N ATIONAL C ENTRE FOR N UCLEAR R ESEARCH
D OCTORAL T HESIS

Indirect Search for Dark Matter with theSuper-Kamiokande Detector

Author:
Katarzyna F RANKIEWICZSupervisors:
Prof. dr hab. Ewa R ONDIODr Piotr M IJAKOWSKI

A thesis submitted in fulfillment of the requirements
for the degree of Doctor of Philosophy

April 2018

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NATIONAL CENTRE FOR NUCLEAR RESEARCH

Abstract
Doctor of Philosophy
Indirect Search for Dark Matter with the Super-Kamiokande Detector
by Katarzyna F RANKIEWICZOne of the strategies for dark matter detection is to search for the products of its
self-annihilation or decay, such as antimatter, photons, or neutrinos. The later are
particularly interesting since they can travel unaffected through the galactic scales.
Therefore, neutrinos can provide valuable information on their source location andinitial energy spectra related to dark matter annihilation/decay processes.
In this dissertation, an indirect search for dark matter induced neutrinos is described.
Two types of analyses are performed: the search for neutrinos originating from dark
matter annihilation or decay in the Milky Way, and a search for neutrinos from dark
matter annihilation inside the Earth’s core. In both presented analyses, atmospheric
neutrino data set collected with the Super-Kamiokande detector from 1996 to 2016 isused. The expected dark matter induced signal would manifest itself as an excess inthe number of neutrinos originating from the direction corresponding to position of
the Galactic Center or the Earth’s core, when compared to the background level ofatmospheric neutrinos. The selection criteria which allows us to effectively distinguish the signal from background are developed in order to estimate the potential
contribution of dark matter induced neutrinos to all detected neutrino interactions.
No statistically significant excess of neutrinos coming from the direction of the considered sources has been found in the performed analyses. The allowed number ofdark matter induced neutrinos which can be contained in the Super-Kamiokande
data so far is estimated. In case of the Galactic Center analysis, obtained limits ondark matter induced neutrino flux are related to the upper limits on the velocityaveraged dark matter self-annihilation cross-section, < σA v >, and lower limits ondark matter particle lifetime, τ. Limits are set for wide range of masses from 1 GeV
up to 10 TeV, and different possible annihilation/decay channels including: νν̄, bb̄,µ+ µ− and W + W − . The influence of the dark matter halo model choice on the obtained results is also estimated for the annihilation scenario.
For the Earth’s core analysis, the spin-independent WIMP-nucleon scattering crosssection is constrained for dark matter particle masses ranging from 10 to 1000 GeV,
and for bb̄, τ + τ − and W + W − annihilation channels. The limits from performed
analysis are compared against the results of other direct and indirect detection experiments. High sensitivity of the Super-Kamiokande detector, allows to set thestrongest limits among all neutrino experiments up to date. For the dark matterparticle mass ∼ 50 GeV, limit for τ + τ − annihilation channel reaches 10−44 cm2 .

NATIONAL CENTRE FOR NUCLEAR RESEARCH

Streszczenie
Jednym ze sposobów na poszukiwanie ciemnej materii jest próba detekcji produktów jej anihilacji lub rozpadów, takich jak antymateria, fotony lub neutrina. Te ostatnie sa˛ szczególnie interesujace,
˛ ponieważ podczas propagacji w przestrzeni kosmicznej ich kierunek oraz energia pozostaja˛ niezmienione i moga˛ one dostarczyć
niezwykle istotnych informacji na temat źródła z którego pochodza.˛W poniższej rozprawie opisane sa˛ poszukiwania neutrin pochodzacych˛z anihilacji lub rozpadów ciemnej materii. Przeprowadzone zostały dwie analizy, poszukiwanie neutrin pochodzacych˛
z centrum Drogi Mlecznej oraz neutrin pochodzacych˛
z wn˛etrza Ziemi. Do obydwu analiz użyto przypadków oddziaływań neutrin zarejestrowanych w japońskim detektorze Super-Kamiokande, w latach 1996-2016. Wśród
wszystkich zarejestrowanych przypadków poszukiwane sa˛ te posiadajace
˛ charakterystyki zgodne z potencjalnym wkładem od neutrin produkowanych w wyniku
anihilacji lub rozpadów ciemnej materii. Poszukiwanym sygnałem jest nadwyżkaneutrin pochodzaca
˛ z centrum Galaktyki lub wn˛etrza Ziemi, w stosunku do tła,
które stanowia˛ neutrina produkowane w atmosferze ziemskiej przez promieniowanie kosmiczne.
W przeprowadzonych analizach nie stwierdzono nadmiaru przypadków zwiazane˛go z rozpatrywanymi źródłami, co pozwoliło na górne ograniczenie liczby przypadków mogacych
˛pochodzić od ciemnej materii, rejestrowanych w detektorze SuperKamiokande. Na tej podstawie dla analizy z centrum Galaktyki obliczono górne
limity na ważony pr˛edkościa˛ przekrój czynny na samo-anihilacj˛e ciemnej materii,< σA v >, i dolne limity na czas życia czastek
˛ciemnej materii, τ. Limity te wyznaczono w szerokim zakresie mas od 1 GeV do 10 TeV i dla czterech rozważanych
kanałów anihilacji/rozpadów ciemnej materii: νν̄, bb̄, µ+ µ− oraz W + W − . W przypadku anihilacji ciemnej materii dodatkowo rozważono wpływ wybranego modelu
galaktycznego halo na otrzymywane wyniki.
W przypadku analizy z centrum Ziemi, wyznaczono górne limity na niezależny
od spinu przekrój czynny na rozpraszanie WIMP-nukleon, σχ− N , dla mas czastek
˛ciemnej materii w zakresie od 10 GeV do 1 TeV, dla trzech rozważanych kanałów anihilacji: bb̄, τ + τ − oraz W + W − . Dzi˛eki dużej czułości detektora Super-Kamiokande
uzyskano najsilniejsze limity pochodzace
˛ z eksperymentów neutrinowych na świecie,si˛egajace
˛ 10−44 cm2 dla czastek
˛ciemnej materii o masie ∼ 50 GeV, przy założeniu
anihilacji w pary leptonów τ + τ − .

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Acknowledgements
First of all, I would like to express my deep gratitude to Prof. Ewa Rondio. She
guided me through my PhD and was an excellent supervisor. I gained a lot from hervast experience in neutrino physics and I am very happy that I decided to join hergroup. She would always find time to discuss physics problems and answer any ofmy questions. Thank you for your support, patience, and encouragement.
I am very thankful to Dr Piotr Mijakowski, who helped supervise my work, especially through the last and most difficult part – preparing this dissertation. He
also introduced me to the Super-Kamiokande experiment, during the last year of
my Masters, what convinced me to pursue a PhD in neutrino physics. In addition to
all his help, he always was a good friend.
Super-Kamiokande is an exceptional experiment, which provides the opportunity
to study a wide range of physics topics. The experiment was built and has been
operated with funding from the Japanese Ministry of Education, Culture, Sports,
Science and Technology and the U.S. National Science Foundation. Special thanks
goes to Kamioka Mining and Smelting Company for helping to host the experiment.
I would like to thank all my collaborators for their dedication and engagement in
the Super-K experiment. In particular, I want to mention the ATMPD working groupconveners: Prof. Ed Kearns and Prof. Masato Shiozawa. They provided excellent
leadership and guidance in my analysis group.
Moreover, a special thanks to Ed for giving me the opportunity to visit Boston andFermilab. I had a great time working with his neutrino group at Boston University.
Thanks to his help I had a chance to broaden my outlook. I really appreciate histime, support and advice.
My greatest debt is to Roger Wendell, who prepared the framework which we alluse in the ATMPD working group. He was a tremendous help when dealing withnearly any kind of problems: software, statistics, physics, and much more. My analysis would not have been possible without his support. Thank you for the time you
spent with us during the WIMP meetings, and for the hundreds of emails with myquestions that you have answered.
Lluis Marti is a great friend and colleague, and I really appreciated his company
during the long days spent in Mozumi. I enjoyed our conversations very much and
I am in debt to you for the delicious coffee and cookies.
I would like to thank my family and friends. Thanks to my parents support I wasable to take up my studies in Warsaw. My sister and brother were always ready tohelp me with every problem I have encountered.
Krzysztof was not only the best flatmate, but above all, the best friend. I don’t knowwhat I would do without his support and great advice. I would like to thank you forall this good times we had during our PhDs.
A special thanks goes to Elżbieta Gaca, my first physics teacher, who aroused myinterest in science. I am very grateful for her time and commitment, and having theviii
faith in me. If it was not for her I would probably never have thought that I could
be a physicist.
Last but not the least, I would like to say thank you to Spencer. For everything.
For his love and understanding, and always being there for me.
My work has been supported by the funds from the National Science Centre, Poland(2015/17/N/ST2/04064) and the European Union (H2020 RISE-GA641540-SKPLUS).

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Contents
Abstract

iii

Streszczeniev

Acknowledgementsvii

1

Introduction

1

2

Dark Matter
2.1 Observational Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Galaxy Rotation Curves . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Gravitational Lensing . . . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Cosmic Microwave Background . . . . . . . . . . . . . . . . . .
2.1.5 Big Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . .
2.1.6 Structure Formation . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Neutralino as a Dark Matter Candidate . . . . . . . . . . . . . .
2.3 Dark Matter Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . .
Antimatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Production in Accelerators . . . . . . . . . . . . . . . . . . . . .

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3

Neutrinos
3.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 In Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 In Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Sources of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4

Super-Kamiokande
4.1 Cherenkov Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . .
4.3 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Water Purification System . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Air Purification System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5

Atmospheric Neutrinos at Super-Kamiokande
5.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Data Reduction and Reconstruction . . . . . . . . . . . . . . . .
5.2 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Atmospheric Neutrino Oscillation Analysis . . . . . . . . . . . . . . . .
5.3.1 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Results of the Oscillation Analysis . . . . . . . . . . . . . . . . .

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WIMPs in the Center of the Milky Way
6.1 Dark Matter Halo Models . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Dark Matter Annihilation . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Dark Matter Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Energy Spectrum of Dark Matter Induced Neutrinos . . . . . . . . . . .

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Search for the Galactic WIMPs at Super-Kamiokande
7.1 Equatorial Coordinate System . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Simulation of WIMP Induced Neutrinos from the Galactic Center . . .
7.3 ON-OFF Source Approach . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Optimization of the ON-Source Region Size . . . . . . . . . . . . . . . .

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Results of the Search for Galactic WIMPs
8.1 Asymmetry Between ON- and OFF-Source Regions . . . . . . . . . . .
8.2 Constraints on Dark Matter Self-Annihilation Cross-Section . . . . . .
8.3 Constraints on the Dark Matter Particles Lifetime . . . . . . . . . . . .

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WIMPs in the Center of the Earth
9.1 Capture Rate of WIMPs in the Earth . . . . . . . . . . . . . . . . . . . .
9.2 WIMP Annihilation in the Earth . . . . . . . . . . . . . . . . . . . . . .
9.3 Neutrino Flux from WIMP Annihilation in the Earth . . . . . . . . . . .
9.4 WimpSim Results for the Earth WIMPs . . . . . . . . . . . . . . . . . .

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10 Search for the Earth WIMPs at Super-Kamiokande
10.1 Global Fit Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 Signal and Background Predictions . . . . . . . . . . . . . . . . . . . . .
10.3 Sensitivity Study for WIMP Induced Neutrinos from the Earth’s Core .
10.3.1 Null WIMP Contribution (β = 0) . . . . . . . . . . . . . . . . . .
10.3.2 Injected WIMP Contribution (β = 0.01) . . . . . . . . . . . . . .
10.4 Binning Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.1 Toy Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . .

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11 Results of the Search for the Earth WIMPs
103
11.1 Fit Results with Standard Binning . . . . . . . . . . . . . . . . . . . . . . 103
11.1.1 Constraints on the WIMP-Nucleon Spin Independent Scattering Cross-Section for Mχ < 100 GeV . . . . . . . . . . . . . . . . 112
11.2 Fit Results with Optimized Binning . . . . . . . . . . . . . . . . . . . . . 113
11.2.1 Constraints on the WIMP-Nucleon Spin Independent Scattering Cross-Section for Mχ up to 1 TeV . . . . . . . . . . . . . . . 120
11.2.2 Comparison with Other Experiments . . . . . . . . . . . . . . . 122
12 Summary and Outlook

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A Galactic WIMP Weights

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B WimpSim Results
133
B.1 bb̄ annihilation channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B.2 τ + τ − annihilation channel . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B.3 W + W − annihilation channel . . . . . . . . . . . . . . . . . . . . . . . . . 139
C Earth WIMP Signal Illustrations
141
C.1 Standard Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
C.2 Optimized Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
D Bayesian Approach

149

Bibliography151

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List of Figures
2.1

2.2

2.3

2.4
2.5
2.6
2.7

2.8

An example of a galaxy rotation curve for NGC 6503 dwarf spiralgalaxy studied by Begeman, Broels, and Sanders. The solid line is
the theoretical rotation curve and the data points with error bars are
the measured object speed. The segmented lines show the contributions from gas, luminous matter, and dark matter. Figure is takenfrom (Begeman, Broeils, and Sanders, 1991) . . . . . . . . . . . . . . . .
Left: Visible light image of the Bullet Cluster from the Magellan Telescope. Right: The Chandra X-ray Observatory image of the Bullet
Cluster showing the location of the x-ray emission of the hot gas. In
both panels the mass density contours are shown with green lines.
Figure taken from (Clowe et al., 2006) . . . . . . . . . . . . . . . . . . .
Simplified diagram showing the three different dark matter detection
channels. The direct detection experiments (→) look for the recoil
introduced by a WIMP (χ) on a SM particle in the detector. Indirect
detection experiments (↓) look for the SM annihilation products of
WIMPs. Collider experiments (↑) look for the creation of WIMPs in
Standard Model particle collisions. . . . . . . . . . . . . . . . . . . . . .
Feynman diagrams contributing to the spin-dependent elastic scattering of neutralinos from quarks. . . . . . . . . . . . . . . . . . . . . . . .
Feynman diagrams contributing to the scalar elastic-scattering amplitude of a neutralino from quarks. . . . . . . . . . . . . . . . . . . . . . .
A sketch idea of dark matter direct detection. . . . . . . . . . . . . . . .
Latest limits on SI WIMP-nucleon scattering cross-section as a function of WIMP mass: results from combined PandaX-II Run 9 and Run
10 data (Cui et al., 2017) (red) (the green band represents the ±1σ sensitivity band), overlaid with results from PandaX-II 2016 (Tan et al.,2016) (blue), LUX 2017 (Akerib et al., 2017) (magenta), and XENON1T
2017 (Aprile et al., 2017) (black). . . . . . . . . . . . . . . . . . . . . . . .
Latest limits on the SD WIMP-proton scattering cross-section as a function of WIMP mass: results from PICO-60 C3 F8 (Amole et al., 2017)(thick blue), along with limits from PICO-60 CF3 I (Amole et al., 2016a)(thick red), PICO-2L (Amole et al., 2016b) (thick purple), PICASSO(Behnke et al., 2017) (green band), SIMPLE (Felizardo et al., 2014)(orange), PandaX-II (Fu et al., 2017) (cyan), IceCube (Aartsen et al.,2017b) (dashed and dotted pink), and SuperK (Choi et al., 2015) (dashedand dotted black). Indirect limits from IceCube and SuperK assume
annihilation to τ leptons (dashed) and b quarks (dotted). The purple
region represents parameter space of the constrained minimal supersymmetric model of (Roszkowski, Austri, and Trotta, 2007). . . . . . .

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2.9

Experimental 90 % C.L. exclusion limit on the SI WIMP-nucleon scattering cross section as a function of WIMP mass for the combined
fit from EDELWEISS-II detectors (Hehn et al., 2016) (solid red). The
green and yellow band represent the 1 and 2 σ confidence band of
the expected median sensitivity (dashed black). Result of the EDELWEISS BDT based analysis (dashed red) is shown for comparison.
Colored regions show possible signals from CDMS-II (Si) (Agnese etal., 2013) (blue), DAMA (Bernabei et al., 2013) (brown), CRESST-II(Angloher et al., 2012) (pink) and CoGeNT (Aalseth et al., 2014) (orange). Other existing exclusion limits are from EDELWEISS-II (Armengaud et al., 2012) (small red dashes), CoGeNT (Aalseth et al.,2013) (orange), CRESST (Angloher et al., 2016) (pink), SuperCDMS(Agnese et al., 2014) (purple), XENON100 (Aprile et al., 2016) (black),
CDMSlite (Agnese et al., 2015) (dashed violet) and LUX (Akerib et al.,2016) (green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 An illustration of a possible products of supersymmetric dark matter
self-annihilation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 The electron flux and the positron flux measured by AMS-02 experiment (Aguilar et al., 2016). . . . . . . . . . . . . . . . . . . . . . . . . . .
2.12 The upper 90% C.L. limits from neutrino experiments on dark matter self-annihilation cross section for the bb̄ (blue), W + W − (maroon),µ+ µ− (purple) and νν̄ (orange) annihilation channels. The limits fromSuper-Kamionkande (Frankiewicz, 2017a) are plotted with solid lines,
IceCube (Aartsen et al., 2017c) with dotted lines and ANTARES (Albert et al., 2017a) with dashed lines. . . . . . . . . . . . . . . . . . . . .
2.13 The upper 90% C.L. limits on the WIMP-proton SD cross section (left)
and WIMP-nucleon SI cross section (right) for the bb̄ (blue), τ + τ −(green) and W + W − (maroon) annihilation channels. The limits fromSuper-Kamionkande (Choi et al., 2015) are plotted with solid line, IceCube (Aartsen et al., 2017b) with dotted lines. For the comparison thestrongest limits from direct detection experiments: LUX (Akerib et al.,2017) (orange) and PICO-60 (Amole et al., 2017) (purple) are plotted,
and possible signal from DAMA (Bernabei et al., 2013). . . . . . . . . .
2.14 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section
from the CMS experiment (Lowette, 2016), for the mono-jet (magenta),mono-photon (red and yellow), and mono-lepton (grey) searches, asa function of the dark matter mass. . . . . . . . . . . . . . . . . . . . . .
2.15 90% C.L. upper limits on SD WIMP-nucleon scattering cross-section
from the CMS experiment (Lowette, 2016), for the mono-jet (magenta),mono-photon (red and yellow), and mono-lepton (gray) searches, as afunction of the dark matter mass. The limits from Super-Kamionkande
come from Solar WIMP search analysis (Choi et al., 2015). . . . . . . . .
3.1
3.2
3.3
3.4

Charged current neutrino interactions via a W boson exchange. . . . .
Summary of the current knowledge of νµ charged-current cross sections. Figure taken from (Formaggio and Zeller, 2012). . . . . . . . . .
Measured and expected fluxes of natural and reactor neutrinos. Figure taken from (Katz and Spiering, 2012) . . . . . . . . . . . . . . . . . .
Schematic view of cosmic rays interactions in the atmosphere. Figure
taken from (Louis et al., 1997). . . . . . . . . . . . . . . . . . . . . . . . .

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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

5.1

5.2

5.3

5.4

5.5

5.6

A schematic view of the detection of Cherenkov light by the photomultipliers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The schematic view of Super-Kamiokande detector and the experimental hall. Figure taken from (Fukuda et al., 2003). . . . . . . . . . . .
A diagram of the module structure of the PMT support frame. Figure
taken from (Fukuda et al., 2003). . . . . . . . . . . . . . . . . . . . . . .
Diagram of 20-inch (50 cm) photomultiplier tube used in Super-K detector (taken from (Fukuda et al., 2003)). . . . . . . . . . . . . . . . . . .
Quantum efficiency of the photocathode as a function of the lightwavelength (taken from (Fukuda et al., 2003)). . . . . . . . . . . . . . .
Super-Kamiokande water purification system (taken from (Fukuda etal., 2003)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Super-Kamiokande air purification system (taken from (Fukuda et al.,2003)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Energy scale stability measured as a function of date since the startof Super-Kamiokande detector operations. The energy scale is taken
as the average of the reconstructed momentum divided by range of
stopping cosmic ray muon data in each bin. The vertical axis shows
the deviation of this parameter from the mean value for each SK period separately. Error bars are statistical. Figure taken from (Abe etal., 2017a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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38

The schematic illustration of event categories used in Super-K: fullycontained (FC), partially-contained (PC) and upward - going muons(UPMU) samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
The expected parent neutrino energy distributions for the FC e-like(left), FC µ-like and PC (middle), and UP-µ (right) samples based on
MC simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
An example event display of single-ring µ-like (left) and e-like (right)
event. The colored points indicate the quantity of the detected lightby each PMT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Atmospheric neutrino fluxes for Kamioka averaged over all directions(left panel), and the flux ratios (right panel), calculated by Honda (Honda
et al., 2011) (solid red), Fluka (Battistoni et al., 2003) (dotted green) andBartol (Barr et al., 2004) (dashed blue) groups, (dash-dotted line is forthe previous Honda calculation (HKKM06)). . . . . . . . . . . . . . . . 45
Data and MC comparisons for the entire Super-K data divided into 19
analysis samples. Samples with more than one zenith angle bin are
shown as zenith angle distributions (second through fifth column)
and other samples are shown as reconstructed momentum distributions (first column). Cyan (orange) lines denote the best f it MC assuming the normal (inverted) hierarchy. Narrow panels below each
distribution show the ratio relative to the normal hierarchy MC. In all
panels, the error bars represent the statistical uncertainty. . . . . . . . . 47
Constraints on neutrino oscillation parameters from the Super-K atmospheric neutrino data fit. Orange lines denote the inverted hierarchy result, which has been offset from the normal hierarchy result,shown in cyan, by the difference in their minimum χ2 values. . . . . . 50

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6.1

6.2
6.3

6.4

6.5

7.1
7.2
7.3

7.4

7.5

7.6

The dark matter density as a function of the distance from the GC for
Moore (Moore et al., 1999) (dotted green), NFW (Navarro, Frenk, andWhite, 1997) (solid red) and Kravtsov (Kravtsov et al., 1998) (dashedblue) halo profiles. The vertical gray line indicates the Solar System
position (Rsc = 8.5 kpc). The plot illustrate Eq. 6.1 with parametersfrom Tab. 6.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Illustration of the line of sight l and the angle Ψ in the coordinate
system related to the Galactic Center. . . . . . . . . . . . . . . . . . . . .
Intensity of dark matter annihilation products versus angular distancefrom the Galactic Center for Moore (green), NFW (red) and Kravtsov(blue) profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Intensity of dark decay products versus angular distance from the
Galactic Center for Moore (green), NFW (red) and Kravtsov (blue)
profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Differential muon neutrino energy spectra for WIMP particle massof 100 GeV annihilating into bb̄ (blue), W + W − (maroon) and µ+ µ−(purple), after taking into account neutrino oscillations through the
Galaxy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52
53

53

54

55

Definition of the coordinates (right ascension, declination) in the equatorial coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Atmospheric neutrino events from SK I-IV data sets in the equatorial
coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Left: Standard atmospheric MC in the equatorial coordinate system(upper left plot for the true and bottom left for the reconstructed directions). Middle: Distribution in the cosine of the angular distancefrom the GC (upper middle plot) and the angular distance from theGC (bottom middle plot). Right: Distribution in right ascension (upper right plot) and declination (bottom right plot). Blue curves in middle and right plots correspond to true neutrino directions and black
curves to the reconstructed directions of leptons produced in neutrino
interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Spherical projections of the expected signal shape in the equatorial coordinate system for Moore (left), NFW (middle) and Kravtsov (right)
halo profiles, assuming the dark matter annihilation scenario. Upper
plots show the true neutrino directions and bottom plots show thereconstructed lepton directions. . . . . . . . . . . . . . . . . . . . . . . . 60
Expected signal shape in RA (upper plots) and DEC (bottom plots) for
Moore (left), NFW (middle) and Kravtsov (right) halo profiles, assuming the dark matter annihilation scenario. Blue curves correspond to
the true direction of neutrino and black curves to the reconstructed one. 61
Expected signal shape in the cosine of the angular distance from theGC, cos (Ψ), (upper plots) and the angular distance, Ψ, from the GC(bottom plots) for Moore (left), NFW (middle) and Kravtsov (right)
halo profiles, assuming the dark matter annihilation scenario. Blue
curves correspond to the true direction of neutrino and black curves
to the reconstructed one. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

xvii
7.7

Signal expectations for the NFW halo profile, assuming dark matter decay scenario. Left: Spherical projections of the expected signal
shape in the equatorial coordinate system (upper left plot for the trueand bottom left for the reconstructed directions). Middle: Distribution in the cosine of the angular distance from the GC (upper middleplot) and the angular distance from the GC (bottom left plot). Right:
Distribution in right ascension (upper right plot) and declination (bottom right plot). Blue curves on middle and right plots correspond totrue neutrino direction and black curves to the reconstructed directionof lepton produced in neutrino interactions. . . . . . . . . . . . . . . . .
7.8 The illustration of the ON-OFF source approach. The ON-source region is defined around the GC where the signal concentration is thehighest. The OFF-source region is shifted in RA by 180◦ . Because
ON- and OFF-source regions are equally sized, the expected numberof background events is the same in both of them. . . . . . . . . . . . .
7.9 Spherical projections of the expected signal shape in the equatorial coordinate system for NFW halo model, assuming the dark matter annihilation scenario for FC SubGeV, FC MultiGeV, PC and UP-µ event
categories. . . . . . . . . . . . . . . . . . . . . . . √. . . . . . . . . . . . .
7.10 The signal to square root of the background (S/ B) ratio as a function of the angular size of the ON-source region for FC SubGeV (blue),
FC MultiGeV (magenta), PC (black), UP-µ (green) and all events together (red). The NFW halo model is assumed and dark matter annihilation scenario is considered. . . . . . . . . . . . . . . . . . . . . . . .
8.1
8.2

8.3

8.4

9.1

The asymmetry in the number of events between the ON- and OFFsource regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The upper 90% C.L. limit on dark matter self-annihilation cross-section
as a function of the dark matter particle mass for bb̄ (blue), W + W −(maroon), µ+ µ− (purple) and νν̄ (orange) annihilation channels. The
influence of the halo model choice is shown as a band around the result for the benchmark NFW profile. . . . . . . . . . . . . . . . . . . . .
The upper 90% C.L. limits on dark matter self-annihilation cross-section
as a function of dark matter particle mass for bb̄ (blue), W + W − (maroon), µ+ µ− (purple) and νν̄ (orange) annihilation channels (solidlines), compared with the results of independent Global Fit analysis(dotted lines) of Super-K data (Mijakowski, 2018). . . . . . . . . . . . .
The lower 90% C.L. limits on the dark matter particle lifetime as afunction of dark matter particle mass for bb̄ (blue), W + W − (maroon),µ+ µ− (purple) and νν̄ (orange) decay channels, compared with limits
from IceCube experiment (dotted lines) (Abbasi et al., 2012). NFW
halo model is assumed. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

63

64

65
69

71

72

73

The capture rate of WIMPs in the Earth for a scattering cross sectionof σ = 10−44 cm2 , calculated in (Sivertsson and Edsjo, 2012). The
normalization of the original calculation performed for σ = 10−42 cm2
was adjusted due to recent exclusions from direct detection (Akerib
et al., 2017). Figure taken from (Aartsen et al., 2017a). . . . . . . . . . . 76

xviii
9.2

9.3

9.4

The differential fluxes of the neutrinos (left panels) and anti-neutrinos(right panels) produced by 6 GeV WIMPs annihilating into bb̄ quarks,
as a function of the neutrino energy Eν , divided by the WIMP massMχ . The different neutrino species are indicated with a different color,
black for νe , red for νµ , and green for ντ . . . . . . . . . . . . . . . . . . . 79
Energy spectra of the dark matter induced muon neutrinos at the
Earth’s surface generated with WimpSim, for 100 GeV WIMPs annihilating into bb̄ (blue line), τ + τ − (green line), and W + W − (maroon line)
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Angular distribution of the dark matter induced muon neutrinos observed at the Earth’s surface, generated with WimpSim for 10 GeV(solid line), 100 GeV (dashed line), and 1 TeV (dotted line) WIMPs
annihilating into b̄ quarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 79

10.1 Atmospheric neutrino background expectation (orange histogram) andthe SK-I-IV data (black points). The momentum (1st column) andzenith angle (2nd -5th columns) distributions are shown for 19 samples
used in the analysis. In all panels, the error bars represent the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2 The signal originating from the annihilation of 25 GeV WIMPs in the
Earth’s core into bb̄ quarks. The momentum (1st column) and zenith
angle (2nd -5th columns) distributions are shown for 19 samples used in
the analysis. The plots contain the expected signal from WIMP annihilation (filled blue histogram) and the SK-I-IV atmospheric neutrino
data (black points). In all panels, the error bars represent the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 The signal originating from the annihilation of 100 GeV WIMPs in
the Earth’s core into τ + τ − leptons. The momentum (1st column) andzenith angle (2nd -5th columns) distributions are shown for 19 samples
used in the analysis. Plots contain expected signal from WIMP annihilation (filled green histogram) and the SK-I-IV atmospheric neutrino
data (black points). In all panels, the error bars represent the statisticaluncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4 The signal originating from the annihilation of 500 GeV WIMPs in the
Earth’s core into W + W − bosons. The momentum (1st column) andzenith angle (2nd -5th columns) distributions are shown for 19 samples
used in the analysis. Plots contain expected signal from WIMP annihilation (filled maroon histogram) and the SK-I-IV atmospheric neutrino data (black points). In all panels, the error bars represent thestatistical uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5 Heat map showing the tested parameter space of WIMP masses (X axis) and WIMP contribution (Y - axis) for three considered annihilation channels: bb̄ (top), τ + τ − (middle) and W + W − (bottom). Null
WIMP contribution (β = 0) is assumed and the color represents χ2
value of the fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6 Sensitivity contours at 68% (blue), 90% (yellow) and 99% (maroon)
C.L for null WIMP contribution (β = 0), for tested parameter space of
WIMP masses (X - axis) and WIMP contribution (Y - axis), plotted forthree considered annihilation channels: bb̄ (top), τ + τ − (middle) andW + W − (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

84

85

86

88

89

xix
10.7 The ∆χ2 = χ2 − χ2min distributions minimized over the corresponding WIMP masses. The horizontal lines correspond to the 68% (blue),
90% (yellow) and 99% (maroon) C.L. for no WIMP hypothesis (β=0),
plotted for τ + τ − annihilation channel. . . . . . . . . . . . . . . . . . . . 90
10.8 The 90% upper limits on the dark matter induced muon neutrino flux
from the sensitivity study for bb̄ (dotted blue), τ + τ − (dotted green)
and W + W − (maroon line) annihilation channel. . . . . . . . . . . . . . 91
10.9 The 90% upper limits on SI WIMP-nucleon scattering cross-section
from the sensitivity study for bb̄ (dotted blue), τ + τ − (dotted green)
and W + W − (maroon line) annihilation channel. Positive result claimed
by DAMA/LIBRA (Bernabei et al., 2013) is shown for comparison. . . 91
10.10Heat map plot showing the tested parameter space of WIMP masses(X - axis) and WIMP contribution β (Y - axis) for three consideredannihilation channels: bb̄ (top), τ + τ − (middle) and W + W − (bottom).
Positive WIMP contribution (β = 0.01) is assumed and the color represents χ2 value of the fit. In bb̄ channel: Mχ = 25 GeV, in τ + τ − :Mχ = 100 GeV, and in W + W − : Mχ = 500 GeV. . . . . . . . . . . . . . . 93
10.11Sensitivity contours at 68% (blue), 90% (yellow) and 99% (maroon)
C.L for positive WIMP contribution (β = 0.01), for tested parameter
space of WIMP masses (X - axis) and WIMP contribution β (Y - axis)
for three considered annihilation channels: bb̄ (top), τ + τ − (middle)
and W + W − (bottom). In bb̄ channel: Mχ = 25 GeV, in τ + τ − : Mχ =100 GeV, and in W + W − : Mχ = 500 GeV. . . . . . . . . . . . . . . . . . . 94
10.12Atmospheric neutrino background expectation (orange histogram) andthe SK-I-IV data (black points) with the optimized binning. The momentum (1st column) and zenith angle (2nd -5th columns) distributions
are shown for 19 samples used in the analysis. In all panels, the error
bars represent the statistical uncertainty. . . . . . . . . . . . . . . . . . . 96
10.13The signal originating from the annihilation of 1000 GeV WIMPs in
the Earth’s core into bb̄ quarks with the optimized binning. The momentum (1st column) and zenith angle (2nd -5th columns) distributions
are shown for 19 samples used in the analysis. Plots contain expectedsignal from WIMP annihilation (filled histogram) and the SK-I-IV atmospheric neutrino data (black points). In all panels the error bars
represent the statistical uncertainty. . . . . . . . . . . . . . . . . . . . . . 97
10.14Signal expectation (filled histogram) from Fig. 10.13 and the SK-I-IV
atmospheric neutrino data (black points) for UP-µ samples. . . . . . . . 98
10.15The distribution of ∆χ2toy = χ2β0 =0 − χ2min for Mχ = 6 GeV, bb̄ annihilation channel. Vertical line shows the critical value ∆χ2c , such that 90%of the ToyMC experiments have ∆χ2toy < ∆χ2c . . . . . . . . . . . . . . . 99
10.16The distribution of β 90 for Mχ = 6 GeV, bb̄ annihilation channel. Vertical lines shows the median (black), ±1σ (green) and ±2σ (yellow). . . 100
10.17The sensitivity expectation for a null WIMP hypothesis (dotted lines)
and its ±1σ (green band) and ±2σ (yellow band) uncertainty is presented for the bb̄ (top), τ + τ − (middle) and W + W − (bottom) annihilation channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
10.18Comparison between 90% upper limits on SI WIMP-nucleon scattering cross-section for bb̄ annihilation channel, calculated with standard(black line) and optimized (blue line) binning. The significant improvement for Mχ > 100 GeV is visible. . . . . . . . . . . . . . . . . . . 102

xx
11.1 The momentum (1st column) and zenith angle (2nd -5th columns) distributions before and after the fit are shown for 19 samples used in theanalysis. See detailed description in text. . . . . . . . . . . . . . . . . . 104
11.2 Heat map plot showing the tested parameter space of WIMP masses(X - axis) and WIMP contribution β (Y - axis) for three consideredannihilation channels: bb̄ (top), τ + τ − (middle) and W + W − (bottom).
The color represents χ2 value of the fit to data. . . . . . . . . . . . . . . 105
11.3 The 68%, 90% and 99% C.L contours of allowed regions in tested parameter space of WIMP masses (X - axis) and WIMP contribution β(Y - axis) for three considered annihilation channels: bb̄ (top), τ + τ −(middle) and W + W − (bottom). . . . . . . . . . . . . . . . . . . . . . . . 106
11.4 The fitted number of dark matter induced neutrinos together with
90% and 99% C.L. sensitivity contours as a function of WIMP mass
for three considered annihilation channels: bb̄ (top), τ + τ − (middle)
and W + W − (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
11.5 The distribution of fitted values of the systematic errors ei , given inunits of σ, at the global best f it point from the fit with standard binning (bb̄ annihilation channel, Mχ = 150 GeV, β = 0.0007). . . . . . . . 108
11.6 Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with standard binning (part I). . . . . . . . . . . 109
11.7 Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with standard binning (part II). . . . . . . . . . . 110
11.8 Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with standard binning (part III). . . . . . . . . . 111
11.9 The 90% upper limits on dark matter induced muon neutrino flux forbb̄ (blue), τ + τ − (green) and W + W − annihilation channel, comparedwith expectations from the sensitivity studies (dashed lines). . . . . . . 112
11.10The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section
for bb̄ (blue) and τ + τ − (green) annihilation channels, for Mχ < 100 GeV.
The visible peaks correspond to resonant capture on the most abundant elements 16 O, 24 Mg, 28 Si, 56 Fe, and their isotopes. Positive result
claimed by DAMA/LIBRA (Bernabei et al., 2013) is shown for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
11.11The momentum (1st column) and zenith angle (2nd -5th columns) distributions before and after the fit are shown for 19 samples used in theanalysis. See detailed description in text. . . . . . . . . . . . . . . . . . 114
11.12The fitted number of dark matter induced neutrinos together with
90% and 99% C.L. sensitivity contours calculated with optimized binning, plotted as a function of WIMP mass for three considered annihilation channels: bb̄ (top), τ + τ − (middle) and W + W − (bottom). . . . . 115
11.13The 90% C.L. upper limit on the fitted number of dark matter induced
neutrinos of all flavors from WIMP annihilation into bb̄ (top), τ + τ −(middle) and W + W − (bottom) channel as a function of the mass ofrelic particles. The sensitivity expectations for a null WIMP hypothesis (dotted lines) and their ±1σ (green bands) and ±2σ (yellow bands)
uncertainty calculated in Sec. 10.4 are shown. . . . . . . . . . . . . . . . 116
11.14The distribution of fitted values of the systematic errors ei , given inunits of σ, at the global best f it point from the fit with optimized binning (W + W − annihilation channel, Mχ = 100 GeV and β = 0.00035).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

xxi
11.15Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with optimized binning (part I). . . . . . . . . . 118
11.16Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with optimized binning (part II). . . . . . . . . . 119
11.17Global best f it values of the systematic error parameters, ei , given inunits of σ, from the fit with optimized binning (part III). . . . . . . . . . 120
11.18The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section
for bb̄ (blue), τ + τ − (green) and W + W − (maroon) annihilation channels. The visible peaks correspond to resonant capture on the mostabundant elements 16 O, 24 Mg, 28 Si, 56 Fe, and their isotopes. The results are compared with previous SK result (Desai et al., 2004) (dottedcyan line), as well as positive result claimed by DAMA/LIBRA (Bernabei et al., 2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
11.19The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section
for bb̄ (blue), τ + τ − (green) and W + W − (maroon) annihilation channels. For comparison the results from IceCube (Aartsen et al., 2017a)(dotted line) and ANTARES (Albert et al., 2017b) (dashed line) are
shown, as well as positive result claimed by DAMA/LIBRA (Bernabei et al., 2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
12.1 Favored regions obtained by interpreting the observed positron andelectron excesses as due to dark matter annihilation in µ+ µ− . Greenregion is favored by PAMELA (at 3σ), red region is favored by the
global fit of FERMI, HESS and PAMELA data (at 3σ) (Meade et al.,2010), and blue region is favored by AMS-02 data (at 2σ) (Di Mauroet al., 2016). The 90% C.L. limits from SK data are plotted with solid
purple line for "ON-OFF souce" analysis (this thesis), and with solidline for "Global fit" approach (Mijakowski, 2018). NFW halo model isassumed in all cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
12.2 The upper 90% C.L. limits on the WIMP-nucleon SI scattering crosssection for the bb̄ (blue), τ + τ − (green) and W + W − (maroon) annihilation channel from the SK data, compared with the results from direct
detection experiments: LUX (Akerib et al., 2017) (orange) and PICO60 (Amole et al., 2017) (purple), and possible signal from DAMA (Bernabei et al., 2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
D.1 An example of a measurement α̂ which can give results in unphysical region. If one assumes that α, the quantity one tries to measure,cannot lie in the unphysical region, but can lie anywhere in the physical region (no prior knowledge), then Bayes’ theorem says the newknowledge of distribution of α (given our measurement α̂) is given by
the shaded function after appropriate normalization. . . . . . . . . . . 150

xxiii

List of Tables
2.1

Table of the SM particles and their SUSY partners. Particles with spinj in the SM have supersymmetric partners with spin | j − 1/2|. . . . . . 10

3.1

The best-fit values and 3σ allowed ranges of the neutrino oscillation
parameters, derived from a global fit of the current neutrino oscillation data (based on (Capozzi et al., 2016)). The values (values inbrackets) correspond to normal (inverted) hierarchy m1 < m2 < m3
(m3 < m1 < m2 ). The definition of ∆m2 used is ∆m2 = m23 − (m22 +m21 )/2. Thus, ∆m2 = ∆m231 − ∆m221 /2 > 0, if m1 < m2 < m3 , and∆m2 = ∆m232 + ∆m221 /2 < 0 for m3 < m1 < m2 . . . . . . . . . . . . . . 23

4.1
4.2

The values of threshold energy for e± , µ± and π ± . . . . . . . . . . . . . 32
Summary of the differences between each of the SK periods. . . . . . . 36

5.1
5.2

Livetime of SK-I, SK-II, SK-III and SK-IV data sets. . . . . . . . . . . . . 41
Summary of event subsamples for atmospheric neutrino events at
Super-Kamiokande. For each subsample, the standard bins in cosineof the zenith angle and momentum (or visible energy) are specified. . . 44
The global best fit values of neutrino oscillation parameters from (Olive,2014) fixed during the fit. The uncertainties on the parameters values
are treated as systematic errors in the fit. . . . . . . . . . . . . . . . . . . 46

5.3

6.1

The parameters of Eq. 6.1 for Moore (Moore et al., 1999), NFW (Navarro,
Frenk, and White, 1997) and Kravtsov (Kravtsov et al., 1998) halo profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7.1

The results of the optimization of an ON-source region size assuming
dark matter annihilation for NFW, Moore and Kravtsov halo profile.
The results for decay scenario are the same for all models, and thesize of 60◦ is the result of the requirement that ON- and OFF-source
regions cannot overlap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

8.1

The number of events observed in ON-source (NON ) and OFF-source(NOFF ) regions for each considered event classes together with resulting asymmetry (A) and the corresponding statistical errors (σ∆N and
σA ). The optimal size of the ON-source region is determined separately for each group of event categories. . . . . . . . . . . . . . . . . . 68
The number of neutrino events observed in ON-source and corresponding OFF-source regions for each considered µ-like event class.
The optimal size of the ON-source region was determined separately
for each class. The last column shows the upper 90% C.L limit on theallowed difference in number of signal events between two considered regions. Results for dark matter annihilation scenario. . . . . . . 70

8.2

xxiv
8.3

The number of neutrino events observed in ON-source and corresponding OFF-source regions for each considered µ-like event class.
The optimal size of the ON-source region is constrained to be 60◦
in order to no not have overlapping between ON- and OFF-source
regions. The last column shows the upper 90% C.L limit on the allowed difference in number of signal events between two consideredregions. Results for dark matter decay scenario. . . . . . . . . . . . . . 73

9.1

The composition of the Earth’s core and mantle (McDonough, 2003). . 76

10.1 Optimized binning in cosine of the zenith angle for FC SubGeV, FC
MultiGeV, PC and UP-µ samples. . . . . . . . . . . . . . . . . . . . . . . 95
10.2 The calculated atmospheric neutrino background expectation for first
four bins in UP-µ samples. . . . . . . . . . . . . . . . . . . . . . . . . . . 98
11.1 The best f it points from the fit with standard binning, for the threeconsidered annihilation channels (bb̄, τ + τ − and W + W − ). The corresponding χ2 values are compared with atmospheric neutrino background only hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
11.2 The best f it points from the fit with optimized binning, for the threeconsidered annihilation channels (bb̄, τ + τ − and W + W − ). The corresponding χ2 values are compared with atmospheric neutrino background only hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

xxv

List of Abbreviations
ATIC
BR
CC
CDM
CDMS
CL
CMB
CMS
CoGeNT
CRESST
DEC
DONUT
EROS
FC
FERMI-LAT
GC
GPS
GUT
HST
ID
LHC
LSP
LUX
MACHO
MC
MOND
MSSM
MSW effect
NC
NOνA
OD
OGLE
PAMELAPANDAXPCPDFPMNS matrix
PMT
PQSM
RA
RENO
SD
SI

Advanced Thin Ionization Calorimeter
Branching Ratio
Charged Current
Cold Dark Matter
Cryogenic Dark Matter Search
Confidence Level
Cosmic Microwave Background
Compact Muon Solenoid
Coherent Germanium Neutrino Technology
Cryogenic Rare Event Search with Superconducting Thermometers
Declination
Direct Observation of the Nu Tau
Expérience pour la Recherche d’Objets Sombres
Fully Contained
Fermi Large Area Telescope
Galactic Center
Global Positioning System
Grand Unification Theory
Hubble Space Telescope
Inner Detector
Large Hadron Collider
Lightest Supersymmetric Particle
Large Underground Xenon experiment
Massive Compact Halo Objects
Monte Carlo
Modified Newtonian Dynamics
Minimal Supersymmetric Model
Mikheyev Smirnov Wolfenstein effect
Neutral Current
NuMI Off-Axis νe Appearance experiment
Outer Detector
Optical Gravitational Lensing Experiment
Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics
Particle and Astrophysical Xenon Detector
Partially Contained
Probability Density Function
Pontecorvo Maki Nakagawa Sakata matrix
Photomultiplier Tube
Peccei-Quinn extended Standard Model
Right Ascension
Reactor Experiment for Neutrino Oscillations
Spin Dependent
Spin Independent

xxvi
SK
SM
SNO
SUSY
T2K
TPC
UPMU
WIMP
WMAP

Super-KamiokandeStandard Model
Sudbury Neutrino Observatory
Supersymmetry
Tokai to Kamioka
Time Projection Chamber
Upward-going Muon
Weakly Interacting Massive Particle
Wilkinson Microwave Anisotropy Probe

1

Chapter 1

Introduction
Detecting and elucidating the nature of a dark matter is one of the main goals of
the astrophysics and particle physics nowadays. Dark matter neither emits or absorbs light, nor does it interact electromagnetically and cannot be observed directlywith telescopes. However, its existence and properties can be inferred from its gravitational effects on visible matter, radiation, and on the large-scale structure of the
Universe. According to studies of the cosmic microwave background and on predictions made by the standard cosmological model (ΛCDM), dark matter is expectedto account for a large part of the total mass in the Universe (Ade et al., 2016).
Various hypotheses regarding the nature of the dark matter have been proposed.
Most of them suggest composition of new type, non-baryonic particles, and theirproduction mechanisms going beyond the Standard Model of particle physics. In
this thesis we will focus on widely accepted proposal that dark matter consist of non
relativistic, neutral, long-lived Weakly Interacting Massive Particles (WIMPs). It is
expected that they are present in the whole Universe forming large invisible structures which encompass visible matter formations (Einasto, 2009). One of the commonly considered example of WIMP is the lightest supersymmetric particle, neutralino χ (Jungman, Kamionkowski, and Griest, 1996)
There are three complementary strategies for dark matter detection consisting of
direct, indirect, and collider-based searches. The direct methods are based on theassumption that WIMPs can be elastically scattered on baryonic nuclei. Many experiments attempt to measure the kinetic energy of the resulting nuclear recoils, butcurrent results are inconsistent and controversial (see Chapter 2). The other, indirect
method, focuses on a search for products of dark matter self-annihilation or decay,such as antimatter, photons or neutrinos. Alternatively, to those methods, there areattempts to produce dark matter particles in the high energy particle accelerators
like Large Hadron Collider (LHC).
This thesis aims at the indirect search for dark matter, concentrating on a search
for WIMP-induced neutrinos. Neutrinos are expected to be produced in the annihilation of WIMPs taking place in the entire cosmic space - both in the center partsof galaxies as well as in their outer regions. The decay of the dark matter is also
discussed in the literature for non-standard WIMP candidates, which may lead to
production of neutrinos as well (Feldstein and Fitzpatrick, 2010).
Neutrinos can provide very precise information on their source position while traversing unaffected through galactic scales. Moreover, their energy remains unchanged
during propagation providing valuable information about energy spectra generated

2

Chapter 1. Introduction

in dark matter annihilation/decay processes. Neutrinos originating from the annihilation/decay of the relic particles could be created directly or in subsequent decays of mesons and heavy leptons. The energy spectrum of these neutrinos andbranching ratio for their production is model dependent. In the following thesis,
various WIMP annihilation/decay scenarios and various models of the anticipateddark matter distribution in the galactic halo are studied.
In the analyses of data from neutrino telescopes, the reconstructed direction of incoming neutrino is the main selection criterion. The searches focus on the regions
where dark matter density is expected to be larger. For instance, it is believed thatmassive celestial objects like the Sun, the Earth, or the region of the Galactic Center
could gravitationally bound dark matter particles. It is expected that non-relativistic
WIMPs present in the halo can interact elastically with baryonic matter inside suchobjects with a cross section of the electroweak scale (< 10−38 cm2 ) and occasionallyloose enough energy so they cannot escape the strong gravitational potential. Dueto the consecutive interactions, WIMPs would naturally accumulate in the core ofheavy celestial objects and effectively annihilate there. Among many annihilation
products, only neutrinos could escape dense annihilation region. Their investigation
could constrain the WIMP-nucleon scattering cross section based on the relationshipbetween capture and annihilation rate.
This thesis presents the search for dark matter induced neutrinos based on the datacollected with the Super-Kamiokande (SK) detector in years 1996-2016. It stars withan overview of the dark matter in Chapter 2, including the observational evidence
and possible candidates, methodology of dark matter searches and current experimental results. Neutrinos which are one of the possible products of dark matterannihilation or decay are described in Chapter 3, which starts with a short historicalintroduction, then discuss neutrino oscillation formalism and their interactions, andat the end, the natural and artificial neutrino sources. The atmospheric neutrinos
are discussed in more details since they cover wide energy range (from hundredsof MeV up to tens of TeV) where dark matter induced neutrinos are expected. The
description of the large water Cherenkov neutrino detector and principle of its operation is the subject of Chapter 4.
The author of this thesis joined the Super-K collaboration in November 2013. The
main author’s activity in the experiment is related to the search for dark matter induced neutrinos using atmospheric neutrino data. The data and Monte Carlo samples, as well as results of standard atmospheric neutrino oscillation analysis are presented in Chapter 5. The two separated analyses were performed during the time of
the PhD by the author. The first one covers the search for dark matter induced neutrinos from the Milky Way, and it is described in Chapters 6 - 8. Chapter 6 discuss
the three different Milky Way halo models investigated in the analysis, dark matterannihilation and decay scenario and resulting expectation for neutrino signal. The
simulation of WIMP induced neutrinos, which was developed for the purpose ofthis analysis is discussed in Chapter 7. This chapter contains also the concept of ONOFF source search. The results including upper limits on the self-annihilation crosssection and lower limits on dark matter lifetime, obtained for dark matter particle
masses ranging from 1 GeV to 10 TeV are presented in Chapter 8. The second analysis performed by the author covers search for dark matter induced neutrinos fromthe Earth’s core and is described in Chapters 9 - 11. Chapter 9 discusses WIMP annihilation in the center of the Earth, including the calculations of annihilation rate andChapter 1. Introduction

3

expected neutrino flux. The analysis technique, signal simulation and performed
sensitivity studies for the Super-Kamiokande detector are discussed in Chapter 10.
Finally Chapter 11 contains the fit results and constraints on WIMP-nucleon spin
independent scattering cross-section. Both of the analysis were performed independently by the author. The results were officially approved by the Super-Kamiokande
Collaboration, presented during international conferences and will be publish. The
last Chapter 12 contains summary and outlook.

5

Chapter 2

Dark Matter
2.1

Observational Evidence

There are many compelling evidence indicating the presence of dark matter in the
Universe (Bertone, Hooper, and Silk, 2005). They originate at very different scales:from cosmological ones (through the analysis of angular anisotropies in the cosmic microwave background radiation), down to galactic scales (considering gravitational lensing and the dynamics of galaxies).

2.1.1

Galaxy Clusters

The first observational clue for the existence of dark matter was by Fritz Zwicky in1933 (Zwicky, 1933). He noticed that galaxies in the Coma Cluster were rotating
faster than expected when only visible matter was considered. Based on these observations, he suggested that the major part of matter is invisible, hence the namedark matter. At first, this claim was not fully approved by most scientists. In time,
however, more evidence have emerged. Similar observations in the Virgo cluster
were made later by Sinclair Smith at the Mount Wilson Observatory in 1936 (Smith,1936). He had came to the same conclusion as Zwicky.

2.1.2

Galaxy Rotation Curves

The distributions of rotational velocities of stars in galaxies are another form of evidence which support the dark matter hypothesis. This observation was first madeby Vera Rubin’s group in the 70s an 80s of the 20th century (Rubin and Ford Jr, 1970).
The rotational velocities of stars were measured at different distances from the galactic center, and did not agree with the theoretical predictions based solely on visible matter contribution. Most notably, the stars in outer region of the galaxy movefaster than expected. This lead to the conclusion that there must be additional invisible mass, which creates large structures that extend far beyond the visible edges ofgalaxies.
In 1991, Begeman, Broels, and Sanders presented an analysis of the rotation curvesof ten carefully selected galaxies (Begeman, Broeils, and Sanders, 1991). Using accurate and high resolution 21 cm emission lines from neutral hydrogen, they modeled
the mass distribution of the galaxies (see example in Fig. 2.1). The study determinedthe contribution to the rotation curve from three types of matter (gas, luminous anddark matter), and showed that the dark matter contribution becomes dominant withincreasing distance from the galactic centre.

6

Chapter 2. Dark Matter

F IGURE 2.1: An example of a galaxy rotation curve for NGC 6503
dwarf spiral galaxy studied by Begeman, Broels, and Sanders. The
solid line is the theoretical rotation curve and the data points witherror bars are the measured object speed. The segmented lines show
the contributions from gas, luminous matter, and dark matter. Figure
is taken from (Begeman, Broeils, and Sanders, 1991)

Dark matter is the widely accepted explanation for this observations, however, numerous alternatives have also been proposed. Most of them postulate a modification to the law of gravity, replacing the laws established by Sir Isaac Newton andAlbert Einstein. These theories can be referred to as Modified Newtonian Dynamics(MOND) (Milgrom, 1983). However, even when MOND is taken into consideration
there is still not enough luminous matter. Further, the MOND theory is incompatible
with general relativity. Later modifications of the theory based on general relativity
have been more successful (and it is still an active area of research), but it is unlikely to be successful at resolving the dark matter problem. Detailed studies of thecosmic microwave background, gravitational lensing and Big Bang primodial nucleosynthesis strongly support the dark matter hypothesis and cannot be explain by
MOND theories.

2.1.3

Gravitational Lensing

Dark mater existence can also be inferred from observations of gravitational lensing.
When light emitted from a distant source passes near a massive object, the trajectoryof the photons is bent due to the gravitational field, and can cause the distant source
image to be magnified or distorted. Based on this effect, the total mass in the gravitational field can be inferred. As one example among many, Fig. 2.2 shows the mass
profile of the Bullet Cluster (as measured in August 2006 (Clowe et al., 2006)). Here,the collision between two galaxy clusters caused a separation of dark and baryonicmatter. The electromagnetic interactions between passing gas particles caused thebaryonic matter to slow down near the impact point, as indicated by the emission of
X-rays. Careful measurements show that the hot gas in the Bullet Cluster contains

2.1. Observational Evidence

7

about 7 times more baryonic matter than the stars in the cluster’s galaxies combined.
On the other hand, gravitational lensing observations show that the majority of themass composition of these galaxies simply passed through each other without interacting. Unlike the galactic rotation curves, this evidence for dark matter existence
cannot be explained by the modification of laws of gravity.

F IGURE 2.2: Left: Visible light image of the Bullet Cluster from theMagellan Telescope. Right: The Chandra X-ray Observatory image of
the Bullet Cluster showing the location of the x-ray emission of the
hot gas. In both panels the mass density contours are shown withgreen lines. Figure taken from (Clowe et al., 2006)

.

2.1.4

Cosmic Microwave Background

The Cosmic Microwave Background (CMB) is the oldest electromagnetic radiationin the Universe, dating back to the epoch of recombination (approximately 300,000
years after the Big Bang). Measurements of the CMB allow for an independent measurement of the total mass and energy contained in the Universe. Dark matter does
not interact directly with electromagnetic radiation, but it does affect the CMB by its
gravitational potential (mainly on large scales) and by altering the density and velocity of ordinary matter. Ordinary and dark matter perturbations therefore evolve
differently with time, and leave different imprints on the CMB.
The Wilkinson Microwave Anisotropy Probe (WMAP) was the first experiment todevelop a full sky map of temperature fluctuations in the CMB, and its measurements played the key role in establishing of the current Standard Model of Cosmology, namely the ΛCDM model. ΛCDM implies a flat Universe dominated bydark energy, supplemented by dark and baryonic matter (Larson et al., 2011). The
latest results obtained by Planck mission team implies that total mass - energy of
the Universe contains lest then 5% ordinary matter, 26% dark matter and 69% darkenergy (Ade et al., 2016).

2.1.5

Big Bang Nucleosynthesis

Big Bang nucleosynthesis (also known as primordial nucleosynthesis) makes predictions on the amount of helium, hydrogen, and lithium contained in the Universe,
and further, the required baryonic matter densities needed to produce these abundances. Big Bang nucleosynthesis predictions match the observed abundances only
when the baryonic matter accounts for 4 - 5% of the critical density of the Universe (Schramm and Turner, 1998). This is strong indication for non - baryonic dark
matter.

8

2.1.6

Chapter 2. Dark Matter

Structure Formation

Dark matter seems to be essential in evolution of the Universe. Its presence is required in cosmological models of the Big Bang. Significant amount of non-baryonic,
cold dark matter (CDM) is necessary to explain the large-scale structure formation of
the Universe (Tegmark, 2004). If the majority of the non-baryonic dark matter consists of the hot dark matter (HDM) - particles that were relativistic at the time whenstructure formed, the small sub-structures in the large scale galaxy are expected to
be flattened, which is inconsistent with observations. If there were only ordinary
matter in the Universe, there would not have been enough time for density perturbations to grow into the galaxies and clusters that we see today.

2.2

Dark Matter Candidates

Despite the evidence for the existence of dark matter, its nature is still unknown.
At first, non-luminous heavy baryonic objects, such as black holes, neutron stars
and brown dwarfs (collectively named as Massive Compact Halo Objects, or MACHOs), were considered a possible candidate for dark matter. However, astronomical surveys for gravitational microlensing, including the MACHO (Alcock et al.,2001), EROS (Tisserand et al., 2007) and OGLE (Udalski et al., 1992) projects, alongwith the Hubble Space Telescope (HST) searches for ultra-faint stars, have not foundenough of MACHOs, and indicated that they could constitute only a very small portion of dark matter (Freese, Fields, and Graff, 2000). Since it has been proved thatneutrinos have mass and are abundant in the Universe, they were also considered agood candidate. However, neutrinos can only form a small fraction of the dark matter, due to limits from a large-scale structure formation models and high-redshift
galaxies observations (Hannestad et al., 2010).
One can distinguish two possible creation mechanisms among the dark matter candidates, thermal creation in the early Universe and non-thermal creation in a phasetransition. Thermal and non-thermal relics have a different relic abundance andproperties such as mass and couplings, so the distinction is especially important for
dark matter detection efforts. Here we focus on thermally created dark matter. In
the early Universe, thermal equilibrium was obtained. In case of particles (which
are created thermally), their number density was roughly equal to the number density of photons. Then, as the Universe cooled, the number of dark matter particles
would decrease until the temperature of Universe finally dropped below the dark
matter particle mass. At this point, their creation would require being on the tailof the thermal distribution, the number density would drop exponentially, and theprobability of pair annihilation would become small. The number density would"freeze-out" and the Universe would be left with a substantial number of dark matterparticles today, approximately ΩW I MP ≈ 10−26 cm3 s−1 / < σA v >, where < σA v >is the thermally averaged cross section for dark matter annihilation into Standard
Model (SM) particles (Steigman, Dasgupta, and Beacom, 2012).
The dark matter must be stable or long-lived, since it was produced after the Big
Bang and is still present today. Dark matter is also required to be dynamically cold
(not relativistic) so that it can clump and form gravitationally bound structures. The
SM does not provide a viable non-baryonic candidates for dark matter particles andthe existence of dark matter is one of the most compelling evidence for physics beyond the Standard Model. The best motivated candidates which would be able to2.2. Dark Matter Candidates

9

fulfill the above criteria are those which arise in high-energy completions of the SM,
which solve also other fundamental problems of particle physics and cosmology.
Examples of the considered particles are:• Neutralinos or Gravitinos in supersymmetric extensions of the SM, whichsolve also the hierarchy problem.
• The lightest sterile neutrino in the νMSM which explains also neutrino masses
and mixing as well as the baryon asymmetry of the Universe via the introduction of right - handed sterile neutrinos featuring a Majorana mass.
• Axion in the Peccei - Quinn extended SM (PQSM) which solves also the strong
CP problem.
In this thesis, we will focus on neutral particles, which would be able to reproduce
the required dark matter density in the Universe derived from CMB measurements,
additionally having a mass of the order of the electroweak scale and belonging toa group referred to as Weakly Interacting Massive Particles (WIMPs). Presently
WIMPs, with mass in the range from several GeV to few TeV, are considered the best
motivated dark matter candidate supported by supersymmetry theories (SUSY),
which provide one of the most popular WIMP candidate: the lightest supersymmetric particle (LSP), namely the neutralino χ (Jungman, Kamionkowski, and Griest,
1996). In this thesis, we will consider neutralino as a dark matter candidate (or any
other with similar phenomenology). More details about neutralinos can be found in
the following Sec. 2.2.1.

2.2.1

Neutralino as a Dark Matter Candidate

Supersymmetry (SUSY) was originally introduced to solve some of the outstanding
problems of the Standard Model (SM), such as the hierarchy problem, gauge coupling unification, and radiative electroweak symmetry breaking. SUSY also predicts
new ideas for matter-antimatter asymmetry of the Universe and prospects for the
GUT/Planck scale where all forces unified.
In SUSY, each SM particle has a supersymmetric partner with spin | j − 1/2|. The
minimal extension of the SM of particle physics is described by the Minimal Supersymmetric Standard Model (MSSM). The MSSM contains the smallest possible fieldcontent necessary to give rise to all the fields of the SM. In Tab. 2.1, the SM particles
and corresponding SUSY partners are shown.
A new symmetry, R-parity is introduced for particles in the SUSY theory, which
is defined as:
R = (−1)3B+ L+2j ,(2.1)
where B is the baryon number, L is the lepton number, and j is particle spin. Thisimplies that R = +1 for SM particles and R = −1 for their supersymmetric partners.
Therefore, if R-parity is conserved, supersymmetric particles can only be created or
annihilated in pairs, in reactions of ordinary particles. It also means that a single
supersymmetric particle can only decay into final states containing an odd numberof supersymmetric particles. In particular, this makes the lightest supersymmetricparticle stable (LSP), since there is no kinematically allowed state with negative Rparity which it can decay to.

10

Chapter 2. Dark MatterIn a supersymmetric extensions of the SM, the superpartners of the Z boson (Zino),
the photon (photino) and two neutral Higgs bosons (higgsino), have the same quantum numbers, so they can mix to form four eigenstates of the mass operator called
neutralinos (χ̃01 , χ̃02 , χ̃03 , χ̃04 ). In many models, the lightest of the four neutralinos χ̃01
(from now on simply noted as χ) turns out to be the LSP. As a heavy, stable particle,
which is electrically neutral and thus neither absorbs nor emits light, the LSP is an
excellent candidate for WIMP.
TABLE 2.1: Table of the SM particles and their SUSY partners. Particles with spin j in the SM have supersymmetric partners with spin
| j − 1/2|.

2.3

Particle

Spin

Name

d, c, b, u, s, t
e, µ, τνe , νµ , ντ
G
W±
Z
γ
g
h

1/2
1/2
1/2
2
1
1
1
1
0

quarksleptons
neutrinos
graviton
weak boson
weak boson
photongluon
higgs boson

Superpartnerd,˜ c̃, b̃, ũ, s̃, t̃ẽ, µ̃, τ̃
ν̄
G̃
W̃ ±
Z̃
γ̃
g̃
h̃

Spin

Name

0
1/2
0
3/2
1/2
1/2
1/2
1/2
1/2

squarks
sleptons
sneutrinos
gravitinoWino
Zino
photinogluinohiggsino

Dark Matter Detection

Weakly Interacting Massive Particle as a dark matter candidate is a well posed scientific hypothesis and a subject of experimental verification. Numerous experiments
attempt to detect dark matter using different methods and a wide variety of techniques. The experiments can be divided into three categories: direct detection experiments, which search for the scattering of dark matter particles off atomic nuclei;
indirect detection, which search for the products of WIMPs annihilations; and analternative approach to the detection of WIMPs is their production in the laboratory
in very high energy collisions (see Fig. 2.3).

2.3.1

Direct Detection

It is expected that dark matter local density in the Galaxy at the Solar system position is 0.3 GeV/cm3 (Yüksel et al., 2007). That implies that many of dark matterparticles must pass through every square centimeter of the Earth in each second. In
direct detection method, one tries to detect the nuclear recoils originated from therare interactions of the dark matter particles with the target nuclei (see Fig 2.6).
Two kind of interactions can be expected from WIMP-nucleon scattering. The firstinteraction is a spin dependent (SD) axial-vector interaction, where WIMPs couple
to the spin content of a nucleon. The cross-section for SD scattering ∝ J ( J + 1), where
J is spin of the nucleus. The SD scattering can be efficient when a nucleus has large
number of unpaired protons or neutrons. The second interaction is a spin independent (SI) scalar interaction, where the WIMP couples to the nucleus as a whole. The2.3. Dark Matter Detection

11

F IGURE 2.3: Simplified diagram showing the three different dark
matter detection channels. The direct detection experiments (→) look
for the recoil introduced by a WIMP (χ) on a SM particle in the detector. Indirect detection experiments (↓) look for the SM annihilation
products of WIMPs. Collider experiments (↑) look for the creation of
WIMPs in Standard Model particle collisions.

cross section for SI scattering ∝ A2 , where A is an atomic mass number. Therefore,
the cross section increases dramatically with the mass of the target nuclei, and typically dominates over spin-dependent scattering in current experiments which use
heavy atoms as targets. The possible tree level Feynman diagrams for SD and SI
scattering are shown in Fig. 2.4 and 2.5 respectively.

F IGURE 2.4: Feynman diagrams contributing to the spin-dependent
elastic scattering of neutralinos from quarks.

The expected energy of nuclear recoils is in the range from several to hundreds ofkeV depending on the mass of dark matter particle and type of the detector. The
most effective scattering can be achieved if target nucleus mass is similar to WIMP
mass. In this energy range the main contribution to the experimental backgroundcomes from interactions of α-particles, neutrons, electrons, and photons on the detector target material. These backgrounds originate from decays of radioactive isotopes present in the materials surrounding the detectors, in airborne contaminants,
or from within the detectors themselves. Therefore, appropriate shielding with passive and active materials as well as veto detectors around the experiment are very
important.

12

Chapter 2. Dark Matter

F IGURE 2.5: Feynman diagrams contributing to the scalar elasticscattering amplitude of a neutralino from quarks.

F IGURE 2.6: A sketch idea of dark matter direct detection.

Depending on the type of detector, energy of nuclear recoils can be transferred toscintillation, ionization, phonon signals, or a combination thereof. Some experiments (e.g. XENON (Aprile et al., 2005), LUX (Akerib et al., 2013), PANDA-X (Caoet al., 2014)) are using liquid xenon (LXe), which has high radiopurity and highdensity, and has proven to be very good target material. In dual phase xenon time
projection chambers (TPC), scintillation light from nuclear recoil and the ionizationfrom electrons accelerated in the electric field can be detected. The ratio of ionization to scintillation signal allows for a very effective separation of electron recoil,from nuclear recoil events. This is very important sice the dominant background fordark matter searches consists of electrons. The flux of neutrons and α-particles isapproximately six orders of magnitude lower than flux of electrons. However, interactions of neutrons and α-particles are expected to yield similar signatures as a
WIMP-induced signal. The only difference is that any WIMPs that interact in the detector will have negligible chance of repeated interaction. Neutrons and α-particles,on the other hand, have a reasonably large chance of multiple collisions within thetarget volume, with the frequency which can be accurately predicted. Therefore,
only the multiple scattering of neutrons and α-particles in the detector allows to distinguish them from interactions of WIMPs, which are not expected to scatter morethan once.

2.3. Dark Matter Detection

13

The technology used in ton-scale detectors yields very strong limits on the SI WIMPnucleon scattering cross-section, reaching below 10−46 cm2 for WIMP masses of 3040 GeV (see Fig. 2.7). Next generation of these experiments plan to increase target
volume to multi-ton scale and is expected to reach solar neutrino floor (the regionof WIMP parameter space where coherent neutrino-nucleus scattering constitute adominant background, see (Billard, Figueroa-Feliciano, and Strigari, 2014) for moredetails).

Counts

60

-1

0

1

2

3

4

NeutronWIMP search

40
20

NN score

0
1
0.5
0

-1

0

1

2

3

4

log(AP)
FIG. 2. Top: AP distributions for AmBe and 252 Cf neutron calibration data (black) and WIMP search data (red) at
3.3 keV threshold. Bottom: AP and NN score for the samedataset. The acceptance region for nuclear recoil candidates,deﬁned before WIMP search acoustic data unmasking using
neutron calibration data, are displayed with dashed lines andF IGURE 2.7: Latest limits on SI WIMPreveal no candidate events in the WIMP search data. Alphas
nucleoncross-section
as atimefuncfrom
the 222 Rnscattering
decay chain canbe identiﬁed by theirsignature
two peaksin the from
WIMP combined
search datationandof populate
WIMPthemass:
results214
at high AP. Higher energy alphas fromPo are producing
PandaX-II
Run 9 and Run 10 data (Cui etlargeracoustic signals.

al., 2017) (red) (the green band represents
the ±1σ sensitivity band), overlaid with reto sults
be 0.25± 0.09(0.96 ± 0.34)
single(multiple)-bubble
fromPandaX-II
2016(Tan et al., 2016)
133
events.
PICO-60
exposedto a et
1 mCi
Ba source(blue),
LUX was2017(Akeribal., 2017)(maboth before and after the WIMP search data, which,genta),andXENON1T2017(Aprileetal.,compared against a Geant4 [21] Monte Carlo simulation,
2017)(black).
gives a measured nucleation eﬃciency for electron recoil
events above 3.3 keV of (1.80 ± 0.38)×10−10. Combining this with a Monte Carlo simulation of the external
gamma ﬂux from [16, 22], we predict 0.026 ± 0.007 events
due to electron recoils in the WIMP search exposure. The
background from coherent scattering of 8 B solar neutrinos is calculated to be 0.055 ± 0.007 events.

SD WIMP-proton cross section [cm 2]

4
10 -37

10 -38

10 -3910 -40
PICO-60 C F

3 8

10

-41

10 1

10 2

2

10 3

WIMP mass [GeV/c ]FIG. 3. The 90% C.L. limit on the SD WIMP-proton crossFsection
IGURE
2.8:
LatestC3limits
on inthethickSD blue,
WIMPfrom
PICO-60
F8 plottedalongwith limitsscatteringfrom PICO-60
CF3 I (thick red)as[10],protoncross-section
a PICO-2L
func(thick purple) [9], PICASSO (green band) [14], SIMPLE (ortionof WIMP mass: results from PICOange) [15], PandaX-II (cyan) [35], IceCube (dashed and dot60
C3 F8[36],(Amoleet (dashedal., 2017)(thickted pink)
and SuperKand dottedblack)blue),[37, 38].
The indirect
from
IceCubeand SuperK
annialongwithlimits
limitsfrom
PICO-60
CF3 Iassume(Amolehilation to τ leptons (dashed) and b quarks (dotted). The
etal., region
2016a)(thickparameter
red), PICO-2L(Amoleetpurplerepresents
space of theconstrained
minimalsupersymmetricmodel of [39].
Additional
limits, notal.,2016b)(thick purple),
PICASSO(Behnkeshown for clarity, are set by LUX [40] and XENON100 [41]etal., 2017)(greenandband),
SIMPLE(comparable
to PandaX-II)
by ANTARES[42, 43](Fe(comparable toet
IceCube).
lizardoal., 2014) (orange), PandaX-II (Fuet al., 2017) (cyan), IceCube (Aartsen et al.,2017b) (dashed and dotted pink), and SuWIMP mass, are shown in Fig. 3 and 4. These limits,
perK(Choi et al., 2015) (dashed and dotcorresponding to an upper limit on the spin-dependent
tedblack). crossIndirect
cm2 for a
WIMP-proton
section limitsof 3.4 ×from
10−41IceCube−2
andSuperK
assumeannihilationto τ leptons
30 GeVc WIMP,are currently
the world-leading
constraints in the
WIMP-proton
sectorand(dashed)andb quarks spin-dependent(dotted). The
purindicate an improved sensitivity to the dark matter signal
ple region represents parameter space of theof a factor of 17, compared to previously reported PICO
constrained
minimal supersymmetric model
results.
of(Roszkowski,
Austri,and Trotta,2007).with
A comparison of our
proton-only
SD limits

We use the same shapes of the nucleation eﬃciency
neutron-only SD limits set by other dark matter search
curves for ﬂuorine and carbon nuclear recoils as found inexperiments is achieved by setting constraints on theRef. [8], rescaled upwards in recoil energy to account foreﬀective spin-dependent WIMP-neutron and WIMPthe 2% diﬀerence in thermodynamic threshold. We adopt
Bubble chamber experiments (e.g. PICO (Amoleet al., 2017))
to be extremely
proton couplings
an and aprovep that are calculated according
the standard halo parametrization [23], with the follow−2
−3
to
the
methodproposed
in
Ref.
[29].
The expectationcompetitive
PICO-60 uses a bubble chamber
filled
=0.3SD
GeVsearches.
c cm , vescFor= 544example,
km/s,
ing
parameters: ρDfor
values for the proton and neutron spins for the 19 F nu=
232
km/s,
and
v
=
220
km/s.
We
use
the
eﬀecvEarthowith 52 kg of C3 F8 located in the SNOLABcleus
undergroundlaboratory,
sets
the
most
are taken from Ref. [24]. The allowed region intive ﬁeld theory treatment and nuclear form factors de−2 crossstringent
direct-detection
constraint
to
date
on
the
WIMP-protonSDscattering
the
a
−
a
plane
is
shown
for
a
50
GeV
c
WIMP
in
n
p
scribed in Refs. [24–27] to determine sensitivity to both−41
2F
improves
theconFig.
5.
We
ﬁnd
that
PICO-60
C
3
8
spin-dependentandspin-independent
dark
matterintersection reaching 10 cm for WIMP masses of 30 GeV (see Fig. 2.8).
straints on an and ap , in complementarity with otheractions. For the SI case, we use the M response of Table
dark matter search experiments that are more sensitive
1 in Ref. [24], and for SD interactions, we use the sum
to the WIMP-neutron
coupling.
usethecryogenic
at very low
temperatures, whichand Σ′′ terms fromsame table.detectors
To im- operated
ofManythe Σ′ experiments
plement
theseinteractions
andform
factors,
we
use
the
The
LHC
has
signiﬁcant
to dark
matter,detect heat produced in electron and nuclear recoils. Cryogenicsensitivity
detectors(suchaspublicly available dmdd code package [27, 28]. The calcubut to interpret LHC searches, one must assume a speCRESST(Angloheretal.,2016),CDMS(Agneseetal.,2015),EDELWEISS(Hehn
lated Poisson upper limits at the 90% C.L. for the spinciﬁc model to generate the signal that is then lookedet
fordependent
WIMP-protonandspin-independent
WIMPin thedata. Despite
this subtlety,
the convention
hasal., 2016)) have proven to be very effective in
exploring
the light
dark matterregionnucleon elastic scattering cross-sections, as a function ofbeen to show LHC limits alongside more general direct

with WIMP mass < 10 GeV (see Fig. 2.9).

14

Chapter 2. Dark Matter

F IGURE 2.9: Experimental 90 % C.L. exclusion limit on the SI WIMPnucleon scattering cross section as a function of WIMP mass for the
combined fit from EDELWEISS-II detectors (Hehn et al., 2016) (solidred). The green and yellow band represent the 1 and 2 σ confidenceband of the expected median sensitivity (dashed black). Result of
the EDELWEISS BDT based analysis (dashed red) is shown for comparison. Colored regions show possible signals from CDMS-II (Si)
(Agnese et al., 2013) (blue), DAMA (Bernabei et al., 2013) (brown),
CRESST-II (Angloher et al., 2012) (pink) and CoGeNT (Aalseth et al.,2014) (orange). Other existing exclusion limits are from EDELWEISSII (Armengaud et al., 2012) (small red dashes), CoGeNT (Aalseth
et al., 2013) (orange), CRESST (Angloher et al., 2016) (pink), SuperCDMS (Agnese et al., 2014) (purple), XENON100 (Aprile et al., 2016)(black), CDMSlite (Agnese et al., 2015) (dashed violet) and LUX (Akerib et al., 2016) (green).

The event rate of a dark matter signal is expected to modulate annually due to relative motion of the Earth around the Sun. The expected event rate R is proportional
to the density of dark matter particles ρ, cross section for WIMP-nucleus elastic scattering σ and the speed of the Earth with respect to the dark matter halo V:
R ∝ ρ · σ · V.

(2.2)

The speed of the Earth with respect to the halo changes throughout a year due tocombination of the Earth’s motion around the Sun and the Sun’s motion aroundthe Galactic Center. Therefore, with a high statistics of collected dark matter particle interactions one would expect to see annual modulation of an observed event
rate. Such an effect was observed by DAMA/LIBRA experiment (Bernabei et al.,2013), which has been in operation since 1996. DAMA/LIBRA claims the observation of modulation at 9.3 σ obtained with a total exposure of 1.33 ton×year collected
over 14 cycles. The observed annual modulation is inconsistent with indirect andother direct detection bounds, but they were obtained using different target materials. The long standing DAMA anomaly is expected to be confirmed or resolvedin the near future with multiple new experiments (e.g. SaBRE (Tomei, 2017), PICOLON (Fushimi et al., 2017), ANAIS (Amaré et al., 2016), COSINE (Adhikari et al.,2.3. Dark Matter Detection

152017)). They are coming on-line now and rely on the identical detector technology
as DAMA/LIBRA.

2.3.2

Indirect Detection

Indirect detection experiments search for WIMP annihilation or decay products in
the Universe by investigating cosmic rays. The annihilation rate is proportional tothe velocity-averaged dark matter self-annihilation cross-section (< σA v >) and numerical density squared (n2χ ):Γ A ∝< σA v > ×n2χ =< σA v > ×

ρ2χ
,
Mχ2

(2.3)

where ρχ corresponds to dark matter particles density in the local halo. Most of the
SUSY models assume that dark matter particles would be their own antiparticles.
The particle-antiparticle pairs of WIMPs could annihilate, and depending on theirmass, produce leptons, quarks, gauge or Higgs bosons (see Fig. 2.10).

F IGURE 2.10: An illustration of a possible products of supersymmetric dark matter self-annihilation.

After subsequent decays of the primal annihilation products, various Standard Modelparticles can be created. The indirect detection searches focus on channels and energy ranges where it is possible to reasonably disentangle dark matter induced signals from the ordinary astrophysical background. There are few viable possibilities
such as gamma rays, neutrinos, and antimatter. Additionally, if the WIMPs are unstable, they could also decay into SM particles. In this case, the decay rate would be
proportional to dark matter density (see Chapter 6).

16

Chapter 2. Dark Matter

Antimatter
Since antimatter is much less abundant in the Universe than the ordinary matter,its excess in the cosmic rays may suggest that it originated in dark mater annihilation or decay. The searches are conducted using detectors placed on the Earth’s
orbit on satellites (FERMI-LAT (Atwood et al., 2009), PAMELA (Picozza et al., 2007)
and AMS-02 (Aguilar et al., 2016)), or on balloons (HEAT (Barwick et al., 1997),
ATIC (Chang et al., 2008) and GAPS (Ong et al., 2017)). High altitudes are required toreduce background induced by primary cosmic ray interactions in the atmosphere.
Data from the PAMELA satellite showed an excess of positrons from 10 GeV up to
100 GeV as compared to standard prediction of positron production in cosmic rays
fluxes. The result was compatible with previous results from HEAT and AMS-01 experiments, and later was confirmed in independent measurements by FERMI-LAT
and AMS-02 experiments. The most recent results from AMS-02 experiment are
shown in Fig. 2.11.

F IGURE 2.11: The electron flux and the positron flux measured by
AMS-02 experiment (Aguilar et al., 2016).

The excess could originate from self-annihilating or decaying dark matter and has
been extensively discussed in the literature, e.g. (Di Mauro et al., 2016). However,this interpretation is in tension with indirect bounds based on gamma-rays and neutrinos. On the other hand, astrophysical sources, such as pulsars could explain theobserved spectra. Recent measurement of nerby pulsars by HAWC and Milagro
indicate that these objects generate significant flux of high-energy positrons that issimilar in spectrum and magnitude to the positron fraction measured by PAMELA
and AMS-02 (Hooper et al., 2017).
Gamma Rays
Since some hints of the dark matter annihilations in the positron spectrum have been
observed, it is very important to consider the associated signals in the gamma ray
fluxes. Photons can be produced in many WIMP annihilation or decay channels.
Moreover, photons propagate in space without significant deflection, so they can

2.3. Dark Matter Detection

17

provide good angular information of the source position, and their observed energy
spectra also could be a good estimate of primary WIMP annihilation/decay spectra.
FERMI-LAT (Albert et al., 2017c) experiment attempts to search for gamma-ray lines
from the sky, looking at satellite galaxies, at the isotropic diffuse background, at clusters of galaxies, and at diffuse gamma rays from wide regions of the galactic halo. In
addition to satellite born experiments, such as FERMI-LAT, the gamma rays can bemeasured in Cherenkov telescopes such as MAGIC (Doro, 2017), HESS (Oakes et al.,2017) or VERITAS (Zitzer, 2017) and HAWC (Yapici, 2017). HESS performed a large
number of studies which are relevant for dark matter searches, such as observations
towards the Galactic Center, the Galactic Ridge, the Galactic Center Halo, a couple ofglobular clusters, a number of dwarf galaxies (Sagittarius, Carina and Sculptor andCanis Major), and the Fornax galaxy cluster. HESS has also looked at possible signals
from spikes of dark matter accumulated around Intermediate Mass Black Holes. The
VERITAS telescope has investigated a few dwarf spheroidal galaxies and the Comagalaxy cluster. The MAGIC telescope has investigated a few dwarf galaxies andthe Perseus galaxy cluster. HAWC performed a search for GeV-TeV photons resulting from dark matter annihilation or decay considering dwarf spheroidal galaxies(dSphs), the M31 galaxy and the Virgo cluster as sources, with 507 days of data collected in the full detector configuration. No statistically significant excess from thesesources has been observed.
Neutrinos
Neutrinos could be one of the direct products of dark matter annihilation/decay
or be produced in subsequent decays of baryons, bosons and leptons. Neutrinos
provide very good information about the source position and they can provide insight into areas where the dark matter induced signal to astrophysical backgroundratio can be maximized. Neutrino telescopes such as IceCube (Aartsen et al., 2017d),
ANTARES (Ageron et al., 2011), and Super-Kamiokande (Fukuda et al., 2003) aresearching for signals originating from the center of the Milky Way, the Sun or the
Earth. The latest results of searches for dark matter induced neutrinos from the center of our Galaxy are presented in Fig. 2.12.
Some fraction of WIMPs passing through the Sun or the Earth may scatter off protonor nuclei and loose energy. Due to these processes a large population of WIMPs may
accumulate at the center of these celestial bodies, increasing the chance that two ofthem will collide and annihilate. As the Sun is a large hydrogen target, the highsensitivity to the spin-dependent dark matter scattering can be achieved. Searches
for dark matter induced neutrinos from the Sun have been performed by various
neutrino detectors. The latest ones are presented in Fig. 2.13. No positive signal inneutrinos has been found so far.
This thesis presents the search for dark matter induced neutrinos from the Galactic Center and the Earth’s core using the data from the Super-Kamiokande detector.
The results of two analysis performed by the author are describes in Chapters 6 - 11.

18

Chapter 2. Dark Matter

F IGURE 2.12: The upper 90% C.L. limits from neutrino experiments
on dark matter self-annihilation cross section for the bb̄ (blue), W + W −(maroon), µ+ µ− (purple) and νν̄ (orange) annihilation channels. The
limits from Super-Kamionkande (Frankiewicz, 2017a) are plottedwith solid lines, IceCube (Aartsen et al., 2017c) with dotted lines and
ANTARES (Albert et al., 2017a) with dashed lines.

F IGURE 2.13: The upper 90% C.L. limits on the WIMP-proton SD
cross section (left) and WIMP-nucleon SI cross section (right) for thebb̄ (blue), τ + τ − (green) and W + W − (maroon) annihilation channels.
The limits from Super-Kamionkande (Choi et al., 2015) are plottedwith solid line, IceCube (Aartsen et al., 2017b) with dotted lines.
For the comparison the strongest limits from direct detection experiments: LUX (Akerib et al., 2017) (orange) and PICO-60 (Amole et al.,2017) (purple) are plotted, and possible signal from DAMA (Bernabei
et al., 2013).

2.3. Dark Matter Detection

2.3.3

19

Production in Accelerators

An alternative approach for the detection of dark matter particles is to produce themin a laboratory. The searches for the supersymmertic WIMP candidates at the accelerators aim at recreating the conditions in the early Universe and production of therelic particles. The evidence of dark matter might present itself in observations ofprocesses that deviate from the SM predictions.
The strategy for WIMP searches in hadron colliders is to use mono-jet, mono-photon
and mono-lepton signatures with energy or momentum imbalance in the final state.
The missing reconstructed energy or momentum could be an indication of a production of heavy neutral stable particles in a collision. The WIMP-nucleon scatteringcross section can be deduced by these searches. However, it is a model dependent
approach relying on effective field theories and assumptions on masses of mediating
particles.
The experiments at Large Hadron Collider (LHC) has not found any signs of the
production of dark matter particles so far. The results of several analysis of the CMS
experiment data are shown in Fig 2.14 for SI and in Fig. 2.15 for SD interactions, andcompared with some of the previously discussed results from direct and indirect
dark matter searches.

F IGURE 2.14: 90% C.L. upper limits on SI
WIMP-nucleon scattering cross-section fromthe CMS experiment (Lowette, 2016), for the
mono-jet (magenta), mono-photon (red andyellow), and mono-lepton (grey) searches, asa function of the dark matter mass.

F IGURE 2.15: 90% C.L. upper limits on SD
WIMP-nucleon scattering cross-section fromthe CMS experiment (Lowette, 2016), for the
mono-jet (magenta), mono-photon (red andyellow), and mono-lepton (gray) searches, asa function of the dark matter mass. The limits from Super-Kamionkande come from Solar WIMP search analysis (Choi et al., 2015).

21

Chapter 3

Neutrinos
3.1

History

The existence of neutrinos was postulated by Wolfgang Pauli in 1930, in an attempt
to explain the observed continuous energy spectrum of β particles emitted in nuclear
decays (Brown, 1978). He considered that the new particle was emitted from the nucleus together with an electron in the process of beta decay in order to conserve
energy, momentum, and angular momentum. The predicted particle was initiallynamed "neutron", but in 1932, a much more massive nuclear particle discoveredby James Chadwick claimed the name. The name "neutrino" (little neutral one in
Italian) was introduced by Enrico Fermi, who used it during the July 1932 Solvay
Conference, hosted in Paris.
Experimental confirmation of the neutrino existence was made by Frederick Reines
and Clyde Cowan in 1956 (Cowan Jr et al., 1991). In their experiment, antineutrinos created in a nuclear reactor via beta decays, reacted with protons to produce
neutrons and positrons:ν̄e + p+ → n0 + e+ .
The positron quickly annihilates with an encountered electron, resulting in two back to - back 511 keV gamma rays. The neutron can be detected by its capture on an
appropriate nucleus, releasing another gamma ray. The coincidence of both events:
positron annihilation and neutron capture, gives a unique signature of an antineutrino interaction.
In 1962, Leon M. Lederman, Melvin Schwartz, and Jack Steinberger showed that
more than one type of neutrino exists by making the first measurement of a muon
neutrino (Danby et al., 1962). After the discovery of a third type of lepton, the tau, in1975 at the Stanford Linear Accelerator Center, the existence of associated neutrino(the tau neutrino) was expected. The first detection of tau neutrino interactions wasannounced in the summer of 2000 by the DONUT collaboration at Fermilab (Kodama et al., 2001).
The first measurement of the electron neutrino flux from the core of the Sun wasmade in the 1960s by the Homestake Experiment. The measured value of the flux
was between one third and one half the number predicted by the Standard Solar
Model (Cleveland et al., 1998). Many subsequent radiochemical and water Cherenkov
detectors confirmed the deficit, including the Kamioka Observatory and Sudbury
Neutrino Observatory (SNO). This discrepancy, known as the solar neutrino problem, remained unresolved for thirty years. The problem was resolved with an improved understanding of the properties of neutrinos. It was realized that neutrinos

22

Chapter 3. Neutrinos

have a non-zero mass and that the masses of the individual states are different. Allowing for the interacting flavor states to be different than the mass states would
manifest itself as an oscillation, where a certain flavor of neutrino produced at somelocation will have a quantifiable probability of being measured as a different flavor
some distance away. This means that some portion of the electron neutrinos created in the Sun would then oscillate into tau and muon flavor neutrinos by the timethey arrive at the Earth. This hypothesis has been investigated by a new series ofexperiments (Shirai, 2005), thereby opening a new major field of research that still
continues.

3.2

Neutrino Oscillations

A practical method for investigating neutrino oscillations was first suggested by
Bruno Pontecorvo in 1957, who proposed that neutrino - antineutrino transitions
may occur in analogy with neutral kaon mixing. Although such matter - antimatter oscillation has not been observed, this idea formed the conceptual foundation
for the quantitative theory of neutrino flavor oscillation, which was first developedby Maki, Nakagawa, and Sakata in 1962 (Maki, Nakagawa, and Sakata, 1962) andfurther expanded on by Pontecorvo in 1967 (Pontecorvo, 1968). Experimental detection and confirmation of the phenomenon of neutrino oscillation led to two Nobel
prizes. First, in 2002, Nobel Prize was divided, and one half was awarded jointly
to Raymond Davis Jr. and Masatoshi Koshiba for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos. Later, in 2015, Nobel
Prize has been awarded to Takaaki Kajita (SK) and Arthur B. McDonald (SNO), fordiscovering that neutrinos can change from one type to another, evidence that theymust have mass.

3.2.1

In Vacuum

Neutrino oscillation is the quantum mechanical effect which arises from the nonequivalence of neutrino mass states and the eigenstates of the weak interaction (theflavor states). The flavor state |να i (α = e, µ, τ ) can be described as a linear combination of different mass eigenstates |νi i with masses (i = 1, 2, 3):3∗|να i = ∑ Uαi|νi i.

(3.1)

i =1

U is 3x3 rotation matrix between these states, called Pontecorvo-Maki-NakagawaSakata (PMNS) matrix:




1
0
0
c13
0 s13 e−iδCPc12 s12 0 −s12 c12 0 ,0
1
0
U = 0 c23 s23  
(3.2)
−
iδ
CP
0 −s23 c23
0
0 1−s13 e0c13where cij = cosθij , sij = sinθij . The propagation of these states according to their vacuum Hamiltonians leads to the standard oscillation formula for relativistic neutrinos
in vacuum:∗∗∗∗P(να → νβ ) = δαβ − 4 ∑ <(UαiUβi Uαj Uβj)sin2 ∆ij ± 2 ∑ =(UαiUβi Uαj Uβj)sin2∆ij ,
ij

ij

(3.3)

3.2. Neutrino Oscillations

23

where
∆ij =

1.27∆m2ij [eV 2 ] L[km]
E[ GeV ].

The sign before second summation is positive for neutrinos and negative for anti neutrinos.
Neutrino oscillations in vacuum are fully characterized by 6 parameters: three mixing angles θ13 , θ12 , θ23 , two mass splittings ∆m221 , ∆m231 , and one CP - violating phaseδCP . Majority of neutrino mixing parameters have been experimentally determinedby reactor, atmospheric, solar, and long-baseline neutrino experiments. This includes parameters such as magnitude of the two mass splittings, the ordering of
the mass states with the smallest splitting, and the values of the mixing angles. In
particular, recent measurements by reactor experiments (Daya Bay, RENO, and Double Chooz) (Olive, 2014) and T2K (Abe et al., 2014) have established that the mixing
angle θ13 is small but non - zero. The values of these parameters were derived from a
global fit of the current neutrino oscillation data (Capozzi et al., 2016), and are listed
in Tab. 3.1.
The two remain unknown parameters in the PMNS formalism are the sign of ∆m223 ,which relates to the ordering of the mass states with the largest splitting (commonlyreferred to as the neutrino mass hierarchy) and CP-violating phase δCP . If δCP is neither 0 nor π then the neutrinos and antineutrinos have a different oscillation probabilities. The precise value of δCP is still unknown, but the T2K (Abe et al., 2017b) andNOvA (Adamson et al., 2017) long-baseline experiments are beginning to constrain
it. It is known that the muon and tau neutrino mixing is nearly maximal, i.e. θ23 isnear π/4, however, it is not known if θ23 takes exactly that value, or is slightly larger
or slightly smaller.
TABLE 3.1: The best-fit values and 3σ allowed ranges of the neutrino oscillation parameters, derived from a global fit of the current
neutrino oscillation data (based on (Capozzi et al., 2016)). The values (values in brackets) correspond to normal (inverted) hierarchy
m1 < m2 < m3 (m3 < m1 < m2 ). The definition of ∆m2 used is∆m2 = m23 − (m22 + m21 )/2. Thus, ∆m2 = ∆m231 − ∆m221 /2 > 0, if
m1 < m2 < m3 , and ∆m2 = ∆m232 + ∆m221 /2 < 0 for m3 < m1 < m2

Parameter∆m212 [10−5 eV2 ]|∆m2 | [10−3 eV2 ]sin2 θ12
sin2 θ23 , ∆m2 > 0
sin2 θ23 , ∆m2 < 0sin2 θ13 , ∆m2 > 0
sin2 θ13 , ∆m2 < 0δCP /πBest fit
7.37
2.50 (2.46)
0.297
0.437
0.569
0.02140.02181.35 (1.32)

3σ6.93 – 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)∗* For the Dirac phase δCP we give the best fit value and the 2 σ allowed ranges (at 3σ no physicalvalues of δCP are disfavored).

24

3.2.2

Chapter 3. Neutrinos

In MatterIf neutrinos travel long distances through matter, they undergo weak interactions.
Due to the presence of electrons in matter, electron neutrinos may additionally interact with them via the W ± boson, while muon and tau neutrinos do not. Thisasymmetry induces an effective potential which is proportional to the density ofelectrons, Ne , in the surrounding matter:√
V = ± 2GF Ne ,(3.4)
where GF is the Fermi constant, the plus sign is for νe , and the negative sign is for ν̄e .
The influence of matter on neutrino oscillations was first pointed out by Wolfenstein,
Mikheyev and Smirnov and is often referred to as the MSW effect (Smirnov, 2005).
Introducing this potential changes the energy levels of the propagation eigenstates(mass eigenstates) of neutrinos. When neutrinos travel through matter, the effective
Hamiltonian is modified from its vacuum form due to the difference in the forward
scattering amplitudes of νe and νµ,τ . In the mass eigenstate basis, the effective Hamiltonian can be written as:
 2



m1
0
0
V 0 0
 2E m2†
2
0 0 0 U,
Hmatter = (3.5)
 0 2E 0  + U
2
m3
0 0 0
0
0
2E

where U is the PMNS matrix. Since the Hamiltonian is now position-dependent, it is
not possible to write a simple closed form for the oscillation probability. Following
the approach presented in (Barger et al., 1980), we can define the matrix X, whoserow vectors are the pure mass eigenstates and therefore contain the evolution of eachof the mass states:"!
#
2EHmatter − M2j I
Mk2 L
X=∑ ∏
,
(3.6)
exp −i2E
Mk2 − M2jk
j6=kwhere Mi2 /2E are the eigenvalues of the constant-density matter Hamiltonian Hmatter ,and I is the identity matrix. The oscillation probability can then be written as:† 2P(να → νβ ) = |UXUαβ
| .

(3.7)

In the two flavor approximation, the solution of the corresponding Schroedinger
equation is simple in case where the matter density is constant. Then, Hmatter canbe re-diagonalised to obtain the mixing matrix and mass eigenstates in matter via arotation matrix, similar to the one for vacuum. If we note the effective mixing angle
in matter as θ M :sin2 2θ
sin2 2θ M =,(3.8)
sin2 2θ + (Γ − cos 2θ )2and the effective difference of squared masses as ∆M2 :q∆M2 = ∆m2 sin2 2θ + (Γ − cos 2θ )2 ,(3.9)

3.3. Neutrino Interactions

25√
where Γ = ±2 2GF Ne E/∆m2 , we can write the equation in matter as:i∂ x Ψ( x ) =

∆M2
4E




cos 2θ M sin 2θ M
Ψ ( x ).
− sin 2θ M cos 2θ M

(3.10)For constant density, the matter evolution leads to an oscillation probability:22P(νe → να ) = sin 2θ M sin

1.27∆M2 LE.

(3.11)

Therefore, to observe significant matter effects, long baselines or high matter densities are required. In the limit ∆M2 L/4E << 1 the vacuum probabilities can be
retrieved. Since the "matter" mixing angle now depends on the local matter density,
maximal mixing occurs when the vacuum mixing angle θ is non-maximal. That is, aresonance condition can be achieved for any set of vacuum mixing parameters if
f ρE
cos 2θ = Γ = ±6.5 × 103 ∆m2


g/cm3 · GeV,
eV 2(3.12)

where ρ is the matter density in g/cm3 and f is the proton to nucleon ratio in thematter. In the resonance region, oscillations can be significantly enhanced. The resonant condition depends on the sign of ∆m2 , which can be used to determine theneutrino mass hierarchy. For example, long baseline experiments, which look forνµ → νe oscillations in the region of ∆m2 ∼ ∆m223 , are sensitive to the mass hierarchy
through matter effects in the Earth if the baseline is sufficiently long and the energy
is sufficiently high, so that matter effects are significant. Oscillation probabilities forneutrinos and antineutrinos can be different due to matter effects (because of the ±sign), even if neutrino interactions with matter do not violate CP.

3.3

Neutrino Interactions

Neutrinos do not have electric charge, which means that they are not affected by theelectromagnetic forces and interact only via weak interactions (and gravity). Therefore, neutrinos pass through normal matter unimpeded and are very difficult to detect. Occasionally neutrinos can interact with the electrons or nuclei and produce a
detectable charged particles (see Fig. 3.1). Neutrino couplings to atomic electrons

F IGURE 3.1: Charged current neutrino interactions via a W boson
exchange.

are typically 3 orders of magnitude smaller then to nucleons, and can be neglectedin most experimental cases. The value of cross section is proportional to the energyof neutrino. The ratio of neutrino to anti-neutrino cross section is approximately 2.

26

Chapter 3. Neutrinos

One can distinguish two types of neutrino interactions based on exchanged boson:• Charged current (CC): ν + N → l + N 0 + .. - with exchange of W ± boson,• Neutral current (NC): ν + N → ν + N 0 + .. - with exchange of Z0 boson.
Here, N, N 0 are nucleons and l is a charged lepton of the same flavor as interacting neutrino. Neutral current processes are usually difficult to reconstruct as part ofthe energy available in the final state is carried away by the unobservable neutrino.
Therefore, neutrino detection is based mostly on the detection of a lepton producedin charged current interactions. There is a correlation between the direction of a parent neutrino and direction of a charged lepton produced in the neutrino interaction.
The more energetic the neutrino is, the closer the lepton follows the original direction of its parent neutrino.
There are a few different types of CC neutrino interactions which are shown in
Fig. 3.2.
• Charged current quasi elastic interactions (CCQE): ν + N → ν + N 0
In these processes, there are no additional particles in the final state apart fromthe charged lepton l and recoiling nucleon N 0 . CCQE processes (red line) are
dominant interaction mode for neutrino energies below 1 GeV. They significantly contribute to the total cross section up to around 10 GeV.
• Resonant production (RES): ν + N → l + r ∗ → l + N 0 + meson(s)Here r ∗ indicates a produced resonance, most commonly a ∆(1232). Mesons
are usually charged or neutral pions, but contribution from heavier particles
like kaons and ρ mesons is also possible. The resonant production processes(blue line) start to play role in neutrino interactions for Eν from around 1 GeV
up to several GeV.
• Deep inelastic scattering (DIS): ν + N → l + other particles
In these processes neutrino interact with partons (quarks and gluons) inside
nucleons and as a result, many particles can be produced. Deep inelastic reactions (green line) are dominant for neutrino energies of several tens of GeV
and higher.
Due to the very small cross-section for neutrino interactions, their detection is very
challenging. It requires high intensity neutrino sources and large neutrino detectors
associated with long exposition time to gather a sufficient number of events.

3.4

Sources of Neutrinos

Neutrinos are the second (after photons) most abundant particles in the Universe.
They can be produce by different nautral and artificial sources. Neutrino energy
spectra from various sources are shown in Fig. 3.3.
Natural sources:• Relic neutrinos:
As the Universe expanded and cooled, neutrinos decoupled from matter. Just
like the cosmic microwave background, these relic neutrinos are still aroundacting as an echo of the Big Bang.

3.4. Sources of Neutrinos

27

F IGURE 3.2: Summary of the current knowledge of νµ chargedcurrent cross sections. Figure taken from (Formaggio and Zeller,2012).

• Solar neutrinos:
Neutrinos are produced in the nuclear fusion reactions inside the Sun andother stars. The dominant process, fusion of proton plus proton (pp) to deuterium (p + p → d + e+ + νe ) is responsible for 98% of the energy production of the Sun. From this reaction, 86% of all solar neutrinos are produced,
however, they have very low energies, so the detectability of solar neutrinos
relies on the presence of fusion side chains giving higher-energy neutrinos
from boron-8 and beryllium-7. The neutrino flux from the Sun is enormous,∼60 billion/cm2 /s.
• Supernova neutrinos:
99% of the energy released by a core-collapse supernova comes in the formof neutrinos. Extreme heat and pressure force protons and electrons to combine together to form neutrons, releasing electron neutrinos νe . Conditions
are so extreme that most of the neutrinos are produced thermally, as neutrinoantineutrino pairs.
• Atmospheric neutrinos:
Cosmic rays striking the Earth’s atmosphere produce showers of pions whichin subsequent decays can produce significant flux of neutrinos.
• Ultra high energy neutrinos (UHE):
High-energy neutrinos produced by astrophysical objects (like active galaxies
or gamma-ray bursts).
• Geoneutrinos:
Neutrinos and antineutrinos emitted in decay of radionuclide naturally occurring in the Earth.

28

Chapter 3. Neutrinos

Artificial sources:• Reactor neutrinos:
In fission reactors, electron-type antineutrinos ν̄e are produced in beta decaysof fission fragments. Fission reactors are the best source of low energy antineutrinos.
• Accelerator neutrinos:
In proton accelerators, the proton beam is directed on to a target, producing
a large number of secondary pions (among other particles). Muon-neutrinos
νµ and antineutrinos ν̄µ can be produced by allowing pions of the appropriate
charge to decay in flight, and then stopping the non-neutrino products with adense absorber.

F IGURE 3.3: Measured and expected fluxes of natural and reactor
neutrinos. Figure taken from (Katz and Spiering, 2012)

Among all that sources it is worth to discuss atmospheric neutrinos in more details,
as they would have the same energies as expected for dark matter induced neutrinos. Atmospheric neutrinos are produced in interactions of primary cosmic rays
with atomic nuclei in the Earth’s atmosphere. Primary cosmic rays mainly consist of
protons (90%) and alpha particles (9%), with small contribution of nuclei of heavier
elements (Berezinskii et al., 1984). The isotropically distributed cosmic rays interact with the air molecule nuclei, producing copious amounts of pions and kaons.
The neutral pion decays and produces gamma rays and leptons, but no neutrinos.
The decay of charged pions π ± leads to the production of two muon neutrinos νµand one electron neutrino νe . The whole reaction chain is shown schematically in3.4. Sources of Neutrinos

29

Fig. 3.4. The average energy of atmospheric neutrinos is several hundreds of MeV
and the energy spectra has a long high energy tail reaching TeV scale. While mostof the neutrinos pass through Earth (travelling 10-10,000 km) without interaction,
small fraction of them could interact and be detected. Detection of Cherenkov radiation from charged leptons produced by neutrino interactions in water or ice is a
widely used technique. Super-Kamiokande is large water Cherenkov neutrino detector operating in the Kamioka Observatory, and it is described in Chapter 4.

F IGURE 3.4: Schematic view of cosmic rays interactions in the atmosphere. Figure taken from (Louis et al., 1997).

If dark matter exist, it is expected that observed atmospheric neutrinos may contain some contribution of dark matter induced neutrinos. The aim of the analysis
presented in this thesis is to evaluate the allowed contribution from this hypothetical additional source.

31

Chapter 4

Super-Kamiokande
The Super-Kamiokande (Super-K, SK) is a large water Cherenkov detector locatedin the Mt. Ikenoyama in Japan (Fukuda et al., 2003). It is run by the Kamioka Observatory of the Institute for Cosmic Ray Research, University of Tokyo. The detector
is operated by the international collaboration of more than 40 institutes from Japan,
United States, Korea, China, Canada, Poland, Spain, UK, Italy and France. The observatory was designed to search for a proton decay, study solar, atmospheric andman-made neutrinos, and keep a watch for Supernovae. Super-K also serves as thefar detector for the Tokai-to-Kamioka (T2K) long baseline neutrino oscillation experiment (Abe et al., 2011).

4.1

Cherenkov Radiation

The detection of neutrinos in the Cherenkov detectors, is based on examining thecharacteristic light emitted by a charged particle produced during the interaction of
a neutrino in water or ice. When the generated charged particle moves faster than
the speed of light in a dielectric medium (water, in the case of Super-K), it produces
electromagnetic shock wave known as Cherenkov radiation. The wavefront of theresulting radiation propagates at an anglecos θc = 1/nβ,(4.1)

where n is refractive index of the medium, and β is velocity of the particle divided
by speed of light, c. In pure water where n ≈ 1.34 and β ≈ 1, this corresponds toθc ≈ 42◦ for 580 nm photons. The number of Cherenkov photons emitted (N) per
unit wavelength (dλ) and per unit length (dx) is given by:
d2 N
2πα 
1 
= 2 1− 2 2 ,
dxdλ
λ
n β

(4.2)

where α is the fine-structure constant. For particles traveling near the speed of light,'3400 photons per cm are emitted between 300 and 500 nm, where the Super-K photomultiplier tubes (PMTs) are most sensitive.
The threshold energy Ethr of a charged particle to emit Cherenkov radiation (if β= 1) can be written as
n
mc2 ,
(4.3)
Ethr = √2
n −1
where m is the mass of the charged particle. For pure water Ethr ∼ 1.5mc2 . In Table
4.1 one can see values of threshold energy for charged particles detected in Super-K.
The cone of Cherenkov light when projected onto the walls of the detector forms a

32

Chapter 4. Super-Kamiokande
TABLE 4.1: The values of threshold energy for e± , µ± and π ± .

Particlee±µ±π±Rest mass (MeV/c2 )
0.511
105.7
139.7

Ethr (MeV)
0.767
157.4
207.9

characteristic shape of rings (see Fig. 4.1). This light is recorded by the PMTs. Theenergy, direction and neutrino interaction point can be reconstructed based on theamount of charge deposited in the PTMs and the time when the light was detected.

F IGURE 4.1: A schematic view of the detection of Cherenkov light by
the photomultipliers.

4.2

Detector

The Super-Kamiokande detector is located 1,000 m underground (2,700 m waterequivalent) in Japan, inside the Mozumi Mine near the Kamioka section of the cityof Hida in Gifu Prefecture, owned and operated by the Kamioka Mining and Smelting Coperation. The geographic coordinates of SK are 36◦ 250 N latitude and 137◦ 180 E
longitude. The mountain above the detector reduces the rate of cosmic ray muonsto ∼3 Hz, which corresponds to a reduction factor of approximately 1/100,000 withrespect to the ground level. The detector is a cylindrical stainless steel tank, 41.4 m
tall and 39.3 m in diameter, holding 50,000 tons of ultra-pure water. The layout of
the experimental site, including a schematic of the SK tank is shown in Fig. 4.2.
The tank volume is divided into an inner detector (ID) region, which is extending
2.7 m inward from the walls of the SK cylinder and 2.6 m from its top and bottom,
and outer detector (OD), which consists of the remaining tank volume with total
mass of 18 kton. The ID and OD are optically isolated from each other. In-between,
there is a 55 cm dead-space spanned by a steel support structure that houses photomultiplier tubes viewing each of the detector regions. The ID contains 11,146 20-inch
PMTs mounted on the tank wall. They are arranged in modules, each one consistingof 3x4 PMTs spaced 70 cm from each other. The space between the PMTs is linedwith a reflective black sheet to prevent light leaks into the OD. In the OD houses
1,885 8-inch PMTs grouped in pairs and installed facing outside (see Fig. 4.3).

4.2. Detector

F IGURE 4.2: The schematic view of Super-Kamiokande detector andthe experimental hall. Figure taken from (Fukuda et al., 2003).

F IGURE 4.3: A diagram of the module structure of the PMT support
frame. Figure taken from (Fukuda et al., 2003).

33

34

Chapter 4. Super-Kamiokande

To enhance total light collection efficiency, the walls, top and bottom of the OD arecovered with the reflective Tyvek. Tyvek’s reflectivity is 90% at 400 nm falling toabout 80% at 340 nm. The OD serves as both an active and passive veto, that is, itenables us to identify muons coming from outside the tank and also to makes theinner part free from gamma rays and neutrons from the rock.
The surface of the Super-Kamiokande dome cavity above the tank is coated withradon-tight plastic material manufactured by Mineguard in order to prevent naturally occurring radon in the rock from finding its way into the detector volume.
To maximize water transparency, water in the detector is ultra-purified by a special
multi-step purification scheme which includes filtration, reverse osmosis, and degasifications (see Sec. 4.4 for more details). To neutralize the geomagnetic field thatwould otherwise affect photoelectron trajectories in the PMTs, 26 sets of horizontal and vertical Helmholtz coils are arranged around the inner surface of the tank.
They reduce magnetic field at the site from 450 mG to 50 mG. While the detector isin operation, the performance and data acquisition is monitored 24 hours a day byphysicists.

4.2.1

Photomultiplier Tubes

The inner detector of Super-K uses custom built, 20-inch (50 cm) type R3600-5 PMTs
developed by Hamamatsu Photonics in cooperation with the Kamiokande collaboration (Suzuki et al., 1993). A schematic view of the ID PMTs is shown in Fig. 4.4.
The photocathode is approximately hemi-spherical in shape and consists of a bialkali(Sb-K-Cs) photocathode with a peak quantum efficiency of about 21% at 360-400 nm,
and a sensitivity ranging from 280-660 nm (see Fig. 4.5). The average transit-time
spread for 1 pe signal is 2.2 ns. The average dark noise rate at the 0.25 pe thresholdused in Super-Kamiokande is about 3 kHz. The ID PMTs are operated with gain of
107 , which corresponds to a supply voltage ranging from 1700 to 2000 V. Since SK-II
phase (see Sec. 4.3), each ID PMT is encased in a fiber reinforced plastic shell (FRP)
at the base and topped with an acrylic window over the photo-sensitive area. The
transparency of the acrylic case is higher than 96% at 350 nm wavelength.

F IGURE 4.4: Diagram of 20-inch (50 cm)
photomultiplier tube used in Super-K detector (taken from (Fukuda et al., 2003)).

F IGURE 4.5: Quantum efficiency of thephotocathode as a function of the lightwavelength (taken from (Fukuda et al.,2003)).

4.3. History

35

The outer detector uses 8-inch (20 cm) Hamamatsu PMTs, which were recycled fromthe IMB experiment (Becker-Szendy et al., 1993), after it was decommissioned in1991. The OD PMTs are distributed as 302 units on the top layer, 308 on the bottom,
and 1275 on the barrel wall. To enhance the light collection efficiency, wavelength
shifting plates are attached to each PMT, which absorbs light in a wide range of
wavelengths, and re-radiates the light at a wavelength where the PMT sensitivity
peaks. The plates are made from 1.3 cm thick by 60 cm square acrylic panels. Thesepanels, increases the light collection efficiency of the OD by approximately 60%, butalso lower the time resolution to approximately 15 ns. Since the OD functions primarily as a veto, this gain in the photon yield provides sufficient compensation forthe loss in the timing resolution.

4.3

History

The Super-Kamiokande is a successor to the Kamioka Nucleon Decay Experiment(KamiokaNDE) (Koshiba, 1986), which was designed to search for a proton decay.
The construction of the detector was completed in April, 1983. It was a tank 16.0 m
in height and 15.6 m in width, containing 3,000 tons of pure water and about 1,000
photomultiplier tubes. After an upgrade in 1985, the detector ran as KamiokaNDE-II
and was able to observe solar and atmospheric neutrinos. It detected neutrinos fromthe Supernova 1987A, and set what was then the world’s best limit on the lifetimeof the proton.
The construction of the Super-Kamiokande detector started in 1991 and the firstdata-run began on April 1st, 1996. It was continually operating until July 2001, when
it was shutdown for scheduled upgrades and refurbishing dead PMTs. This period
of operation is called SK-I.
In November 2001, when tank was refilling with water, one of the bottom PMTs
imploded. 6,779 ID PMTs and 885 OD PMTs were broken in a chain reaction due tothe resulting shock wave. Since this accident, each ID tube is is covered by acrylic
covers and an FRP case to protect against shock waves from imploding neighboring
tubes. The detector was rebuilt using the remaining PMTs for the ID, and remaining
and newly-introduced PMTs for the OD. It was working from October 2002 to October 2005. In this period, called SK-II, 5182 ID PMTs with acrylic covers and 1885 OD
PMTs were used, and the photo-coverage of ID was 20%.
In July 2006, after a break to restore lost PMTs, the experiment resumed full operation with 11,129 working ID PMTs, reaching 40% of photo-coverage. In addition,a vertical layer of Tyvek was installed to optically separate the barrel and end cap
regions. The optical segmentation was done in order to better separate backgroundcorner-clipping cosmic ray muons from neutrino interactions with an exiting lepton.
This period is known as SK-III and lasted until September 2008, when the detector
was shutdown once more for an upgrade of electronics. Thanks to the new electronics, the dead time associated with the data acquisition system was reduced, thedynamic range was expanded, and the energy threshold lowered. The period whichstarted in September 2008 and continues to this day is calld SK-IV. A summary ofthe detector configuration for the SK experiment phases up to the current moment
can be found in Table 4.2.

36

Chapter 4. Super-Kamiokande
TABLE 4.2: Summary of the differences between each of the SK periods.

Phase
Start of data taking
End of data taking
Number of ID PMTs
Number of OD PMTs
Photo-coverage
Anti-implosion PMT cases
OD segmentation
Energy threshold
Front-end electronics

SK-I
1996 Apr.
2001 Jul.
11146

SK-II
SK-III
2002 Oct. 2006 Jul.
2005 Oct. 2008 Sep.
5182
11129
1885
40%
19%
40%
no
yes
yes
no
no
yes
5 MeV
7 MeV
4.5 Mev
ATM (ID), OD QTC (OD)

SK-IV
2008 Sep.
(running)
11129
40%
yes
yes
4 MeV
QBEE

In 1998, the Super-Kamiokande Collaboration announced the evidence of atmospheric neutrino oscillation, which was the first experimental observation supporting the theory that the neutrino has a non-zero mass (Fukuda et al., 1998). Soon
after, in 2001, solar neutrino oscillations were confirmed (Fukuda et al., 2001). The
precision measurement of the solar neutrino flux opened a new window that enabled scientists to study the inner workings of the Sun. The experiment continues
to operate, collecting data on various natural sources of neutrinos, as well as acting
as the far detector for the Tokai-to-Kamioka (T2K) long baseline neutrino oscillation
experiment (Abe et al., 2011).
On June 2015, the Super-Kamiokande Collaboration approved the SuperK-Gd project,which aim at dissolving gadolinium to the Super-K water. By adding gadolinium
into water Cherenkov detector, inverse beta decay reactions will have two signals,
the prompt one is positron signal and the delayed one is a ∼ 8 MeV gamma cascadefrom neutron capture on gadolinium. Due to this effect, background for Supernova
Relic Neutrino (SRN) can be largely reduced by detecting prompt and delayed signals in coincidence. It is expected to detect ∼ 5 neutrinos from SNR after a year of
detector operation. Moreover, SuperK-Gd will also have the ability to distinguishneutrino and anti-neutrino (see (Beacom and Vagins, 2004) for more details).

4.4

Water Purification System

Water conditions affect photon propagation in the tank, so it is very important tokeep the water transparency as high as possible. The water used in SK is sourced
from natural water inside the Kamioka mine. It is purified by a dedicated system(see Fig. 4.6) and is continually recirculated through parts of that system during normal detector operation. Water passes throug a 1µm filter in order to remove large
particles, a heat exchanger maintains the temperature at 13◦ C to suppress bacteria
growth, ion exchangers remove metal ions in the water, and any bacteria remaining
in the water are killed by an ultra-violet sterilizer. Radon-less air (Rn-less-air) systems dissolve radon free air into the water to improve the radon removal capabilitiesof the vacuum degasifier. Reverse osmosis (RO) filter stops the contaminants heavier than a mass of 100 molecular weight using a high performance membrane. A
vacuum degasifier is used to remove gas dissolved in the water. It is able to remove4.5. Air Purification System

37

F IGURE 4.6: Super-Kamiokande water purification system (takenfrom (Fukuda et al., 2003)).

about 99% of the oxygen gas and 96% of the radon gas. Cartridge Ion Exchangers selectively remove ions with 99% elimination efficiency. To remove small dust even of
the order of nanometers Ultra filter is used. Membrane Degasifier further removes
dissolved radon and oxygen gases. The water is taken from the top of the tank using
a pump and returned to the bottom of the tank at a flow rate of 50 tons/hour. Thissystems enables the water to be transparent up to ∼90 m.

4.5

Air Purification System

Purified (Rn-reduced) air is supplied to the gap between the water surface and the
top of the Super-Kamiokande tank. A schematic view of the air purification system
is shown in Fig. 4.7. It consists of three compressors, a buffer tank, dryers, filters,
and an activated charcoal filter.

F IGURE 4.7:

Super-Kamiokande air purification system (takenfrom (Fukuda et al., 2003)).

38

Chapter 4. Super-Kamiokande

The air in the mine housing SK naturally contains 100-5,000 Bq/m3 of radon throughout the year. Varied concentrations occur due to changes in the ventilation of air inthe mine. In the cool season, air flows from the mine entrance closest to the experiment. In the summer months though, air flows in the opposite direction andis exposed to more rock before reaching SK and picks up more radon. To limit theamount of this background reaching the detector volume, radon free air is provided
to the control room and dome areas of the experiment.
Air collected from outside the mine, with intake far from the mine entrance, is purified in a "radon hut" located outside of the mine via a series of compressors andactivated charcoal filters and pumped in at a rate of 10 m3 /min. Radon concentrations at the dome are consistently below 100 Bq/m3 throughout the year. Typicalradon concentration inside the top of SK tank is measured to be 20-30 Bq/m3 .

4.6

Calibration

Neutrino oscillations studied with the Super-Kamiokande experiment are a function of the neutrino energy. Therefore, in the determination of particle’s energy it isimportant to know the relation between the number of photoelectrons recorded in
PMTs and the total deposited energy. That matching is called the energy scale determination and it is crucial for precision measurements.

F IGURE 4.8: Energy scale stability measured as a function of datesince the start of Super-Kamiokande detector operations. The energy
scale is taken as the average of the reconstructed momentum divided
by range of stopping cosmic ray muon data in each bin. The verticalaxis shows the deviation of this parameter from the mean value foreach SK period separately. Error bars are statistical. Figure takenfrom (Abe et al., 2017a).

During the detector operation, changes in the run conditions are unavoidable. They
may impact the water transparency and subsequent performance of the detector.
Therefore, they must be corrected through calibrations. Since the range of energies
of interest to atmospheric neutrino analysis spans from tens of MeVs to tens of TeVs,

4.6. Calibration39

the calibration through radioactive isotopes is impossible. The water transparency is
continuously monitored using cosmic ray muons as a calibration source (see (Ashie,2005) for the detailed description).
A plot showing the energy scale stability since SK-I is presented in Fig. 4.8. Notethe SK-III period was subject to poor and volatile water transparency conditions,
resulting in a comparatively turbulent energy scale. The stability seen in the SK-IV
period is a result of improvements in the water purification system and in corrections for the time variation of the PMT response.

41

Chapter 5

Atmospheric Neutrinos at
Super-Kamiokande
The search for dark matter induced neutrinos is based on atmospheric neutrino datacollected with the Super-Kamiokande detector from 1996 to 2016 (SK-I, SK-II, SK-III
and SK-IV data taking periods). The livetime of each sample, which corresponds tothe period of time when the detector was operational, is listed in Table 5.1.
TABLE 5.1: Livetime of SK-I, SK-II, SK-III and SK-IV data sets.

Sample
FC/PC
UP-µ

SK-I
1489.2 days
1645.9 days

SK-II
798.6 days
827.7 days

SK-III
518.1 days
635.6 days

SK-IV
2519.9 days
2519.9 daysALL
5325.8 days
5628.2 days

Before we discuss the search for dark matter induced neutrinos, we must first describe the atmospheric data and Monte Carlo samples used in analysis, and the standard oscillation analysis.

5.1

Data Samples

In the Super-Kamiokande detector, the observed atmospheric neutrino events are
divided into three main categories: fully-contained (FC), partially-contained (PC),and upward - going muons (UP-µ), which are schematically illustrated in Fig. 5.1.
These categories are further sub-divided into final 19 analysis samples.

F IGURE 5.1: The schematic illustration of event categories used inSuper-K: fully-contained (FC), partially-contained (PC) and upward going muons (UPMU) samples.

If the charged particle produced in neutrino interaction stops in the inner detector,

42

Chapter 5. Atmospheric Neutrinos at Super-Kamiokande

the interaction is classified as fully-contained. FC events have a reconstructed vertex within the 22.5 kton fiducial volume, which is defined as the region located morethan 2 m from the ID wall. In additon, we require there to be no activity in the
OD. The FC data is further subdivided based on the number of observed Cherenkov
rings (single- or multi-ring), the particle ID (PID) of the most energetic ring (e-like orµ-like), and visible energy or momentum (SubGeV with E < 1.33 GeV or MultiGeV
with E > 1.33 GeV). There are also additional selections made based on the number of observed electrons from muon decays and the likelihood of containing a π 0(detailed description can be found in (Wendell et al., 2010)). After all the selections,
there are 14 FC analysis samples.
Events are classified as partially-contained (PC) if they have a reconstructed vertex inside the fiducial volume, but the produced high energy lepton exits the ID anddeposit energy also in the outer veto region. Based on the energy deposition within
the OD, PC events are further classified into "stopping" and "through-going" subsamples. The energies of neutrinos which produce PC events are typically 10 times
higher that those which produce FC events.
Neutrinos can also interact with the rocks surrounding the detector and produce
high energy muons which intersect the tank. Downward-going muons producedin neutrino interactions cannot be distinguished from the constant flux of cosmic
ray muons. However, muons travelling in upward direction must be neutrino induced. The upward-going muon (UP-µ) sample, based on light deposition in both
the OD and ID, is further divided into "through-going" and "stopping" subsamples
for events that cross or stop within the ID, respectively. Through-going events withenergy deposition consistent with radiative losses are separated into a "showering"subsample.
The expected number of neutrino events in each class as a function of the true neutrino energy for the FC, PC, and UP-µ events is presented in Fig. 5.2. The event rateof each subsample over the lifetime of the experiment have been stable at 8.3 FC
events per day, 0.73 PC events per day, and 1.49 UP-µ events per day. A summary of
all 19 subsamples defined for atmospheric events at the Super-Kamiokande is presented in Table 5.2. Each subsample is binned in momentum or visible energy andthe cosine of the zenith angle. In this way, 520 analysis bins are created for each of
the SK period (2080 bins in total). Note that for FC and PC events, the cos θz bins
cover the full sky:(−1, −0.8. − 0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6, 0.8, 1),
and for UP-µ events the are defined only below the horizon:(−1, −0.9, −0.8, −0.7, −0.6, −0.4, −0.3, −0.2, −0.1, 0).
In this way, the size of the UP-µ bins is half of the size of FC and PC bins. The
binning is choosen is such a way to have at least 6 events expected in each bin after
scaling to data livetime of this analysis.

5.1. Data Samples

43

F IGURE 5.2: The expected parent neutrino energy distributions for
the FC e-like (left), FC µ-like and PC (middle), and UP-µ (right) samples based on MC simulation.

5.1.1

Data Reduction and Reconstruction

At Super-Kamiokande, roughly 10 atmospheric neutrino interaction events per day
are expected, but the detector records approximately 106 events per day. The majority of them come from the low background radioactivity surrounding the detector(around 11 Hz) and cosmic ray muons (around 3 Hz). Therefore, dedicated reduction algorithms are implemented to select neutrino events from this background.
Special care is taken to ensure high efficiency of the selection. The initial steps ofthe reduction are not computationally intense and are designed to remove apparent
backgrounds quickly and efficiently, while later steps focus on finer subtleties between events. Data reduction is done separately for each category of events. The
details of the reduction process can be find in (Li, 2017).

F IGURE 5.3: An example event display of single-ring µ-like (left) ande-like (right) event. The colored points indicate the quantity of thedetected light by each PMT.

Following the reduction, the remaining events are put through a reconstruction algorithm in order to convert the PMT charge and timing information into physicalvariables. The reconstruction of the initial interaction vertex is based on PMT timing information, with a correction implemented for the photon time of flight. The
type of the charged particle produced in neutrino interaction can be inferred from

44

Chapter 5. Atmospheric Neutrinos at Super-Kamiokande
TABLE 5.2: Summary of event subsamples for atmospheric neutrino
events at Super-Kamiokande. For each subsample, the standard bins
in cosine of the zenith angle and momentum (or visible energy) are
specified.

SampleFully Contained (FC) SubGeV
e-like 0 decay-ee-like 1 decay-e
Single-ring π0 -likeµ-like 0 decay-eµ-like 1 decay-eµ-like 2 decay-e
Multi-ring π0 -like
Fully Contained (FC) MultiGeVνe -likeν̄e -likeµ-likeMultiRing νe -like
MultiRing ν̄e -like
MultiRing µ-like
MultiRing Other
Partially Contained (PC)
Stopping
Through-going
Upward-going Muons (UP-µ)Stopping
Through-going Non-showering
Through-going Showering

Energy/momentum binscos θz bins

5 e± momentum
5 e± momentum
5 e± momentum
5 µ± momentum
5 µ± momentum
5 µ± momentum
5 π 0 momentum

10 in [-1,1]
1 in [-1,1]
1 in [-1,1]
10 in [-1,1]
10 in [-1,1]
1 in [-1,1]
1 in [-1,1]

4 e± momentum
4 e± momentum
2 µ± momentum
3 visible energy
3 visible energy
4 visible energy
4 visible energy

10 in [-1,1]
10 in [-1,1]
10 in [-1,1]
10 in [-1,1]
10 in [-1,1]
10 in [-1,1]
10 in [-1,1]

2 visible energy
4 visible energy

10 in [-1,1]
10 in [-1,1]

3 visible energy
1
1

10 in [-1,0]
10 in [-1,0]
10 in [-1,0]

the sharpness of the edge of the ring and the opening angle. Muons and charged pions are classified as µ-like or non-showering, because they do not form electromagnetic showers, and as a result, they produce Cherenkov rings with sharp edges (seeFig. 5.3 left). On the other hand, particles are divided into e-like or showering categories if they produce electromagnetic showers, resulting with fuzzy edges caused
by many overlapping rings (see Fig. 5.3 right). Moreover, based on the topology of
the ring pattern, the particle directions can be determined. Based on the observed
number of photons in the ring, the momentum is assigned to each reconstructed ringin an event. Particles with higher momentum produce more photons in Cherenkov
ring. The momentum of a multi-ring event is a sum of individual ring momenta. The
only exception from this rule is the momentum estimation of π 0 -like events which
is based only on the most energetic gamma-induced ring which is e-like. In case of
events with decay electrons (originated from muon), the delayed electron ring is notincluded in the estimation of an event direction and momentum.

5.2

Monte Carlo

Atmospheric neutrinos at Super-Kamiokande are simulated with large statistics, corresponding to 500 years of livetime for each running period (SK-I, SK-II, SK-III and
SK-IV). The Monte Carlo (MC) simulation is performed in stages: first modeling the5.2. Monte Carlo45

initial neutrino interactions in the water, then tracking subsequent particles inside ofthe detector volume, and finally checking the detector’s response to those particles.
The simulation of atmospheric neutrinos is performed following the flux calculation of Honda (Honda et al., 2011), presented in Fig. 5.4. Two other flux calculations,
the Fluka flux (Battistoni et al., 2003) and Bartol flux (Barr et al., 2004), are used tocompute flux - related systematic errors.

F IGURE 5.4: Atmospheric neutrino fluxes for Kamioka averaged overall directions (left panel), and the flux ratios (right panel), calculatedby Honda (Honda et al., 2011) (solid red), Fluka (Battistoni et al., 2003)(dotted green) and Bartol (Barr et al., 2004) (dashed blue) groups,(dash-dotted line is for the previous Honda calculation (HKKM06)).

Neutrino interactions within the detector and in the surrounding rocks are simulated using the NEUT (Hayato, 2002) model (software version 5.3.6). In NEUT, theinteractions of neutrinos on protons, oxygen, and sodium are considered throughthe following modes:• quasi-elastic elastic scattering ν + N → l + N 0• single meson production ν + N → l + N 0 + m• meson exchange current ν + NN ? → l + N 0 N 0?
• coherent pion production ν + 16 O → l + 16 O + π• deep inelastic scattering ν + N → l + other particles
where l is a lepton, m is a meson and N, N 0 are nucleons. Charged-current quasielastic interactions are simulated using the Llewellyn-Smith model (Smith, 1972)
with nucleons distributed according to the Smith-Moniz relativistic Fermi gas (Smith
and Moniz, 1972) assuming an axial mass M A = 1.21 GeV/c2 and form factors from
(Bradford et al., 2006). Interactions on correlated pairs of nucleons, so-called meson exchange currents (MEC), have been included following the model of Nieves(Nieves, Amaro, and Valverde, 2004). Pion-production processes are simulated using the Rhein-Seghal model (Rein and Sehgal, 1981) with Graczyk form factors (Graczyk
and Sobczyk, 2008). Since the MEC simulation includes delta absorption processes,

46

Chapter 5. Atmospheric Neutrinos at Super-Kamiokande

the pionless ∆ decay process, ∆ + N 0 → N 00 + N 0 , in NEUT’s previous pion production model has been removed in the present version.
Detector simulation provide an accurate model of the Super-K tank itself as wellas its electronic response to particles propagating in the detector volume. It includes
tracking the particles, modeling the Cherenkov radiation and photon propagation,and simulating the PMT response. The Super-K has custom detector simulation
package called SKDETSIM, based on GEANT3 (Brun et al., 1993).
The same data reduction and reconstruction procedure is applied to MC events as
to real data. Therefore after scaling to the data livetime, one can obtain expected
number and characteristics of the atmospheric neutrino interaction events seen in
the experiment.

5.3

Atmospheric Neutrino Oscillation Analysis

The fit using atmospheric neutrino data is performed to estimate the values of theoscillation parameters sin2 θ23 and |∆m232 | (normal hierarchy)/|∆m231 | (inverted hierarchy). The value of the other oscillation parameters is fixed in the fit at the global
best fit values listed in Table 5.3, but their uncertainties are treated as a source ofsystematic error in the analysis.
TABLE 5.3: The global best fit values of neutrino oscillation parameters from (Olive, 2014) fixed during the fit. The uncertainties on theparameters values are treated as systematic errors in the fit.

Parameter∆m221
sin2 θ12
sin2 θ13Value(7.53 ± 0.18) × 10−5 eV20.304 ± 0.014
0.0219 ± 0.0012

The zenith angle distributions of data and MC for each sample are shown in Fig. 5.5.
MC predictions for normal hierarchy are plotted with cyan, while the inverted hierarchy is shown in orange. Note that the predictions for normal hierarchy are plottedon top of predictions for inverted hierarchy, which makes the latter ones difficult to
noticed.
The likelihood is based on Poisson probabilities and can be written as:
MC

L( N

MC

,N

DATA

DATA

e− Nn ( NnMC ) Nn)=∏
NnDATA !
n

,

(5.1)

where NnMC and NnDATA are expected and observed number of events in the n-th bin.
According to Wilks’ theorem (Wilks and Daly, 1939), log likelihood ratio follows χ2
distribution with n degrees of freedom:L( N MC , N DATA )NnDATA
MC
DATA
DATA. (5.2)χ ≡ −2 ln= 2 ∑ Nn − Nn
+ Nnln
L( N DATA , N DATA )
NnMC
n
2

5.3. Atmospheric Neutrino Oscillation Analysis

47

F IGURE 5.5: Data and MC comparisons for the entire Super-K data
divided into 19 analysis samples. Samples with more than one zenith
angle bin are shown as zenith angle distributions (second throughfifth column) and other samples are shown as reconstructed momentum distributions (first column). Cyan (orange) lines denote thebest f it MC assuming the normal (inverted) hierarchy. Narrow panels
below each distribution show the ratio relative to the normal hierarchy MC. In all panels, the error bars represent the statistical uncertainty.

In order to incorporate the effect of systematic errors into the bin expectation for
independent sources of error, we use the prescription given in (Fogli et al., 2002).
The expected number of events in each bin changes within an added systematic
error parameter:
NnMC → NnMC (1 + ∑ f ni ei ),(5.3)
iwhere f ni represents the fractional change in the number of events in n-th bin due toa variation of the systematic error parameter ei . This is the so called "pull" method.
For each systematic error, the parameter ei is estimated during the fit and resulting
distribution of the ei /σi is Gaussian univariate. In this way, the strength of systematic error’s is constrained through the addition of a penalty term to Eq. 5.2. The full
χ2 can be written as:
χ = 2∑2n



N DATA
NnMC − NnDATA + NnDATA ln n MC
Nn



+∑
i



ei
σi

2
(5.4)

48

Chapter 5. Atmospheric Neutrinos at Super-Kamiokandeχ = 2∑
2

NnMC (1 +n∑f ni ei ) − NnDATA + NnDATA lni

NnDATA
NnMC (1 + ∑i f ni ei )

!

+∑



i


ei 2
σi
(5.5)

In the fit, χ2 is minimized over ei , and at the minimum ∂χ2 /∂ei = 0 for every i.

5.3.1

Systematic Uncertainties

In the "pull" method we use, the effect of systematic errors is incorporated by the systematic error coefficients f ni . Calculation of these coefficients is based on atmospheric
MC simulations. It is assumed that they have a linear effect on the bin content B0 ,with f ni being the slope of the line between its contents at Bn (+σi ) and Bn (−σi ):f ni =

Bn (+σi ) − Bn (−σi )
.
2Bn0

(5.6)

In the analysis, we consider 160 systematic error sources, which are listed below.
More details about systematic errors can be found in (Abe et al., 2017a).
Neutrino flux and production errors - common for all SK periods:• Flux normalization• Flux ratio (νµ + ν̄µ )/(νe + ν̄e )• Flux ratio ν̄e /νe• Flux ratio ν̄µ /νµ• Up/down ration• Horizontal/vertical ratio• K/π ratio in flux calculation• Neutrino production height• Energy spectrum and sample-by-sample normalization• Matter effects
Neutrino interaction, particle production, and PMNS oscillation parameter systematic errors that are common to all SK run periods:• Axial mass in quasi-elastic CC interaction• Single π production• CCQE cross section• CCQE ν̄/ν ratio• CCQE µ/e ratio• DIS cross section• DIS model comparisons5.3. Atmospheric Neutrino Oscillation Analysis• DIS Q2 distribution• Coherent π production• NC/CC ratio• ντ cross section• NC fraction from hadron simulation• π + decay uncertainty• Meson exchange current• ∆m221• sin θ12 2• sin θ13 2
Systematic errors that are independent in SK-I, SK-II, SK-III, and SK-IV:• FC reduction• PC reduction• FC/PC separation• PC stopping/through-going separation• Non-ν background• Fiducial volume• Ring separation• Particle identification• Energy calibration• Up/down asymmetry energy calibration• UP-µ reduction• UP-µ stopping/through-going separation• Energy cut for stopping UP-µ
• Path length cut for through-going UP-µ• Through-going UP-µ showering separation• Background subtraction for UP-µ• νe /ν̄e Separation• SubGeV 1-ring π 0 selection• SubGeV 2-ring π 0• Decay-e tagging• Solar Activity

49

50

Chapter 5. Atmospheric Neutrinos at Super-Kamiokande

5.3.2

Results of the Oscillation Analysis

The results presented in this section are based on the official analysis published by
the Super-Kamiokande collaboration (Abe et al., 2017a). The constraints on neutrino
oscillation parameters |∆m232,31 |, sin2 θ23 and δCP are based on ∆χ2 = χ2 − χ2min distributions, where χ2min is the χ2 value at the best f it in the parameter space. The results
for normal and inverted hierarchy are shown in Fig. 5.6 with cyan and orange lines
respectively. The fit results show that data prefer the normal hierarchy over the inverted hierarchy with ∆χ2 = ∆χ2NH,min − ∆χ2I H,min = −4.34.
The normal hierarchy fit to the atmospheric mixing parameters yield:013−3 eV2 ,• |∆m232 | = (2.50+−0.20 ) × 10
0.031
• sin2 θ23 = 0.588+−0.067 ,1.37• δCP = 4.19+−1.59 .

The full list of the best f it values of the 160 systematic error parameters ei can befound in (Abe et al., 2017a). Note that the Super-K has vey small sensitivity to δCPparameter and its value cannot be constrained within 3σ by Super-K data.

F IGURE 5.6: Constraints on neutrino oscillation parameters from theSuper-K atmospheric neutrino data fit. Orange lines denote the inverted hierarchy result, which has been offset from the normal hierarchy result, shown in cyan, by the difference in their minimum χ2values.

51

Chapter 6

WIMPs in the Center of the MilkyWay
Indirect searches aim at detecting dark matter annihilation/decay products, such as
charged particles, photons, or neutrinos (e± , p̄, γ, ν) in the cosmic ray flux. Since theexpected signals depend on the square of the dark matter density for annihilation,or are proportional to the density in case of decay, the distribution of dark matter in
the Universe is crucial for robust predictions.

6.1

Dark Matter Halo Models

The Milky Way is one of the considered sources in the searches for dark matter induced signals, due to an expected increase in the density towards the Galactic Center. The largest source of uncertainty in the dark matter density profile of the underlying halo model, comes from the cuspiness of the inner gradient. However, thesignal averaged over larger regions of the halo is much less dependent on the model
as long as the density normalization is chosen such that it is consistent with the observed data, e.g., rotation curves.
It is expected that the dark matter halo envelops the galactic disk and extends far
beyond the edge of the visible galaxy. In the ΛCDM model (Frieman, Turner, and
Huterer, 2008), dark matter halos are assumed to form hierarchically via gravitational amplification of initial density fluctuations (bottom-up). Cosmological Nbody simulations with large dynamic range (Diemand, Kuhlen, and Madau, 2007)
and gravitational lensing observations (Clowe et al., 2006) seem to indicate that thedark matter density profiles can be described in the form:ρ (r ) =ρ0,γ(r/rs ) [1 + (r/rs )α ]( β−γ)/α(6.1)

where the parameters α, β, γ and rs take different numerical values for different models. Parameter γ is the inner cusp index, rs is the scale radius, and the normalization ρ0 is chosen so that the mass contained within the solar circle (Rsc = 8.5 kpc)
provides the appropriate dark matter contribution to the local rotational curves. In
addition, to avoid numerical divergences due to very cuspy profiles (which may be
an artifact of simulations), one assumes a flat core for all the profiles in the innermost
0.1◦ around GC.
The three commonly used profiles are NFW (Navarro, Frenk, and White, 1997),
Moore (Moore et al., 1999) and Kravtsov (Kravtsov et al., 1998), and parameters
corresponding to these models are listed in Table 6.1. The comparison of the dark

52

Chapter 6. WIMPs in the Center of the Milky Way
TABLE 6.1: The parameters of Eq. 6.1 for Moore (Moore et al., 1999),
NFW (Navarro, Frenk, and White, 1997) and Kravtsov (Kravtsov etal., 1998) halo profiles.

Halo Model
NFW
Moore
Kravtsov

α
1
1.5
3

β
3
3
3

rs [kpc]
20
28
10

γ
1
1.5
0.4

ρ( Rsc ) [GeV/cm3 ]
0.3
0.27
0.37

F IGURE 6.1: The dark matter density as a function of
the distance from the GC for
Moore (Moore et al., 1999)(dotted green), NFW (Navarro,
Frenk, and White, 1997) (solidred) and Kravtsov (Kravtsov etal., 1998) (dashed blue) halo
profiles. The vertical gray line
indicates the Solar System position (Rsc = 8.5 kpc). The plot
illustrate Eq. 6.1 with parameters from Tab. 6.1.

matter density distribution, ρ(r ), as a function of distance from the Galactic Centerfor considered profiles is shown in Fig. 6.1. For the outer regions of the halo (several
kpc away from the Galactic Center) one can observe very similar behavior and good
agreement between the models. However, the inner gradient of the halo profile is themost uncertain part, due to the spatial resolution limit of the existing simulations.
In the analysis presented in this thesis, the NFW profile will be used as a benchmark
model, while the Moore and Kravtsov profiles will be applied as extreme cases toestimate the influence of halo model choice on the obtained results.

6.2

Dark Matter Annihilation

The intensity J (number flux per solid angle) of dark matter annihilation products in
the galactic halo at an angle Ψ with respect to the GC direction is proportional to thedark matter density squared integrated along the line of sight (Yüksel et al., 2007)(see Fig. 6.2 for definition of the variables):1
J (Ψ) =
Rsc ρ2sc

lmax
Z

ρ2 (

q

R2sc − 2lRsc cos Ψ + l 2 )dl.

(6.2)

0

The prefactor R 1ρ2 , where ρsc = ρ( Rsc ), is an arbitrary scaling which makes J (Ψ)
sc scdimensionless. The upper limit for integration lmax is defined as:qlmax = R2MW − R2sc sin2 Ψ,(6.3)
where R MW = 40 kpc is the adopted Milky Way halo size. Any enhancement of
the density would result in a sharp increase in the flux of annihilation products.

6.2. Dark Matter Annihilation

53

F IGURE 6.2: Illustration of the line of sight l and the angle Ψ in thecoordinate system related to the Galactic Center.

Since dark matter radial halo profiles are peaked towards the Galactic Center, one
can expect very large enhancements for small angles Ψ around this point. This ispresented in Fig. 6.3 for the NFW, Moore, and Kravtsov profiles. One can see thatthe intensity strongly depends on the chosen profile and the differences can be several orders of magnitude at small angles. Presented density and intensity profiles
had been calculated based on Eq. 6.1 and 6.2 using computational software program
Mathematica (Wolfram, 1999).

F IGURE 6.3: Intensity of dark
matterannihilation
products versus angular distancefrom the Galactic Center for
Moore (green), NFW (red) andKravtsov (blue) profiles.

The relevant quantity in a measurement is related to overall intensity of dark matterannihilation products received from a given cone half-angle. The integral of J (Ψ)
over the solid angle ∆Ω = 2π (1 − cos Ψ) can be defined as:
J∆Ω =

1
∆Ω

Z
∆Ω

J (Ψ)dΩ,

(6.4)

54

Chapter 6. WIMPs in the Center of the Milky Way

where ∆Ω is the chosen search region. Then, the differential flux of annihilation
products from this field of view can be expressed in the form:dΦ∆Ω< σA v >Rsc ρ2sc dN
=
J∆Ω
.
dE
2
4πMχ2 dE

(6.5)

The factor 1/2 accounts for dark matter being its own antiparticle, 1/4π is for isotropic
emission of the annihilation products, Mχ is assumed mass of the dark matter particle and dN/dE is the spectrum of the annihilation products.

6.3

Dark Matter Decay

For decaying dark matter, the expected neutrino flux can be written in form:dΦ∆Ω
1
Rsc ρsc dN= Jd∆Ω,
dEτ
4πMχ dE(6.6)

where τ is the dark matter particle lifetime. The intensity Jd is the line of sight integral over the dark matter density,1
Jd (Ψ) =Rsc ρsc

lmax
Z

ρ(

q

R2sc − 2lRsc cos Ψ + l 2 )dl.

(6.7)

0

The calculated intensity of dark matter decay products is shown in Fig. 6.4. In thiscase the differences between the halo models are smaller.

F IGURE 6.4: Intensity of dark
decay products versus angulardistance from the Galactic Center for Moore (green), NFW(red) and Kravtsov (blue) profiles.

6.4

Energy Spectrum of Dark Matter Induced Neutrinos

In the presented analysis four generic annihilation/decay channels of the relic particles are considered: νν̄, bb̄, W + W − and µ+ µ− . When considering the annihilation/decay of dark matter into pairs of neutrinos, νν̄, the spectrum of neutrinos per
flavor is a monochromatic line with dN/dE = 23 δ( E − Mχ ), where the prefactor
2/3 arises under the assumption that 2 neutrinos are produced per one annihilationof dark matter particles pair and all neutrino flavors are equally populated. Suchmono-energetic neutrinos are of a specific interest as they can be used to set a model
independent limit on the total dark matter self-annihilation cross-section or decay
livetime into Standard Model final states.

6.4. Energy Spectrum of Dark Matter Induced Neutrinos

55

F IGURE 6.5: Differential muon
neutrino energy spectra for
WIMP particle mass of 100 GeV
annihilating into bb̄ (blue),
W + W − (maroon) and µ+ µ−(purple), after taking into
account neutrino oscillations
through the Galaxy.

For the calculation of the neutrino energy spectrum dN/dE, each time 100% branching ratio (BR) to a given annihilation/decay channel is assumed. The realistic annihilation/decay neutrino energy spectra, will be a mixture of different channels.
Therefore, the spectra assuming 100% BR to "hard" leptonic channel µ+ µ− and "soft"
hadronic channel bb̄ will bracket the realistic scenario.
Differential multiplicity spectra for bb̄, W + W − and µ+ µ− dark matter annihilation
or decay modes are obtained using DarkSUSY (Gondolo et al., 2001) simulator . The
example, differential muon neutrino energy spectra from annihilation of 100 GeV
WIMPs is shown in Fig. 6.5.
Full mixing due to long-baseline oscillations is assumed for the calculation of thedark matter induced neutrino flux at the Earth. The expected number of neutrino
events observed in the detector can be found by integrating the differential neutrino flux dΦdE∆Ω over the detector live-time and the direction- and energy-dependent
effective area for annihilation. Therefore, using Eq. 6.5 one can relate the velocityaveraged self-annihilation cross-section < σA v > with dark matter induced flux andconvert it into expected number of neutrinos.
DarkSUSY is a publicly-available advanced numerical package for neutralino dark
matter calculations (Gondolo et al., 2001). The neutralino density in the Universe,the direct detection rate with various nuclei, and indirect detection rates for neutrinos, gamma rays, and charged particles today can be computed. In this analysis,
version 5.0.6 is used in order to predict differential multiplicity spectra of neutrinos
produced in dark matter annihilation into one of considered channels (bb̄, W + W − ,µ+ µ− ), in the Milky Way. The hadronization and/or decay of the annihilation products are simulated with Pythia (Sjöstrand, Mrenna, and Skands, 2006) (v.6.154).

57

Chapter 7

Search for the Galactic WIMPs at
Super-Kamiokande
The methodology of the indirect search for dark matter with the Super-Kamiokande
detector is presented in this chapter. It is assumed that Super-K atmospheric neutrino data could have one additional origin related to dark matter induced neutrinos
from the center of the Milky Way. The goal of the search is to evaluate the allowed
contribution from such a source.
The presented analysis focuses on the search for angular anisotropy in the number ofobserved neutrino events between the region around the Galactic Center (GC) andthe other part of the sky, where the expected flux of dark matter annihilation/decay
products is low. It is referred to as an "ON-OFF source approach". In this method,
Monte Carlo simulation of WIMP induced neutrinos is used to optimize the analysis. In order to estimate the background, we use data itself, which allows to avoid
dependence on the simulation and related systematic uncertainties. The impact ofthe dark matter halo model choice is discussed.

7.1

Equatorial Coordinate System

In the search for dark matter induced neutrinos originating in the Galactic Center, it
is very convenient to use the equatorial coordinate system (see Fig. 7.1). Its origin isdefined at the center of the Earth and the fundamental plane is formed by the projection of the Earth’s equator onto the celestial sphere, forming the celestial equator.
The primary direction is pointing towards the vernal equinox, which is one of thetwo points where the ecliptic intersects the celestial equator.
To determine the position of a point in this system, two coordinates are used. The
first one is the declination (DEC), which measures the angular distance of an object
perpendicular to the celestial equator. It extends from 0◦ at the celestial equator to+90◦ at the north celestial pole, and to −90◦ at the south celestial pole. Declination
is analogous to terrestrial latitude. The second coordinate is right ascension (RA)which measures the angular distance of an object eastward along the celestial equator from the vernal equinox and is similar to terrestrial longitude. It can be measured
in degrees or hours, from 0◦ /0h at the vernal equinox up to 360◦ /24h.
One of the advantages of the equatorial coordinate system is the fact that it does
not rotate with the Earth, but remains fixed against the background stars. This isvery convenient since then the stars positions do not depend on the position of
the observer and the position of the GC is fixed, which is crucial for this analysis.

58

Chapter 7. Search for the Galactic WIMPs at Super-Kamiokande

F IGURE 7.1: Definition of the coordinates (right ascension, declination) in the equatorial coordinate system.

The distribution of atmospheric neutrino events in equatorial coordinate system isshown in Fig. 7.2. In contrast, in the horizontal coordinate system, the stars positions differ among observers based on their positions on the Earth’s surface, and arecontinuously changing with the Earth’s rotation.

F IGURE 7.2: Atmospheric neutrino events from SK I-IV data sets inthe equatorial coordinate system.

7.2

Simulation of WIMP Induced Neutrinos from the Galactic Center

The GC region is expected to contain the largest density of dark matter. For the halomodels (NFW, Moore and Kravtsov) considered in Chapter 6, neutrinos originatingfrom dark matter annihilation/decay would introduce a significant modification to7.2. Simulation of WIMP Induced Neutrinos from the Galactic Center

59

distribution of neutrino events observed at Super-K in equatorial coordinate system, where the position of the Galactic Center is fixed. The intensity of expecteddark matter induced neutrino signal is proportional to the square of the dark matter density in the halo (in case of annihilation) or to the density (in case of decay).
Therefore, the distribution of dark matter in the Milky Way is crucial for any robust predictions. For the assumed halo profile one can simulate the dark matter
induced neutrino events based on calculations of the intensity of dark matter annihilation/decay products (see Fig. 6.3 and Fig. 6.4), in order to investigate expectedsignal properties.
The Monte Carlo simulation of the dark matter induced neutrino signal is basedon the standard atmospheric MC described in Chapter 5, which is available for theSuper-K data in large statistics (500 years for each data taking period, 2000 years intotal). Standard atmospheric MC plotted in the equatorial coordinates (RA, DEC andΨ-angular distance from the GC) is shown in Fig. 7.3. For each plot, the true neutrino direction and reconstructed direction (based on direction of lepton produced inneutrino interaction) are shown. Due to Earth’s rotation, the detector gets an equal
exposure for atmospheric neutrinos in RA.

F IGURE 7.3: Left: Standard atmospheric MC in the equatorial coordinate
system (upper left plot for the true and bottom left for the reconstructed
directions). Middle: Distribution in the cosine of the angular distancefrom the GC (upper middle plot) and the angular distance from the GC(bottom middle plot). Right: Distribution in right ascension (upper rightplot) and declination (bottom right plot). Blue curves in middle and rightplots correspond to true neutrino directions and black curves to the reconstructed directions of leptons produced in neutrino interactions.

Based on the "date" and "time" information of each event, the position of GC at a
certain time can be calculated. Technically this calculation is done using Super-K
astrophysical libraries. First, the fixed position of GC in right ascension and declination is translated to the local frame (azimuth and zenith angle), and then, the GC
position in the local frame can be compared with the position of the given event.
Right ascension and declination of each event are calculated as well. The MC "time"

60

Chapter 7. Search for the Galactic WIMPs at Super-Kamiokandeand "date" are assigned randomly based on the distribution of the year, month, day,hour, minute, second of the real data for each SK period. Therefore, MC reflects datataking periods of the real events.
In order to simulate the dark matter induced neutrinos, for every event in atmospheric MC, a WIMP weight is assigned. The WIMP weight value is based on theintensity of dark matter annihilation/decay products, that can retrieve the characteristic shape associated with dark matter density distribution for a given halo model.
At a certain angular distance Ψ > 1◦ from the GC, the WIMP weight is proportional
to intensity in 1◦ intervals:(
J (Ψ) for dark matter annihilation,
WIMP weight(Ψ) ∼(7.1)
Jd (Ψ) for dark matter decay.
In this analysis, six sets of WIMP weights were used in order to reproduce the signal
shape for three considered dark matter halo models (NFW, Moore, and Kravtsov),and for both the dark matter annihilation and decay scenarios. The numerical values of the calculated weights used in this analysis are listed in Appendix A. The
intensity profiles for dark matter annihilation scenario have a very sharp shape forsmall angular distances from the GC. To take this effect into account, a finer binningscheme is used for Ψ < 1◦ (see Appendix A).

F IGURE 7.4: Spherical projections of the expected signal shape inthe equatorial coordinate system for Moore (left), NFW (middle) andKravtsov (right) halo profiles, assuming the dark matter annihilation
scenario. Upper plots show the true neutrino directions and bottom
plots show the reconstructed lepton directions.

The resulting event distribution obtained in the reweighting procedure are presented
in Fig 7.4 - 7.7. Fig. 7.4 shows the spherical projections of the expected dark matter
neutrino signal in the equatorial coordinate system, for the three halo profiles considered in the analysis, assuming dark matter annihilation scenario.

7.2. Simulation of WIMP Induced Neutrinos from the Galactic Center

F IGURE 7.5: Expected signal shape in RA (upper plots) and DEC (bottom plots) for Moore (left), NFW (middle) and Kravtsov (right) halo
profiles, assuming the dark matter annihilation scenario. Blue curves
correspond to the true direction of neutrino and black curves to thereconstructed one.

F IGURE 7.6: Expected signal shape in the cosine of the angular distance from the GC, cos (Ψ), (upper plots) and the angular distance,Ψ, from the GC (bottom plots) for Moore (left), NFW (middle) andKravtsov (right) halo profiles, assuming the dark matter annihilation
scenario. Blue curves correspond to the true direction of neutrino andblack curves to the reconstructed one.

61

62

Chapter 7. Search for the Galactic WIMPs at Super-Kamiokande

The 1D projections showing RA (upper row) and DEC (lower row) distributions
are presented in Fig. 7.5. The visible peak corresponds to GC direction (266◦ RA,−29◦ DEC). In Fig. 7.6 the projections showing the cosine of the angular distancefrom the GC, cos (Ψ) (upper plots) and the angular distance Ψ from the GC (bottom
plots) are presented.
The results of the simulation are consistent with expectations. For each halo model,
the annihilation signal is peaked and pointing towards to the GC direction. The
differences between the three considered profiles and the effect of reconstruction
procedure are clearly visible. One can expect differences in the obtained results dueto the adopted halo model.
For the dark matter decay scenario, the expected signal intensity is linearly proportional to the dark matter density distribution in the halo. Therefore, the differences
between halo models are smaller. The dark matter decay signal expectations for the
NFW halo profile are shown in Fig. 7.7.

F IGURE 7.7: Signal expectations for the NFW halo profile, assuming dark matter decay scenario. Left: Spherical projections of the expected signal shape in the equatorial coordinate system (upper left
plot for the true and bottom left for the reconstructed directions).
Middle: Distribution in the cosine of the angular distance from the
GC (upper middle plot) and the angular distance from the GC (bottom left plot). Right: Distribution in right ascension (upper right plot)
and declination (bottom right plot). Blue curves on middle and rightplots correspond to true neutrino direction and black curves to thereconstructed direction of lepton produced in neutrino interactions.

7.3. ON-OFF Source Approach

7.3

63

ON-OFF Source Approach

The dark matter induced neutrino flux would manifest itself through a large scaleanisotropy, with the largest excess of neutrinos at the area of the GC, as shown in
the previous section. To test this hypothesis, two regions on the sky are defined. The
ON-source region is centered on the GC position (266◦ RA, -29◦ DEC) and definedby a circle around this point with a half-opening angle Ψ. The OFF-source region isequally-sized, but offset by 180◦ in RA (see Fig. 7.8).

F IGURE 7.8: The illustration of the ON-OFF source approach. The
ON-source region is defined around the GC where the signal concentration is the highest. The OFF-source region is shifted in RA by 180◦ .
Because ON- and OFF-source regions are equally sized, the expected
number of background events is the same in both of them.

In both regions, signal and background events are expected. Signal events are defined as dark matter induced neutrinos and they are concentrated in the ON-source
region around the GC. Background events consist of atmospheric neutrinos and are
expected to be equally distributed in the ON- and OFF-source regions. Therefore, thedifference in the number of neutrino events between ON- and OFF-source regions
should contain no background events. In this way, the background can be estimateddirectly from the data. This method is independent of the atmospheric Monte Carlosimulations and related systematic uncertainties as they should equally affect ONand OFF-source regions. The difference in the number of neutrino events between
ON- and OFF-source regions correspond to difference in the signal events:
bkg

sig

bkg

sig

sig

sig

∆N = ( NON + NON ) − ( NOFF + NOFF ) ≈ NON − NOFF = ∆N sig .

(7.2)

The difference in signal events is directly proportional to the velocity-averaged dark
matter self-annihilation cross-section < σA v >, or inversely proportional to dark
matter particle lifetime τ, if dark matter decay is considered.

7.4

Optimization of the ON-Source Region Size

The accuracy of the neutrino direction reconstruction strongly depends on its energy.
Leptons produced in the interactions of low energy neutrinos (< few GeV) loosely
follow the direction of the parent neutrinos. The average neutrino energy differs

64

Chapter 7. Search for the Galactic WIMPs at Super-Kamiokande

between event categories used in Super-K atmospheric data analyses (see Fig. 5.2).
Therefore, it is advantageous to carry out the optimization separately for FC SubGeV, FC MultiGeV, PC and UP-µ events. The expected neutrino signal shape fromdark matter annihilation for NFW halo model is shown in Fig. 7.9 for FC SubGeV,
FC MultiGeV, PC and UP-µ event categories.

F IGURE 7.9: Spherical projections of the expected signal shape in theequatorial coordinate system for NFW halo model, assuming the dark
matter annihilation scenario for FC SubGeV, FC MultiGeV, PC and
UP-µ event categories.

The goal of the optimization procedure is to choose the size of the ON-source region,
so that the signal to background ratio is maximal. In order to do this, we calculate theratio between the expected number of signal events, S (for arbitrary chosen annihilation cross section), and square root of the expected number of background events,
B, for a range of different angular sizes of the ON-source region. The procedure isrepeated for ON-source region radius varying from 5◦ to 60◦ , with the step of 5◦ .
The maximal tested region sized is set to be 60◦ in order to avoid overlapping between ON- and OFF-source regions. The results of optimization of the ON-source
region size for different event classes are listed in Tab. 7.1. The optimization results
performed for our benchmark model, the NFW profile, are used in further analysis.
They are shown in Fig. 7.10, for the dark matter annihilation scenario.
The optimization of the size of the ON-source region was performed entirely withthe simulated events. However, this is the only part of analysis where the Monte7.4. Optimization of the ON-Source Region Size

65

TABLE 7.1: The results of the optimization of an ON-source region size assuming dark matter annihilation for NFW, Moore andKravtsov halo profile. The results for decay scenario are the samefor all models, and the size of 60◦ is the result of the requirement thatON- and OFF-source regions cannot overlap.

Event class
FC SubGeV
FC MultiGeV
PC
UPMU
ALL

Optimal size [◦ ]Annihilation
Decay
NFW Moore Kravtsov All Models
60
60
60
60
30
25
55
60
20
10
45
60
10
5
40
60
35
20
60
60

√
F IGURE 7.10: The signal to square root of the background (S/ B)
ratio as a function of the angular size of the ON-source region for
FC SubGeV (blue), FC MultiGeV (magenta), PC (black), UP-µ (green)
and all events together (red). The NFW halo model is assumed anddark matter annihilation scenario is considered.

Carlo events are used, later, the analysis is based solely on data in order to exclude
any dependence on the MC simulations and related systematic uncertainties.

67

Chapter 8

Results of the Search for Galactic
WIMPs
This chapter presents results of the searches for dark matter induced neutrino eventswith SK-I, II, III and IV data sets, using the ON-OFF source approach. The search
for a large-scale neutrino anisotropy in equatorial coordinate system is performed.
The analysis is focused on the area of the Galactic Center (ON-source) where theexpected contribution from dark matter induced neutrinos should be higher than in
the other part of the sky (OFF-source).
The results presented here were officially approved by the Super-Kamiokande Collaboration and presented by the author during XXIX Rencontres de Physique de laVallee d’Aoste (La Thuile 2015) in Italy (Frankiewicz, 2016) and the Meeting of theAmerican Physical Society, Division of Particles and Fields (DPF 2015) in Michigan,
USA (Frankiewicz, 2015).

8.1

Asymmetry Between ON- and OFF-Source Regions

The comparison between the number of observed events in ON- and OFF-source regions is shown in Table 8.1. Different event categories are considered separately, andfor each group of classes (FC SubGeV, FC MultiGeV, PC and UP-µ), the optimal sizeof the ON-source region is determined based on the simulated dark mater induced
neutrino interactions (see previous Chapter 7). Optimization assumes dark matterannihilation and NFW profile as a benchmark halo expectation.
The resulting asymmetries between the ON- and OFF-source regions, defined as
A = ( NON − NOFF )/( NON + NOFF ) are also shown in the Table 8.1, and are plottedin Fig. 8.1. No excess of dark matter induced neutrino events from the Galactic Center has been observed. This is the main result of the performed analysis, which canbe further interpreted under the assumption of various dark matter halo models and
WIMP annihilation modes.

68

Chapter 8. Results of the Search for Galactic WIMPs

TABLE 8.1: The number of events observed in ON-source (NON ) andOFF-source (NOFF ) regions for each considered event classes together
with resulting asymmetry (A) and the corresponding statistical errors(σ∆N and σA ). The optimal size of the ON-source region is determined
separately for each group of event categories.

SampleFully Contained (FC) SubGeV
e-like 0 decay-ee-like 1 decay-e
Single-ring π0 -likeµ-like 0 decay-eµ-like 1 decay-eµ-like 2 decay-e
Multi-ring π0 -like
Fully Contained (FC) MultiGeVνe -likeν̄e -likeµ-likeMultiRing νe -like
MultiRing ν̄e -like
MultiRing µ-like
MultiRing Other
Partially Contained (PC)
Stopping
Through-going
Upward-going Muons (UP-µ)*Stopping
Through-going Non-showering
Through-going Showering

NON

NOFF

∆N sig

σ∆N

A

σA

2597
283
154
677
1909
146
475

2576
290
141
710
1924
167
477

21
-7
13
-33
-15
-21
-2

71.92423.93717.17637.24261.911
17.69230.8540.004-0.0120.044-0.024-0.004-0.067-0.002

0.014
0.042
0.058
0.027
0.016
0.056
0.032

47
158
150
75
45
139
100

58
193
160
62
47
137
120

-11
-35
-10
13
-2
2
-20

10.24718.73517.60711.7059.592
16.61314.832-0.105-0.100-0.0320.095-0.0220.007-0.091

0.097
0.053
0.057
0.085
0.104
0.060
0.067

18
81

11
91

7
-10

5.385
13.1150.241-0.058

0.180
0.076

9.73
49.68
5.54

14.01
49.61
12.52

-4.29
0.07
-6.98

4.872
9.964
4.249

-0.1810.001-0.387

0.202
0.100
0.217

∗ In case of UP-µ samples, estimated rate of background events due to horizontal cosmic ray muons is

subtracted from the final data set resulting in fractional entries.

8.2. Constraints on Dark Matter Self-Annihilation Cross-Section

69

F IGURE 8.1: The asymmetry in the number of events between theON- and OFF-source regions.

8.2

Constraints on Dark Matter Self-Annihilation Cross-Section

Based on the null results in the considered samples, one can derive the upper limits on the allowed number of dark matter induced neutrinos, which can be furthertranslated to upper limits on the velocity-averaged dark matter self-annihilation
cross-section < σA v >. In order to do this, we have to assume the dark matter
halo model and the annihilation channel.
The νν̄ annihilation channel is considered separately, since the annihilating dark
matter particles of a given mass are resulting with neutrinos of the same energy.
In order to investigate νν̄ annihilation channel we would consider only νµ ν̄µ (1/3of the expected total νν̄ flux), as muon neutrinos are the most abundant in SK dataand cover the whole tested energy range. We group together µ-like events fromFC SubGeV, FC MultiGeV, PC and UP-µ categories, keeping the optimal size of the
ON-source region (60◦ , 30◦ , 20◦ and 10◦ respectively). For these samples, the difference in number of events between the ON- and OFF-source regions (∆N sig ) and thesig
90% C.L. upper limit on this value (∆N90 ) are calculated. These results are listed
in Table 8.2. If the difference in number of signal events happen to be negative (inunphysical region), the upper limit is calculated using the Bayesian approach described in details in Appendix D.
For the remaining annihilation channels: bb̄, W + W − and µ+ µ− , the energy spectraof neutrinos produced in the dark matter annihilation processes covers wide rangeof the energies (see example in Fig. 6.5). In this case we expect that the dark matter
induced neutrinos would be present in all event categories. Again, for the purpose

70

Chapter 8. Results of the Search for Galactic WIMPs

of this calculation we use only muon neutrino flavor. Therefore we group together
all µ-like events, and choose the ON-source region size to be 35◦ . The resulting numbers are shown in the last row of Table 8.2.
TABLE 8.2: The number of neutrino events observed in ON-source
and corresponding OFF-source regions for each considered µ-likeevent class. The optimal size of the ON-source region was determined separately for each class. The last column shows the upper
90% C.L limit on the allowed difference in number of signal events
between two considered regions. Results for dark matter annihilation scenario.

Sampleµ-like FC SubGeVµ-like FC MultiGeV
PC
UP-µ∗
ALL

Size [◦ ]
60
30
20
10
35

On-source
2732
289
99
64.95
2503.78

Off-source
2801
297
102
76.14
2626.69∆N sig-69± 74.38-8± 24.21-3± 14.18-11.19±11.88-122.91± 71.63

sig

∆N90
87.51
35.24
21.56
13.91
65.25

∗ In case of UP-µ samples, estimated rate of background events due to horizontal cosmic ray muons is

subtracted from the final data set resulting in fractional entries.

It is possible to translate the upper limit on a difference in number of dark matsig
ter induced muon neutrinos (∆N90 ) to corresponding difference in average dark
matter induced muon neutrino fluxes between ON-source ((dΦ∆ΩOFF) regions:dEdΦ∆ΩON) and OFF-sourcedEdΦ∆ΩONdΦ∆ΩOFF
−
.
(8.1)
dE
dE
The translation from the number of events to the flux value can be done based on
MC samples of the atmospheric neutrinos. One can match the number of observed
atmospheric events ( Natm ) with corresponding true value of neutrino flux ( dΦdEatm ) fora given neutrino energy. The same relation can be obtained for signal events. The
ratio of upper limit on number of dark matter induced neutrino events to the upper limit on corresponding difference in fluxes between ON-source and OFF-source
region should be the same as similar ratio for atmospheric neutrinos:
sig∆N90 →NatmdΦ atm
dE

sig

= dΦ

∆N90
∆ΩON

dE

−

dΦ∆ΩOFFdE· scaling factor.

(8.2)

Thus, from the following proportion one can derive the upper limit on a difference influxes of signal events in the investigated region of the sky (∆Ω = ∆ΩON = ∆ΩOFF )as:sigdΦ∆ΩONdΦ∆ΩOFF
4π ∆N90 dΦ atm livetime(MC)
−
=
·
·
,
(8.3)
dE
dE
∆Ω NatmdE
livetime(data)
where one takes into account the scaling for the adopted size of ON-source region
4π) and the different livetime for data and atmospheric MC.
( ∆ΩBased on the theoretical expectations on dark matter halo profile (see Sec. 6.1), one
can translate the limit on the dark matter induced neutrino flux (obtained for different event classes with the corresponding ON-source region ∆Ω) into the upper
limit for velocity-averaged self-annihilation cross-section < σA v >. The Eq. 6.5 can8.2. Constraints on Dark Matter Self-Annihilation Cross-Section

71

be rewritten in the form:dΦ∆ΩONdΦ∆ΩOFF< σA v >Rsc ρ2sc dN−=( J∆ΩON − J∆ΩOFF )
.
dE
dE
2
4πm2χ dE

(8.4)

This upper limit can be evaluated for NFW, Moore and Kravtsov profiles, by using the different average signal intensities J∆Ω corresponding to the assumed model.
The spectrum of annihilation products dN
dE for the considered annihilation channel iscalculated using DarkSUSY (see Sec. 6.4).
In this way one can determine the corresponding limit on < σA v > for assumed
mass of dark matter particle and annihilation channel. For the νν̄ annihilation channel, the upper limit in the given WIMP mass range is determined based on thatsample of FC SubGeV, FC MultiGeV, PC or UP-µ events, which dominates in thatenergy range (see Fig. 5.2). The results for bb̄, W + W − and µ+ µ− are based on allµ-like events together, considered within 35◦ around GC. The results for the threeconsidered profiles are presented in Fig. 8.2. Each time 100% BR to a given annihilation channel is assumed.

F IGURE 8.2: The upper 90% C.L. limit on dark matter selfannihilation cross-section as a function of the dark matter particle
mass for bb̄ (blue), W + W − (maroon), µ+ µ− (purple) and νν̄ (orange) annihilation channels. The influence of the halo model choice
is shown as a band around the result for the benchmark NFW profile.

The derived constraints on the value of < σA v > strongly depend on the adopted
halo model. Obtained differences between benchmark model (NFW) and models
used as extreme cases (Moore and Kravtsov) can reach the order of magnitude. If
the size of an ON-source region is smaller, the difference between obtained limits
is even greater due to large discrepancies in the expected intensity of dark matterannihilation products close to the Galactic Center for considered halo profiles (seeFig. 6.3). Therefore, focusing on the GC makes the results very sensitive to the chosen
profile, but on the other hand, allows to obtain the best sensitivity for dark matter

72

Chapter 8. Results of the Search for Galactic WIMPs

induced neutrino signal.
The results for NFW profile are compared to limit obtained in the independent analysis of Super-Kamiokande data referred to as "Global Fit" (Mijakowski, 2018), whichis shown in Fig. 8.3. This independent analysis was performed by different author.
It relies on a fit of simulated dark matter induced neutrino signal and the atmospheric neutrino background to the same data sample as used in this analysis. In the
Global Fit analysis, all SK data samples (FC, PC, UP-µ) including both electron andmuon neutrinos, are binned in angular and momentum bins and are used in the fit
providing the best search sensitivity among the two presented methods. The ONOFF source approach was designed as an independent cross-check for the Global
Fit method. The advantage of ON-OFF source approach is being data driven andindependent on atmospheric MC and related systematic uncertainties.

F IGURE 8.3: The upper 90% C.L. limits on dark matter selfannihilation cross-section as a function of dark matter particle massfor bb̄ (blue), W + W − (maroon), µ+ µ− (purple) and νν̄ (orange) annihilation channels (solid lines), compared with the results of independent Global Fit analysis (dotted lines) of Super-K data (Mijakowski,2018).

8.3

Constraints on the Dark Matter Particles Lifetime

In analogical way, one can calculate the limits on WIMP particles lifetime. The same
ON-OFF source number of events comparison is repeated in the cone of 60◦ aroundthe GC. In this case the expected signal covers significant part of the sky (see Fig. 7.7),
and size of the ON-source region is limited by the requirement that ON- and OFFsource regions cannot overlap with each other. The comparison between the number
sigof observed events in ON- and OFF-source regions and obtained limits for N90 are
shown in Table 8.3. Since there is no statistically significant excess in the search cone,
one can derive the upper limits on dark matter particle lifetime τ, using the Eq. 6.6.
The results for four considered decay channels bb̄, W + W − , µ+ µ− and νν̄, assuming
NFW halo profile are shown in Fig. 8.4. Each time 100% BR to a given decay channel
is assumed.

8.3. Constraints on the Dark Matter Particles Lifetime73

The results are compared with the limits form IceCube experiment (Abbasi et al.,2012). Super-Kamiokande detector is located in the northern hemisphere which
gives better conditions to search for dark matter induced neutrino flux from the GC,
as it can be seen with UP-µ events ∼71% of the time. Given IceCube’s location at
the South Pole, a search for a neutrino flux from the GC, located in the southern sky
is impacted by a significant background of cosmic-ray induced atmospheric muonsand atmospheric neutrinos. Part of the detector has to be used as a veto for cosmic
muons.
TABLE 8.3: The number of neutrino events observed in ON-source
and corresponding OFF-source regions for each considered µ-likeevent class. The optimal size of the ON-source region is constrained
to be 60◦ in order to no not have overlapping between ON- and OFFsource regions. The last column shows the upper 90% C.L limit on
the allowed difference in number of signal events between two considered regions. Results for dark matter decay scenario.

Sampleµ-like FC SubGeVµ-like FC MultiGeV
PC
UP-µ∗
ALL

Size [◦ ]
60
60
60
60
60

On-source
2732
1133
783
2353.55
7001.55

Off-source
2801
1087
777
2453.857118.85∆N sig-69±74.38
46±47.12
6±39.50-100.30±69.34-117.30±118.83

sig

∆N90
87.51
111.1068.76
68.69
136.99∗ In case of UP-µ samples, estimated rate of background events due to horizontal cosmic ray muons is

subtracted from the final data set resulting in fractional entries.

F IGURE 8.4: The lower 90% C.L. limits on the dark matter particle lifetime as a function of dark matter particle mass for bb̄ (blue), W + W −(maroon), µ+ µ− (purple) and νν̄ (orange) decay channels, comparedwith limits from IceCube experiment (dotted lines) (Abbasi et al.,2012). NFW halo model is assumed.

75

Chapter 9

WIMPs in the Center of the Earth
Neutrinos can be used as a probe of dark matter present in massive baryonic bodies like the Sun or the Earth. It is expected that WIMPs from the Galactic Halo canbe bound in the gravitational potential of the Solar system, as it passes through theMilky Way. WIMPs can scatter off a nucleus inside a massive celestial bodies (theSun or the Earth), lose energy, and be gravitationally trapped. Once captured, they
eventually sink to the core due to subsequent scatters and then annihilate into leptons, quarks or bosons, producing neutrinos in the subsequent decays. Among theannihilation products, only neutrinos can escape from the center of the Sun or the
Earth.
The idea to search for dark matter induced neutrino flux was proposed by Pressand Spergel (Press and Spergel, 1985), where capture rates for dark matter particles
in the Sun have been calculated. The dedicated analysis to search for neutrinos fromthe annihilation of the captured low-mass WIMPs in the Sun was previously performed with the Super-Kamiokande data (Choi et al., 2015). The analysis dedicatedto the Earth, performed by the author, will be described in the next three chapters.

9.1

Capture Rate of WIMPs in the Earth

The history of determining the capture rates in the Earth has gone through a seriesof significant changes over the years, summarized in (Lundberg and Edsjo, 2004).
This thesis follows the approach presented in (Sivertsson and Edsjo, 2012).
The capture rate of WIMPs depends on their mass, velocity in the halo, and local
density. When the WIMP mass (Mχ ) matches the mass of an element present in the
Earth, the Earth can efficiently capture relic particles directly from the galactic halo.
Therefore, the capture rate depends on the mass and distribution of the elements inthe Earth. The most important elements are listed in Table 9.1. The Earth’s density
profile, given in (Seyfert, 1998) is used.
The WIMP velocity in the halo cannot be measured and it is estimated through simulations. A Maxwell-Boltzmann WIMP velocity distribution is assumed, with a velocity dispersion of 270 km/s, and circular velocity at the Solar system’s location of
220 km/s. The local dark matter halo density can be estimated from observations
and it is taken to be ρχ = 0.3 GeV/cm3 (Yüksel et al., 2007). Fig. 9.1 shows the rate at
which dark matter particles are captured to the interior of the Earth, for a scatteringcross-section of σ = 10−44 cm2 . The visible peaks correspond to resonant capture on
the most abundant elements 16 O, 24 Mg, 28 Si, 56 Fe, and their isotopes.

76

Chapter 9. WIMPs in the Center of the EarthTABLE 9.1: The composition of the Earth’s core and mantle (McDonough, 2003).

Element
Oxygen, O
Silicon, Si
Magnesium, Mg
Iron, Fe
Calcium, Ca
Phosphor, P
Sodium, Na
Sulphur, S
Nickel, Ni
Aluminum, Al
Chromium, Cr

Atomic Number
16
28
24
56
40
30
23
32
59
27
52

Core mass fraction
0.0
0.06
0.0
0.855
0.0
0.002
0.0
0.019
0.052
0.0
0.009

Mantle mass fraction
0.440
0.210
0.228
0.06260.02530.00009
0.00270.000250.001960.02350.0026

F IGURE 9.1: The capture rate of WIMPs in the Earth for a scatteringcross section of σ = 10−44 cm2 , calculated in (Sivertsson and Edsjo,
2012). The normalization of the original calculation performed for
σ = 10−42 cm2 was adjusted due to recent exclusions from direct detection (Akerib et al., 2017). Figure taken from (Aartsen et al., 2017a).

9.2

WIMP Annihilation in the Earth

The differential equation governing the time evolution of the number of WIMPs, N,
in a celestial body can be written in the form:dN= CC − C A N 2 − CE N,
dt

(9.1)

where the three constants describe rate of WIMP capture (CC ), annihilation (C A ), andevaporation (CE ). WIMP evaporation, means that once captured, WIMPs could beejected from the celestial body by hard elastic scattering from nuclei. Only WIMPS

9.3. Neutrino Flux from WIMP Annihilation in the Earth77

with low masses < 5 GeV may undergo this process (Jungman, Kamionkowski, andGriest, 1996), so this term can be neglected in our calculations.
WIMP annihilation, depends on the WIMP annihilation cross-section (σA ) and effective volumes available for WIMP capture in the Earth:CA =hσA vi · ( Mχ /(10 GeV))3/2√.
2 8 · 1025 cm3(9.2)

The total annihilation rate (Γ A ) can be written as:
ΓA =1
CA N 2 .
2(9.3)

The capture of WIMPs mainly depends on the WIMP-nucleon scattering cross-section(σχ− N ), the WIMP mass (Mχ ), and the mass and distribution of the elements in the
Earth. Therefore, for capture in the Earth, the main contribution comes from the SI
component σχ− N , which is quadratically proportional to the atomic mass of the elements in the Earth. If the capture rate is constant in time and we solve Eq. 9.1 for theannihilation rate, we find:
 
1
t
2
Γ A (t) = CC tanh
,
(9.4)
2
τ
where τ is the time scale for capture and annihilation equilibrium to occur, and isequal to
1
τ= √
.
(9.5)
CC C AThe present rate can be calculated using age of the Solar system, t = t ∼ 4.6 · 109
years. If t/τ >> 1, the annihilation and capture are in equilibrium and dN/dt = 0.
In this case, the annihilation rate depends only on the capture rate:
ΓA =

1
CC .
2

(9.6)

The equilibrium time scale (τ) is determined by the WIMP-nucleon scattering crosssection σχ− N , the WIMP self-annihilation cross section < σA v >, and the WIMP massMχ . For the Earth, this equilibrium time is of the order of 1011 years for the SI WIMPnucleon scattering cross-section, σχSI− N ∼ 10−43 cm2 (Jungman, Kamionkowski, andGriest, 1996). As t /τ << 1, the equilibrium between capture and annihilation has
typically not been reached in the Earth and the annihilation rate goes as the squareof the capture rate:Γ A ∝ CC2 .
(9.7)
Therefore, for the higher capture rate, we have higher annihilation rate and thus the
expected dark matter induced neutrino flux.

9.3

Neutrino Flux from WIMP Annihilation in the Earth

WIMPs accumulated in the Earth’s core can self-annihilate at the rate Γ A , which is
proportional to the square of its density (see Eq. 9.3). The neutrino flux produced at

78

Chapter 9. WIMPs in the Center of the Earththe Earth’s surface can be written as:
dΦ
ΓA
=
dEν
4πR2⊕



dNν
dEν


,

(9.8)

where R⊕ is the Earth radius and dNν /dEν is neutrino spectrum for all annihilation
channels.
In order to calculate the neutrino flux from WIMP annihilation in the Earth, weneed an explicit WIMP candidate. We consider the lightest neutralino (χ), that arises
as a natural dark matter candidate in supersymmetric extensions of the standard
model (see Sec. 2.2.1). In the considered model, the direct annihilation into neutrinos χχ → νν̄ is strongly suppressed. We will consider three annihilation channels:bb̄, which gives the softest (less energetic) spectrum, and τ + τ − and W + W − , whichgive the hardest (the most energetic) spectrum. In this case µ+ µ− channel is not considered, since produced muons will be stopped before they have a chance to decay
and produce neutrinos. Neutrino spectra at the detector from the considered annihilation channels are generated with WimpSim (Blennow, Edsjö, and Ohlsson, 2008)
software (see following Sec. 9.4).

9.4

WimpSim Results for the Earth WIMPs

Neutrino yields from WIMP annihilation in the Earth’s core are simulated with the
WimpSim simulation package (Edsjö, 2007), which is based on DarkSusy (Gondolo
et al., 2001). The simulation includes WIMP captured in the Earth, annihilation into
11 channels, hadronization of the products, and their decays leading to the production of neutrinos. The propagation through the Earth to the detector is also covered.
Neutrino oscillations are included in a full three-flavor framework including both
vacuum and matter oscillations.
For the purposes of this analysis, the simulation was performed by the author for
the following WIMP masses: 3, 6, 10, 25, 50, 80.3, 91.2, 100, 150, 176, 200, 250, 350,
500, 750, and 1000 GeV and three annihilation channels: bb̄, W + W − , and τ + τ − . For
each mass and annihilation channel, 2.5 · 106 annihilations were simulated, keeping
track of the all produced neutrinos and antineutrinos, and their flavors.
The example of dark matter induced neutrino spectra at the surface of the Earth generated with WimpSim is shown in Fig. 9.2 for 6 GeV WIMPs annihilating into the bb̄
channel. Plots for a wide range of WIMP masses and three annihilation channels
considered in the analysis can be find in Appendix B.
The output of WimpSim, used in this analysis, consists of text files containing 50
lines for each neutrino and antineutrino flavor. Each line is for one of 50 bins in z =0.01, 0.03, . . . , 0.99, where z is the ratio between neutrino energy and assumed dark
matter particle mass: z = Eν /Mχ . Each line contains 91 values corresponding to
d2 N/dzdθ, where θ is the angular distance from the Earth’s core, and is binned in 91
bins from 0 to 30◦ . The θ bins are as follows:• The first 50 bins are for θ = 0.1◦ , 0.3◦ , . . . , 9.9◦
• The next 40 bins are for θ = 10.25◦ , 10.75◦ , . . . , 29.75◦• The final bin in θ is for θ > 30◦ .

9.4. WimpSim Results for the Earth WIMPs

79

F IGURE 9.2: The differential fluxes of the neutrinos (left panels) andanti-neutrinos (right panels) produced by 6 GeV WIMPs annihilating
into bb̄ quarks, as a function of the neutrino energy Eν , divided by the
WIMP mass Mχ . The different neutrino species are indicated with adifferent color, black for νe , red for νµ , and green for ντ .

The comparison of dark matter induced muon neutrino spectra at the surface of the
Earth generated for the same WIMP mass and for the three annihilation channels
considered in the analysis is presented in Fig. 9.3. The fact that WIMP annihilation
does not occur exactly in the center of the Earth (the size of the region depends on
the WIMP mass) is also taken into account, and is shown in Fig. 9.4. The annihilation
region radius scales as ∼ 1/Mχ2 , so for higher WIMP masses, neutrinos produced indark matter annihilation are more concentrated around the Earh’s core.

F IGURE 9.3: Energy spectra of the dark
matter induced muon neutrinos at the
Earth’s surface generated with WimpSim,
for 100 GeV WIMPs annihilating into bb̄
(blue line), τ + τ − (green line), and W + W −(maroon line) channel.

F IGURE 9.4: Angular distribution of the dark
matter induced muon neutrinos observed at
the Earth’s surface, generated with WimpSim for 10 GeV (solid line), 100 GeV (dashedline), and 1 TeV (dotted line) WIMPs annihilating into b̄ quarks.

The results from WimpSim allow us to obtain the angular and energy characteristics expected for dark matter induced neutrinos from the center of the Earth. These
distributions are used as a first step in the simulation of the signal in the Super-K detector, which is described in the next chapter. WimpSim also provides a conversion
script that can convert between neutrino flux, annihilation rate, and corresponding
SI WIMP-nucleon scattering cross-section for an assumed dark matter particle mass
and annihilation channel, taking into account different thresholds and angular cuts

80

Chapter 9. WIMPs in the Center of the Earthfor the detector. This conversion script is used for the interpretation of results discussed in Chapter 11.

81

Chapter 10

Search for the Earth WIMPs at
Super-Kamiokande
In this chapter, the methodology of the search for dark matter induced neutrinos
from the Earth’s core with the Super-Kamiokande data is presented. The approach
applied here is different than the "ON-OFF source" technique used in the previously
presented analysis focused on neutrinos from the Galactic Center, and the latter one
would be referred to as a "Global fit" approach.
In this analysis, it is assumed that the atmospheric neutrino data collected with
the SK detector can be described by two components: atmospheric neutrinos (background) and neutrinos produced in dark matter annihilation in the Earth’s core (signal). The goal of the search is to evaluate the allowed signal contribution. In orderto do this, a fit method similar to the one used in the standard neutrino oscillation
analysis (see Section 5.3) is adopted. Instead of scanning the oscillation parameters(∆m232 , sin2 θ23 and δCP ), we will be scanning over the WIMP masses (Mχ ) and dark
matter contribution (β), which is normalized to the number of atmospheric neutrino
data.

10.1

Global Fit Approach

Similarly to the standard oscillation analysis, data is fit to the combination of signal and background MC, using a binned χ2 method that is built assuming Poisson
statistics and incorporating systematic errors as a scaling factors on the MC in eachbin (Fogli et al., 2002):
χ = 2∑
2

n

NnMC



1+∑
i

f ni ei+ βNnDM

1+∑

f nk ek



k

!
DATA
N
n
− NnDATA ln MC
Nn (1 + ∑i f ni ei ) + βNnDM (1 + ∑k f nk ek )
 2
 2
ei
e
+∑
+∑ k .
σiσkik(10.1)In this equation, NnMC represents the background MC expectation (atmospheric neutrinos with oscillations), NnDM represents the signal MC expectation (DM induced
neutrinos) and NnDATA is the corresponding data in the n-th analysis bin. Systematic
errors are incorporated into the fit via the systematic error parameter ei , where i is
the systematic error index and f ni is the fractional change in the MC expectation in
the n-th bin for a σi change in the i-th systematic error. Systematic errors penalize

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

the χ2 based on their corresponding fitting parameters ei . Parameter β represents
the varied normalization of the simulated signal and the determination of its value
is the main goal of this analysis.
In the fit, the system of equations defined by the requirement ∂χ2 /∂ei = 0, is solved
for each systematic error, which brings the data and MC into the best agreement
allowed by the systematic errors. This minimization in the systematic error parameters is repeated over a grid of WIMP parameters (Mχ and β), and global minimumof χ2 defines the best f it point.
The following WIMP parameters are considered in this analysis:• β: 301 points from -0.01 to 0.02
• Mχ : 15 points for bb̄ annihilation channel(6, 10, 25, 50, 80.3, 91.2, 100, 150, 176, 200, 250, 350, 500, 750, 1000 GeV)
16 points for τ + τ − annihilation channel(3, 6, 10, 25, 50, 80.3, 91.2, 100, 150, 176, 200, 250, 350, 500, 750, 1000 GeV)
11 points for W + W − annihilation channel(80.3, 91.2, 100, 150, 176, 200, 250, 350, 500, 750, 1000 GeV)
The lower value of the tested WIMP mass range for a given annihilation channel
is due to kinematical restrictions on the production of b quarks, τ leptons, and W
bosons. The upper analysis threshold, Mχ = 1000 GeV, is related to limited statistics
in the MC samples which are used to simulate signal and background component atsuch high neutrino energies.
There are 160 sources of systematic uncertainties taken into account in the analysis(see Sec. 5.3.1). All of them are applied to the background part describing atmospheric neutrinos. For the signal part describing WIMP induced contribution, solar
activity and flux related systematic errors are not taken into account. Uncertainties corresponding to neutrino interactions, particle production, PMNS oscillation
parameters and detector related are applied to signal in the same way as for the
background.
The simulated component describing background predictions (N MC ) depends onthe values of neutrino oscillation parameters: three mixing angles θ13 , θ12 , θ23 , twomass splittings ∆m221 , ∆m232 , and one CP-violating phase δCP .
Oscillation parameters: θ13 , θ12 and ∆m221 are treated in the same way as during
standard oscillation analysis described in Chapter 5. They are fixed at the values
from the global fit, listed in Tab. 5.3, and varied only through the systematic errors.
The values of θ23 and ∆m232 are fixed during the fit at their best f it point from thestandard oscillation analysis of SK data, assuming normal mass hierarchy: sin2 θ23 =
0.588 and |∆m232 | = 2.50 × 10−3 eV2 . Since super-Kamiokande has a very small sensitivity to δCP , this parameter is set to be 0.
The fit is performed using 19 data samples, including both e-like and µ-like event
categories. Each sample is binned in lepton momentum and cosine of the zenith
angle, which gives in total 520 analysis bins for each of the SK running period (seeChapter 5 for detailed description).

10.2. Signal and Background Predictions

10.2

83

Signal and Background Predictions

In order to simulate the detector response for the signal (WIMP induced neutrinos
from the Earth’s core), the existing simulation of atmospheric neutrino interactions
is used (see Sec. 5.2). This Monte Carlo assumes realistic fluxes of neutrinos, andincludes their interactions in the Super-K tank or in the rock surrounding the detector. The simulation also includes the detector response for the produced Cherenkov
light. The same set of data reduction steps and classification cuts are applied to simulated events and to the real data.
The background component is described by the half of the events from the standard atmospheric MC (250 years for each SK period). The plot with the backgroundexpectations is shown in Fig. 10.1.
Background illustration with the standard binning

F IGURE 10.1: Atmospheric neutrino background expectation (orange
histogram) and the SK-I-IV data (black points). The momentum (1stcolumn) and zenith angle (2nd -5th columns) distributions are shownfor 19 samples used in the analysis. In all panels, the error bars represent the statistical uncertainty.

Second half of the events from the standard atmospheric MC is reweighted in a way
to obtain characteristics expected for dark matter induced neutrinos. The assigned
weights are based on the results obtained using WimpSim simulation (see Sec. 9.4 forthe details). The Earth WIMP weight is assigned to each event, based on its energy

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

and angular distance from the Earth’s core. After the reweighting, the signal partof MC is normalized to the background part (describing atmospheric neutrinos),
therefore the β parameter used in the fit correspond to the fraction of atmospheric
neutrinos.
The dark matter induced neutrino signal from the Earth’s core is simulated for threeannihilation channels: bb̄, τ + τ − , and W + W − . Plots of the signal contributions areshown in Fig. 10.2 for 25 GeV WIMPs annihilating into bb̄ quarks, in Fig. 10.3 for
100 GeV WIMPs annihilating into τ + τ − leptons, and in Fig. 10.4 for 500 GeV WIMPs
annihilating into W + W − bosons.
Signal illustration for Mχ = 25 GeV, β = 0.02, bb̄ annihilation channel

F IGURE 10.2: The signal originating from the annihilation of 25 GeV
WIMPs in the Earth’s core into bb̄ quarks. The momentum (1st column) and zenith angle (2nd -5th columns) distributions are shown for
19 samples used in the analysis. The plots contain the expected signal from WIMP annihilation (filled blue histogram) and the SK-I-IV
atmospheric neutrino data (black points). In all panels, the error bars
represent the statistical uncertainty.

All data samples which are being used in the analysis are presented there. The
samples in the first column (SubGeV e-like 1 decay electron, SubGeV π 0 -like andSubGeV µ-like 2 decay electron) have only one angular bin, therefore the reconstructed momentum distributions are shown. Other samples with more than one

10.2. Signal and Background Predictions

85

Signal illustration for Mχ = 100 GeV, β = 0.02, τ + τ − annihilation channel

F IGURE 10.3: The signal originating from the annihilation of 100 GeV
WIMPs in the Earth’s core into τ + τ − leptons. The momentum (1stcolumn) and zenith angle (2nd -5th columns) distributions are shownfor 19 samples used in the analysis. Plots contain expected signal
from WIMP annihilation (filled green histogram) and the SK-I-IV atmospheric neutrino data (black points). In all panels, the error bars
represent the statistical uncertainty.

zenith angle bin are shown as zenith angle distributions (second through fifth column). More illustrations for the wide range of considered WIMP masses can be findin Appendix C.
The WIMP induced signal appears in various samples, depending on the assumed
WIMP mass and annihilation channel. According to the expectations, the signal isalways located in bins close to the Earth core (cos θ = −1) .
All neutrino flavors (νe ν̄e , νµ ν̄µ and ντ ν̄τ ) are used in the signal and backgroundMC simulations. Tau neutrinos are produced in the subsequent decays of WIMP
annihilation products. They would be mainly categorized as MultiGeV e-like andMulti-Ring event samples due to the complex topology of secondary particles produced in tau neutrino interactions (τ decays immediately producing leptons andmesons).

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

Signal illustration for Mχ = 500 GeV, β = 0.02, W + W − annihilation channel

F IGURE 10.4: The signal originating from the annihilation of 500 GeV
WIMPs in the Earth’s core into W + W − bosons. The momentum (1stcolumn) and zenith angle (2nd -5th columns) distributions are shownfor 19 samples used in the analysis. Plots contain expected signal
from WIMP annihilation (filled maroon histogram) and the SK-I-IV
atmospheric neutrino data (black points). In all panels, the error bars
represent the statistical uncertainty.

10.3

Sensitivity Study for WIMP Induced Neutrinos from the
Earth’s Core

Dedicated studies are performed in order to estimate the SK detector sensitivity to
the dark matter induced neutrino signals from the Earth’s core. Based on the prepared simulation sets, the expected sensitivity to each of the WIMP parameters (Mχ ,β) can be computed. In order to do this, we choose a point in the WIMP parameter space, for which we have prepared the signal and background expectations.
This point is treated as the observed data. Then, we preform "pulled" χ2 test for all10.3. Sensitivity Study for WIMP Induced Neutrinos from the Earth’s Core87

points from our parameter space against the template that is the assumed observation. Based on the obtained χ2 value of the fit, we can draw sensitivity contours.
Note that the background expectation is the same for all tested points from WIMP
parameter space.
During the analysis we consider three annihilation channels separately: (bb̄, τ + τ −and W + W − ). Each time, a 100% branching ratio (BR) to a given annihilation modeis assumed as a model independent approach.

10.3.1

Null WIMP Contribution (β = 0)First of all, we want to test null hypothesis when β = 0. This case corresponds
to the result from the standard oscillation analysis (described in Sec. 5.3). Here weassume that all data observed by the SK detector can be explained by atmospheric
neutrino oscillations. We calculate "pulled" χ2 for this hypothesis against all points
in our WIMP parameter space (defined in Sec. 10.1) . Results of this test are plottedin Fig. 10.5 for the three considered annihilation channels. For each tested WIMP
mass (Mχ - X axis) and WIMP contribution (β - Y axis), the resulting χ2 value of the
fit against no WIMP contribution hypothesis is plotted as color, creating so called"heat map". It is visible that the lowest χ2 values are located around β = 0 line (darkblue) as expected. As we move away from β = 0 line, χ2 values are getting higher,
which corresponds to increasing WIMP contribution. The same results can be presented as sensitivity contours. The 68% (blue), 90% (yellow) and 99% (maroon) C.L.
contours for β = 0 hypothesis are shown in Fig. 10.6.

One can notice that the sensitivity contours are getting wider for lower WIMP masses(the left side of top and middle plots). Also If we compare the sensitivity contours
in Fig. 10.6 between bb̄ and τ + τ − for the same WIMP mass, the contour for thesoft channel (bb̄) is wider then for the hard channel (τ + τ − ). In general, it is easier
to distinguish a signal when it consists of neutrinos of higher energies. This effect can be explain by the fact that the WIMP annihilation does not occur exactly inthe center of the Earth, and the size of the region depends on the WIMP mass (seeSec. 9.4). The annihilation region radius scales as ∼ 1/Mχ2 . Therefore, for higher
WIMP masses, neutrinos produced through dark matter annihilation are more concentrated around the Earth’s core, and it makes them easier to distinguish from theatmospheric neutrino background. Moreover, the angular resolution of the detector
strongly depends on the energy of the parent neutrinos. Leptons produced in interactions of low energy neutrinos (< few GeV) loosely follow the direction of theparent neutrino. Therefore, the average angular separation between the true parent
neutrino direction and the reconstructed lepton direction is greater. These effects
are also visible in the signal plots for τ + τ − channel presented in Appendix C. For
low WIMP masses (Mχ = 3 GeV), the signal is distributed over many angular bins
and present in many samples. For high masses (Mχ ≈ 1000 GeV), almost the whole
signal is concentrated in narrow UP-µ bins.

88

Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

F IGURE 10.5: Heat map showing the tested parameter space of WIMP
masses (X - axis) and WIMP contribution (Y - axis) for three considered annihilation channels: bb̄ (top), τ + τ − (middle) and W + W −(bottom). Null WIMP contribution (β = 0) is assumed and the color
represents χ2 value of the fit.

10.3. Sensitivity Study for WIMP Induced Neutrinos from the Earth’s CoreF IGURE 10.6: Sensitivity contours at 68% (blue), 90% (yellow) and
99% (maroon) C.L for null WIMP contribution (β = 0), for tested
parameter space of WIMP masses (X - axis) and WIMP contribution(Y - axis), plotted for three considered annihilation channels: bb̄ (top),τ + τ − (middle) and W + W − (bottom).

89

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

In order to better illustrate the sensitivity of the fit, we can plot 1D projection of∆χ2 value as a function of β parameter (see Fig. 10.7), for each considered WIMP
mass. The ∆χ2 is defined as a difference between χ2 obtained for a given value ofbeta parameter and χ2min , the value obtained for the best f it point. In case of a null
WIMP contributions, χ2min = 0 for β = 0, where all obtained ∆χ2 parabolas havetheir minimum. The horizontal lines show the ∆χ2 equal to 1 (blue), 2.71 (yellow),and 6.63 (maroon), corresponding to 68%, 90% and 99% C.L. limit on β value respectively. The intersection between ∆χ2 parabola and 90% C.L. horizontal line defines
β 90 value. One can notice that the width of ∆χ2 parabola is changing with mass.

F IGURE 10.7: The ∆χ2 = χ2 − χ2min distributions minimized overthe corresponding WIMP masses. The horizontal lines correspond to
the 68% (blue), 90% (yellow) and 99% (maroon) C.L. for no WIMP
hypothesis (β=0), plotted for τ + τ − annihilation channel.

Based on the obtained values of β 90 corresponding to 90% C.L. limit on dark matter induced neutrino contribution for a given WIMP mass, the upper limits on the
WIMP induced muon neutrino flux are calculated using MC (in analogical way as
described in Sec. 8.2) and shown in Fig. 10.8. These results are translated to limits on the SI WIMP-nucleon scattering cross-section presented in Fig. 10.9. Since
the equilibrium between WIMP capture and annihilation in the Earth core has not10.3. Sensitivity Study for WIMP Induced Neutrinos from the Earth’s Core91

been achieved (see Sec. 9.2), this limits depend on the velocity averaged dark matter self-annihilation cross-section. For the calculation we assumed a typical value of< σA v >= 3 · 10−26 cm3 s−1 , for which the WIMP is a thermal relic (see Sec. 2.2). For
the translation, we use conversion script provided by WimpSim (see Sec. 9.4).

F IGURE 10.8: The 90% upper limits on thedark matter induced muon neutrino flux
from the sensitivity study for bb̄ (dottedblue), τ + τ − (dotted green) and W + W −(maroon line) annihilation channel.

F IGURE 10.9: The 90% upper limits on SI
WIMP-nucleon scattering cross-section fromthe sensitivity study for bb̄ (dotted blue), τ + τ −(dotted green) and W + W − (maroon line) annihilation channel. Positive result claimed by
DAMA/LIBRA (Bernabei et al., 2013) is shownfor comparison.

The structure of the limits corresponds to enhanced WIMP capture in the Earth’s
core, when WIMP mass (Mχ ) matches the mass of an element present in the Earth.
The peaks visible in Fig. 10.9 correspond to most abundant elements: 16 O, 24 Mg, 28 Si,
56 Fe, and their isotopes (see Fig. 9.1 for comparison).
From the sensitivity study results, we can estimate the possible range of SI WIMPnucleon scattering cross-section that can be probed with Super-Kamiokande data.
One can see that most of the region of the positive signal claimed by DAMA/LIBRA
experiment can be accessed with this analysis.
The presented results of the sensitivity study for null WIMP contribution were officially approved by the Super-Kamiokande Collaboration in June 2016. They were
presented by the author during the 38th International Conference on High Energy
Physics (ICHEP 2016) in Chicago, USA (Frankiewicz, 2017b), and XXVII International Conference on Neutrino Physics and Astrophysics (Neutrino 2016) in London,
UK (Frankiewicz, 2017a).

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

10.3.2

Injected WIMP Contribution (β = 0.01)

After testing null hypothesis, we also test the fit behavior for the positive WIMP
contribution. The three example points:• Mχ = 25 GeV, β = 0.01, bb̄ annihilation channel,• Mχ = 100 GeV, β = 0.01, τ + τ − annihilation channel,• Mχ = 500 GeV, β = 0.01, W + W − annihilation channel,
are now treated as the observed data and we fit all points from our parameter spaceagainst these presumed observations. The results are shown in Fig. 10.10, as the heatmaps. One can clearly see that the lowest χ2 values are located around tested points
with β = 0.01 and at injected WIMP masses. The same results presented as 68%(blue), 90% (yellow) and 99% (maroon) C.L. contours are shown in Fig. 10.11.
This simple test shows that the fitting procedure is sensitive to the possible WIMP
contribution. Therefore, if the Super-Kamiokande data contains dark matter induced neutrinos on a level greater than the limits derived from the null hypothesis,
we will be able to distinguish it from atmospheric neutrino background. We haveworking framework which can be used to analyze the data.

10.3. Sensitivity Study for WIMP Induced Neutrinos from the Earth’s CoreF IGURE 10.10: Heat map plot showing the tested parameter spaceof WIMP masses (X - axis) and WIMP contribution β (Y - axis) for
three considered annihilation channels: bb̄ (top), τ + τ − (middle) andW + W − (bottom). Positive WIMP contribution (β = 0.01) is assumed
and the color represents χ2 value of the fit. In bb̄ channel: Mχ =25 GeV, in τ + τ − : Mχ = 100 GeV, and in W + W − : Mχ = 500 GeV.

93

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

F IGURE 10.11: Sensitivity contours at 68% (blue), 90% (yellow) and
99% (maroon) C.L for positive WIMP contribution (β = 0.01), fortested parameter space of WIMP masses (X - axis) and WIMP contribution β (Y - axis) for three considered annihilation channels: bb̄ (top),τ + τ − (middle) and W + W − (bottom). In bb̄ channel: Mχ = 25 GeV, inτ + τ − : Mχ = 100 GeV, and in W + W − : Mχ = 500 GeV.

10.4. Binning Optimization

10.4

95

Binning Optimization

During the preformed sensitivity studies, it was noticed that for the higher WIMP
masses (Mχ > 100 GeV), the signal is located very close to the direction of the Earth’s
core (cos θz = −1), even for the "soft" bb̄ annihilation channel. As it is shown in
Fig. 9.4, for Mχ = 1 TeV, dark matter induced neutrinos are expected to be contained in a region with radius smaller than 3◦ , which is much smaller than the bin
size used in the oscillation analysis 5.1.
The size of the first bin in the standard oscillation analysis is 36.9◦ (0.2 in cos θz )for FC and PC, and 25.8◦ (0.1 in cos θz ) for UP-µ events. This size was chosen toprovide at least 6 background events expected in each bin after scaling to the data
livetime of the analysis. We decided to perform the analysis with the finer binning,which is defined in the Table 10.1.

TABLE 10.1: Optimized binning in cosine of the zenith angle for FC
SubGeV, FC MultiGeV, PC and UP-µ samples.

SampleFully Contained (FC) SubGeV
Fully Contained (FC) MultiGeV
Partially Contained (PC)
Upward-going Muons (UP-µ)cos θz bins
10 in [-1,1]
12 in [-1,1]
12 in [-1,1]
13 in [-1,0]

FC SubGeV events are binned in the cos θz in the same way as in the standard oscillation analysis (see Sec. 5.1):(−1, −0.8. − 0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6, 0.8, 1).
For FC MultiGeV and PC events we divide the first and the last bin (for symmetry)in half:(−1, −0.9, −0.8. − 0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6, 0.8, 0.9, 1),
and for UP-µ events, which are defined only below the horizon, we divide the firstbin in four:(−1.0, −0.9994, −0.9962, −0.94, −0.9, −0.8, −0.7, −0.6, −0.5, −0.4, −0.3, −0.2, −0.1, 0.0).
The extra UP-µ bins correspond to 2◦ , 5◦ , 20◦ and 25.8◦ angular distance from the
Earth’s core. As a result of this procedure, 595 analysis bins are created for each of
the SK periods (2380 bins in total).

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

The plot with the atmospheric neutrino background expectations with the optimized
binning is shown in Fig. 10.12.
Background illustration with the optimized binning

F IGURE 10.12: Atmospheric neutrino background expectation (orange histogram) and the SK-I-IV data (black points) with the optimized binning. The momentum (1st column) and zenith angle (2nd 5th columns) distributions are shown for 19 samples used in the analysis. In all panels, the error bars represent the statistical uncertainty.

Fig. 10.13 shows the SK data and the signal expectations for Mχ = 1000 GeV andbb̄ annihilation channel, with the optimized binning. Majority of the signal is concentrated in very narrow UP-µ bins, close to the Earth’s core. More illustrations forthe wide range of considered WIMP masses can be find in Appendix C. This optimized binning improves the sensitivity for dark matter induced neutrino signal
from the Earth’s core.

10.4. Binning Optimization

97

Signal illustration for Mχ = 1000 GeV, β = 0.02, bb̄ annihilation channel

F IGURE 10.13: The signal originating from the annihilation of1000 GeV WIMPs in the Earth’s core into bb̄ quarks with the optimized binning. The momentum (1st column) and zenith angle (2nd 5th columns) distributions are shown for 19 samples used in the analysis. Plots contain expected signal from WIMP annihilation (filled
histogram) and the SK-I-IV atmospheric neutrino data (black points).
In all panels the error bars represent the statistical uncertainty.

To better present this effect, the first four bins from the Earth’s core are plotted separately in Fig. 10.14, for the three UP-µ samples. Note that first four new bins together
cover the size of 25.8◦ , which is a size of the first UP-µ bin in standard analysis. Dueto the very small size of the new bins, the number of expected background events
could be very low. This expectation is calculated based on the MC simulation andshown in Table 10.2. For this reason, we have to use different method to computethe sensitivity, which is based on Toy MC data sets and described in the following
section.

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

Bin
Expected bkg
Up Stop µ0◦ − 2◦
0.65
◦
◦
2 −5
3.07
5◦ − 20◦47.91
20◦ − 28.5◦
35.46
Non showering µ0◦ − 2◦
0.87
◦
◦
2 −5
4.62
5◦ − 20◦117.5020◦ − 28.5◦
97.83
Showering µ0◦ − 2◦
0.42
◦
◦
2 −5
1.99
5◦ − 20◦38.63
20◦ − 28.5◦
29.04
TABLE 10.2: The calculated
atmospheric neutrino background expectation for first
four bins in UP-µ samples.

F IGURE 10.14: Signal expectation(filled histogram) from Fig. 10.13
and the SK-I-IV atmospheric neutrino data (black points) for UP-µsamples.

10.4.1

Toy Monte Carlo Method

For the analysis with optimized binning, we use a method to compute confidence
intervals numerically, developed by Feldman and Cousins (Feldman and Cousins,1998). The method is based on toy Monte Carlo (ToyMC) experiments, which are
simulated data sets drawn from the assumed probability density function (PDF). We
adopt this method in order to determine 90% C.L. upper limit on dark matter induced neutrino contribution (β) for a given WIMP mass (Mχ ), assuming null WIMP
contribution (β = 0).
The algorithm proposed by Feldman and Cousins computes the interval [β 1 , β 2 ]for each value of the true parameter (β 0 ) in a sufficiently fine grid. We test 401 β

10.4. Binning Optimization

99

values from 0 to 0.02 for each assumed WIMP mass and annihilation channel. In
case of this analysis we do not test negative β contribution. This is motivated by avery low atmospheric background expectation in the narrow UP-µ bins around theEarth’s center (see Table 10.2). If we would add the negative contribution from thedark matter induced neutrino signal, we may end up with resulting negative number of events (signal+background) expected in these bins, which we want to avoid.
The steps of the procedure for each tested WIMP mass and assumed annihilation
channel, are as follow:• Generate 1,000 ToyMC experiments at the considered value of the true parameter β 0 , in our case with null WIMP contribution (β 0 = 0). We generate thefake data sets representing atmospheric neutrino background by setting thenumber of events in each bin according to a Poisson distribution. During the
ToyMC generation we fluctuate data set according to the data livetime andwithin systematic errors (see Sec. 5.3.1).
• For each generated ToyMC experiment perform a pulled χ2 test and calculate∆χ2toy = χ2β0 =0 − χ2min , where χ2min corresponds to the best f it point from a given
Toy data set, and χ2β0 =0 corresponds to point β 0 = 0 from the same data set.
• Find the critical value ∆χ2c , such that 90% of the ToyMC experiments have∆χ2toy < ∆χ2c . Note that the ∆χ2c is different for each tested WIMP mass andassumed annihilation channel. The example for 6 GeV WIMPs annihilation
into bb̄ quarks is shown in Fig. 10.15.

F IGURE 10.15: The distribution of ∆χ2toy = χ2β0 =0 − χ2min for Mχ =6 GeV, bb̄ annihilation channel. Vertical line shows the critical value∆χ2c , such that 90% of the ToyMC experiments have ∆χ2toy < ∆χ2c .

• For each generated ToyMC calculate β 90 , such that χ2β90 − χ2min = ∆χ2c .
• 90% C.L. upper limit on β (β 90%CL ) at given Mχ and annihilation channel, isgiven by the median from β 90 distribution. The example for 6 GeV WIMPs

100

Chapter 10. Search for the Earth WIMPs at Super-Kamiokandeannihilation into bb̄ quarks is shown in Fig. 10.16. The ±1σ and ±2σ fluctuation of the β 90%CL value are given by 68.27% and 95.45% of the β 90 distribution
respectively (green and yellow vertical lines).

F IGURE 10.16: The distribution of β 90 for Mχ = 6 GeV, bb̄ annihilation channel. Vertical lines shows the median (black), ±1σ (green)and ±2σ (yellow).

• The procedure is repeated for each tested WIMP mass and annihilation channel.
The summary of the sensitivity study with the ToyMC data sets is shown in Fig 10.17.
The resulting β 90%CL is translated to allowed number of dark matter induced neutrinos in the fit, and plotted as a function of WIMP mass for three considered annihilation channel. The ±1σ and ±2σ systematic and statistical uncertainty is plotted as agreen and yellow band respectively.
The 90% C.L. upper limit on allowed number of dark matter induced neutrinos fromsensitivity can be translated to the limit on SI WIMP-nucleon scattering cross-sectionin the same way as described is Sec. 10.3.1. For bb̄ channel, the limit resulting fromsensitivity studies with standard binning (see Fig. 10.9) is compared with the new
result with the optimized binning. This comparison is shown in Fig. 10.18. One cannotice that for low tested WIMP masses below 100 GeV, we achieve only slight improvement, but for higher WIMP masses > 100 GeV, the improvement is significant.
The optimized binning gives ∼ 3 times stronger limits.

10.4. Binning Optimization

F IGURE 10.17: The sensitivity expectation for a null WIMP hypothesis (dotted lines) and its ±1σ (green band) and ±2σ (yellow band)
uncertainty is presented for the bb̄ (top), τ + τ − (middle) and W + W −(bottom) annihilation channel.

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Chapter 10. Search for the Earth WIMPs at Super-Kamiokande

F IGURE 10.18: Comparison between 90% upper limits on SI WIMPnucleon scattering cross-section for bb̄ annihilation channel, calculated with standard (black line) and optimized (blue line) binning.
The significant improvement for Mχ > 100 GeV is visible.

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Chapter 11

Results of the Search for the Earth
WIMPs
In this chapter, the results of the search for dark matter induced neutrinos from the
Earth’s core are presented. The atmospheric neutrino data collected with the SuperKamiokande detector in years 1996-2016 is used in the analysis (see Chapter 5 for thedetailed description). In the first section (11.1), we present the results of the analysis
with standard binning (2080 bins in cosine of zenith angle and momentum or visibleenergy). This part was approved by the Super-Kamiokande Collaboration in June2017 and results were presented by the author during the Meeting of the American
Physical Society, Division of Particles and Fields (DPF 2017) and 26th International
Workshop on Weak Interactions and Neutrinos 2017 (WIN2017) conferences (Rott,2017). The second part of this chapter (Sec. 11.2), presents the results with finer bins,
described in Section 10.4, optimized for WIMP masses > 100 GeV. They were approved by the Collaboration in November 2017 and presented by Piotr Mijakowski
during the 53rd Recontres de Moriond 2018 (Mijakowski, 2018).

11.1

Fit Results with Standard Binning

In order to find the allowed contribution of dark matter induced neutrinos in the SK
data, the "pulled" χ2 fit described in Sec. 10.1 is performed. For one of the tested
hypothesis: 150 GeV WIMPs annihilating into bb̄ channel, Fig. 11.1 shows:• expected signal contribution from the dark matter induced neutrinos before
the fit (filled blue histogram), enlarged for better visibility,• atmospheric neutrino background before the fit (orange histogram),• the best configuration of signal and background after the fit (purple histogram),• SK I-IV data (black points) with error bars represent statistical uncertainty.
The minimal value of the χ2 corresponds to β = 0.0007. Due to extremely small
signal contribution, result after the fit (purple) is very close to background only expectations (orange). Note that subtle differences can be visible e.g. in first bin for
stopping UP-µ events (upper right corner).
In the analysis, three annihilation channels are considered: bb̄, τ + τ − and W + W − .
The resulting χ2 value of the fit is shown in Fig. 11.2 with color (Z axis), for thetested parameter space of WIMP masses (Mχ - X axis) ranging from 3 GeV to 1 TeV,
and added WIMP contribution (β - Y axis) ranging from -0.01 to 0.02. It is visiblethat the low χ2 regions (dark blue) are concentrated around β = 0. The same results

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.1: The momentum (1st column) and zenith angle (2nd -5thcolumns) distributions before and after the fit are shown for 19 samples used in the analysis. See detailed description in text.

are presented as 68% (blue), 90% (yellow) and 99% (maroon) C.L. contours and areshown in Fig. 11.3.
For each tested WIMP mass, Mχ , the point with dark matter contribution β resultingwith the lowest χ2 value is called best f it point. The value of β parameter corresponding to best f it for a given WIMP mass, can be translated to number of dark
matter induced neutrinos of all flavors. The results for three considered annihilation
channels are shown in Fig. 11.4 together with 90% and 99% C.L. sensitivity contours
corresponding to null WIMP contribution hypothesis (described in Sec. 10.3.1). It isvisible that no significant signal contribution is allowed by the SK data in addition to
the atmospheric neutrino background. All results are consistent with null hypothesis, β = 0.

11.1. Fit Results with Standard Binning

F IGURE 11.2: Heat map plot showing the tested parameter spaceof WIMP masses (X - axis) and WIMP contribution β (Y - axis) for
three considered annihilation channels: bb̄ (top), τ + τ − (middle) andW + W − (bottom). The color represents χ2 value of the fit to data.

105

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.3: The 68%, 90% and 99% C.L contours of allowed regionsin tested parameter space of WIMP masses (X - axis) and WIMP contribution β (Y - axis) for three considered annihilation channels: bb̄(top), τ + τ − (middle) and W + W − (bottom).

11.1. Fit Results with Standard Binning

F IGURE 11.4: The fitted number of dark matter induced neutrinos
together with 90% and 99% C.L. sensitivity contours as a functionof WIMP mass for three considered annihilation channels: bb̄ (top),τ + τ − (middle) and W + W − (bottom).

107

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Chapter 11. Results of the Search for the Earth WIMPs

The best f it points for three considered annihilation channels are listed in Table 11.1,
together with the corresponding χ2 values from the fit. For the reference, the resultof the fit for atmospheric neutrino background only (β = 0) is shown in the last row
of the table. The obtained differences ∆χ2 = χ2atm − χ2best are very small. From allof the tested hypothesis, the lowest χ2 value corresponds to bb̄ annihilation channel,Mχ = 150 GeV and β = 0.0007 (global best f it point). Corresponding ∆χ2 is equal
to 1.627.
For the global best f it point the fitted values of systematic parameters ei in units ofσ are plotted in Fig. 11.6 - 11.8 for all considered sources described in Sec. 5.3.1. The
resulting distribution of systematic errors values in units of σ is plotted in Fig. 11.5.
According to expectations, fitted values are distributed around 0.
TABLE 11.1: The best f it points from the fit with standard binning, forthe three considered annihilation channels (bb̄, τ + τ − and W + W − ).
The corresponding χ2 values are compared with atmospheric neutrino background only hypothesis.

Channelbb̄
τ+ τ−
W +W −
Bkg onlyMχ [GeV]
150
25
80.3
−

β
0.00070.00080.00070.0

χ2580.108
580.496580.554581.735

χ2 syst.
39.75939.92838.62039.3268

χ2/bins
1.116
1.116
1.116
1.119

F IGURE 11.5: The distribution of fitted values of the systematic errors
ei , given in units of σ, at the global best f it point from the fit with standard binning (bb̄ annihilation channel, Mχ = 150 GeV, β = 0.0007).

For other points from the fit, the resulting distributions of systematic errors values
have very similar behavior. This proofs that fit is stable and no anomalies have been
observed.

11.1. Fit Results with Standard Binning

F IGURE 11.6: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with standard binning (part
I).

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.7: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with standard binning (partII).

11.1. Fit Results with Standard Binning111

F IGURE 11.8: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with standard binning (partIII).

Based on the fit results, the upper limit on allowed dark matter contribution andthe corresponding neutrino flux can be calculated for each tested WIMP mass. If
the resulting best f it β for a given WIMP mass happens to be negative, the upper limit on allowed dark matter contribution is calculated using the Bayesian approach, described in details in Appendix D. The 90% C.L. limits on muon neutrino
flux are presented in Fig. 11.9, for the three considered annihilation channels. They
are compared with the sensitivity predictions calculated in the previous chapter (seeFig 10.8).
The limits obtained from data are very close to the predictions from sensitivity. Thisis consistent with fit results being close to zero, as it is shown in Fig. 11.4.

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.9: The 90% upper limits on dark matter induced muon
neutrino flux for bb̄ (blue), τ + τ − (green) and W + W − annihilation
channel, compared with expectations from the sensitivity studies(dashed lines).

11.1.1

Constraints on the WIMP-Nucleon Spin Independent Scattering
Cross-Section for Mχ < 100 GeV

The upper limit on muon neutrino flux can be further translated to limit on SI WIMPnucleon scattering cross section. For this purpose, the conversion script provided
with the WimpSim software (Edsjö, 2007) is used. The calculation is done for each
assumed dark matter particle mass and annihilation channel, taking into accountdifferent thresholds and angular cuts of the detector. In the calculation, a typicalvalue for the dark matter self-annihilation cross-section < σA v >= 3 · 10−26 cm3 s−1 ,for which the WIMP is a thermal relic, is assumed.
The results presented in Fig. 11.10, covering WIMP masses < 100 GeV for bb̄ andτ + τ − annihilation channels, were approved by the Super-Kamiokande Collaboration in June 2017. However, based on results from sensitivity studies presented in
Section 10.4, the Collaboration made a decision to use optimized binning for thewhole range of tested WIMP masses. These results are discussed in the following
section.

11.2. Fit Results with Optimized Binning

113

F IGURE 11.10: The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section for bb̄ (blue) and τ + τ − (green) annihilation channels, for Mχ < 100 GeV. The visible peaks correspond to resonant
capture on the most abundant elements 16 O, 24 Mg, 28 Si, 56 Fe, andtheir isotopes. Positive result claimed by DAMA/LIBRA (Bernabei
et al., 2013) is shown for comparison.

11.2

Fit Results with Optimized Binning

In this section we discuss the results of the "pulled" χ2 fit performed with optimized
binning described in Sec. 10.4. For one of the tested hypothesis: 100 GeV WIMPs
annihilating into W + W − channel, Fig. 11.11 shows:• expected signal contribution from the dark matter induced neutrinos before
the fit (filled maroon histogram), enlarged for better visibility,• atmospheric neutrino background before the fit (orange histogram),• the best configuration of signal and background after the fit (purple histogram),• SK I-IV data (black points) with error bars represent statistical uncertainty.
The minimal value of the χ2 corresponds to β = 0.00035. Due to extremely small
fitted signal contribution, result after the fit (purple) is very close to background
only expectations (orange). Therefore, the difference between purple and orange
histograms is hardly visible.
The best f it points resulting with the lowest χ2 value for each tested WIMP massMχ , are shown in Fig. 11.12 for the three considered annihilation channels. Here,the β parameter from the fit is translated to allowed number of the dark matter induced neutrinos of all flavors. The expected sensitivity contours at 90% and 99%
C.L. calculated for null WIMP contribution hypothesis in Sec. 10.4.1 are also shownfor comparison. The obtained results are consistent with null WIMP hypothesis.

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.11: The momentum (1st column) and zenith angle (2nd 5th columns) distributions before and after the fit are shown for 19
samples used in the analysis. See detailed description in text.

Based on critical χ2 values determined for each WIMP mass and annihilation channel, the upper limit on fitted number of WIMP-induced neutrinos of all flavors is
calculated and presented in Fig. 11.13. It is compared with the sensitivity expectations and their ±1, 2σ systematic and statistical uncertainties, which are plotted as agreen and yellow bands respectively. It is visible that limits from data are consistent
with sensitivity results for null WIMP hypothesis. All tested points are within ±2σband (yellow).
The best f it points from the fit with optimized binning are listed in Table 11.2, forthree considered annihilation channels. The corresponding χ2 values from the fit
are also shown. For the reference, the result of the fit for atmospheric neutrino background only (β = 0) is shown in the last row of the table. Note that due to the optimized binning, number of bins in the analysis changed from 520 to 595, resultingwith the different χ2 value for background only scenario. The obtained differences∆χ2 = χ2atm − χ2best are slightly larger than for the fit with standard binning. From
all of the tested hypothesis, the lowest χ2 value correspond to W + W − annihilation
channel, Mχ = 100 GeV and β = 0.00035 (global best f it point). Corresponding∆χ2 = 2.631.

11.2. Fit Results with Optimized Binning

F IGURE 11.12: The fitted number of dark matter induced neutrinos
together with 90% and 99% C.L. sensitivity contours calculated with
optimized binning, plotted as a function of WIMP mass for three considered annihilation channels: bb̄ (top), τ + τ − (middle) and W + W −(bottom).

115

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.13: The 90% C.L. upper limit on the fitted number of dark
matter induced neutrinos of all flavors from WIMP annihilation intobb̄ (top), τ + τ − (middle) and W + W − (bottom) channel as a functionof the mass of relic particles. The sensitivity expectations for a null
WIMP hypothesis (dotted lines) and their ±1σ (green bands) and ±2σ(yellow bands) uncertainty calculated in Sec. 10.4 are shown.

11.2. Fit Results with Optimized Binning

117

TABLE 11.2: The best f it points from the fit with optimized binning, for the three considered annihilation channels (bb̄, τ + τ − andW + W − ). The corresponding χ2 values are compared with atmospheric neutrino background only hypothesis.

Channelbb̄
τ+ τ−
W +W −
Bkg onlyMχ [GeV]
176
100
100
−

β
0.00040.00040.000350.0

χ2668.715669.638
667.962670.593

χ2 syst.
39.51939.58439.45639.373

χ2/bins
1.124
1.125
1.123
1.127

For the global best f it point with optimized binning, (W + W − annihilation channel, Mχ = 100 GeV and β = 0.00035), the fitted values of systematic parameters ei in units of σ are plotted in Fig. 11.15 - 11.17 for all considered sources (seeSec. 5.3.1). The resulting distribution of systematic errors values in units of σ is plotted in Fig. 11.14. Similar to the results for standard binning, again, fitted values are
distributed around 0. This is in agreement with expectations and proofs that fit isstable and there are no anomalies. The resulting distributions of systematic errors
values for other points tested in the fit have very similar behavior.

F IGURE 11.14: The distribution of fitted values of the systematic errors ei , given in units of σ, at the global best f it point from the fit with
optimized binning (W + W − annihilation channel, Mχ = 100 GeV andβ = 0.00035).

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.15: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with optimized binning (partI).

11.2. Fit Results with Optimized Binning

F IGURE 11.16: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with optimized binning (part
II).

119

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Chapter 11. Results of the Search for the Earth WIMPs

F IGURE 11.17: Global best f it values of the systematic error parameters, ei , given in units of σ, from the fit with optimized binning (partIII).

11.2.1

Constraints on the WIMP-Nucleon Spin Independent Scattering
Cross-Section for Mχ up to 1 TeVOnce again we can translate the upper limits on number of dark matter induced
neutrinos to the limits on the SI WIMP-nucleon scattering cross section. This time
the limits are set for the whole tested WIMP mass range and three annihilation channels (bb̄, τ + τ − and W + W − ). The results are presented in Fig. 11.18, together withthe previous result published by the Super-Kamiokande Collaboration (Desai et al.,2004).

11.2. Fit Results with Optimized Binning

121

F IGURE 11.18: The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section for bb̄ (blue), τ + τ − (green) and W + W − (maroon)annihilation channels. The visible peaks correspond to resonant capture on the most abundant elements 16 O, 24 Mg, 28 Si, 56 Fe, and theirisotopes. The results are compared with previous SK result (Desaiet al., 2004) (dotted cyan line), as well as positive result claimed by
DAMA/LIBRA (Bernabei et al., 2013).

The previous official result of indirect WIMP search was based only on upward
through-going muons. In the analysis presented in this thesis all SK samples, including FC, PC and UP-µ, are used. This results in significant increase of signal
acceptance, especially in the resonant capture region (Mχ < 100 GeV). Moreover,the livetime of analyzed data increased from 1679.6 days to 5325.8 days for FC/PC,
and 5628.2 days for UP-µ samples.
The adopted analysis methods are very different. The old analysis simply search
for an excess of high energy muon neutrinos from WIMP annihilation, as comparedto the number expected from the atmospheric neutrino background, in the smallcone around the Earth’s core. In a way, it is similar to "ON-OFF source" approachdescribed in Chapter 7, but in this case, we cannot define the proper "OFF source"
region and background cannot be estimated directly from data. The MC simulation
has to be used, so we lose the advantages of the method. The new method used inthis thesis is based on the global fit of simulated WIMP induced neutrino signal andexpected atmospheric neutrino background to SK data. All available information(angular and energy distributions of signal and background components) are usedin the fit, providing the best search sensitivity. Moreover, the 160 sources of systematic uncertainties are taken into account during the fit.
The other difference is that in the previous analysis, the limit on SI WIMP-nucleon
scattering cross section was based on WIMP-induced muons from both, the Sun and122

Chapter 11. Results of the Search for the Earth WIMPs

the Earth. In case of WIMP masses < 80 GeV, the strength of the limit is dominatedby the constraints from the Earth, due to resonant capture on heavy elements in thecore, but for WIMP masses > 80 GeV, limit is dominated by constraints from theSun. Therefore, the previous limit is stronger for high WIMP masses. The visible
discontinuities in the old limit around 80 GeV and 174 GeV are the result of using
the annihilation channel, which gives the strongest constraints. For Mχ < 80 GeV,
limit is based on bb̄ annihilation channel, for Mχ > 80 GeV and < 174 GeV limit isbased on W + W − channel, and finally for Mχ > 174 GeV limit is based on τ + τ − .
Therefore, the two limits cannot be compared directly in the whole range of tested
WIMP masses. However, in the region corresponding to the iron peak (Mχ ≈56 GeV), the old limit is based on bb̄ annihilation channel, and is dominated by
the constraints from the Earth. Here, we can compare it with the new limit frombb̄ channel (blue line). The significant improvement of the limit strength is visible,
reaching the order of magnitude.

11.2.2Comparison with Other Experiments

Finally, the limits on SI WIMP-nucleon scattering cross-section from the Super-Kamiokande experiment can be compared with the results of the searches performed byother experiments. In Fig. 11.19, the latest results from IceCube (Aartsen et al., 2017a)and ANTARES (Albert et al., 2017b) neutrino telescopes are plotted together with thepositive result claimed by DAMA/LIBRA (Bernabei et al., 2013).

F IGURE 11.19: The 90% C.L. upper limits on SI WIMP-nucleon scattering cross-section for bb̄ (blue), τ + τ − (green) and W + W − (maroon) annihilation channels. For comparison the results from IceCube (Aartsen et al., 2017a) (dotted line) and ANTARES (Albert etal., 2017b) (dashed line) are shown, as well as positive result claimed
by DAMA/LIBRA (Bernabei et al., 2013).

11.2. Fit Results with Optimized Binning123

The limits from the Super-Kamiokande experiment are the strongest among all neutrino experiments due to high sensitivity of the SK detector. For ∼ 50 GeV WIMPs,
the limit from τ + τ − annihilation channel can reach 10−44 cm2 . This high sensitivity
can be achieved by including FC and PC events in the WIMP search sample, whichsignificantly increase signal acceptance, especially for WIMP masses in the resonant
capture region. In the analysis, we take into account all neutrino flavors (νe , ν̄e , νµ ,
ν̄µ , ντ , ν̄τ ), and available momentum or visible energy information. Together withgood angular resolution of the detector, they allow to effectively distinguish the signal from the atmospheric neutrino background. Moreover, the Super-K limits ruleout a majority of the WIMP parameter space favored by the DAMA/LIBRA experiment, using independent technique.
This final results of the analysis provide strong constrains on SI WIMP-nucleon scattering cross-section in wide range of tested dark matter particle masses, from 10 GeV
up to 1 TeV. The obtained results were approved by the Super-Kamiokande Collaboration in November 2017.

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Chapter 12

Summary and Outlook
Dark matter searches are very difficult, but also extremely interesting. In spite ofoverwhelming observational evidence for the dark matter existence, and many detection attempts, its nature remains unknown. Various attempts to determine what
the dark matter is and what are its properties, led to many discoveries, but did notgive the definitive answers. The multi-messenger approach is required in order tocreate a consistent picture, and any positive results have to be verified before claiming the discovery. Only one observation method is not sufficient to fully investigate
and understand the nature of dark matter.
As it is outlined in Chapter 2, the existing results from various searches for dark matter particles are inconsistent with each other and require verification in the independent measurements. In particular, the positive signal claimed by DAMA/LIBRA has
been already excluded by many direct detection experiments, e.g. PANDA, XENON
and LUX. Moreover, recent LHC results provide tight constraints on supersymmetry models, hence on the most popular dark matter candidate, supersymmetirc neutralino χ. However, over the last several years few unexplained astrophysical observations have been interpreted as potential dark matter signals. It is very importantto verify the excess in positron fraction seen by PAMELA, FERMI and AMS-02 experiments, which may be explained by dark matter annihilation, using observationsof other annihilation products, such as neutrinos. The positive results from direct
detection experiment DAMA/LIBRA also require independent verification, and investigation of the signal region with a very different indirect method is very valuable.
According to many theoretical expectations, a significant flux of dark matter induced
neutrinos produced in dark matter annihilation or decay processes is anticipated.
This gives a strong motivation for an indirect search for dark matter with neutrinos.
The two analyses presented in this dissertation aim at searching for dark matter
induced neutrinos with the Super-Kamiokande water Cherenkov detector. SuperKamiokande is an exceptional experiment, which provides the opportunity to study
a wide range of physics topics, search for proton decay, study solar and atmospheric
neutrinos, and keep watch for supernovae. Almost 50,000 atmospheric neutrino
events collected by the detector over 20 years of operation is analyzed in order tofind characteristics expected for neutrinos produced in dark matter annihilation or
decay processes.
The first analysis described in this thesis (see Chapters 6 - 8) focuses on the MilkyWay. Self-annihilating or decaying dark matter in our Galaxy might produce a largescale anisotropy in observed neutrino flux. The excess of dark matter induced neutrinos is expected from the direction of the Galactic Center due to increased dark

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Chapter 12. Summary and Outlook

matter density in this region. The search was performed in the equatorial coordinate
system, where the position of the GC is fixed, and the signal is easy to distinguishfrom atmospheric neutrino background. The adopted method, so called "ON-OFF
source" approach, was used for the first time to analyze the Super-Kamiokande neutrino data. Its great advantages are the simplicity and possibility to estimate thebackground directly from data. Therefore, it was possible to be independent onMonte Carlo simulations and related systematic uncertainties.
The expected anisotropy in neutrino flux has not been observed. Main outcomeof this analysis, not observing any asymmetries in data (see Sec. 8.1), is a data driven
and model independent result. Introduction of additional assumptions (halo model,
dark matter particle mass and annihilation/decay channel) allows to constrain thevelocity-averaged dark matter self-annihilation cross section, < σA v >, in case ofdark matter annihilation scenario, or dark matter particle lifetime, τ, in case of the
decay. The resulting limits are calculated for various WIMP masses in range from
1 GeV to 10 TeV, and for four considered annihilation channels: νν̄, bb̄, µ+ µ− andW + W − . For the dark matter annihilation scenario, the significant impact of assumed dark matter halo model on the obtained results is shown. The differences
between the benchmark model (NFW) and models used as extreme cases (Moore
and Kravtsov) can reach the order of magnitude. Hence, focusing on the central region of our Galaxy makes the results very sensitive to the chosen profile, but on theother hand, allows to obtain stronger constraints on dark matter induced neutrino
flux.

F IGURE 12.1: Favored regions obtained by interpreting the observed
positron and electron excesses as due to dark matter annihilation inµ+ µ− . Green region is favored by PAMELA (at 3σ), red region isfavored by the global fit of FERMI, HESS and PAMELA data (at 3σ)(Meade et al., 2010), and blue region is favored by AMS-02 data (at 2σ)(Di Mauro et al., 2016). The 90% C.L. limits from SK data are plottedwith solid purple line for "ON-OFF souce" analysis (this thesis), andwith solid line for "Global fit" approach (Mijakowski, 2018). NFW
halo model is assumed in all cases.

Chapter 12. Summary and Outlook

127

The preferred regions obtained by interpreting the positron excess seen by AMS02 (Di Mauro et al., 2016) and PAMELA, and electron data from HESS and FERMI(Meade et al., 2010) as being due to dark matter annihilation into µ+ µ− are shown in
Fig 12.1. They are compared to limits for µ+ µ− annihilation channel from the SuperKamiokande experiment. It is visible that interesting region of parameter space canbe probed with neutrino data.
The second performed analysis (see Chapters 9 - 11) presents the search for the neutrinos from dark matter annihilation in the Earth’s core, using so called "Global fit"
approach. This method is based on a fit of a simulated signal component (dark matter induced neutrinos) and background component (atmospheric neutrinos) to thedata. The simulation is based on the existing simulation of atmospheric neutrino
interactions performed for the Super-Kamiokande detector. This Monte Carlo simulation assumes the realistic fluxes of neutrinos, their interaction in the detector orin the surrounding rocks. It includes also the detector response for the produced
Cherenkov light. The signal part is reweighted in such a way that retrieves characteristics expected for dark matter induced neutrinos based on the results from the
WimpSim software. In this way, the angular distributions peaked from the directionof the Earth’s core and energy spectra as expected for various dark matter particle
masses and annihilation channels are obtained. All available Super-K data samples
binned in angular and momentum or visible energy (595 bins in total), are used in
the fit providing the best search sensitivity. For each tested WIMP mass and annihilation channel, the "pulled" χ2 fit to the collected data is perform and the number ofdark matter induced neutrinos that could be contained in the SK data is estimated.

F IGURE 12.2: The upper 90% C.L. limits on the WIMP-nucleon SI
scattering cross section for the bb̄ (blue), τ + τ − (green) and W + W −(maroon) annihilation channel from the SK data, compared with theresults from direct detection experiments: LUX (Akerib et al., 2017)(orange) and PICO-60 (Amole et al., 2017) (purple), and possible signal from DAMA (Bernabei et al., 2013).

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Chapter 12. Summary and Outlook

The obtained results are consistent with null WIMP contribution. Therefore, the upper limits on the dark matter induced neutrino flux and SI WIMP-nucleon scatteringcross-section, σχ− N , are set as a function of mass of dark matter particles, for thethree considered annihilation channels: bb̄, τ + τ − and W + W − . Due to high sensitivity of the Super-Kamiokande detector, the obtained limits are the strongest among
all neutrino experiments. They can reach 10−44 cm2 for 50 GeV WIMPs annihilating
into τ + τ − pairs.
Such a search is complementary to direct detection experiments, which look for aninteraction of WIMPs with a nucleus in a low background detector. Both direct andindirect detection experiments can probe the coupling of WIMPs to nuclei which isshown in Fig 12.2. The direct detection experiments are able to set stronger limits
than indirect searches for dark matter induced neutrinos. However, the constraints
obtain in this analysis allow to rule out a majority of the WIMP parameter spacefavored by the DAMA/LIBRA experiment, with a very different, independent technique. The analysis presented in this thesis is the first one entirely dedicated to thesearch for dark matter induced neutrinos from the WIMP annihilation in the Earth’s
core, with the data collected by the Super-Kamiokande experiment.
The analyses presented in the dissertation are of a great interest to the scientificcommunity. Their results were presented during the important conferences in thefield. In particular, the author had a chance to present them during six international
conferences (including La Thuile 2015, Neutrino 2016, ICHEP 2016, WIN 2017 and
DPF 2015 and 2017), and three domestic ones (TMEX 2014, Astroparticle Physics
in Poland 2015 and Polish Physical Society Meeting 2017). The posters with presented results were awarded with "Best Astrophysics Poster" (DPF 2015) and "Distinguished Poster Award" (ICHEP 2016) prizes. Moreover, the obtained results were
the subject of a few seminar presentations given by the author.
The results of both presented analyses were officially approved by the Super-Kamiokande Collaboration. The first analysis from the Galactic Center will be a part of thepaper "Indirect Search for Dark Matter from the Galactic Center and Halo with theSuper-Kamiokande Detector", together with the independent Milky Way analysis ofSuper-Kamiokande data referred to as "Global Fit" (see Sec. 8.2). The results of thesecond analysis will be published in the dedicated paper "Search for Neutrinos from
Dark Matter Annihilation in the Earth’s Core with the Super-Kamiokande Detector".
Both publications are currently under the internal review in Super-Kamiokande Collaboration.
Dark matter search is a highly challenging field, encompassing very different experimental techniques and detection methods. The existing results in the field, which
are not conclusive, demonstrate the importance of a multi-messenger approach todark matter searches and validate the interest in a neutrino channel. Moreover, thenull results of the searches also make a big contribution to the field. They reduce
the available dark matter parameter space, inform the future search strategies andprovide better guidance where to look next. In recent years, dark matter searches
are expanding in their diversity. Further research in this area is extremely important, because the nature of dark matter is still a huge gap in our knowledge about
the Universe.

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Appendix A

Galactic WIMP Weights
The numerical values of Galactic WIMP weights used to reproduce the signal shapefor three considered dark matter halo models (NFW, Moore, and Kravtsov). Weights
are calculated for the dark matter annihilation and decay scenarios.
...
Angle
0.1
0.2
0.4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

Annihilation
NFW
Moore
7319.7600 722448.0000
3624.8600 181116.0000
1779.0400 45265.6000
678.5680
7232.8800
317.1910
1802.7000
199.1760
798.2230
141.3530447.1210107.3590
284.8600
85.1553
196.8680
69.6197143.9100
58.2074
109.6080
49.5146
86.140842.7047
69.393137.249157.031232.7979
47.6526
29.110540.372926.0162
34.6124
23.391029.978121.1422
26.1963
19.1998
23.071417.5096
20.4607
16.029118.2583
14.7247
16.3839
13.5693
14.7762
12.540913.3874
11.6216
12.1800
10.7965
11.1240
10.0532
10.1955
9.38129.37508.77208.64678.21787.99747.71257.41637.2505
6.8943Kravtsov
41.5995
39.370436.8077
32.8201
29.261126.9183
25.1186
23.633122.3547
21.2240
20.2047
19.2730
18.4124
17.611116.8604
16.1535
15.4852
14.8516
14.2492
13.6755
13.1281
12.6053
12.1054
11.6271
11.1691
10.7305
10.31039.90769.52179.15188.79738.45758.1319NFW
17.4933
14.6826
13.042211.8820
10.9854
10.2560
9.64239.11368.64998.2376
7.8671
7.53127.22446.94256.68216.44046.21536.00495.80755.62195.44715.28185.12554.97724.83634.7023
4.57474.45294.33674.2255

Decay
Moore
37.9280
25.7160
20.3075
17.0849
14.8869
13.2656
12.0066
10.9927
10.15399.44528.83638.30607.83907.4236
7.05136.7151
6.40976.13075.87475.63875.42045.21775.02894.85264.68754.53254.38664.2492
4.1194
3.9965

Kravtsov
7.68337.48927.32897.18577.0533
6.92816.80836.6925
6.57986.46966.3616
6.25546.15076.04745.94555.84475.74515.64675.54935.45315.35795.26395.17105.07934.98884.89954.81144.72454.63894.5547

130

Appendix A. Galactic WIMP Weights

31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

6.8271
6.43826.08035.75025.4451
5.16274.90094.65774.43144.22074.02413.84053.66883.50803.35723.21573.08272.95762.83992.72892.62422.52532.43192.34352.25992.18062.10552.0342
1.96651.9022
1.84101.78281.72751.67471.6244
1.57641.53061.48691.44511.4052
1.36701.33051.29551.26201.22991.1991
1.1696
1.1412
1.11401.08796.42395.99855.61285.26194.94204.64964.38164.13553.90913.70033.50743.32883.16333.00962.86662.73342.60912.49312.38452.28282.18752.09802.01391.93471.8602
1.78991.72361.66091.60171.54561.49251.4422
1.39451.34921.30611.26521.2263
1.1892
1.15391.1202
1.0881
1.05751.02821.0003
0.97350.94800.92350.90010.87760.85617.81997.52097.23456.9601
6.69736.4457
6.20475.97405.7531
5.5416
5.33925.14544.96004.78254.61274.45014.29464.14574.00323.86683.7362
3.61133.49163.3771
3.2674
3.16243.06182.96542.87312.78472.69992.61862.54072.46602.39442.32572.25982.19652.13582.07752.0215
1.96781.91611.86651.81881.77291.72891.68651.64571.60644.1191
4.0172
3.91953.82573.73563.64903.56573.4856
3.40843.33403.2622
3.19303.1262
3.06172.99932.93902.88072.82442.76982.71692.66572.61612.56812.52152.47622.43242.38982.34852.30842.26942.2316
2.19482.15902.12432.09052.05762.02561.9945
1.9643
1.93481.90611.8782
1.85101.8245
1.79871.77361.74911.72521.70191.67923.8801
3.76973.66473.56483.46963.37883.29203.20913.12983.05382.98102.91112.84402.77952.71752.65792.60042.54512.49182.44032.39072.34272.29652.25172.2085
2.16662.12612.08692.04902.0122
1.9766
1.94211.9086
1.87611.84461.81401.78431.7554
1.72741.7002
1.67371.64801.62301.59871.57501.55201.52971.50791.48671.46604.47174.39014.30984.23094.15344.07724.00243.92903.85703.7864
3.71723.64943.58293.51783.4541
3.39173.3306
3.27093.2125
3.15533.09953.04492.99152.93932.88842.83862.78992.74242.69602.65072.60652.56332.52122.48002.43982.40062.36242.32502.28862.25302.2183
2.18442.15142.11912.08762.05692.02701.99771.9692
1.9414

Appendix A. Galactic WIMP Weights

81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130

1.06281.03871.01550.9932
0.97180.95110.93120.91210.89360.87590.85870.84220.82630.81090.79600.78170.76790.75450.74160.72910.71710.70540.69410.68320.67270.66250.65260.6431
0.63390.62490.61620.60790.59970.59190.58430.57690.56970.56280.5561
0.5496
0.54330.53720.53130.52560.52000.51470.50950.50440.49950.49480.83550.81570.79670.77840.76090.74410.72790.71230.69730.68290.66910.65570.64280.63040.61850.60700.59580.58510.57480.56480.55510.54580.53680.52810.51970.5116
0.50370.4961
0.48880.48170.47480.4682
0.46170.45550.44950.44370.43800.43250.42730.42210.41720.41240.40770.4032
0.39880.39460.39050.3866
0.38270.37901.56861.5323
1.4973
1.46351.4311
1.39981.36961.34051.31251.28551.2594
1.23421.21001.1865
1.16391.14211.12101.10061.08091.06191.04351.02581.0086
0.99200.97590.96040.94540.93090.91680.90320.89000.87730.86500.85300.84150.83030.81940.80890.79880.78900.77940.77020.76130.75260.74420.73610.72830.72070.71330.7062131

1.6571
1.63561.61451.59401.57401.55451.53551.51701.49891.4812
1.46391.44711.43071.4147
1.39901.38381.36891.35431.34011.3263
1.31271.29951.28661.27401.26171.24971.23801.22661.21541.20451.19391.18351.1734
1.1635
1.15391.14441.1353
1.1263
1.1176
1.10901.1007
1.09261.08471.07701.06951.0622
1.05501.0481
1.04131.03471.44591.42631.4073
1.38871.37061.35301.33581.31911.30271.28681.2713
1.2562
1.24141.2271
1.21301.1994
1.18601.17301.1603
1.14791.13591.1241
1.1126
1.10141.09041.07981.0693
1.0592
1.04931.03961.0302
1.02101.01201.0032
0.99470.98640.97820.97030.9626
0.95500.94770.94050.9336
0.92680.9201
0.91370.90740.90130.89530.88951.9142
1.8877
1.86181.83661.81191.78791.76451.7416
1.7192
1.6974
1.67621.6554
1.6352
1.6154
1.5961
1.5773
1.55901.54101.52361.50651.48991.47361.45781.4423
1.4272
1.4125
1.39811.38411.3704
1.35711.34411.33141.31901.30691.2952
1.28371.27251.26161.25091.24061.23041.2206
1.21101.2016
1.1925
1.1837
1.17501.1666
1.15841.1505

132

Appendix A. Galactic WIMP Weights

131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180

0.49020.48580.48150.47730.47330.46940.4657
0.46200.45850.45510.45180.44870.44560.44260.43980.43700.43440.43180.42940.42700.42480.42260.42050.41850.4166
0.41480.41310.41140.40980.40830.40690.40560.40430.40320.40210.40100.40010.3992
0.39840.3976
0.39700.39640.39590.39540.39500.39470.39450.39430.3942
0.39410.37540.37190.36860.36530.36220.35910.35620.35330.3506
0.34790.34540.34290.34050.3382
0.33600.33380.33170.32980.32780.32600.32420.32260.32090.31940.31790.31650.31510.31380.3126
0.31140.31030.30930.30830.30740.30650.30570.30500.30430.30370.30310.30260.30210.30170.30140.30110.30080.30060.30050.30040.30040.69930.6926
0.68620.67990.67390.66800.66240.65690.6516
0.64650.6416
0.63690.63230.62790.6236
0.61950.61550.61170.60810.60450.60120.59790.59480.59180.58900.58630.58370.58120.57890.57670.5746
0.57260.57070.56890.56730.56580.56430.56300.56180.56070.55970.55880.55810.5574
0.55680.5564
0.55600.55570.5556
0.55551.0283
1.02201.01601.01011.00430.9987
0.99330.98800.98290.97800.9731
0.96850.96390.9596
0.95530.9512
0.9472
0.94340.93970.93620.93270.92940.92620.92320.92030.91750.91480.91220.90980.90750.90530.90320.90130.89940.89770.89610.8946
0.89320.89190.89080.88970.88880.88790.88720.8866
0.88610.88570.88550.88530.88530.88390.87840.87300.86780.86280.85790.85310.84850.84400.83960.83540.83130.82730.82350.81980.81620.81270.80940.80610.80300.80000.79710.79430.79170.78910.7866
0.78430.78210.77990.77790.77600.77420.77250.77090.76930.76790.7666
0.76540.76430.76330.76240.76150.76080.76020.75970.75920.75890.75870.75850.7585

1.14271.1352
1.12791.1208
1.11381.10711.1006
1.09431.08811.08211.07641.07081.06531.06011.05501.0501
1.04541.04081.03641.03211.02801.02411.02031.01661.01311.00981.00661.00361.00070.99790.99530.99280.99050.98830.98630.98430.98260.98090.97940.97800.97680.97570.9747
0.97380.9731
0.97250.9721
0.97170.97150.9715

133

Appendix B

WimpSim Results
The differential fluxes of the neutrinos (left panels) and anti-neutrinos (right panels)
originating from dark matter annihilation in the Earth’s core, plotted as a functionof the neutrino energy, Eν , divided by the WIMP mass, Mχ . The different neutrino
species are indicated with a different colors. The presented spectra are calculated at
the Earth’s surface, using the WimpSim software (Edsjö, 2007). Neutrino oscillations
are included in a full three-flavor framework including both vacuum and matter oscillations.

B.1bb̄ annihilation channel

134

Appendix B. WimpSim Results

B.1. bb̄ annihilation channel

135

136

B.2

Appendix B. WimpSim Results

τ + τ − annihilation channel

B.2. τ + τ − annihilation channel

137

138

Appendix B. WimpSim Results

B.3. W + W − annihilation channel

B.3 W + W − annihilation channel

139

140

Appendix B. WimpSim Results

141

Appendix C

Earth WIMP Signal Illustrations
The neutrino signal originating from dark matter annihilation in the Earth’s core, expected at the Super-Kamiokande detector. The momentum (1st column) and zenith
angle (2nd -5th columns) distributions are shown for 19 samples used in the analysis. The plots contain the expected signal from WIMP annihilation (filled histogram)and the SK-I-IV atmospheric neutrino data (black points). In all panels, the error
bars represent the statistical uncertainty.

C.1

Standard Binningτ + τ − annihilation channel, Mχ = 3 GeV, β = 0.02

142

Appendix C. Earth WIMP Signal Illustrations
τ + τ − annihilation channel, Mχ = 6 GeV, β = 0.02

τ + τ − annihilation channel, Mχ = 10 GeV, β = 0.02

C.1. Standard Binningτ + τ − annihilation channel, Mχ = 25 GeV, β = 0.02

τ + τ − annihilation channel, Mχ = 50 GeV, β = 0.02

143

144

Appendix C. Earth WIMP Signal Illustrations
τ + τ − annihilation channel, Mχ = 100 GeV, β = 0.02

τ + τ − annihilation channel, Mχ = 500 GeV, β = 0.02

C.1. Standard Binningτ + τ − annihilation channel, Mχ = 1000 GeV, β = 0.02

145

146

C.2

Appendix C. Earth WIMP Signal Illustrations

Optimized Binningτ + τ − annihilation channel, Mχ = 3 GeV, β = 0.02

C.2. Optimized Binningτ + τ − annihilation channel, Mχ = 6 GeV, β = 0.02

τ + τ − annihilation channel, Mχ = 10 GeV, β = 0.02

147

148

Appendix C. Earth WIMP Signal Illustrations
τ + τ − annihilation channel, Mχ = 100 GeV, β = 0.02

τ + τ − annihilation channel, Mχ = 1000 GeV, β = 0.02

149

Appendix D

Bayesian ApproachThis is the description of the procedure which is used to derive the upper limit on thenumber of signal events, in case when the results of ON-OFF approach (see Chapter 8), or fitted parameter β (see Chapter 11) are negative. This approach is adaptedfrom (Barnett et al., 1996) and referred in literature to as "Bayesian approach".
In this method, for the statistical variable α, α̂ is the estimator of α from a measurement. Therefore, the measurement provide conditional probability density functionf (α̂|α). We want to know the probability g(α|α̂)dα, which is telling that "true" valueof α lies between α and α + dα, when we have measured α̂. Bayes’ theorem provide
the connection between f and g:g(α|α̂) = R

f (α̂|α)π (α).
f (α̂|α)π (α)dα(D.1)

In this equation, π (α) represents prior knowledge of α value. We do not have any
prior knowledge of α, which means that all physically reasonable values of α areequally probable. Therefore, π (α) is a constant over the region of interest and 0 in
the unphysical region. In our case, for testing the possible dark matter contribution,
the region of interest is α ≥ 0, and:(Rf (α̂|α)π (α)/ f (α̂|α)π (α)dα for α ≥ 0,g(α|α̂) =(D.2)
0for α < 0.
The integral is over the physical region. If the experiments would provide the valuesof α̂ as shown in Fig. D.1, so with the significant probability of obtaining results inunphysical region, with assumed step function π (α), the Eq. D.2 will replace this
distribution with the function shown by the shaded region.
In order to derive the 90% C.L. on α value, one needs to find such a value of α90 thatthe integral:
Z
α90

0

g(α|α̂)dα,

yields 90% of the total area of g(α|α̂) distribution. In Fig. D.1, confidence limit levelis indicated as (1 − e) and equals 0.9 in our case.
In the analyses presented in this thesis, the upper limit on the fitted number of dark
matter induced neutrinos can be obtained for the negative (unphysical) and positive(physical) result, by using the method described above. The upper limit calculationis computed numerically.

150

Appendix D. Bayesian Approach

F IGURE D.1: An example of a measurement α̂ which can give resultsin unphysical region. If one assumes that α, the quantity one tries tomeasure, cannot lie in the unphysical region, but can lie anywhere in
the physical region (no prior knowledge), then Bayes’ theorem says
the new knowledge of distribution of α (given our measurement α̂) is
given by the shaded function after appropriate normalization.

151

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