
0.348
0.353
-0.817-0.990-0.023
0.553
0.526
0.630
0.883
-0.226
0.115
0.201
0.082
0.002
-0.077

Table 7.12: Mode, mean, RMS and skewness of the pull distributions for the visible energy and the H-neutron corrected energy.

Samples
SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like
SubGeV νµ -like
SubGeV ν µ -like
SubGeV 1ring-π 0 -like
SubGeV π 0 -like
MultiGeV νe -like
MultiGeV νe + ν e -like
MultiGeV ν e -like
MultiGeV νµ -like
MultiGeV ν µ -like
MultiRing NC-like
MultiRing DIS-νµ -like
MultiRing νe -like
MultiRing ν e -like
MultiRing νµ -like
MultiRing ν µ -like

Evis
Mean RMS
0.538 0.181
0.298 0.179
0.361 0.208
0.319 0.196
0.351 0.199
0.685 0.211
0.786 0.158
0.311 0.195
0.139 0.135
0.206 0.163
0.160 0.116
0.194 0.122
0.462 0.242
0.408 0.203
0.323 0.194
0.254 0.184
0.442 0.181
0.338 0.200

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7.3. OSCILLATION ANALYSIS

7.3

Oscillation Analysis

All the previous developments, due to H-neutron tagging, are applied to SK-IV for
proving their benefits to the atmospheric neutrino oscillation analysis. The oscillation
analysis is done for all SK periods, being the SK-I, SK-II and SK-III treated as in
the current official SK analysis, described in [Pik12]. For the implementation of the
new sample definition and the neutron-corrected energy, the SK analysis tools are
modified to accommodate them. The sensitivity of this analysis is computed, as
explained previously in Section 6.6.5.1, by the binned χ2 method.
First, in Section 7.3.1 all the systematic errors involved in this analysis, including
those associated to the new sample selection and energy correction for the SK-IV
are described. Then, an oscillation study is performed, in Section 7.3.2, for all
SK periods assuming their corresponding exposure times, shown in Table 7.1. The
current official analysis is applied to SK-I, SK-II and SK-III, and the new sample
selection and energy corrections of Section 7.2, only for the SK-IV phase, where Hneutron tagging is available.
In Section 7.3.3, a global oscillation analysis of the actual atmospheric neutrino data
including the neutron tagging tools developed for SK-IV, is performed.

7.3.1

Systematic Errors

In this analysis, 77 systematic error sources are considered. Some of them are common to all SK periods, such as those associated to the neutrino flux (except thatassociated with the solar activity as it is time-dependent) and interactions. The uncertainty in the oscillation parameters is also considered as a systematic error sourceand shared by all SK phases as well. Other sources of systematics depend on the per-261

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK
formance of the detectors and therefore, on the SK phase, like the errors induced by
the reduction and reconstruction of events. Finally, three new systematic errors aredefined, two of them account for the uncertainty in the new sample selection methods, and the other for the uncertainty in neutron-corrected energy. These systematic
errors affect only the fully contained data of SK-IV.

7.3.1.1

Neutrino Flux Errors

The systematic uncertainties related to the neutrino fluxes are shared by all SK
phases and summarised in Table 7.13.
Neutrino flux Errors
Eν < 1 GeV
Absolute normalisation
Eν > 1 GeV
Eν < 1 GeV
ν/ν
1 GeV < Eν < 10 GeV
Eν > 10 GeV
Eν < 1 GeV
ν e /νe
1 GeV < Eν < 10 GeV
Eν > 10 GeV
Eν < 1 GeV
ν µ /νµ1 GeV < Eν < 10 GeV
Eν > 10 GeV
Up/down ratio
Horizontal/vertical ratio
κ/π ratio
Neutrino path length
FC MultiGeV
Relative normalisation
PC, UpMu stop
Matter effect
SK-I
SK-II
Solar activity
SK-III
SK-IV

σ (%)
25.0
15.0
2.0
3.0
5.0
5.0
5.0
8.0
2.0
6.0
15.0
1.0
1.0
10.0
10.0
5.0
5.0
6.8
20.0
50.0
20.0
10.0

Table 7.13: Systematic uncertainties for the atmospheric oscillation analysis related to theneutrino flux.

262

7.3. OSCILLATION ANALYSIS
Absolute Normalisation
This is the uncertainty of the absolute neutrino flux and calculated in [Sanuki07],
taking into account the atmospheric pion and kaon production in the hadronic interaction model, the hadronic interaction cross sections and the atmospheric density
profile. The systematic error is divided into two energy regions, below and above 1
GeV, as seen in Figures 7.44 and 7.45.

Figure 7.44: Relative uncertainty of each factor entering the computation of the neutrino
flux. δπ , δκ , δσ , and δair are the uncertainties on pion production, kaon production,
hadronic interaction cross sections and atmospheric density profile.

Figure 7.45: Calculated uncertainty of the absolute normalisation of the neutrino flux as afunction of the neutrino energy.

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OSCILLATION ANALYSIS WITH SK
Neutrino Flux Ratios
The relative amount of muon neutrinos compared with the amount of electron neutrinos is analysed for different flux models. In SK, the so called Honda flux [Honda11]
is used along with other models like the FLUKA [Battistoni03] and Bartol fluxes[Barr04]. This procedure is done also for the rest of the flux ratios, ν µ /νµ and ν e /νe .
Figures 7.46 to 7.48 show the ratio for FLUKA and Honda models for each of theneutrino flux ratios.

Figure 7.46: The (νµ + ν µ )/(νe + ν e ) ratio between the FLUKA and Honda models (blacksolid line) and between Bartol and Honda models (red dashed line).

Figure 7.47: The ν µ /νµ ratio between the FLUKA and Honda models (black solid line) andbetween Bartol and Honda models (red dashed line).

2647.3. OSCILLATION ANALYSIS

Figure 7.48: The ν e /νe ratio between the FLUKA and Honda models (black solid line) andbetween Bartol and Honda models (red dashed line).

κ/π Ratio
At energies below 10 GeV, neutrino production is mainly due to pion decay and as
the cosmic ray energy increases the neutrino production is dominated by kaons. This
uncertainty is estimated using data from [Ambrosini98].
Solar Activity
The 11-year solar cycle slightly changes the Earth’s magnetic field, affecting thecosmic ray flux. The uncertainty of the solar cycle is taken to be ±1 year and it istranslated into a neutrino flux systematic error.
Neutrino Production
This systematic error deals with the height at which the neutrinos are produced.
This affects the length travelled by neutrinos and therefore, the oscillation probability. This error is negligible for upward-going neutrinos compared to the matter effect265

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
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OSCILLATION ANALYSIS WITH SK
error. The atmosphere density uncertainty is the main reason for this error and estimated by comparing the US-standard 76 and the MSISE90 experiments [Hedin91].
Matter Effect
The oscillation probability of neutrinos passing though the Earth depend on its electron density. The exact composition of the Earth’s layers is of great importance. The
different composition and its uncertainty is propagated to the oscillation probability
uncertainty and used as a systematic error.
7.3.1.2

Neutrino Interaction Errors

7.14 shows the errors related to the neutrino interactions. Some of the largest uncertainties can be found in this group due to the little data available from neutrino
cross-section experiments.
Neutrino interaction errors
Axial massCC ντ cross-section
CCQE cross-section ratio
Coherent π production
DIS cross-section model (Eν < 10 GeV)DIS cross-section
DIS Q2 spectrum (W < 1.3 GeV/c2 )DIS Q2 spectrum (W > 1.3 GeV/c2 )Hadronic simulation
NC/CC ratio
Single π production (ν/ν ratio)
Single π production (π 0 /π ± ratio)
Single meson production cross-section
Decay-electron tagging (from π interaction)

σ (%)
10.0
25.0
10.0
100.0
10.0
5.0
10.0
10.0
10.0
20.0
10.0
40.0
20.0
10.0

Table 7.14: Systematic uncertainties for the atmospheric oscillation analysis related to theneutrino interactions.

266

7.3. OSCILLATION ANALYSISCCQE Cross-Section
For modelling the CCQE cross-section in SK, the Fermi-gas model in [Smith72] isused. For the estimation of the systematic uncertainty, the difference between thismodel and [Nieves04] is evaluated.

Axial Mass
The axial mass used in the SK Monte Carlo simulation is MA = 1.21 GeV, andfor accounting for the uncertainty on this value various experimental results are
considered, [Gran06, Nieves12].

Single Meson Production
The estimate of this error is done by comparing the 1π ± production experimental
measurements. For the case of 1π 0 production and due to the lack of enough measurements, the experimental results are also compared with the model in [Hernandez07].

Coherent Pion Production
This uncertainty is set to 50% due to the difference between the Rein&Sehgal modeland experimental data [Nakajima11] for NC and CC νe interactions. There is noexperimental measurement for CC νµ coherent pion production, so the uncertainty
is taken to be 100%.

Deep Inelastic Scattering
The deep inelastic scattering cross-section expectations agree with experiments
within 5%. This uncertainty becomes larger at low energies, making necessary an
additional error is estimated by comparison to the CKMT model [Capella01].

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OSCILLATION ANALYSIS WITH SK
Other Cross-Sections
The Hagiwara model is considered for the ντ CC cross-section [Hagiwara03].

7.3.1.3

Event Reduction Errors

Table 7.15 shows the errors related to the event reduction, their values and the valueof  for the best fit point.

Reduction errors
FC reduction
Fiducial volume
Non-ν background (µ-like)
Non-ν background (SubGeV e-like)
Non-ν background (MultiGeV 1ring e-like)
Non-ν background (MultiGeV MultiRing e-like)
FC-PC separation
PC reduction
PC stop-through separation (barrel)
PC stop-through separation (bottom)
PC stop-through separation (top)
UpMu stop-through separation
UpMu reduction
UpMu stop background
UpMu stop energy cut
UpMu through path cut
UpMu Non-showering background
UpMu Showering–non-showering separation
UpMu Showering background

SK-I
σ
0.2
2.0
1.0
1.0
13.2
12.1
0.6
2.4
7.0
22.7
46.1
0.4
1.0
16.0
0.9
1.5
18.0
3.4
18.0

SK-II
σ
0.2
2.0
1.0
1.0
38.1
11.1
0.5
4.8
9.4
12.9
19.4
0.6
1.0
21.0
1.3
2.3
14.0
4.4
14.0

SK-III
σ
0.8
2.0
1.0
1.0
26.7
11.4
0.9
0.5
28.7
12.1
86.6
0.4
1.0
20.0
2.0
2.8
24.0
2.4
24.0

SK-IV
σ
0.3
2.0
1.0
1.0
17.6
11.6
0.9
1.0
8.5
6.8
40.3
0.6
1.0
17.0
1.7
1.5
17.0
3.0
24.0

Table 7.15: Systematic uncertainties for the atmospheric oscillation analysis related to theevent reduction for all SK periods.

268

7.3. OSCILLATION ANALYSIS

Fiducial Volume
This systematic uncertainty takes into account the migration of events because of
the fiducial volume cut.

FC, PC, UpMu Reductions
The reduction uncertainties are estimated by comparing the distributions of each cut
variable for the observed data and Monte Carlo and the remaining contamination
background.
The separation between FC and PC and between UpMu stopping and through-going
muons is done using the number of OD hits. For this, data and Monte Carlo distributions are compared to estimate the uncertainty associated to these migrations.

UpMu Showering and Non-Showering Backgrounds
UPMU non-showering and showering events are separated by using the difference
between the observed charge and expected charge of non-showering muons and theuncertainty is estimated by comparing this distribution for data and Monte Carlo.

7.3.1.4

Event Reconstrucion Errors

Table 7.16 shows the errors related to the event reconstruction.

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OSCILLATION ANALYSIS WITH SK
Reconstruction errors
SingleRing PID
MultiRing PID
Ring separation
SingleRing π 0 selection
TwoRing π 0 selection
Decay-electron tagging efficiency
Neutron tagging efficiency
Energy calibration
Energy calibration up/down ratio

SK-I
σ
1.0
10.0
10.0
10.0
5.6
10.0
–
1.1
0.6

SK-II
σ
1.0
10.0
10.0
10.0
4.4
10.0
–
1.7
0.6

SK-III
σ
1.0
10.0
10.0
10.0
5.9
10.0
–
2.7
1.3

SK-IV
σ
1.0
10.0
10.0
10.0
5.6
(10.0)(10.0)
2.3
0.3

Table 7.16: Systematic uncertainties for the atmospheric oscillation analysis related to theevent reconstruction for all SK periods.

The ring separation is based on a likelihood distribution and its uncertainty is estimated by comparing data and Monte Carlo distributions. In a similar fashion, theparticle identification systematic errors is extracted from the comparisons, between
data and Monte Carlo, of the likelihood distributions used for separating between
e-like and µ-like events. The energy calibration error is estimated by using the calibration data from .
The error associated to the decay-electron tagging for SK-IV is also of 10%, but it
will be treated differently in the Section 7.3.1.5 because it takes part in the sample
separation methods, having different impact on each of the newly defined SK-IV
samples. In a similar manner, there is only neutron tagging at SK-IV and is of 10%,but its impact will be also analysed for each sample in Section 7.3.1.5.

7.3.1.5

Fully Contained Event Selection Errors

This systematic errors are newly calculated specifically for the new sample selectionof fully contained events in SK-IV. These uncertainties come from the event migration

2707.3. OSCILLATION ANALYSIS

between samples after the uncertainty in the variables used for the sample selection
is propagated.
In the case of samples selected by applying cuts on the number of neutrons and decayelectrons, the systematic uncertainty is induced by the propagation in the tagging
efficiency of neutrons and decay-electrons, which are both of 10% [Irvine14].
N (ntag, +10%) − N (ntag, −10%)
2N (ntag)(7.4)

N (decay − e, +10%) − N (decay − e, −10%)
2N (decay − e)(7.5)

σ ntag =σ decay−e =On the other hand, for those samples where multivariate methods are applied forthe construction of a likelihood distribution, and, in addition to the errors inducedby neutrons and decay-electrons (principal variables for the sample selection), thelikelihood distributions are compared for data and Monte Carlo. This last estimate
uses two parameters to shift (β) and smear (α) the Monte Carlo distribution to builda χ2 map. The systematic error is estimated as the relative variation of the numberof events in the samples between the point with minimum χ2 value and the point at
1σ (i.e. ∆χ2 =2.3).
σ shif t =N (bestf it) − N (1σ)
N (bestf it)(7.6)

SubGeV e-likeFigures 7.49 and 7.50 below show the nominal and ±10% distributions for theneutron and decay-electron multiplicities.

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Figure 7.49: Number of H-tagged neutrons for the default Monte Carlo, plus
and minus 10% uncertainty in the tagging efficiency and SK-IV atmospheric
data (black dots) for the SubGeV e-likesample.

Figure 7.50: Number of decay-electrons
for the default Monte Carlo, plus andminus 10% uncertainty in the tagging
efficiency and SK-IV atmospheric data
(black dots) for the SubGeV e-like sample.

Table 7.17 shows the estimated systematic errors associated to the SubGeV e-likesample selection. The SubGeV νe sample does not require any cut on the number ofneutrons and, therefore, the associated systematic is null.

SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like

σ ntag
0.0%
-1.5%
5.8%

σ decay−e
8.2%
-0.8%
-1.3%

Table 7.17: Systematic uncertainties associated to the H-neutron and decay-electron tagging
in the selection of the three SubGeV e-like samples.

MultiGeV e-like
The results for these samples are very similar to those from the SubGeV e-like case.
The ±10% variation and the nominal distributions for the number of H-tagged
neutrons and for the number of decay-electrons are shown in Figures 7.51 and 7.52.

272

7.3. OSCILLATION ANALYSIS

Table 7.18 shows the estimated systematic errors associated to this sample selection.

Figure 7.51: Number of H-tagged neutrons for the default Monte Carlo, plus
and minus 10% uncertainty in the tagging efficiency and SK-IV atmospheric
data (black dots) for the MultiGeV e-likesample.

Figure 7.52: Number of decay-electrons
for the default Monte Carlo, plus andminus 10% uncertainty in the tagging
efficiency and SK-IV atmospheric data
(black dots) for the MultiGeV e-like sample.

MultiGeV νe -like
MultiGeV νe ν e -like
MultiGeV ν e -like

σ ntag
0.0%
-2.1%
4.0%

σ decay−e
7.3%
-1.8%
-3.6%

Table 7.18: Systematic uncertainties associated to the H-neutron and decay-electron tagging
in the selection of the three MultiGeV e-like samples.

SubGeV µ-likeFigures 7.53 and 7.54 show the nominal and ±10% distributions for the neutron anddecay-electron multiplicities for SubGeV µ-like events.

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Figure 7.53: Number of H-tagged neutrons for the default Monte Carlo, plus
and minus 10% uncertainty in the tagging efficiency and SK-IV atmospheric
data (black dots) for the SubGeV µ-likesample.

Figure 7.54: Number of decay-electrons
for the default Monte Carlo, plus andminus 10% uncertainty in the tagging
efficiency and SK-IV atmospheric data
(black dots) for the SubGeV µ-like sample.

The estimated systematic errors for both defined samples are summarised inTable 7.19.

SubGeV νµ -like
SubGeV ν µ -like

σ ntag1.2%
5.2%

σ decay−e
-1.7%
7.5%

Table 7.19: Systematic uncertainties associated to the H-neutron and decay-electron tagging
in the selection of the two SubGeV µ-like samples.

MultiGeV µ-like
The results for these samples are very similar to those from the SubGeV µ-like case.
The neutron and decay-electron multiplicities are shown in Figures 7.55 and 7.56.

274

7.3. OSCILLATION ANALYSIS

Figure 7.55: Number of H-tagged neutrons for the default Monte Carlo, plus
and minus 10% uncertainty in the tagging efficiency and SK-IV atmospheric
data (black dots) for the MultiGeV µ-likesample.

Figure 7.56: Number of decay-electrons
for the default Monte Carlo, plus andminus 10% uncertainty in the tagging
efficiency and SK-IV atmospheric data
(black dots) for the MultiGeV µ-like sample.

The estimated systematic errors are presented in Table 7.20.

MultiGeV νµ -like
MultiGeV ν µ -like

σ ntag-1.4%
5.0%

σ decay−e
-1.7%
6.6%

Table 7.20: Systematic uncertainties associated to the H-neutron and decay-electron tagging
in the selection of the two MultiGeV µ-like samples.

MultiRing e-likeIn this group of samples three neural networks are used for the separation.
The first one is the NC-CC separation. Its corresponding likelihood distribution isshown in Figure 7.57 for the uncertainty in the neutron and decay-electron tagging,and for the 1σ point from the best fit with data in the χ2 -map. In Figure 7.57, thelikelihood distributions for all cases are presented.
With all the previous, one can extract the systematic errors from each method.

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OSCILLATION ANALYSIS WITH SK

Figure 7.57: Neural network output variations for estimating systematic errors for NC-CC
separation in the MultiRing e-like sample.

Table 7.21 shows that the neutron and decay-electron tagging errors are larger thanthose from obtained from the χ2 -map and, hence, considered as the systematic
errors associated to this separation.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
5.5%
-2.7%
-1.3%
-0.4%

σ decay−e
-0.5%
0.4%
-0.0%
-0.0%

σ shif t
-3.9%
2.3%
1.1%
0.4%

Table 7.21: Systematic uncertainties associated to the H-neutron, decay-electron tagging
and shift and smearing of the Monte Carlo simulation in the selection of the four MultiRing
e-like samples due to the NC-CC separation.

(−)

(−)

For the second step, the CC-DIS ν µ -CC ν e separation, the same procedure applies.
The neural network output for all the cases considered is shown in Figure 7.58.
In this case, there are only three of the four samples affected by this uncertainty
and, again, the estimate with the larger value for the systematic error is that due to276

7.3. OSCILLATION ANALYSIS

Figure 7.58: Neural network output variations for estimating systematic errors for νµ − νeseparation in the MultiRing e-like sample.

the neutrons and decay-electrons, as shown in Table 7.22.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
1.2%
-1.0%
-0.3%

σ decay−e
0%
3.4%
-3.8%
-0.1%

σ shif t
0%
0.9%
-1.0%
-0.1%

Table 7.22: Relative variation of contents for the three MultiRing e-like samples due to the
induced systematics of the νµ − νe separation.

The final step splits the remaining events into neutrino-like and antineutrino-like. Its
likelihood, taking into account the neutron and decay-electron tagging uncertainties
and that 1σ away from the best fit point of Monte Carlo to the data, is plotted in
Figure 7.59.

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Figure 7.59: Neural network output variations for estimating systematic errors for νe − ν eseparation in the MultiRing e-like sample.

Because the separation is much less efficient than in the previous sample selections,the effect of the uncertainties is also significantly smaller. This can be found in
Table 7.23.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
0%
0.8%
-0.5%

σ decay−e
0%
0%
3.5%
-2.2%

σ shif t
0%
0%
1.4%
-1.1%

Table 7.23: Relative variation of contents for the three MultiRing e-like samples due to the
induced systematics of the νe − ν e separation.

MultiRing µ-likeIn this case, a neural network is also considered, but this time with only one step.
The procedure is the analogous as in the paragraph before and the separation
likelihood distribution is plotted in Figure 7.60.

278

7.3. OSCILLATION ANALYSIS

Figure 7.60: Neural network output variations for estimating systematic errors for νµ − ν µseparation in the MultiRing µ-like sample.

The systematic uncertainties associated to this samples selection are shown in
Table 7.24.

MultiRing νµ -like
MultiRing ν µ -like

σ ntag-0.1%
0.2%

σ decay−e
3.0%
-3.4%

σ shif t
-0.2%
0.3%

Table 7.24: Relative variation of contents for the three MultiRing e-like samples due to the
induced systematics of the νµ − ν µ separation.

Summary
For MultiRing samples, the estimated errors induced by the neutron tagging and the
decay-electron tagging efficiency uncertainties are larger than that compute by theχ2 -map method. Therefore, the formers are taken, for all cases, as the two systematic
sources for the sample selection.
Table 7.25 summarises the previous study for the estimation of the systematic errors
for the sample selection for fully contained events in SK-IV, and that will be included
to the oscillation analysis.

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SK-IV FC samples

FC event selection errors
SK4 SubGeV νe -like
SK4 SubGeV νe + ν e -like
SK4 SubGeV ν e -like
SK4 SubGeV νµ -like
SK4 SubGeV ν µ -likeSK4 MultiGeV νe -likeSK4 MultiGeV νe + ν e -likeSK4 MultiGeV ν e -likeSK4 MultiGeV νµ -likeSK4 MultiGeV ν µ -likeSK4 MultiRing NC-likeSK4 MultiRing DIS-νµ -likeSK4 MultiRing νe -likeSK4 MultiRing ν e -likeNC sep.
DISmu sep.
NC sep.
DISmu sep.
ν − ν sep.
NC sep.
DISmu sep.
ν − ν sep.

SK4 MultiRing νµ -likeSK4 MultiRing ν µ -likeσ (%)
Neutron tagging Decay-e tagging
0.0
8.2
-1.5
-0.8
5.8
-1.3
1.2
-1.7
5.2
7.5
0.0
7.3
-2.1
-1.8
4.0
-3.6
-1.4
-1.7
5.0
6.6
5.5
-0.5
-2.7
0.4
1.2
3.4
-1.3
0.0
-1.0
3.8
0.8
3.5
-0.4
0.0
-0.3
-0.1
-0.5
2.2
-0.1
3.0
0.2
-3.4

Table 7.25: Sample selection systematic errors for the SK-IV atmospheric oscllation analysis.

7.3.1.6

Neutron Energy Corrections for Fully Contained Events

As the correction function depends strictly on the neutron multiplicity, the relativechange in its magnitude is computed to include it as an additional systematic error
source. As with the systematics treated before, this only applies to SK-IV fully
contained events.

∆f =

H
H
Erec
(H-neutrons + 10%) − Erec
(H-neutrons + 10%)
H (H-neutrons)
Erec

280

(7.7)

7.3. OSCILLATION ANALYSISThe quantity ∆f will be taken to calculate the migration of events between bins,
which will be the actual systematic uncertainty due to the neutron energy corrections.

SK-IV FC samples

Neutron energy correction errors
SK4 SubGeV νe -like
SK4 SubGeV νe + ν e -like
SK4 SubGeV ν e -like
SK4 SubGeV 1ring π-like
SK4 SubGeV νµ -like
SK4 SubGeV ν µ -like
SK4 SubGeV π-likeSK4 MultiGeV νe -likeSK4 MultiGeV νe + ν e -likeSK4 MultiGeV ν e -likeSK4 MultiGeV νµ -likeSK4 MultiGeV ν µ -likeSK4 MultiRing NC-likeSK4 MultiRing DIS-νµ -likeSK4 MultiRing νe -likeSK4 MultiRing ν e -likeSK4 MultiRing νµ -likeSK4 MultiRing ν µ -like∆f (%)
0.8
0.0
1.3
0.5
1.5
1.1
1.3
0.9
0.0
1.0
0.3
0.6
1.6
0.9
0.7
0.7
1.1
0.9

Table 7.26: Relative change in the neutron energy correction functions due to the neutron
tagging uncertainty.

7.3.2

Oscillation Sensitivity Study

The oscillation analysis will be done for the whole SK dataset, being only able toapply the neutron improvement discussed earlier in SK-IV.
The binning for the analysis in cosine of the zenith angle and in Gd-neutron corrected has a total of 1221 bins, 520 for each of SK-I, SK-II and SK-III, merged in
the analysis, and 701 for the SK-IV period.

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The true oscillation parameters used for the sensitivity studies are those alreadyused for the SuperK-Gd atmospheric oscillation depicted in Table 6.13.
Two sensitivity studies are performed, one assuming true normal hierarchy and theother for the inverted mass ordering. The χ2 distributions, in the normal hierarchy
scenario, for ∆m232 , sin2 θ23 and δCP are shown in Figures 7.61 to 7.63, respectively.

Figure 7.61: χ2 distributions for ∆m232 assuming normal mass hierarchy and for H-tag(green) analysis and current official SK (black) analysis. The horizontal dashed lines represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1, 2.71
and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

282

7.3. OSCILLATION ANALYSIS

Figure 7.62: χ2 distributions for sin2 θ23 assuming normal mass hierarchy and for Htag (green) analysis and current official SK (black) analysis. The horizontal dashed lines
represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1,
2.71 and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

Figure 7.63: χ2 distributions for δCP assuming normal mass hierarchy and for H-tag(green) analysis and current official SK (black) analysis. The horizontal dashed lines represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1, 2.71
and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

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Assuming nature is inverted hierarchy, the analogous χ2 distributions are shownin Figures 7.64 to 7.66.

Figure 7.64: χ2 distributions for ∆m232 assuming inverted mass hierarchy and for H-tag(green) analysis and current official SK (black) analysis. The horizontal dashed lines represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1, 2.71
and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

Figure 7.65: χ2 distributions for sin2 θ23 assuming inverted mass hierarchy and for Htag (green) analysis and current official SK (black) analysis. The horizontal dashed lines
represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1,
2.71 and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

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7.3. OSCILLATION ANALYSIS

Figure 7.66: χ2 distributions for δCP (left) assuming inverted mass hierarchy and for Htag (green) analysis and current official SK (black) analysis. The horizontal dashed lines
represent the 68%, 90% and 99% confidence levels, which correspond to χ2 values of 1,
2.71 and 6.64, respectively. The dataset corresponds to that presented in Table 7.1.

The H-tag analysis improves the sensitivity to the neutrino mass ordering andthe CP phase. The comparison between the official and H-tag analyses can besummarised in Table 7.27.

∆χ2 (N H − IH)
δCP fraction
over 1σStandard(true NH)
-2.78

H-tag
(true NH)
-3.71

Standard(true IH)
1.51

H-tag
(true IH)
1.89

33.2%

38.7%

27.7%

33.5%

Table 7.27: Mass hierarchy sensitivities and fraction of δCP more than 1σ away from thebest fit point, assuming as true, normal (left) and inverted (right) hierarchies. Comparison
between official SK analysis and H-tag analysis.

285

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK
The sensitivity to the mass hierarchy as function of the value of sin2 θ23 assuming
two scenarios, true normal hierarchy and true inverted hierarchy, is displayed in
Figure 7.67. This plots shows that the H-tag analysis improves the sensitivity to therejection of the wrong mass hierarchy for all cases, but specially for large values ofsin2 θ23 .

Figure 7.67: Wrong mass hierarchy sensitivity as function of the θ23 oscillation parameterusing atmospheric neutrinos for the H-neutron tagging (green) and current SK standard(black) analyses. The analysis assumes both possible mass orderings, normal (solid lines)
and inverted (dashed), and fixed δCP = 4.19 and |∆m232 |= 0.0025 eV2 . The horizontal
dashed lines represent the 68%, 90% and 99% confidence levels, which correspond to χ2values of 1, 2.71 and 6.64, respectively. The exposure time is considered to be 2519.9 days,
the same as currently for the SK-IV dataset and shown in Table 7.1, and for the oscillation
parameters listed in Table 6.13.

7.3.3

Data Fit Results

The Monte Carlo simulation is fitted to the dataset from SK-I to SK-IV (summarised in Table 7.1), letting fixed sin2 θ13 = 0.0219, ∆m221 = 7.65 · 10−5 eV2 and286

7.3. OSCILLATION ANALYSIS
sin2 θ12 = 0.309.
At every point in the oscillation parameter space, a fit was performed over thesystematic errors to find the minimum χ2 value. The overall minimum χ2 is chosen
as the best fit point. This is performed twice, for normal and inverted neutrino mass
hierarchies. The obtained χ2 distributions for the sin2 θ23 , ∆m232 and δCP oscillation
parameters are displayed for both neutrino hierarchies and for the H-tag analysis in
Figures 7.68 to 7.70, respectively. The best fit points and the 90% confidence level
allowed ranges, for all the fitted parameters and both mass orderings are summarisedin Table 7.28. The 90% confidence levels are defined for each mass hierarchies (MH)at χ2 = χ2min (M H) + 2.71.

Figure 7.68: ∆χ2 = χ2 − χ2min distributions for ∆m232 for SK atmospheric neutrino dataset
and for H-tag analysis. The horizontal dashed lines represent the 68%, 90% and 99%
confidence levels, which correspond to χ2 values of 1, 2.71 and 6.64, respectively. The
dataset corresponds to that presented in Table 7.1.

287

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK

Figure 7.69: ∆χ2 = χ2 − χ2min distributions for sin2 θ23 for SK atmospheric neutrino
dataset and for H-tag analysis. The horizontal dashed lines represent the 68%, 90% and
99% confidence levels, which correspond to χ2 values of 1, 2.71 and 6.64, respectively. The
dataset corresponds to that presented in Table 7.1.

Figure 7.70: ∆χ2 = χ2 − χ2min distributions for δCP (left) for SK atmospheric neutrino
dataset and for H-tag analysis. The horizontal dashed lines represent the 68%, 90% and
99% confidence levels, which correspond to χ2 values of 1, 2.71 and 6.64, respectively. The
dataset corresponds to that presented in Table 7.1.

288

7.3. OSCILLATION ANALYSIS
Analysis
SK-I – SK-IV
H-tag (dof=1219)

Hierarchy
NH
IH

χ21333.631338.25

sin2 θ23
0.438+0.199−0.0500.438+0.187−0.050|∆m232,31 | (eV2 )0.00217+0.00019−0.00017
0.00217+0.00018−0.00025

δCP
4.19+1.38−2.09
3.84+1.41−2.09

Table 7.28: Best fit points and 90% C.L. allowed ranges for sin2 θ23 , ∆m232 and δCP of the
H-tag oscillation analysis on the SK-I to SK-IV atmospheric neutrino dataset.

The results show a sizeable indication for values of δCP different from zero and apreference for neutrino normal mass hierarchy.

∆χ2 (N H − IH) = χ2min (N H) − χ2min (IH) = −4.6

(7.8)

The results for the θ23 parameter offer no clear conclusion about the octant determination. The minimum χ2 is in the first octant, but there is a local minimum inthe second octant and less than 1σ away.
In order to compare these results with those obtained with the standard analysis,Table 7.29 lists the best fit values and 90% confidence level ranges, and the mass hierarchy preference for both the H −tag and the current official analyses, [Moriyama16].

Analysis
SK-I – SK-IV
H-tag (χ2 /dof=1.09)
SK-I – SK-IV
Standard (χ2 /dof=1.11)∆χ2 (N H − IH)

sin2 θ23|∆m232,31 | (eV2 )

δCP

4.6

0.438+0.199−0.0500.00217+0.00019−0.00017+1.38
4.19−2.09

4.3

0.575+0.048−0.1670.00250+0.00030−0.00038+2.49
4.19−2.48

Table 7.29: Best fit points values and 90% C.L. ranges for sin2 θ23 , ∆m232 and δCP with the
H-tag and current official oscillation analyses for the SK-I to SK-IV atmospheric neutrino
dataset.

289

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK
The results with the H-neutron tagging improvements are similar to those fromthe current official analysis, being the value of χ2 /dof slightly lower for the H-tag
analysis. The zenith angle distributions for the data and the oscillated Monte Carloprediction can be found in Figure 7.71, for the SK-1, SK-II and SK-III combined
samples, and in Figure 7.72, for the SK-IV samples.
Nevertheless, although compatible, there exists a tension between the best fit values
from both analyses for the θ23 and |∆m232,31 | parameters. The H-tag analysis prefers
the first octant, whereas, in the current official analysis, the best fit occurs in thesecond octant. Concerning ∆m232 , the H-tag analysis indicates a lower value than
the standard analysis, existing between them, a tension a little bigger than 1σ.
The best fit value for the δCP and mass hierarchy preference agree in the twoanalyses, being the former better constrained in the H-tag analysis.

Also, thenormal mass hierarchy preference is enhanced, in the H-tag, by 0.3 units of χ2 ascompared with the current official analysis.
The results presented are still preliminary and further systematic studies are ongoing.

2907.3. OSCILLATION ANALYSIS

200

Sub-GeV e-like 1-dcy e

Sub-GeV e-like 0-dcy e

Sub-GeV µ -like 0-dcy e

Sub-GeV µ -like 1-dcy e

200

Up Stop µ

500
500

200

100

100

0

200

0

0

Multi-GeV e-like νe

Sub-GeV π0-like 1-R0Multi-GeV e-like νe0

PC StopNon-showering µ

200

500
50

50
100
100

0

0

0

Multi-Ring e-like νe

Sub-GeV µ -like 2-dcy e
100

100

50

50

0

0

100

0

Multi-Ring e-like νe0Showering µ

PC Thru
200

200
50

100

0

0

0
-1

-0.5

0

200

Sub-GeV π0-like M-R

Multi-GeV µ -like

Multi-Ring µ -like

Multi-Ring Unclassified

200

400
200

100
200

0

100

100

500

1000

lepton momentum (MeV)

0
-1

0

cos zenith

1

0
-1

0

cos zenith

1

0
-1

0

cos zenith

1

cos zenith

Figure 7.71: Zenith angle and lepton momentum (only for samples with one bin in zenith
angle, the SubGeV e-like 1decay-e, the SubGeV µ-like 2decay-e, the SubGeV 1 ring π 0 like and the SubGeV π 0 -like samples) distributions for the SK-I, SK-II and SK-III merged
atmospheric data (black dots) and oscillated Monte Carlo with the parameters at the best
fit point assuming normal (light blue) and inverted hierarchy (orange).

291

CHAPTER 7. NEUTRON-TAGGING WITH HYDROGEN IN
SUPER-KAMIOKANDE IV: GLOBAL ATMOSPHERIC NEUTRINO
OSCILLATION ANALYSIS WITH SK

Figure 7.72: Zenith angle and lepton momentum (only for samples with one bin in zenith
angle, the SubGeV 1 ring π 0 -like and the SubGeV π 0 -like samples) distributions for the
SK-IV atmospheric data (black dots) and oscillated Monte Carlo with the parameters at
the best fit points for normal (light blue) and inverted hierarchy (orange).

292

8. Conclusions (English)
Neutron tagging is a major improvement in neutrino experimental physics withwater-Čerenkov detectors.
Super-Kamiokande has approved an upgrade consisting of dissolving a gadolinium
salt to 0.2% in its water; with it, SK will be capable of tagging neutrons at a very
high efficiency (∼80%). The project is called SuperK-Gd (former GADZOOKS!).
The EGADS demonstrator has proven the feasibility of the project. In this Doctoral Work we have contributed extensively to the success of EGADS: mainly atconstruction, at calibrations and at continous monitoring.
We have developed a highly efficient and realistic Gd-neutron tagging detection
method for SuperK-Gd based on the current operation of the Super-Kamiokande
detector.
We have thoroughly studied potential radioactive contamination in the system,
mainly in the Gd salt, and its impact on relevant measurements by SuperK-Gd:
namely the diffuse supernova neutrino background, the neutrinos from the Siburning phase of a close-enough star, the characteristics of reactor neutrinos andthe measurement of the solar neutrino spectrum at very low energy.
We have developed a series of algorithms based on Gd-neutron tagging that discriminate neutrino from antineutrino interactions in SuperK-Gd rather efficiently.
Further, similar algorithms have been created to characterise CC and NC neutrino

293

CHAPTER 8. CONCLUSIONS (ENGLISH)

interactions.
We have developed a second-step in the reconstruction of the interacting neutrino’s
energy based on the neutron multiplicity measured in the final sate by the Gdneutron tagging. It reduces very significantly the amount of non-visible energy, thus
providing a better match between the measured and the true energy of the neutrino.
We have studied the impact of Gd-neutron tagging in a global oscillation analysis of atmospheric neutrinos by SuperK-Gd.

The global sensitivity study, atsin2 θ23 = 0.575, δCP = 4.189 and ∆m232 = 0.0025 eV2 , for the current 2519.90 daysof SK-IV, shows that the inverted mass hierarchy sensitivity rejection is improved
as compared with the current official analysis (2.7 units of χ2 with Gd, 1.6 current
official). In addition, the sensitivity to the δCP phase is similarly improved.
Corresponding studies have been performed for the T2K long-base-line experiment,
and for the next generation Hyper-Kamiokande experiment with Gd loading, showing also improvements.
The current phase of Super-Kamiokande, SK-IV, has already some, low efficiency,
neutron tagging capability by deuterium production from neutron captures onhydrogen. In this thesis, we have adapted the Gd-neutron tagging improvements
for atmospheric oscillation analysis, to the currently available H-neutron tagging
in Super-Kamiokande. This proves the significant improvements neutron tagging
in water-Čerenkov detectors bring to the atmospheric neutrino oscillation analysis,
providing better constraints on the neutrino mass hierarchy.
The global oscillation analysis of SK data shows a preference for normal hierarchyof 4.6 units of χ2 (Note: results are preliminary), whereas in the current official
analysis the preference in 4.3 units of χ2 .

294

After the more than twenty years of extremely successful operation of the SuperKamiokande experiment, the SuperK-Gd project will bring already in the next years
a wealth of new and exciting physics measurements.

295

9. Conclusiones (Spanish)
La detección de neutrones es una gran mejora en la fı́sica experimental de neutrinos
en detectores de agua-Čerenkov.
Super-Kamiokande ha aprobado una actualización consistente en disolver una sal
de gadolinio al 0,2% en su agua; Con él, SK será capaz de detectar neutros con una
eficiencia muy alta (∼80%). Este es el proyecto SuperK-Gd (antes GADZOOKS!).
El prototipo EGADS ha demostrado la factibilidad del proyecto. En este trabajo
doctoral se ha contribuido ampliamente al éxito de EGADS: principalmente en laconstrucción, en las calibraciones y en el seguimiento continuo de su operación.
Hemos desarrollado un método de reconstrucción altamente eficiente y realista deneutrones capturados por Gd para SuperK-Gd basado en la operación actual deldetector Super-Kamiokande.
Se ha estudiado minuciosamente la posible contaminación radioactiva en el sistema,principalmente en la sal de Gd, y su impacto en las medidas relevantes de SuperKGd: el fondo difuso de neutrinos de supernova, los neutrinos de la fase de combustiónde Si de una estrella suficientemente cercana, las caracterı́sticas de los neutrinos delreactor y la medición del espectro de neutrinos solares a muy baja energı́a.
Hemos desarrollado una serie de algoritmos basados en la detección de neutrones
Gd que discriminan de forma eficiente las interacciones neutrinos y antineutrinos en
SuperK-Gd.

297

CHAPTER 9. CONCLUSIONES (SPANISH)

Además, se han creado algoritmos similares para caracterizar las interacciones decorrientes cargadas y neutras de los neutrinos.
Se ha desarrollado un segundo paso en la reconstrucción de la energı́a de interacciónneutrino, basada en la multiplicidad de los neutrones medida en el estado final,
mediante Gd. Esto reduce drásticamente la cantidad de energı́a no visible, proporcionando ası́ un mejor acuerdo entre la energı́a medida y la verdadera del neutrino.
Se ha estudiado el impacto de la detección de neutrones con Gd en un análisis global
de oscilación de neutrinos atmosféricos en SuperK-Gd. El estudio de sensibilidad
global, con sin2 θ23 = 0,575, δCP =4,189 y ∆m232 = 0,0025 eV2 , para los actuales
2519,90 dı́as de SK-IV, muestra que la sensibilidad al rechazo de la jerarquı́a demasas invertida se incrementa en en comparación con el análisis oficial actual (2.7
unidades de χ2 con Gd, 1.6 analysis oficial actual). Además, la sensibilidad a la fasede violación CP también mejora de manera similar.
Se han realizado estudios correspondientes para el experimento T2K y para lapróxima generación de experimentos, Hyper-Kamiokande con Gd, mostrando sus
notables mejoras.
La fase actual de Super-Kamiokande, SK-IV, ya tiene alguna capacidad de detecciónde neutrones con baja eficiencia mediante la producción de deuterio en la captura deneutrones por el hidrógeno. En esta tesis, hemos adaptado las mejoras desarrolladaspara el caso de la detección de neutrones con Gd, al caso de detección con H.
Esto demuestra la mejora significativa de la detección de neutrones en detectoresagua-Čerenkov. El análisis de los datos muestra una preferencia por la jerarquı́anormal de 4.6 unidades de χ2 (Nota: los resultados son preliminares), mientras queen el actual análisis oficial la preferencia es de 4.3 unidades de χ2 .
Tras más de veinte aõs de grandes éxitos del experimento Super-Kamiokande, el

298

proyecto SuperK-Gd proporcionará una gran cantidad de nuevas e interesantes
medidas en la fı́sica fundamental de partı́culas.

299

A. Evaluation of Systematic Errors in the Neutrino Oscillation
Analyses with SuperK-Gd

A.1

Fully Contained Event Selection Errors

The systematic errors associated to the sample selection defined are estimated.

301

APPENDIX A. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH SUPERK-GD

SubGeV e-likeFigure A.1: Number of Gd-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for the
SubGeV e-like sample.

SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like

σ ntag
0.0%
-1.8%
2.9%

σ decay−e
8.2%
-0.8%
-1.3%

Table A.1: Relative variation of contents for the three SubGeV e-like samples.

302

A.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiGeV e-likeFigure A.2: Number of Gd-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for theMultiGeV e-like sample.

MultiGeV νe -like
MultiGeV νe ν e -like
MultiGeV ν e -like

σ ntag
0.0%
-2.6%
1.9%

σ decay−e
7.3%
-1.8%
-3.6%

Table A.2: Relative variation of contents for the three MultiGeV e-like samples.

303

APPENDIX A. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH SUPERK-GD

SubGeV µ-likeFigure A.3: Number of Gd-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for the
SubGeV µ-like sample.

SubGeV νµ -like
SubGeV ν µ -like

σ ntag-1.5%
2.8%

σ decay−e
-1.7%
7.5%

Table A.3: Relative variation of contents for the two SubGeV µ-like samples.

304

A.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiGeV µ-likeFigure A.4: Number of Gd-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for theMultiGeV µ-like sample.

MultiGeV νµ -like
MultiGeV ν µ -like

σ ntag-1.3%
2.2%

σ decay−e
-1.7%
6.6%

Table A.4: Relative variation of contents for the two MultiGeV µ-like samples.

305

APPENDIX A. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH SUPERK-GD

MultiRing e-likeFigure A.5: Neural network output variations for estimating systematic errors for NC-CC
separation in the MultiRing e-like sample.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
6.6%
-2.2%
-0.4%
-0.0%

σ decay−e
0.2%
0.0%
-0.1%
-0.0%

Table A.5: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the NC-CC separation.

Figure A.6: Neural network output variations for estimating systematic errors for νµ − νeseparation in the MultiRing e-like sample.

306

A.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
1.5%
-1.7%
-0.3%

σ decay−e
0%
2.8%
-3.5%
-0.2%

Table A.6: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νµ − νe separation.

Figure A.7: Neural network output variations for estimating systematic errors for νe − ν eseparation in the MultiRing e-like sample.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
0%
0.4%
-0.3%

σ decay−e
0%
0%
3.3%
-2.5%

Table A.7: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νe − ν e separation.

307

APPENDIX A. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH SUPERK-GD

MultiRing µ-likeFigure A.8: Neural network output variations for estimating systematic errors for νµ − ν µseparation in the MultiRing µ-like sample.

MultiRing νµ -like
MultiRing ν µ -like

σ ntag-0.8%
0.2%

σ decay−e
4.5%
-3.5

Table A.8: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νµ − ν µ separation.

A.2

Neutron Energy Corrections for Fully Contained Events

As the correction function depends strictly on the neutron multiplicity, the relativechange in its magnitude is computed to include it as an additional systematic error
source. As with the systematics treated before, this only applies to SK-IV fully
contained events.

∆f =

Gd
Gd
Erec
(Gd-neutrons + 5%) − Erec
(Gd-neutrons + 5%)
Gd (Gd-neutrons)
Erec

308

(A.1)

A.2. NEUTRON ENERGY CORRECTIONS FOR FULLY CONTAINEDEVENTS

The quantity ∆f will be taken to calculate the migration of events between bins,
which will be the actual systematic uncertainty due to the neutron energy corrections.

Neutron energy correction errors
SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like
SubGeV 1ring π-like
SubGeV νµ -like
SubGeV ν µ -like
SubGeV π-like
MultiGeV νe -like
MultiGeV νe + ν e -like
MultiGeV ν e -like
MultiGeV νµ -like
MultiGeV ν µ -like
MultiRing NC-like
MultiRing DIS-νµ -like
MultiRing νe -like
MultiRing ν e -like
MultiRing νµ -like
MultiRing ν µ -like∆f (%)
0.7%
0.0%
1.5%
0.7%
0.3%
1.0%
0.6%
0.5%
0.0%
0.5%
0.2%
0.5%
1.3%
1.1%
0.6%
0.8%
0.7%
0.6%

Table A.9: Relative change in the neutron energy correction functions due to the 5% neutron
tagging uncertainty.

309

B. Evaluation of Systematic Errors in the Neutrino Oscillation
Analyses with Hyper-Kamiokande

B.1

Fully Contained Event Selection Errors

The systematic errors associated to the sample selection defined are estimated.

311

APPENDIX B. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH HYPER-KAMIOKANDE

SubGeV e-likeFigure B.1: Number of H-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for the
SubGeV e-like sample.

SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like

σ ntag
0.0%
-1.7%
3.1%

σ decay−e
8.2%
-0.8%
-1.3%

Table B.1: Relative variation of contents for the three SubGeV e-like samples.

312B.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiGeV e-likeFigure B.2: Number of H-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for theMultiGeV e-like sample.

MultiGeV νe -like
MultiGeV νe ν e -like
MultiGeV ν e -like

σ ntag
0.0%
-2.6%
2.1%

σ decay−e
7.3%
-1.8%
-3.6%

Table B.2: Relative variation of contents for the three MultiGeV e-like samples.

313

APPENDIX B. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH HYPER-KAMIOKANDE

SubGeV µ-likeFigure B.3: Number of H-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for the
SubGeV µ-like sample.

SubGeV νµ -like
SubGeV ν µ -like

σ ntag-1.4%
3.0%

σ decay−e
-1.7%
7.5%

Table B.3: Relative variation of contents for the two SubGeV µ-like samples.

314

B.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiGeV µ-likeFigure B.4: Number of H-tagged neutrons for the default Monte Carlo, plus and minus
5% uncertainty in the tagging efficiency and SK-IV atmospheric data (black dots) for theMultiGeV µ-like sample.

MultiGeV νµ -like
MultiGeV ν µ -like

σ ntag-1.2%
2.5%

σ decay−e
-1.7%
6.6%

Table B.4: Relative variation of contents for the two MultiGeV µ-like samples.

315

APPENDIX B. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH HYPER-KAMIOKANDE

MultiRing e-likeFigure B.5: Neural network output variations for estimating systematic errors for NC-CC
separation in the MultiRing e-like sample.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
7.5%
-3.2%
-0.4%
-0.1%

σ decay−e
-1.9%
1.3%
0.0%
0.0%

Table B.5: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the NC-CC separation.

Figure B.6: Neural network output variations for estimating systematic errors for νµ − νeseparation in the MultiRing e-like sample.

316

B.1. FULLY CONTAINED EVENT SELECTION ERRORS

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
2.2%
-1.0%
-0.2%

σ decay−e
0%
5.5%
-2.9%
-0.1%

Table B.6: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νµ − νe separation.

Figure B.7: Neural network output variations for estimating systematic errors for νe − ν eseparation in the MultiRing e-like sample.

MultiRing NC-like
MultiRing CCDIS νµ -like
MultiRing νe -like
MultiRing ν e -like

σ ntag
0%
0%
-0.1%
0.1%

σ decay−e
0%
0%
2.2%
-2.4%

Table B.7: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νe − ν e separation.

317

APPENDIX B. EVALUATION OF SYSTEMATIC ERRORS IN THE
NEUTRINO OSCILLATION ANALYSES WITH HYPER-KAMIOKANDE

MultiRing µ-likeFigure B.8: Neural network output variations for estimating systematic errors for νµ − ν µseparation in the MultiRing µ-like sample.

MultiRing νµ -like
MultiRing ν µ -like

σ ntag0.1%-0.2%

σ decay−e
1.9%
-1.9%

Table B.8: Relative variation of contents for the four MultiRing e-like samples due to the
induced systematics of the νµ − ν µ separation.

B.2

Neutron Energy Corrections for Fully Contained Events

As the correction function depends strictly on the neutron multiplicity, the relativechange in its magnitude is computed to include it as an additional systematic error
source. As with the systematics treated before, this only applies to SK-IV fully
contained events.

∆f =

70%
70%
Erec
(70%-neutrons + 5%) − Erec
(70%-neutrons + 5%)
70% (70%-neutrons)
Erec

318

(B.1)

B.2. NEUTRON ENERGY CORRECTIONS FOR FULLY CONTAINEDEVENTS

The quantity ∆f will be taken to calculate the migration of events between bins,
which will be the actual systematic uncertainty due to the neutron energy corrections.

Neutron energy correction errors
SubGeV νe -like
SubGeV νe + ν e -like
SubGeV ν e -like
SubGeV 1ring π-like
SubGeV νµ -like
SubGeV ν µ -like
SubGeV π-like
MultiGeV νe -like
MultiGeV νe + ν e -like
MultiGeV ν e -like
MultiGeV νµ -like
MultiGeV ν µ -like
MultiRing NC-like
MultiRing DIS-νµ -like
MultiRing νe -like
MultiRing ν e -like
MultiRing νµ -like
MultiRing ν µ -like∆f (%)
0.7%
0.0%
1.3%
0.4%
0.6%
1.0%
0.6%
0.3%
0.0%
0.7%
0.2%
0.5%
1.5%
1.4%
0.6%
0.7%
0.9%
0.7%

Table B.9: Relative change in the neutron energy correction functions due to the 5% neutron
tagging uncertainty.

319

C. Neutron-Corrected Energy for
Fully Contained Events in SuperKamiokande with H-Neutron
Tagging
In this additional chapter, the H-neutron correction functions are shown in Figures C.1 and C.2.
The energy pull distributions are computed for the visible and H-neutron corrected energies and plotted in Figures C.3 and C.4.

321

APPENDIX C. NEUTRON-CORRECTED ENERGY FOR FULLY CONTAINEDEVENTS IN SUPER-KAMIOKANDE WITH H-NEUTRON TAGGING

Figure C.1: H-Neutron correction functions for each of the FC samples for atmospheric
neutrino Monte Carlo (1 of 2). Y-axis is the averaged fraction of invisible and visibleenergies and X-axis is the Gd-neutron multiplicity. The box in each plot shows the fitted
polynomial parameters and the χ2 value of the fit.

322

Figure C.2: H-Neutron correction functions for each of the FC samples for atmospheric
neutrino Monte Carlo (2 of 2). Y-axis is the averaged fraction of invisible and visibleenergies and X-axis is the Gd-neutron multiplicity. The box in each plot shows the fitted
polynomial parameters and the χ2 value of the fit.

323

APPENDIX C. NEUTRON-CORRECTED ENERGY FOR FULLY CONTAINEDEVENTS IN SUPER-KAMIOKANDE WITH H-NEUTRON TAGGING

Figure C.3: Energy pulls of visible and neutron-corrected energies of the different FC samples for atmospheric Monte Carlo (1 of 2).

324

Figure C.4: Energy pulls of visible and neutron-corrected energies of the different FC samples for atmospheric Monte Carlo (2 of 2).

325

D. Systematic Errors at Best Fit
Point in the Global Atmospheric
Neutrino Oscillation Analysis
with H-neutron Tagging in SK
In Appendix D, all the fitted systematic errors for the H-tag atmospheric oscillation
analysis in Super Kamiokande are shown for the best fit point. Of special interestfor this analysis are the newly introduced ones for the new sample selection and theneutron corrected energy.

327

APPENDIX D. SYSTEMATIC ERRORS AT BEST FIT POINT IN THE
GLOBAL ATMOSPHERIC NEUTRINO OSCILLATION ANALYSIS WITH
H-NEUTRON TAGGING IN SK

Figure D.1: Value of the variation coefficient, j , over the error size, σj , for each of thesystematic uncertainties described in Section 7.3.1, and for the best fit point of the SK
analysis.

328

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