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ACTA UNIVERSITATIS UPSALIENSIS

Uppsala Dissertations from the Faculty of Science and Technology 143

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Alexander Burgman

Bright Needles in a Haystack

A Search for Magnetic Monopoles Using

the IceCube Neutrino Observatory

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Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, 10134, Uppsala, Wednesday, 3 February 2021 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor David Milstead (Stockholm University, Stockholm, Sweden).

Abstract

Burgman, A. 2020. Bright Needles in a Haystack. A Search for Magnetic Monopoles Using the IceCube Neutrino Observatory. (Ljusstarka Nålar i en Höstack. En Sökning efter Magnetiska Monopoler med Neutrino-Observatoriet IceCube). Uppsala Dissertations from

the Faculty of Science and Technology 143. 166 pp. Uppsala: Acta Universitatis Upsaliensis.

ISBN 978-91-513-1083-1.

The IceCube Neutrino Observatory at the geographic South Pole is designed to detect the light produced by the daughter-particles of in-ice neutrino-nucleon interactions, using one cubic kilometer of ice instrumented with more than 5000 optical sensors.

Magnetic monopoles are hypothetical particles with non-zero magnetic charge, predicted to exist in many extensions of the Standard Model of particle physics. The monopole mass is allowed within a wide range, depending on the production mechanism. A cosmic flux of magnetic monopoles would be accelerated by extraterrestrial magnetic fields to a broad final velocity distribution that depends on the monopole mass.

The analysis presented in this thesis constitutes a search for magnetic monopoles with a speed in the range [0.750;0.995] in units of the speed of light. A monopole within this speed range would produce Cherenkov light when traversing the IceCube detector, with a smooth and elongated light signature, and a high brightness.

This analysis is divided into two main steps. Step I is based on a previous IceCube analysis, developed for a cosmogenic neutrino search, with similar signal event characteristics as in this analysis. The Step I event selection reduces the acceptance of atmospheric events to lower than 0.1 events per analysis livetime. Step II is developed to reject the neutrino events that Step I inherently accepts, and employs a boosted decision tree for event classification. The (astrophysical) neutrino rate is reduced to 0.265 events per analysis livetime, corresponding to a 97.4 % rejection efficiency for events with a primary energy above 1E+5 GeV.

No events were observed at final analysis level over eight years of experimental data. The resulting upper limit on the magnetic monopole flux was determined to 2.54E–19 per square centimeter per second per steradian, averaged over the covered speed region. This constitutes an improvement of around one order of magnitude over previous results.

Keywords: magnetic monopole, IceCube, astroparticle physics, neutrino telescope

Alexander Burgman, Department of Physics and Astronomy, High Energy Physics, Box 516, Uppsala University, SE-751 20 Uppsala, Sweden.

© Alexander Burgman 2020 ISSN 1104-2516

ISBN 978-91-513-1083-1

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This thesis is dedicated to my children Olivia and Victor, who are all that is best in me.

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Contents

1 Units and Conventions . . . 13

1.1 High Energy Physics Natural Units . . . 13

1.2 Speed and Relativistic Lorentz Factor . . . 13

2 Magnetic Monopoles . . . .15

2.1 Electric-Magnetic Duality . . . 15

2.2 The Dirac Monopole . . . 16

2.3 The ’t Hooft-Polyakov Monopole . . . .18

2.4 The Cosmic Monopole Population . . . 20

2.5 Magnetic Monopole Search Methods . . . 21

2.6 Monopole Search Results from Neutrino Telescopes. . . 23

3 The IceCube Neutrino Observatory. . . .26

3.1 The Detector . . . .26

3.1.1 The Detector Constituent Arrays. . . 27

3.1.2 The DOM . . . 29

3.1.3 The Detector Medium . . . 31

3.1.4 Coordinate System . . . 32

3.2 Data Acquisition and Triggering. . . .33

3.2.1 Data Filter Stream. . . .34

3.3 Typical Events . . . 34

3.4 High Energy Neutrinos in IceCube . . . .35

3.4.1 Typical Event Signatures. . . .36

3.5 Interpreting an Event View . . . .38

4 Magnetic Monopoles in IceCube. . . .40

4.1 Energy Loss in Matter . . . .40

4.2 Light Production. . . .41

4.2.1 Cherenkov Radiation. . . 42

4.2.2 Indirect Cherenkov Radiation. . . 44

4.3 Magnetic Monopole Signatures in IceCube . . . 45

5 Magnetic Monopole Event Simulation in IceCube . . . 48

5.1 Magnetic Monopole Generation . . . 48

5.1.1 Generation Disk Radius . . . 50

5.1.2 Generation Disk Distance . . . 51

5.2 Magnetic Monopole Propagation . . . .54

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5.4 Simulation Validation . . . 55

5.4.1 Validation with Experimental Data . . . 56

5.4.2 Magnetic Monopole Light Yield Validation . . . 58

6 Event Cleaning and Reconstruction Methods. . . .60

6.1 Event Cleaning Algorithms . . . 60

6.1.1 The SeededRadiusTime Cleaning Method . . . 60

6.1.2 The TimeWindow Cleaning Method . . . .61

6.2 Event Reconstruction Algorithms . . . .62

6.2.1 A Particle Track Representation. . . 62

6.2.2 The LineFit Track Reconstruction Method. . . .62

6.2.3 The EHE Reconstruction Suite . . . .63

6.2.4 The CommonVariables Event Characterization Suite. . . 66

6.2.5 The Millipede Track Reconstruction Method. . . 67

6.2.6 The BrightestMedian Track Reconstruction Method. . . . 68

7 Data Analysis and Statistical Tools . . . 72

7.1 Analysis Strategies . . . 72

7.1.1 Cut-and-Count Analyses . . . .72

7.1.2 Multi-Variate Analyses. . . .73

7.1.3 Analysis Blindness . . . 73

7.2 Determining an Upper Limit . . . 74

7.2.1 Effective Area . . . 74

7.2.2 Upper Limit. . . .74

7.2.3 Sensitivity. . . .75

7.2.4 Including Uncertainties in the Upper Limit. . . 75

7.3 Model Rejection and Discovery Potentials . . . 76

7.3.1 Model Rejection Potential. . . .77

7.3.2 Model Discovery Potential. . . .77

7.4 Boosted Decision Trees . . . 78

8 Analysis Structure, Exposure and Assumptions . . . .80

8.1 Analysis Structure . . . 80 8.1.1 Step I . . . 80 8.1.2 Step II . . . 80 8.2 Analysis Exposure. . . .81 8.2.1 Livetime . . . 81 8.2.2 Solid Angle . . . 82

8.3 Signal and Background Parameter Space . . . 82

8.3.1 Magnetic Monopole Flux Assumptions . . . .82

8.3.2 Astrophysical Neutrino Flux Assumptions. . . 84

9 Simulated Event Samples. . . .85

9.1 Signal Monte Carlo Event Samples . . . 85

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10 Event Selection . . . 87

10.1 Event Triggers and Filters . . . 87

10.2 Step I . . . 88

10.2.1 The Offline EHE Cut. . . 88

10.2.2 The Track Quality Cut. . . .88

10.2.3 The Muon Bundle Cut . . . .92

10.2.4 The Surface Veto . . . 93

10.3 Step II . . . .93

10.3.1 Additional Reconstruction . . . 96

10.3.2 Step II Variables. . . .96

10.3.3 BDT Implementation and Performance . . . 104

10.3.4 Placing the Cut Criterion . . . 108

10.4 Expected Numbers of Events . . . 115

11 Sensitivity. . . .118

11.1 Effective Area . . . .118

11.2 Sensitivity . . . 120

12 Uncertainty on the Magnetic Monopole Efficiency . . . 122

12.1 Systematic Variation of Monte Carlo Settings . . . 123

12.2 Total Uncertainty . . . .127

13 Uncertainty on the Astrophysical Neutrino Flux . . . .128

13.1 Statistical Uncertainty. . . .128

13.2 Uncertainties in the Astrophysical Flux Measurement. . . .128

13.3 Alternative Neutrino Flux Assumptions . . . 129

13.4 Expected Flux outside of the Simulated Energy Range . . . 131

13.5 Expected Background at Final Analysis Level . . . 133

14 Result. . . .134

14.1 Experimental Event Rate . . . 134

14.1.1 Step I Accepted Events . . . 134

14.1.2 Step II Accepted Events . . . .138

14.2 Final Result. . . .138

15 Summary and Outlook . . . 142

16 Swedish Summary — Svensk Sammanfattning . . . 145

16.1 Vad är en Magnetisk Monopol? . . . 145

16.2 Vad är IceCube? . . . 146

16.3 Att Söka Magnetiska Monopoler med IceCube . . . 148

16.4 Resultat . . . 149

17 Acknowledgements . . . 150

A The IceCube EHE Analysis . . . 152

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Preface

This Thesis

The topic of this thesis is an analysis that was conducted by the author with the goal of discovering a cosmic flux of magnetic monopoles with a speed above the Cherenkov threshold in ice, here restricted to the speed region between 0.750 c and 0.995 c. The analysis was conducted on data collected with the IceCube detector over the course of 8 yr, and the author has been associated with Uppsala University and the IceCube collaboration for the entire duration of the project.

The contents of this thesis can roughly be divided into three main groups of chapters — background, tools and methods, and the work by the author. In addition to this, there are a few supplementary chapters, such as Preface (this chapter), Acknowledgements and the Appendices.

The background chapters, Chapters 1–4, contain the background know-ledge needed to fully grasp the remainder of the thesis. These cover mag-netic monopoles, the IceCube detector, and the expected interactions between a magnetic monopole and the IceCube detector medium, as well as a few use-ful units and conventions.

The next set of chapters (5–7), cover different tools and methods that have been used in this thesis. The IceCube magnetic monopole event simulation methods are described in Chapter 5, and the relevant event reconstruction and cleaning methods are described in Chapter 6. Chapter 7 covers the tools that have been used for data analysis, statistical analysis and machine learning.

Finally, the work by the author is covered in Chapters 8–14. Chapter 8 marks the beginning by covering the overall strategy of this analysis, the anal-ysis scope, and additional parameter space constraints that may exist. Next, the Monte Carlo samples that were used to develop this thesis are detailed in Chapter 9. Chapter 10 covers the event selection developed for this thesis, from beginning to end, and the results that can be expected from the applica-tion of this event selecapplica-tion is covered in Chapter 11. After this, Chapters 12 and 13 cover the uncertainty on the analysis efficiency for magnetic mono-poles and the uncertainty on the neutrino astrophysical flux, respectively. The final chapter, Chapter 14 covers the final results produced by this analysis.

Author’s Contributions

The majority of the time I have spent as a Ph.D. student with Uppsala Univer-sity has been devoted to the development of the analysis that is described in

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this thesis. During this time, I have been an active collaborator in the IceCube collaboration, and have attended six IceCube collaboration meetings where I have presented and discussed my work, discussed the work of my collab-orators, and formed strong professional bonds. I also attended the Particle Physics with Neutrino Telescopes conference in October 2019, PPNT-2019, where I presented my own work along with other active and finished magnetic monopole analyses in IceCube. Additionally, my work has been presented twice at the International Conference for New Frontiers in Physics, in Au-gust 2017 and July 2018, ICNFP-2017 and -2018 respectively, for the latter of which I co-authored the presentation material.

I have attended four Partikeldagarna meetings, the Particle Days, which is the annual meeting of the Swedish particle physicist community. I have had the opportunity of presenting my work during several of these.

During my Ph.D. student time, I have also completed a number of courses, both in and outside of Uppsala University. Within Uppsala University I have completed courses for a total of 42.5 HP, covering a wide scope of topics rele-vant for my Ph.D. education. I have also attended the Neutrinos Underground & in the Heavens summer school, given by the Niels Bohr Institute (Copen-hagen University) and the Detector Technologies for Particle Physics course, jointly given by the Niels Bohr Institute and Helsinki University. Addition-ally, I have attended two internal IceCube courses — the IceCube bootcamp on collaboration and analysis, and the IceCube advanced course on C++.

Before commencing my IceCube data analysis work, I conduced an antenna characterization study for the ARIANNA collaboration over ∼ 6 months. The primary measurements were conducted by myself and my Ph.D. student col-league Lisa Unger, and secondary measurements were conducted later by a project worker. I performed the data analysis in this project, which resulted in an internal ARIANNA report documenting the measurements and concluded antenna characteristics. The results of the study were also used as benchmarks in an antenna Monte Carlo study conducted at the University of California, Irvine.

In addition to my main tasks with IceCube and ARIANNA, I have also taken on various smaller engagements:

• I was a part of the IceCube Software Strike Team for two years, with monthly code sprints to maintain and develop the IceCube software • I have conducted the Uppsala University monitoring shifts for the

Ice-Cube detector over three years

• I have performed teaching duties in laboratory exercises for two Upp-sala University courses, on the topics of shearing in classical mechan-ics and the photoelectric effect in quantum mechanmechan-ics

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1. Units and Conventions

1.1 High Energy Physics Natural Units

In high energy physics it is common to adopt a simplified unit convention, usually denoted by high energy physics natural units, where:

c= ε0= ¯h = kB= 1 (1.1)

Here, c is the speed of light in vacuum, ε0 is vacuum permittivity, ¯h is the reduced Planck constant and kB is Boltzmann’s constant. Additionally, the vacuum permeability is one, µ0= 1, due to:

1

c2 = ε0µ0 (1.2)

These constants are commonly omitted in equations, such that all units can be given as different powers α of energy, usually on the form GeVα. Below follows a non-exhaustive list of the units used for different physical quantities in high energy physics natural units and how they relate to the International System of Units, SI, we are familiar with.

Energy α= 1 , 1 GeV ⇔ 1.60 × 10−10J Mass α= 1 , 1 GeV ⇔ 1.78 × 10−27kg Time α= −1 , 1 GeV−1 ⇔ 6.58 × 10−25s Distance α= −1 , 1 GeV−1 ⇔ 1.97 × 10−16m Temperature α= 1 , 1 GeV ⇔ 1.16 × 1013K

High energy physics natural units will be used for energy and mass through-out this thesis, while time and length will be given in SI units.

1.2 Speed and Relativistic Lorentz Factor

A central quantity in the work described in this thesis is speed. Speed will here be denoted by β , which is the speed given in units of the speed of light in vacuum, c:

β=v

c (1.3)

The Lorentz factor γ is used to quantify how relativistic a particle is, and is directly related to the speed of the particle:

γ= p 1

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The Lorentz factor also relates to the mass and the relativistic total energy of the particle through:

γ= Etot m0

=(Ekin+ m0) m0

(1.5) where m0is the rest mass of the particle, Etotis its relativistic total energy and Ekinis its relativistic kinetic energy.

It is common to describe the speed of a high energy particle in terms of how relativistic it is, e.g. nonrelativistic, relativistic or ultrarelativistic. These terms are vague, and can be adapted to the use-case at hand. In IceCube, magnetic monopoles below a speed β ∼ 0.1 are usually referred to as nonrelativistic, while a speed of β ∼ 0.5 or above is commonly said to be relativistic. The ultrarelativistic regime usually denotes Lorentz factors above γ ∼ 102to ∼ 104, i.e. speeds above β ∼ 0.99995 to ∼ 0.999999995.

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2. Magnetic Monopoles

The existence of magnetic monopoles seems like one of the safest bets that one can make about physics not yet seen. It is very hard to predict when and if monopoles will be discovered. [...] But we must continue to hope that we will be lucky, or unexpectedly clever, some day.

J. Polchinski [1] The quote above is an apt illustration of the current state of the pursuit of magnetic monopoles. On the one hand, magnetic monopoles are explicitly al-lowed in most current theories describing the fundamental laws of physics. On the other hand, several properties, such as the monopole mass and its current abundance, are unknown and vary over many orders of magnitude between theories.

This chapter is an introduction to magnetic monopoles and current experi-mental efforts to find them. Magnetic monopole matter-interactions and their detectable signatures in the IceCube detector are described in Chapter 4.

2.1 Electric-Magnetic Duality

The electromagnetic interaction is classically described by J. C. Maxwell’s equations of electromagnetism: ¯ ∇ · ¯E= ρe (2.1) ¯ ∇ · ¯B= 0 ¯ ∇ × ¯E= −∂ ∂ t ¯ B ¯ ∇ × ¯B= ∂ ∂ t ¯ E+ ¯je

Where ¯E and ¯B are the electric and magnetic fields, and ¯je and ρe are the electric current and charge density, respectively.

Isolated magnetic charges are not included in these equations due to their absence in observation. They can, however, be trivially included in the form

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of a magnetic current ¯jmand charge density ρm: ¯ ∇ · ¯E= ρe (2.2) ¯ ∇ · ¯B= ρm ¯ ∇ × ¯E= −∂ ∂ t ¯ B− ¯jm ¯ ∇ × ¯B= ∂ ∂ t ¯ E+ ¯je

This would introduce a symmetry to Maxwell’s equations known as electric-magnetic duality, which entails that the equations remain unchanged when introducing the substitutions [2]:

¯

E, ¯je, ρe → B, ¯j¯ m, ρm (2.3) ¯

B, ¯jm, ρm → − ¯E, − ¯je, −ρe

2.2 The Dirac Monopole

The electromagnetic interaction may also be expressed using the scalar and vector potentials φ and ¯A, replacing the electric and magnetic fields of Maxwell’s equations via [2]: ¯ E= −∂ ∂ t ¯ A− ¯∇φ (2.4) ¯ B= ¯∇ × ¯A

This disallows a magnetic charge density, ρm= ¯∇ · ¯B, as the divergence of the curl of a vector field is zero, ¯∇ · ¯B= ¯∇ · ∇ × ¯¯ A= 0. The physical interpreta-tion of this is that magnetic field lines may not have a beginning or end.

However, in 1931 P. A. M. Dirac included magnetic monopoles in quan-tum mechanics by modeling each pole as the end of a semi-infinitely long and infinitesimally thin idealized solenoid, a Dirac string [2; 3]. This allows the magnetic field around the end of the solenoid to be identical to that of a sin-gle magnetic pole, without explicitly including isolated magnetic charges in the theory. The apparent charge of the pole, g, corresponds to the magnetic flux inside of the Dirac string, ΦB= g. The Dirac monopole is illustrated in Figure 2.1.

In order for the Dirac monopole to truly act as a free pole, the Dirac string must be experimentally undetectable. Classically, an infinitesimally thin ob-ject is undetectable. However, in quantum mechanics, a solenoid with mag-netic flux ΦB can be observed by the phase shift of qΦB that is introduced to the complex phase of a particle with electric charge q that is transported around the solenoid. In order for the solenoid to be undetectable, this phase

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Figure 2.1. An illustration of a Dirac magnetic monopole, with the magnetic field lines represented in blue and the Dirac string extending to the left. The shaded area represents the region where the magnetic field does not look like the field of a point charge, but like the end of a solenoid. This region is infinitesimally small for a Dirac monopole. Figure by the author.

shift must be a multiple of 2π [2], i.e. satisfy: qΦB

2π = qg

2π ∈ Z (2.5)

This requires that both the electric and magnetic charges are quantized if mag-netic monopoles exist, and the statement is known as the Dirac charge quanti-zation condition [2].

Inserting the elementary electric charge as the charge of the transported particle, q= e, and the fine structure constant as α = e2

4π, into Equation 2.5 yields that magnetic charges, g, are allowed as:

g= n 1

2αe (2.6)

where n is an integer. Setting n = 1 yields the smallest allowed magnetic charge, known as the Dirac charge, gD, as:

gD= 1

2αe≈ 68.5e (2.7)

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2.3 The ’t Hooft-Polyakov Monopole

The three fundamental forces that are included in the Standard Model of par-ticle physics are each described by a symmetry gauge group — U(1) for elec-tromagnetism, SU(2) for the weak interaction, and SU (3) for the strong in-teraction [4]. So-called grand unified theories, GUTs, attempt to unify these three symmetries into a single symmetry group at high energy scales, a sym-metry which is broken at lower energy scales into the three gauge groups that are observed today. The energy scale of the grand unification, ΛGUT, depends on the details of the theory, with a current lower bound of ∼ 1016GeV.

With this is mind, G. ’t Hooft and A. M. Polyakov independently described a different type of magnetic monopole than Dirac [2; 5; 6; 7]. ’t Hooft and Polyakov considered the Standard Model Higgs field, which contains several components φiin internal space that may be considered as individual compo-nents of a vector. At the high energy scales of a GUT symmetry, the values of these may vary arbitrarily, but in the vacuum state their vector magnitude, v, is fixed. The magnitude v corresponds to the radius of the minimum of the Mexican hat potential. A higher symmetry, such as a GUT symmetry, may independently break into the electromagnetic U(1) symmetry in different spa-tial domains simultaneously, potenspa-tially resulting in vastly different direction of the Higgs field in adjacent domains. These domains may be arranged such that the field is always pointing away from (or always towards) a particular point in space, in the so-called hedgehog configuration. In this point the field direction is undefined, and the magnitude must be zero. This is not the vacuum configuration of the Higgs field, and it cannot be continuously transformed to the vacuum state. Thus, the point constitutes a (stable) topological soliton, and must contain a localization of energy to uphold the unbroken symmetry [2]. This results in an effective massive particle with mass mMM:

mMM& ΛSB αSB

(2.8) where ΛSBis the energy scale of the symmetry breaking and αSBis the cou-pling constant at this scale (αSB∼ 10−2for the simplest allowed GUT gauge groups [8]).

Topologically, the ’t Hooft and Polyakov soliton (in the hedgehog con-figuration) can arise when any gauge symmetry of a grand unifying theory breaks into the electromagnetic U(1) symmetry. It is also shown that this topological soliton carries magnetic charge, and thus constitutes a magnetic monopole [2; 6]. Thus, all grand unified theories that unify the three forces (electromagnetism, weak and strong) predict ’t Hooft-Polyakov magnetic mo-nopoles [2].

In the case that a GUT symmetry breaks directly into the U(1) symmetry, the resulting magnetic monopole mass would be given by the energy scale of the GUT and the coupling constant at this scale. These are known as GUT

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10−15m

10−18m

10−31m

[Point charge magnetic field]

[Confinement] [EW unification] [Grand unification] XY Z Z W+ W µ+µ τ+τ ss¯ c¯c b¯b t ¯t uu ¯¯ds γ ¯ u¯u ¯de+ g νµν¯µ d ¯d γ νeν¯e uude uu¯ g e+e ντν¯τ

Figure 2.2. An illustration of the inner structure of a GUT scale magnetic monopole. Figure by the author, inspiration from [9].

scale monopoles, with a mass between mMM ∼ 1014GeV and 1017GeV, de-pending on the details of the theory [2; 9]. If, on the other hand, the GUT symmetry does not break immediately into the U(1) symmetry, but does so via an intermediate symmetry at a lower energy scale, monopoles would arise with a correspondingly lower mass [2]. These monopoles are known as inter-mediate mass monopoles, and would have a mass between mMM∼ 105GeV and 1013GeV, depending on theoretical details [2; 9].

The mass of the magnetic monopole subsequently determines the inner structure of the monopole, illustrated in Figure 2.2 for a GUT scale monopole. A GUT scale monopole would have a core (radius r 10−31m) where the GUT symmetry is upheld, containing virtual X and Y GUT gauge bosons [2; 9]. Here, otherwise forbidden baryon number violating processes, such as proton decay, are allowed, and a proton that passes this region may decay via p→ π0+ e+. Outside of this region, there would be the electroweak unifi-cation region (r 10−18m) containing virtual Z and W bosons, and yet out-side of this would be the confinement region (r 10−15m), containing virtual photons, gluons, fermion-antifermion pairs and four-fermion structures, e.g.

¯

uu ¯¯de+. Further out from the core, only the “classical” monopole magnetic field is observed.

An intermediate mass monopole would have a similar structure, but with the inner region extending to the scale of its corresponding symmetry break-ing. This scale does not reach the grand unification scale, i.e. the scale where baryon number violation is allowed, implying that intermediate mass mono-poles do not induce baryon number violating processes.

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2.4 The Cosmic Monopole Population

If the grand unification hypothesis is correct, GUT scale magnetic monopoles would have formed as the ambient temperature of the early Universe decreased below the energy scale of the GUT symmetry breaking. As described above, the monopole formation takes place where several domains of simultaneous symmetry breaking meet, resulting in a monopole number density on the same order as that of the domains. This mechanism is known as the Kibble mecha-nism [2; 10].

Due to magnetic charge conservation, the only magnetic monopole destruc-tion channel is annihiladestruc-tion with an oppositely charged monopole. This pro-cess is made exceedingly rare because of the expansion of the Universe, imply-ing that a significant fraction of the monopoles that were formed in the early Universe should remain today. Calculations based on the Kibble mechanism suggest a present GUT scale magnetic monopole number density comparable to that of baryons [8], which clearly opposes everyday observations. This is known as the monopole problem in cosmology, and is resolved by postulat-ing a period of rapid cosmic inflation in the early Universe, thus dilutpostulat-ing the monopole density to the currently unobserved abundance [2; 8; 9].

The speed distribution of the cosmic monopole population would depend on the magnetic monopole mass, as well as the magnitude of the ambient accelerating magnetic fields. A magnetically charged particle is accelerated linearly along a magnetic field, in analogy to an electrical charge accelerated by an electric field. The Lorentz force, ¯FL, acting on a particle with magnetic charge ngDand velocity ¯β is given by:

¯

FL= ngD B¯+ ¯β × ¯E (2.9) The gained kinetic energy, Ekin, over a distance L along a path d ¯sis calcu-lated as the integral of the Lorentz force over the path. Assuming a vanishing electric field, ¯E= ¯0, this is given by [9]:

Ekin= Z

L ¯

FLds¯= ngD| ¯B| L (2.10) Here, the traversed distance L represents the coherence length of the ambi-ent magnetic field, i.e. the size of the domain where the magnetic field direc-tion remains constant.

The typical domain length of the Milky Way galaxy is ∼ 300 pc with a magnetic field strength ∼ 3 µG. Given these values, a Dirac charged monopole would gain a kinetic energy of Ekin∼ 6 × 1010GeV [11].

Other astrophysical environments, with higher magnetic fields or larger sizes, would yield even higher kinetic energy. For example, active galactic nuclei jets, with ∼ 100 µG over. 10 kpc, yield Ekin. 2 × 1013GeV and large scale extragalactic magnetic field structures, called sheets, with . 1 µG over . 30 Mpc, yield . 5 × 1014GeV [11].

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The total kinetic energy, Ekintot, of a magnetic monopole is then the sum of the kinetic energy gained in each domain passing:

Ekintot=√N× Ekin (2.11) where the factor of√N approximates the effect of a random walk through an average of N domains.

A relic magnetic monopole is expected to pass N ∼ 102extragalactic mag-netic sheets, acquiring a total kimag-netic energy of ∼ 1016GeV. This allows mag-netic monopoles within a broad range of masses to be accelerated to relativis-tic, or even ultrarelativisrelativis-tic, speeds.

The heaviest magnetic monopoles, on the other hand, are expected to be gravitationally bound to various astronomical systems. A magnetic monopole orbiting our solar system, the Milky Way galaxy or the local galaxy cluster would gain an orbital speed of β ∼ 10−4, 10−3or 10−2, respectively.

2.5 Magnetic Monopole Search Methods

Magnetic monopoles may be detectable through several different channels here at Earth — trapped in terrestrial or extraterrestrial material, produced in high energy colliders or in the form of a cosmic flux [9]. Each of these channels can also be probed using several different experimental techniques. The available magnetic monopole search channels, and different experimental search techniques, are summarized in this section, and several current results on the cosmic flux of magnetic monopoles can be found in Figure 2.3.

The hypothetical cosmic flux of magnetic monopoles can be searched for using, for example, neutrino telescopes (e.g. IceCube [12; 13], ANTARES [14], BAIKAL [15]), where a large volume of water or ice is instrumented with a large number of optical modules that detect visible light. The typical scale of a neutrino telescope is. 1 km3, with isotropic acceptance. For a wide portion of the allowed spectrum of magnetic monopole speeds, a monopole that passes through ice or water should interact with the medium in such a way that it produces optical light that is readily registered with the detector. The relevant matter-interactions of a magnetic monopole in ice are described in Chapter 4. The work described in this thesis is an example of a search for magnetic mo-nopoles with a neutrino telescope, and previous results of similar analyses are given in Section 2.6.

An alternative technique to search for a cosmic flux of magnetic monopoles is to use large area cosmic ray air shower detectors (e.g. the Pierre Auger Ob-servatory [16]). These are designed to register the particle showers produced by cosmic rays as they enter the atmosphere. Magnetic monopoles that enter the atmosphere with an ultrarelativistic speed produce similar particle showers

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Figure 2.3.Current upper limits on the cosmic magnetic monopole flux as a function of speed, v/c, and of the base-10 logarithm of the Lorentz factor, log10γ), over a broad interval. Credit: A. Pollmann [19]. Included are results from IceCube [12; 13], ANTARES [14], BAIKAL [15], MACRO [20], RICE [17], ANITA [18] and the Pierre Auger Observatory [16], along with the Parker bound [21; 22; 5].

continually along their entire track, and can thus be readily detected by such detector arrays. Cosmic ray detector arrays are usually deployed over large areas of land in order to observe a large volume of the atmosphere, which also yields a very large effective volume for magnetic monopole detection. How-ever, in order to produce enough atmospheric particle showers to be detected, the magnetic monopoles must be in the regime ofγ  108, thus limiting cos-mic ray detectors to search for monopoles with mass mMM  108GeV.

Ultrarelativistic magnetic monopoles may also be detected by the Cheren-kov radiation that they produce in the radio frequency range. This is produced as a magnetic monopole traverses a dielectric medium, and is detectable if the medium is transparent to radio waves. Upper limits on the cosmic monopole flux have been determined through radio observations of the Antarctic ice (e.g. RICE [17], ANITA [18]).

A dedicated magnetic monopole experiment, MACRO [20], used a com-bination of different detector techniques (liquid scintillation counters, lim-ited streamer tubes and nuclear track detectors) to search for a cosmic mag-netic monopole flux. This allowed them to analyze a wide range of allowed magnetic monopole speeds, from β = 10−5 to 1, with an acceptance for an isotropic flux of monopoles of∼ 104m2sr (compare to the∼ km2 scale and 4πsr acceptance of neutrino telescopes).

Another approach to search for a cosmic monopole flux is by using a mag-netometer, where the passage of a magnetic monopole through a supercon-ducting coil would be registered by the induced current [23]. This type of device has an ideal detection efficiency for magnetic monopoles, independent

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of the monopole speed. The limiting factor of this technique is, however, the effective area, as the magnetic monopole must pass through the loop of the su-perconducting coil in order to be detected, with a typical scale of. 1 m2[24]. A magnetometer can also be used to detect terrestrially bound magnetic monopoles, i.e. monopoles that have been trapped in a piece of material. The piece of material is thus passed through the superconducting coil of the mag-netometer, and a magnetic monopole present in the material would be readily detected. Searches of this type have been conducted on several classes of ma-terial, e.g. volcanic rocks [25] and meteoritic material [26].

Additionally, instrumentation components that have been close to the colli-sion point at high energy particle colliders have also been examined for trapped magnetic monopoles (e.g. HERA [27]) that were produced in the collision. Due to magnetic charge conservation, collider produced magnetic monopoles must be produced in pairs with opposite magnetic charge, and are thus limited to a mass that is lower than half of the center-of-mass energy of the collision. In addition to searching for magnetic monopoles that are trapped in the detec-tor material, collider produced magnetic monopoles can be sought by looking for highly ionizing tracks in general purpose detectors surrounding the colli-sion point (e.g. ATLAS [28]) or in dedicated detectors (e.g. MoEDAL [29]).

2.6 Monopole Search Results from Neutrino Telescopes

Several efforts have been made to experimentally examine the hypothetical flux of magnetic monopoles with a speed in the range that is relevant to the analysis that is described in this thesis. As previously mentioned, no mag-netic monopole has been detected, but in this section four different works are highlighted, each producing an upper limit on the cosmic monopole flux in the speed range from β = 0.5 to 0.995. The resulting upper limits are shown in Figure 2.4 along with the so-called Parker bound [21]. The Parker bound lim-its the galactic flux of magnetic monopoles to less than 10−15cm−2s−1sr−1, by arguing that a higher flux would disallow the presently observed galac-tic magnegalac-tic fields. This limit is valid for magnegalac-tic monopole masses below 1017GeV, above which the monopole is only slightly deflected by galactic fields [5; 22].

Each of the highlighted analyses is produced with neutrino telescopes where optical modules have been immersed in large volumes of (liquid or solid) wa-ter. Each analysis is performed by first identifying a number of characteristic signatures of a magnetic monopole event that distinguishes them from back-ground events. From the characteristic event signatures, a number of analysis-specific variables were constructed, and used to reduce the background rate. All of the analyses are focused on events with a track-like event signature, as magnetic monopoles should have large penetrative power in matter (see Chap-ter 4.1), and an upwards directed light distribution, in order to reject events

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Figure 2.4. The (current) lowest upper limits on the magnetic monopole flux as a function of speed, in a speed interval relevant for the analysis presented in this the-sis. These results (barring the Parker bound) were produced by the analysis of data collected with neutrino telescopes.

induced by atmospheric muons. After additional event selection the remaining events are used to obtain an upper limit on the flux of magnetic monopoles.

The IceCube-40 1 yr result was produced by the analysis of one year of data from the IceCube detector in the 40 string configuration [13]. For this analysis, four benchmark magnetic monopole speeds β were selected (β = 0.760, 0.800, 0.900 and 0.995) and a sample of simulated magnetic monopoles was produced for each. The event selection criteria were the same for all magnetic monopole speeds, but differed for events that exhibited a higher or lower average number of detected photons per optical module. The selection criteria accepted a total of three events over the 1 yr of data collection with the IceCube-40 detector configuration, which is not compatible with the included atmospheric background. However, the light distributions of the three events do not correspond well to the expected distribution from a magnetic monopole event. The events may have been the product of the not-included background flux of astrophysical neutrinos. An upper limit was set for each of the four selected monopole speeds (see Figure 2.4), where the three observed events were treated as upwards fluctuations of the background flux.

A similar analysis was performed on the first year of data collected with the completed IceCube detector array, denoted by IceCube-86 1 yr [13]. This analysis targets magnetic monopoles in the speed range fromβ = 0.5 to 0.75, where the dominant light production process is indirect Cherenkov light (see Chapter 4.2.2). A continuous spectrum of magnetic monopole events was sim-ulated in the speed range fromβ = 0.4 to 0.99, and a boosted decision tree was

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used to distinguish between possible magnetic monopole event candidates and background events at the final level of the analysis. The event selection criteria of this analysis accepted a total of three events in the experimental data of the first year of data taking with the IceCube-86 detector configuration, which is compatible with the expected background. Conservatively, the resulting upper limit was calculated using an expected background of 0 events, and was locally worsened around the reconstructed speeds of the observed events. The upper limit is world-leading between magnetic monopole speeds of about β = 0.5 and 0.8 (see Figure 2.4).

In addition to the two IceCube analyses, an analysis of five years of data collected with the ANTARES detector is included, denoted by ANTARES 5 yr [14]. This analysis targets magnetic monopoles over a wide speed range, from β = 0.5945 to 0.9950, and selects magnetic monopole candidate events based on their detected brightness and track-likeness. The speed range was divided into nine equal width bins, and an individual upper limit was set for each bin. Two events were observed in the full 5 yr of collected data, which is compatible with the expected atmospheric muon background. The resulting upper limit is world-leading above a speed of β = 0.8615 (see Figure 2.4).

Finally, I highlight the upper limit produced by the analysis of five years of data collected by the BAIKAL collaboration, here denoted by BAIKAL 5 yr [15]. In this analysis, a magnetic monopole event candidate was mainly identified by its track-likeness and brightness, and quality cuts considering the event apparent direction and position relative the detector array were ap-plied. A total of 3.9 ± 2.2 background events were expected to be accepted by this event selection over the five years of collected data, and zero events were observed. This resulted in then world-leading upper limits for each of the three speeds β = 0.8, 0.9 and 1.0. These have now been superseded by more than one order of magnitude, but are included here for completeness (see Figure 2.4).

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3. The IceCube Neutrino Observatory

The IceCube Neutrino Observatory is a multi-purpose facility that can be used for a wide range of physics topics. One of the primary objectives of IceCube has been to discover the diffuse cosmic flux of high energy neutrinos, which was achieved in 2013, through the observation of an excess of high energy neutrino events over the expected background [30].

In addition to this, IceCube has contributed in many areas, including: Neutrino astronomy Where IceCube has several world leading searches

for point-like neutrino emitters, both steady [31] and transient [32], and an excellent sensitivity for discovering a nearby supernova [33]. Neutrino oscillations Using atmospheric neutrinos, where IceCube is

sensitive to baseline lengths from ∼ 10 km (directly above the detec-tor) to ∼ 104km (≈ 2REarth, directly below the detector) [34], several neutrino oscillation parameters have been measured.

Dark matter Searches for neutrinos as dark matter decay or annihila-tion products from the galactic center [35], the Sun [36] or the center of the Earth [37].

New physics A wide category, including searches for non-standard in-teractions [38], sterile neutrinos [39], and magnetic monopoles [13], the latter of which the work described in this thesis is an example of.

3.1 The Detector

The IceCube detector is designed to detect the Cherenkov light produced by the neutrino interaction products in the deep Antarctic ice. In addition to neu-trinos (astrophysical and atmospheric) the IceCube detector measures atmo-spheric muons, muon bundles and potentially also exotic particles. See Fig-ure 3.1 for a schematic illustration of the IceCube detector and its constituent components.

The first IceCube string was deployed in 2005, and the detector was com-pleted in 2010 [40]. During the construction years IceCube operated and col-lected data in partial configuration modes, where the detector grew larger with each year. Since 2011, the completed detector has operated in its full configu-ration.

Each year of operations, denoted by detector season, is identified with a designation such as “IceCube-XX” where XX is given by the number of op-erating strings, e.g. 40, 79, 86. The seasons of full configuration are also

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Figure 3.1. A schematic illustration of the IceCube detector. Credit: IceCube col-laboration. An illustration of the Eiffel Tower in Paris (height 324 m) is inserted to demonstrate the scale.

appended with a roman numeral, representing the year since completion. The first full configuration season (2011) is thus denoted by IceCube-86 I, and the roman numeral is incremented by 1 for each subsequent year. The season des-ignation may also be abbreviated as ICXX-I, where the XX numeral and final roman numeral behave correspondingly.

3.1.1 The Detector Constituent Arrays

The IceCube detector array consists of three sub-arrays, each one with a differ-ent purpose. Each sub-array is instrumdiffer-ented with a number of digital optical modules (DOMs), and they all feed their data to the IceCube Laboratory (ICL) at the surface for readout [40].

The main in-ice array makes up the bulk of the IceCube detector, and is also the main tool for the majority of the measurements, e.g. astrophys-ical neutrinos, atmospheric neutrinos and muons, and exotic particles. The main in-ice array consists of 78 cables extending deep into the ice, commonly called strings. These are placed in a hexagonal grid (see Figure 3.2) with a nearest-neighbor average spacing of 125 m. Each string is instrumented with 60 DOMs with a nearest-neighbor spacing of 17 m, deployed between depths of 1450 m and 2450 m. The DOMs on each string are labeled with a numeral from 1 to 60, increasing with depth. As such, the main in-ice array can be

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Globen Arena

Figure 3.2.A schematic view of the surface footprint of the IceCube detector. Credit: IceCube collaboration. An illustration of the Globen Arena in Stockholm (diameter 110 m) is inserted to demonstrate the scale.

divided into 60 layers of DOMs at similar depths, by selecting DOMs with identical identification numbers.

An additional eight strings, distributed around the center of the main in-ice array, allow the definition of the DeepCore sub-detector [41] (see Figure 3.2). The purpose of DeepCore is to lower the energy detection threshold for inci-dent neutrinos in a region of the detector, for use in analyses on e.g. neutrino oscillations, astrophysical neutrino sources or various exotic topics. Similar to the main in-ice array, the DeepCore strings also hold 60 DOMs each, but with a denser spacing. Of these, 50 are placed below the main dust layer with a 7 m inter-DOM spacing, and the remaining 10 DOMs are placed above the dust layer with a 10 m spacing. The DOMs on the eight DeepCore strings cannot be trivially included in the DOM layers of the main array, due to the differing instrumentation depths. The definition of the DeepCore sub-detector varies by use-case, but always includes the bottom 50 DOMs of the eight DeepCore strings, often along with the DOMs on the adjacent main array strings that are vertically close to the DeepCore instrumented volume. The DeepCore strings are instrumented with DOMs with a higher quantum detection efficiency, apart from strings 79 and 80, that carry both standard and high quantum efficiency DOMs.

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The main in-ice array and DeepCore together instrument the deep Antarctic ice with 5160 DOMs.

In addition to the deep detector arrays, IceCube includes a surface array, the IceTop array, that instruments the surface footprint of the deep detector array. The IceTop array consists of a total of 162 frozen ice containers, tanks, (approximately 1 m3), each instrumented with two DOMs facing downwards. The tanks are placed in pairs at the surface coordinates of each of the 78 main array strings, and the DeepCore strings numbered 79, 80 and 82. IceTop is used as a detector for cosmic ray air showers, with a primary cosmic ray energy from E = 300 TeV to 1 EeV. It can be used to measure the arrival direction, the flux and the mass composition of the southern hemisphere cosmic rays. Additionally, IceTop enables a veto for the in-ice constituents against events originating in a cosmic ray atmospheric interaction by measuring the resulting particle air-shower, and correlating the arrival times of the air shower and the in-ice detection.

3.1.2 The DOM

The basic building-block of the IceCube detector is the digital optical module (DOM). A total of 5484 DOMs constitute the IceCube detector, 5160 frozen into the deep Antarctic ice (the main in-ice array and DeepCore) and 324 frozen into ice-tanks at the surface level (IceTop). Each DOM operates as an independent photon detector, and communicates continuously with the sur-rounding DOMs and the control unit in the IceCube Laboratory (ICL) at the surface [40].

The main constituents of a DOM are a photo-multiplier tube (PMT) several calibration LEDs and a processing main-board. These are encased in a spher-ical pressure resistant 13 mm thick glass housing, made up by two equally dimensioned hemispheres. The glass housing is pierced by a cable for data exchange and power supply. See Figure 3.3 for a schematic illustration of a DOM.

The photo-detector in each DOM is a 10 inch (25.4 cm) R7081-02 HAMA-MATSU PMT. Each PMT is operated with an individually calibrated voltage in order to achieve a gain (amplification factor) of ∼ 107, thereby allowing single-photon detection. The overall detection efficiency of a DOM also de-pends on the quantum efficiency of the PMT, i.e. the probability that an elec-tron is ejected by a photon incident on the photo-cathode. By default, the IceCube DOMs have a quantum efficiency of ∼ 25 % (for λ ∼ 390 nm), while some (the majority of DOMs deployed on DeepCore strings) are instrumented with a higher efficiency PMT (model HAMAMATSU R7081-02 MOD) and therefore have a higher quantum efficiency of ∼ 34 %.

One source of noise in an IceCube event is the noise originating in the PMT itself. For example, a ∼ 300 Hz noise rate is caused by thermal electrons

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Figure 3.3. A schematic illustration of a digital optical module, DOM. Credit: Fig-ure 2 from reference [42].

that evaporate from the PMT dynodes, and may cause a detection unrelated to an incident photon. Additionally, photo-production on the first dynode (as opposed to the photo-cathode), or electrons that scatter past one or more dyn-odes, produce so-called pre-pulses. So-called after-pulses are produced by ionization of residual gas in the PMT. Finally, radioactive decays in the DOM glass housing contribute an additional ∼ 350 Hz noise rate.

The glass housing has a 93 % transmission efficiency for photons with a wavelength of λ = 400 nm, and 50 % and 10 % for 340 nm and 315 nm respec-tively. The PMT is coupled to the glass housing with an optical gel, which is transparent to light with wavelengths from λ ≈ 350 nm to 650 nm, and encased in a mu-metal grid for partial shielding against the Earth magnetic field. The air is evacuated from the spherical glass housing and replaced with nitrogen gas at a pressure of ∼ 0.5 atm. The lack of oxygen prevents corrosion of the electronics and the low pressure ensures the tightness of the seal between the two hemispheres prior to deployment, even at the minimum recorded South Pole air pressure.

Mounted in the top hemisphere of the DOM is also the processing main-board. This is where the digitization of the registered PMT signal takes place before transmission from the DOM to the ICL. The digitization is done with two different systems, the fast Analog to Digital Converter (fADC) and the Analog Transient Waveform Digitizer (ATWD). Each DOM contains one fADC and two ATWDs, where the fADC allows a longer and coarser detection (256 samples at 40 MHz) and the ATWDs yield a more detailed and short readout (128 samples at 300 MHz) The two ATWDs alternate operations in order to minimize dead-time. Additionally, the ATWDs digitization can be done with

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one of three different multiplication factors (16, 2 or 0.25), which is deter-mined by the amplitude of the incoming signal.

In order for a detected signal to be designated as a DOM launch (also known as a hit or pulse), the total registered charge by the PMT must sur-pass a discriminator threshold of 0.25 PE, where PE denotes photo-electron. A photo-electron is a unit of electric charge that represents the average charge detected in a PMT per single detected photon. Thus, the total charge measured in an event is often given in units of PE, or as the number of photo-electrons, nPE=[total registered charge]1 PE .

Each DOM also holds a flasher-board instrumented with 12 calibration LEDs. These are placed in pairs at equal intervals around the horizontal plane of the DOM, with each pair producing light directed horizontally through the ice as well as 48° upwards. The majority of the DOMs are instrumented with LEDs that produce light with a wavelength of λ = 399 nm, while sixteen are instrumented with LEDs that yield light with λ = 340 nm, 370 nm, 450 nm and 505 nm for wavelength dependence calibration.

3.1.3 The Detector Medium

The Antarctic glacial ice, where the IceCube detector is placed, was formed over many millenia as consecutive layers of snow were compressed to ice by the pressure of new snow above. Therefore, the top layer of the glacier consti-tutes a cover of snow. Below the snow comes a layer of firn which transitions into ice with trapped air bubbles. These air bubbles scatter light substantially, rendering the shallow ice opaque to optical light. As the depth increases fur-ther, the high pressure forces the air to diffuse into the ice and form air-hydrate crystals, so-called clathrates, with optical properties very similar to ice [43]. The majority of the air bubbles have dissipated into the ice around a depth of ∼ 1400 m, which is why the in-ice constituents of the IceCube detector are placed below 1450 m of depth.

Figure 3.4 shows the absorptivity a and the effective scattering coefficient beas functions of in-ice depth and photon wavelength. The absorptivity is the reciprocal of the characteristic absorption length, λa, a= λa−1, where the char-acteristic absorption length is the distance traversed by a photon as it reaches a 1 −1eprobability of having been absorbed. Correspondingly, the effective scattering coefficient is the reciprocal of the effective scattering length, λe, be= λe−1. The effective scattering length relates to the scattering mean free path, λs, through Equation 3.1, where avg(cos (θ )) is the average cosine of the scattering angle [43].

λe=

λs

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Figure 3.4. The effective scattering coefficient be(left) and the absorptivity a (right) as functions of in-ice depth and photon wavelength. Credit: Figure 22 from refer-ence [43].

Below the depth of 1400 m the main scattering and absorbing agent consists of micron-sized dust particles frozen in the ice. These mainly include mineral grains, sea salt, soot and drops of acid, and are concentrated in several roughly horizontal layers. The dust layers correspond to ancient geological events resulting in higher concentration of dust particles in the air, and, thus, in the Antarctic snow. A photon incident on a dust particle has an average cosine of the scattering angle of avg(cos (θ)) ≈ 0.94 [43].

The region in the instrumented ice with the highest concentration of dust, known as the main dust layer, is found around a depth of 2000 m. The ice in this region was formed ∼ 65000yr ago [44], and the effective scattering and absorption lengths here are∼ 5m and ∼ 20m respectively for light with a wavelengthλ = 400nm [43]. This can be compared to the typical scattering and absorption lengths in the instrumented volume, ranging within[20; 50] m and[80; 200] m, respectively. The ice is clearer below the main dust layer than above it, with the longest effective scattering and absorption lengths,∼ 100m and∼ 250m, respectively, for λ = 400nm [43].

The (group velocity) index of refraction, nλ, decreases monotonically from nλ= 1.38 to 1.33 for wavelengths fromλ = 337nm to 532nm [43; 45]. Some IceCube first-guess algorithms assume a constant index of refraction over the whole detector, with a value of nλ = 1.34.

3.1.4 Coordinate System

An IceCube-local coordinate system is defined. The (x, y, z) coordinates of IceCube follow a right-handed configuration where the x-y plane is horizon-tally directed, with the y axis directed along the Global prime meridian, and the z axis is vertically directed. The origin of the IceCube coordinate

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sys-tem, (0, 0, 0)IC, is located close to the center of the instrumented volume, at a vertical depth of 1946 m. The origin of the IceCube coordinate system is sometimes referred to as the center of the IceCube detector.

The direction of a particle in IceCube can thus be given in terms of an (x, y, z) unit vector, or in spherical (azimuth, zenith) coordinates, (φ , θ ), where:

tan(φ ) =y

x, cos(θ ) =

z p

x2+ y2+ z2 (3.2) The instrumented volume of IceCube can be defined in many ways, depend-ing on the purpose of the definition. For the purpose of the analysis presented in this thesis, the IceCube instrumented volume has been defined as a hexag-onal prism extending 62.5 m outside of the outermost DOMs. This is used when determining if a set of coordinates represents a point inside or outside of the detector, e.g. when calculating the geometric length of a particle trajectory through the detector (see Chapter 6.2.1). The 62.5 m margin was chosen as half of the average horizontal nearest-neighbor distance between DOMs, thus containing the volume within which the detector is evenly instrumented (aside from the denser DeepCore volume).

3.2 Data Acquisition and Triggering

The majority of IceCube data readout triggers are based on so-called hard local coincidence hits (HLC hits). An HLC hit is designated as any hit that is registered within a 1 µs time window around another hit in an adjacent or second-adjacent DOM on the same string. If a hit does not fulfill this condition it is labeled as a soft local coincidence hit (SLC hit) [40]. HLC hits are often required by the IceCube trigger conditions as SLC hits are more likely to arise from noise.

Several trigger conditions are in place for triggering the data readout of the detector, where some are general purpose and others are tuned to specific use-cases. The most general trigger is the simple multiplicity trigger (SMT), which requires eight or more registered HLC hits within a 5 µs time window to trigger data readout. Other triggers may require fewer hits or longer time windows by setting additional spatial requirements (e.g. a certain number of hits occurring on the same string), or be specially designed for selecting slowly moving particles. In the analysis presented in this thesis, data collected with any active trigger is considered.

The data readout triggering system continuously monitors the detector for any satisfied trigger conditions. As a trigger condition is met a time window of [−4 µs; +6 µs] is spanned around the trigger time window (of length 5 µs in the case of the SMT) to define the period of data readout. Overlapping periods of data readout are merged, excepting the longer running triggers (e.g. the slow

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particle trigger, for which the time window is 102–103 times longer than a regular event). Next, the (merged) readout time window is sent to the event builder software. The event builder collects all hits (HLC as well as SLC) within the time window into a so-called pulse-map for the event, which forms the basis for further data analysis.

The average total trigger rate is 2.7 kHz, with a < ±10 % annual modulation that depends on atmospheric conditions, which yields an average daily data readout of ∼ 1 TB d−1.

Both the trigger conditions and filter algorithms are implemented solely in software, and may therefore technically be changed at any time. However, it is agreed that these procedures should be changed no more than once per year, in the transition between data collection seasons.

3.2.1 Data Filter Stream

A number of higher level filters exist that monitor the event stream. These are designed to define specialized data substreams with different character-istics, e.g. cascade-like events, events that start inside the detector or events contained in the DeepCore sub-detector. An event that passes one or several data filter(-s) is transferred via satellite to the central IceCube data storage for further analysis. This constitutes a transfer rate of ∼ 100 GB d−1[40].

The majority of the current data filters base their analysis on a common pulse map, called InIcePulses. As a part of the filter procedure, the filter algo-rithms construct a custom set of variables for use in further data analysis.

In the analysis presented in this thesis, events that pass the EHE filter are selected. The EHE filter was designed to be used as an initial step of the EHE analysis, searching for extremely high-energy neutrinos with energies in and above the PeV range (see Appendix A). The filter is set to reject events where the number of registered photo-electrons, nPE, is less than 103, and the average data rate is 0.8 Hz [46].

3.3 Typical Events

The majority of events registered with the IceCube detector are caused by muons, and bundles of muons, that were produced by cosmic ray interactions in the atmosphere. Atmospheric muons are detected at a rate between 2.5 kHz and 2.9 kHz, depending on atmospheric conditions.

The second most common class of events is induced by atmospheric neu-trinos. These are detected with a typical rate a factor of ∼ 10−6 lower than the atmospheric muon rate. Like atmospheric muons, these neutrinos are pro-duced when cosmic rays interact with nuclei in the atmosphere.

In addition to the atmospheric neutrinos and muons, certain IceCube events are induced by extra-terrestrially produced neutrinos, commonly called

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astro-physical neutrinos. The diffuse flux of astroastro-physical neutrinos can be experi-mentally measured by large neutrino telescopes, such as IceCube [30], but at very high energies the neutrino flux measurement suffers from low statistics and therefore exhibits a large uncertainty. At the highest energies the local flux is further reduced by neutrino absorption in the Earth.

In addition to the event classes described above, very low energy neutrinos may arrive at the IceCube detector, originating in e.g. the atmosphere, the Sun or a nearby supernova. Such low energy neutrinos may give rise to only a single photo-electron, and thereby mainly contribute to the ambient stochastic noise background in IceCube. However, a close enough supernova might still produce enough low energy neutrinos to be detected as a significant increase in the collective rate of the ambient background [33].

3.4 High Energy Neutrinos in IceCube

A neutrino interacts rarely with matter, and is only detectable in IceCube after a collision with the detector medium. The possible interaction channels are neutral current, NC, and charged current, CC, interactions with both the ambi-ent nuclei (dominantly) and electrons. Neutral currambi-ent interactions take place through the exchange of a Z boson, via:

ν/ ¯ν + X −−→ ν/ ¯ν + XZ ∗ (3.3)

where a momentum exchange between the neutrino ν (antineutrino ¯ν ) and nucleus X has taken place. If the momentum transfer is large enough, the nucleus X will break up (indicated by the final state asterisk) and cause a particle shower through the medium. Charged current interactions take place through the exchange of a W boson, via:

ν/ ¯ν + X −−→ lW± −/l++Y (3.4) where the W exchange implies the production of an (electrically) charged lep-ton l±, as well as the conversion of the nucleus X into Y . Similar to the NC case, a momentum transfer takes place between the neutrino and the nucleus, which may break up in the impact.

In the analysis that is described in this thesis, neutrino events that deposit a high amount of light in the detector are interesting as the background channel that is most difficult to reject. This implies neutrino events induced by very high energy neutrinos. For neutrinos with Eν & 10 TeV the neutrino-nuclear interaction cross sections for NC and CC, σNC and σCC respectively, are very similar for neutrinos and antineutrinos. Both increase with the neutrino energy,

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and are approximately given by the power laws [47]: σν XNC=  Eν 1 GeV α × 2.31 × 10−36cm2 (3.5) σν XCC=  Eν 1 GeV α × 5.53 × 10−36cm2 (3.6)

with the exponent α = 0.363 (for comparison, 10−36cm2= 1 pb). This is illustrated by the fact that a 30 TeV neutrino has a ∼ 50 % absorption probabil-ity when traversing the whole Earth, while this probabilprobabil-ity increases to above 95 % for 300 TeV neutrinos.

In addition to the mainly dominant neutrino-nucleon interaction, electron antineutrinos incident on ambient electrons can produce resonant W− bosons when the collision center-of-mass energy coincides with the W boson mass, i.e. for an incident neutrino energy of Eν ≈ 6.3 PeV. This is known as the Glashow resonance [48], and locally increases the electron antineutrino matter-interaction cross section by several orders of magnitude.

A neutral current interaction induced by a neutrino always manifests as a hadronic cascade in the IceCube detector, originating from the break-up prod-ucts of the target nucleus. A charged current interaction may also yield a hadronic cascade, along with the final state charged lepton. This enables vastly different signatures, determined by the lepton flavor:

• A final state electron (or positron) produces a local electromagnetic shower in the detector.

• A final state (anti-)muon propagates long distances through the ice (energy dependent), producing light along its path both through Cher-enkov and radiative loss processes.

• A final state (anti-)tauon propagates shorter than a muon, as its path is promptly ended by a tauon decay (producing yet another particle shower). A tauon may thus produce a so-called double bang event, where two consecutive particle showers are produced and connected by the track of the tauon.

3.4.1 Typical Event Signatures

The great majority of all events detected by IceCube can be categorized into one of two main event categories, track-like and cascade-like events.

A track-like event is an event that displays a clearly elongated light signa-ture in the detector. The elongation arises when a particle produces light while propagating through the detector, usually more than several hundred meters, which requires a particle with high penetrative power in ice. Outside of the realm of exotics, such as magnetic monopoles, this limits the particle options to muons or tauons, where the tauon is required to be highly energetic in order

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Figure 3.5. Event view of a track-like event, here represented by a simulated muon antineutrino event with energy Eν= 3.1 × 106GeV.

Figure 3.6. Event view of a cascade-like event, here represented by a simulated electron neutrino event with energy Eν= 5.2 × 106GeV.

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to propagate sufficiently before decaying. A track-like event may have a parti-cle shower at the beginning, or at the end in the case of tauons. See Figure 3.5 for an event view of a simulated track-like event.

The track may start inside or outside of the detector. A track starting inside the detector, a starting track, must be induced by a neutrino (again, outside of the realm of exotics such as boosted dark matter), which enables the outer lay-ers of strings of the detector to be used as a veto against non-neutrino events. A track that starts outside of the detector, a non-starting track, may still be induced by a neutrino, but may also be an atmospheric muon or muon bundle. It is impossible to distinguish a non-starting track induced by a muon neutrino from an atmospheric muon, so this must be done on a statistical level based on the directions and energies of the incoming tracks.

The light of a muon or tauon track is mainly produced as Cherenkov ra-diation from secondary interaction products that are produced by stochastic collisions along the trajectory of the particle. The radiative cross section in-creases with energy, with the result that more energetic particles produce more secondary light than less energetic particles do.

A cascade-like event displays a shorter and broader light signature in the detector. A cascade-like event is induced by a neutrino that interacts with the ice to produce a large particle shower, and may be either hadronic or electromagnetic. These are characteristically produced by electron and tauon neutrino charged current interactions, or neutral current interactions involv-ing any neutrino flavor. The light is produced as direct Cherenkov light from the secondary charged particles in the particle shower, which spread out over a short distance, typically less than ∼ few meters. Therefore, the light in a cascade-like event appears to have a point-like production vertex compared to the characteristic instrumentation scale of the detector, and has a broad angu-lar distribution. See Figure 3.6 for an event view of a simulated cascade-like event.

3.5 Interpreting an Event View

This thesis, as well as other IceCube literature, contains visual representations of registered events in the form of so-called event views. An example event view of a magnetic monopole event is shown in Figure 3.7.

In Figure 3.7, the colored and gray spheres represent DOMs with and with-out registered charge in the selected pulse-map, respectively. The apparent size of a sphere represents the registered charge magnitude, with a customiz-able size-to-magnitude ratio. The color scale of the colored DOMs, from red to blue, represents the detection time of the first registered pulse in the DOM, from early to late, respectively. The time interval represented by the color scale is also customizable, in order to allow meaningful viewing of events with varying time widths.

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Figure 3.7. Event view of a simulated magnetic monopole event, displaying the In-IcePulses pulse-map along with the Monte Carlo true trajectory of the particle. The horizontal deficiency of registered pulses close to the center of the track is caused by the main dust layer present in the ice.

An event view may also contain one or several straight lines. These repre-sent (reconstructed or Monte Carlo) particle trajectories through the detector (see Chapter 6.2.1).

Note the horizontal deficiency of registered pulses close to the center of the track in the example event view, Figure 3.7. This is caused by the increased absorption in main dust layer present in the detector volume.

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4. Magnetic Monopoles in IceCube

As a magnetic monopole propagates through the IceCube detector medium it interacts with the surrounding matter via a number of different processes. Several of these processes produce optical light around the trajectory of the monopole, which is readily detected by the IceCube optical modules.

This chapter is dedicated to the interactions between a magnetic monopole and the IceCube ice, the light that is produced, as well as the characteristic signatures of a magnetic monopole event in IceCube.

4.1 Energy Loss in Matter

As a magnetic monopole traverses a medium, it will inevitably lose energy through interactions with the surrounding matter. These energy losses occur through several different processes, depending on the speed of the monopole. Over a large portion of the speed range, from β ∼ 0.1 to 0.99995 (γ ∼ 100), the interactions between a magnetic monopole and the surrounding medium can be modeled as the interactions of a heavy electrically charged particle with a charge corresponding to the effective charge of the magnetic monopole [49; 50]. Formally, the substitution ze → gβ is made, where ze is the charge of the electrically charged particle, g is the monopole charge and β is the speed of the monopole in units of the speed of light.

In this speed region, the monopole mainly loses energy by ionizing and exciting the electrons in the surrounding medium, so the average energy loss dE per unit length dx is given by Equation 4.1 below [51; 52], similar to the Bethe-Bloch formula. −  dE dx  =4πg 2e2n e mec2  ln  2β2γ2mec2 I  +K 2 − 1+ δ 2 − B  (4.1) Here, neis the number density of electrons in the medium, meis the electron mass, and β and γ are the monopole speed and Lorentz factor respectively. Additionally, I is the mean excitation energy, δ is a density effect correction, Kis the correction given by the δ -electron ionization cross section [53] (given by the Kazama-Yang-Goldhaber (KYG) cross section, see Section 4.2.2) and B is the Bloch correction. The Bloch correction accounts for interactions where the wavefunction of the incident monopole does not fully cover the scattering center of the ambient target electron.

References

Outline

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