Searches for Dark Matter with Icecube and Deepcore

Matthias Danninger

Searches for Dark Matter with IceCube and DeepCore

New constraints on theories predicting dark-matter particles

Department of Physics Stockholm University 2013 Doctoral Dissertation 2013 Oskar Klein Center for Cosmoparticle Physics

Fysikum Stockholm University Roslagstullsbacken 21 106 91 Stockholm Sweden

ISBN 978-91-7447-716-0 (pp. i-xii, 1-112)

(pp. i-xii, 1-112) c Matthias Danninger, Stockholm 2013

Printed in Sweden by Universitetsservice US-AB, Stockholm 2013 Distributor: Department of Physics, Stockholm University Abstract

The cubic-kilometer sized IceCube neutrino observatory, constructed in the glacial ice at the South Pole, searches indirectly for dark matter via neutrinos from dark matter self-annihilations. It has a high discovery potential through striking signatures. This thesis presents searches for dark matter annihilations in the center of the Sun using experimental data collected with IceCube. The main physics analysis described here was performed for dark matter in the form of weakly interacting massive particles (WIMPs) with the 79-string configuration of the IceCube neutrino telescope. For the first time, the Deep- Core sub-array was included in the analysis, lowering the energy threshold and extending the search to the austral summer. Data from 317 days livetime are consistent with the expected background from atmospheric muons and neutrinos. Upper limits were set on the dark matter annihilation rate, with conversions to limits on the WIMP-proton scattering cross section, which initiates the WIMP capture process in the Sun. These are the most stringent spin- dependent WIMP-proton cross-sections limits to date above 35 GeV for most WIMP models. In addition, a formalism for quickly and directly comparing event-level Ice- Cube data with arbitrary annihilation spectra in detailed model scans, considering not only total event counts but also event directions and energy estima- tors, is presented. Two analyses were made that show an application of this formalism to both model exclusion and parameter estimation in models of supersymmetry. An analysis was also conducted that extended for the first time indirect dark matter searches with neutrinos using IceCube data, to an alternative dark matter candidate, Kaluza-Klein particles, arising from theories with extra space- time dimensions. The methods developed for the solar dark matter search were applied to look for neutrino emission during a flare of the Crab Nebula in 2010.

List of Papers

Papers included in this thesis Paper I R. Abbasi et al., (IceCube Collaboration). Limits on a Muon Flux from Kaluza-Klein Dark Matter Annihilations in the Sun from the IceCube 22-string Detector. Physical Review D81 (2010) 057101.

Paper II R. Abbasi et al., (IceCube Collaboration). Neutrino Analysis of the 2010 September Crab Nebula Flare and Time-Integrated Constraints on Neutrino Emission from the Crab using IceCube. Astrophysical Journal 745 (2012) 45.

Paper III P. Scott, C. Savage, J. Edsjö and the IceCube Collaboration. Use of Event-Level Neutrino Telescope Data in Global Fits for Theories of New Physics. Journal of Cosmology and Astroparticle Physics 11 (2012) 057.

Paper IV H. Silverwood, P. Scott, M. Danninger, C. Savage, J. Edsjö, J. Adams, A.M. Brown and K. Hultqvist. Sensitivity of IceCube-DeepCore to Neutralino Dark Matter in the MSSM-25. Journal of Cosmology and Astroparticle Physics 03 (2013) 027.

Paper V M.G. Aartsen et al., (IceCube Collaboration). Search for dark matter annihilations in the Sun with the 79-string IceCube detector. Physical Review Letters 110 (2013) 131302.

Proceedings not included in this thesis Paper VI M. Danninger and K. Han for the IceCube Collaboration. Search for the Kaluza-Klein Dark Matter with the AMANDA/IceCube Detectors. Proceedings of the 31st International Cosmic Ray Conference, Łód´z, Poland, 7–15 July 2009, session HE.2.3, contribution 1356; arXiv:0906.3969. vi

Paper VII M. Danninger and E. Strahler for the IceCube Collaboration. Searches for Dark Matter Annihilations in the Sun with IceCube and DeepCore in the 79-string Conﬁguration. Proceeding of the 32nd International Cosmic Ray Conference, Beijing, China, 11–18 August 2011, session HE.3.4, contribution 292; arXiv:1111.2738.

Paper VIII M. Danninger for the IceCube Collaboration. Searches for Dark Matter with the IceCube Detector. Proceedings of the 12th International Conference on Topics in Astroparticle & Underground Physics, Munich (Germany), September 2011; Journal of Physics: Conference Series 375 (2012) 012038 (JPCS).

Paper IX M. Danninger for the IceCube Collaboration. Latest Results on Searches for Dark Matter from IceCube. Proceedings of the 36th International Conference on High Energy Physics, Melbourne (Australia), July 2012: To be published in Proceedings of Science. Contents

Abstract...... iii List of Papers...... v Contents...... vii Acknowledgements...... xi Preface...... 1

Part I: Dark matter: Motivation, constraints & indirect search with neutrinos using the IceCube detector 1 Dark matter...... 7 1.1 Observational evidence for dark matter...... 7 1.2 WIMP dark matter...... 10 1.3 The MSSM and the neutralino...... 11 1.4 Extra dimensions and Kaluza-Klein dark matter...... 13 1.5 Dark matter detection...... 13 1.5.1 Direct detection...... 14 1.5.2 Indirect detection...... 16 1.5.3 Accelerator searches...... 17 1.6 Indirect solar search for WIMP dark matter...... 17 1.7 Discussion on astrophysical uncertainties...... 20 2 Expected background...... 23 2.1 Atmospheric muon background...... 23 2.2 Atmospheric neutrino background...... 23 2.3 Neutrinos from the solar atmosphere...... 24 3 Neutrino detection and the IceCube neutrino observatory...... 27 3.1 Neutrino detection in ice...... 27 3.1.1 Neutrino-nucleon interactions...... 27 3.1.2 Muons in ice...... 30 3.1.3 Cherenkov radiation...... 30 3.1.4 Propagation of light in the South Pole ice...... 31 3.2 IceCube neutrino observatory...... 33 3.2.1 IceCube digital optical module...... 36 3.2.2 Data acquisition...... 38 3.2.3 Calibration...... 39 Part II: Search for dark matter annihilations in the Sun with the 79- string IceCube detector 4 Event simulation...... 43 4.1 Event generators...... 43 4.1.1 Atmospheric background...... 43 4.1.2 WIMP signal...... 44 4.2 Particle propagators...... 46 4.3 Detector response...... 47 5 Event reconstruction and event observables...... 49 5.1 Waveform calibration & feature extraction...... 49 5.2 Reconstruction algorithm...... 52 5.2.1 Coincident event splitting...... 54 5.3 Event observables...... 55 6 Analysis method...... 57 6.1 Probability densities...... 57 6.2 Shape analysis...... 57 6.3 Calculation of WIMP signal quantities...... 61 7 IceCube 79-string data analysis...... 63 7.1 Experimental dataset...... 65 7.2 Online filter level...... 66 7.3 Filter level L2...... 69 7.4 Analysis specific data processing...... 69 7.5 Filter level L3...... 70 7.5.1 L3, summer event selection...... 70 7.5.2 L3, winter event selection...... 71 7.6 Filter level L4...... 71 7.6.1 L4, SL event selection...... 72 7.6.2 L4, WH event selection...... 72 7.6.3 L4, WL event selection...... 73 7.7 Multivariate event classification...... 73 7.7.1 SL event selection...... 74 7.7.2 WH event selection...... 77 7.7.3 WL event selection...... 80 7.8 Filter level L5...... 83 7.8.1 L5, SL event selection...... 84 7.8.2 L5, WH event selection...... 85 7.8.3 L5, WL event selection...... 86 7.9 Sensitivity...... 88 7.10 Results...... 89 7.11 Systematic uncertainties...... 94 7.12 Final results and discussion...... 95 7.13 Search for Kaluza Klein dark matter...... 99 Sammanfattning på svenska...... 101 8 Bibliography...... 103 Part III: Papers

Paper I ...... 118

Paper II ...... 126

Paper III ...... 138

Paper IV ...... 172

Paper V ...... 192

Acknowledgements

This work would not have been possible without the help of a large number of people. First and foremost I want to thank the Stockholm-IceCube triumvirate, Klas Hultqvist, Per-Olof Hulth, and Christian Walck, for their indefatigable supervision during the last four years. You always created a great atmosphere to work in and had made time to listen to all my unconventional ideas, both professional and personal. Klas, with your unique way to challenge my new ideas, you taught me to act with more caution and guided me through my research work. I admire your skill to spot weaknesses and inconsistencies without slowing progress unnecessarily. Unsaid, I greatly appreciate the amount of time you spent on proofreading my paper and thesis drafts, which you persistently returned dyed red. Peo, you are a true particle physics enthusiast! You had me believe for four years that I surely will find some WIMPs (well done!). Your passionate attitude inspired me to constantly work hard and think about new ways and methods to improve my work. I am also grateful for your support and guid- ance regarding conferences, which gave me the opportunity to present Ice- Cube research at numerous conferences. I want to thank Christian, the unof- ficial publication-guru, for helping me bring order to citations and references and his continuous support as a statistician. I also had the pleasure of having Chad Finley as a ‘substitute’-supervisor, who started off the bench during my first years and has now changed into the starting line-up of the Stockholm- IceCube triumvirate. Thank you very much for all the advice and help in the last years, especially with the quest of getting a new position. I owe a great deal of thanks to the members of the IceCube Collaboration for past and present work, as it forms the base of my research efforts. In particular I want to thank the members of the last drill-season night shift deployment team, the Moops (Breckenridge, tack för hjälpen). We had good fun during many meetings, peaking with the memorable win of the Berkeley IceCube- trivia night. I also want to thank Pat Scott, Joakim Edsjö, Chris Savage, and Hamish Silverwood for their patient collaboration with an experimental physi- cist on our ambitious projects. Many thanks also to my colleagues and friends in the ATLAS group, the Oskar Klein Center, and the Uppsala IceCube group. Especially, I want to thank Allan Hallgren for his support and dedication during the Oden icebreaker project. I also want to thank my office mates and fel- low PhD students, old and new - Gustav, Henrik, Olle, Maja, Marcel, Samuel, and Martin - for great company and messing about with a ‘proud’ Bavarian. Special thanks to my parents for their full support throughout the years, despite my vagabond life. And for everything I thank Aroha, who makes all things worthwhile.

Preface

This thesis contributes to seraches to reveal the identity of dark matter, which remains one of the outstanding problems in both particle and astrophysics. The research concentrates on the most promising and experimentally accessible candidates for dark matter, so-called Weakly Interacting Massive Particles (WIMPs). Current models predict a WIMP mass in the range from a few GeV to a few TeV. As a member of the IceCube Collaboration, I have mainly worked on analyses of IceCube data that probe the mass, nuclear cross-section and annihilation cross-section of dark matter particle candidates.

The thesis is roughly divided into three main parts: Part I gives an introduction to the field of dark matter physics. Part II describes a search for dark matter annihilations in the Sun using the 79-string configuration of IceCube. Part III includes published articles most pertinent to the aims of this thesis. Part I, chapter1, lists observational evidence for dark matter, various proposed dark matter candidate models, and discusses different dark matter search strategies. Part I, chapter2, is a discussion of expected background components for an indirect solar search for WIMP dark matter. The final chapter in part I, chapter3, is a review of neutrino detection in ice with the IceCube neutrino observatory. Part II, chapters4 and5, begin by giving a description of methods used in simulation and event reconstruction. The analysis method (maximum likelihood) that is used to estimate the number of dark matter induced signal events within the experimental data set is introduced in chapter6. Chapter7 presents analysis details and results for a search for muon neutrinos from dark matter annihilation in the center of the Sun using the 79-string configuration of the IceCube neutrino telescope. This concludes part II and the monograph-section of this thesis. In part III papers I-V are chronologically ordered. The work detailed in chapters4-7 is summarized and presented in paper V. The other papers were also performed as a part of this project, but are separate analyses that are not discussed in detail in parts I and II. They are self-contained publications, including introduction, analysis and results sections, and therefore should not be viewed as appendices. Instead, these publications are included as part of the main body of this thesis. 2

Author’s contribution Below, I summarize my contributions to papers I-V, and how these are connected to the main topic of the thesis, searches for dark matter using IceCube and DeepCore. Further, I list my main additional contributions to IceCube during my thesis work.

Contribution to papers In paper I, G. Wikström and I extended for the first time indirect dark matter searches with neutrinos (using IceCube data) to an alternative dark matter candidate, Kaluza-Klein (KK) particles, arising from theories with extra space-time dimensions. I initiated the analysis that lead to the publication and demonstrated that the analysis strategy used in [1] (hard annihilation spectra) is already optimized for the search of KK dark matter. I performed the required simulations, wrote most of the text, and interpreted the obtained limits with respect to theoretical models. Paper II is a direct application of an IceCube sensitivity study for dark matter searches in the full 86-string detector configuration (detailed in [2] and paper VII). Because of the unusual flare state of the Crab Nebula, IceCube initiated a fast analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed X-rays and γ-rays. Two different data selections were performed, where one was a selection based on the solar WIMP analysis. I performed this analysis and wrote the corresponding sections in the paper. I collaborated with theorists and phenomenologists for the work presented in papers III and IV (mainly P. Scott, C. Savage, J. Edsjö, H. Silverwood, J. Adams and K. Hultqvist). We performed an analysis that is based on explicit exploration of theoretical SUSY parameter spaces, including a model- by-model comparison with fluxes observed by IceCube (paper III). I ran all detector simulations and studies that were necessary as ‘experimental input’ in the global statistical analysis framework. I actively contributed to the development of the statistical framework, the verification of results and wrote the ‘experimental’ sections of the paper. The work described in paper IV was performed outside of the IceCube Collaboration. Thus, it was necessary to perform the analysis without IceCube internal software tools, using only published data. I generated background models, using a bootstrap Monte-Carlo re-simulation of the expected background rates away from the Sun. I further contributed in the interpretation of the results and the final review. For the work described in paper V (also chapters4-7), I collaborated with E. Strahler (IceCube collaboration). I performed all simulations, designed and implemented the analysis structure (event selection steps) and framework as such. E. Strahler handled most of the analysis specific data processing and 3 performed a number of consistency and cross-checks. I wrote most of the text in the paper and interpreted the results.

Contribution to IceCube More details of some of the contributions to IceCube listed here are summarized in my licentiate thesis [2].

IceCube DAQ trigger development and detector assembly: In an effort to improve IceCube’s low WIMP mass sensitivity, I worked on a new DAQ trigger algorithm to capture low energy events that would not activate standard IceCube triggers. I achieved this through the implementa- tion of a simple majority trigger, running on a special topologically motivated sub-detector volume. This new trigger was integrated into the DAQ and has been operational since 2011. Additionally, I was involved in a more ambitious trigger development project together with D. Nygren, P.-O.Hulth, C. Bohm, K. Hultqvist, C. Walck, G. Wikström, C. Robson, C. Wernhoff and H.Kavianipour. Here, we attempted to drop the trigger-input requirement of so-called hard local coincidences between neighboring modules on the same string (this condition is the standard input requirement for IceCube trigger algorithm). This method is an attempt to trigger on the full ﬂow of hits inside IceCube without early restrictions, using only topological features of a straight line, typical for muon track detection. We deployed a ﬁrst system at the South Pole for initial test runs and further study. As part of my work with IceCube, I assembled, tested and deployed detector components at sites in Sweden, as well as at the South Pole, Antarctica. Additionally, I was responsible for data acquisition and detector operations during a latitude survey with an ice Cherenkov detector unit, as used in the surface air shower array which is part of IceCube. This detector was mounted in a portable freezer on the icebreaker Oden. We recorded data during the entire sea voyage from Sweden to Antarctica and return.

DeepCore analysis integration: A key element in my work on indirect dark matter searches is the understanding of DeepCore data and its successive integration and effective use within IceCube data analyses. Extending the search for a neutrino signal from the Sun to the time when the Sun is above the Horizon at the South Pole, meant facilitating for the ﬁrst time the search for neutrino source candidates in the Southern equatorial sky in a DeepCore data analysis. In order to gauge the dark matter physics potential of IceCube as well as the impact of the Deep- Core subarray, I performed a detailed study during the beginning of my thesis work, to determine the sensitivity of the 86-string detector to signals originating from dark matter annihilations in the center of the Sun. In contrast to previous estimates, this study was performed as a full analysis in all details, 4 including detailed data processing and event selection, while making conservative choices where possible.

Additionally, I represented the IceCube Collaboration with contributed presentations at a series of conferences: IPA (Madison, USA, May 2013), IDM (Chicago, USA, July 2012), The LHC, Particle Physics and the Cosmos (Auckland, New Zealand, July 2012), ICHEP (Melbourne, Australia, July 2012), TAUP (Munich, Germany, September 2011), ICRC (Beijing, China, August 2011), TeVPA (Paris, France, July 2010), Low-energy Neutrino workshop (Pennsylvania, USA, June 2010), Novel Searches for DarkMatter (Columbus, USA, June 2010) and ICRC (Łód´z,Poland, July 2009). Part I: Dark matter: Motivation, constraints & indirect search with neutrinos using the IceCube detector

1 Dark matter

Dark matter embodies one of the great experimental and theoretical challenges in modern physics. Based on strong observational evidence, the existence of dark matter is not heavily disputed. Beyond this fact, very little is known about the nature of dark matter. This ﬁrst chapter lists some of the most compelling observational evidence for dark matter, and its implications on dark matter properties. In this context, dark matter candidates are discussed, with a focus on weakly interacting massive particles (WIMPs). An overview of the main search techniques for WIMPs is presented, and a review of the current status of these searches. Finally, the search for dark matter annihilations in the Sun with neutrino-telescopes is detailed. In the following, matter and energy densities (Ωi) are expressed in terms of the critical density (ρc) required to close the Universe, where Ωi ρi/ρc. ≡

1.1 Observational evidence for dark matter As early as 1933 [3], the first indication that large quantities of ‘unseen’ or dark mass exist was noted by Fritz Zwicky after studies of the Coma galaxy cluster. He observed that galaxies outside of the central cluster region move too quickly to be simply tracing the gravitational potential of the visible mass. For this observation to be consistent with the virial theorem, an additional dark mass was postulated. In 1970, this problem became more apparent when Vera Rubin [4] studied rotation curves of individual galaxies. Rubin observed that stars in the outer reaches of spiral galaxies rotate at far greater speeds than predicted by the total visible matter (stars and interstellar gas). Taking into account only such luminous matter, the orbital velocity of stars as a function of their distance from the galaxy center should drop beyond the optical disc. This is in conflict with the observed rotation curves, which have a characteristic flat behavior. Such a constant orbital velocity implies the existence of an additional halo of dark matter, extending beyond the observed stellar disc.

Further evidence for dark matter comes from gravitational lensing. Gen- eral relativity predicts a curvature of space in the presence of mass. Thus light, traveling on such a curved geodesic, is bent around a massive body. This causes light from distant objects to be ‘lensed’ in the gravitational ﬁeld of foreground objects, and can be used to precisely infer their mass. Obser- vations of distant galaxies, with galaxy clusters in the foreground, indicate a 8 Chapter 1: Dark matter

Figure 1.1: Large-scale redshift-space correlation function of the SDSS sample. The inset shows an expanded view with a linear vertical axis. The lines show, from top to 2 2 bottom, models with Ωmh =0.12 (0.13 and 0.14), all with Ωbh =0.024. The bottom 2 line shows a pure cold dark matter model (Ωmh =0.105), which lacks the acoustic peak. Figure from [7]. much stronger lensing effect than predicted by the observed distribution of luminous matter, thus concluding that there is an additional dark matter component present [5,6].

Baryonic acoustic oscillations (BAO) provide an experimental constraint on the total matter density of the Universe. BAO characterize acoustic density perturbations in the early Universe. Assuming small perturbations in the hot dense plasma of electrons, baryons and photons, pressure waves are created. During the early expansion of the Universe, photons and baryons initially moved together, until the Universe cooled enough to form hydrogen (recombination epoch). This decouples baryons and photons, where the latter quickly diffuse away leaving the baryon wave ‘crests’ stalled. These over-dense shells of baryons remained and are predicted at a co-moving separation scale of 1 approximately 100 h− Mpc. Here, h is the dimensionless Hubble parameter, 1 1 defined by the Hubble constant (H0), as h H0/100 km s− Mpc− . This peak has been observed in large-scale galaxy surveys≡ e.g., with the Sloan Digital Sky Survey (SDSS) [7] (figure 1.1). The observation shows that the galaxy super structure reflects the history of gravitational clustering of matter since the Big Bang. Thus, structure formation should be influenced by dark matter, if it was present during this epoch. Additionally, cosmological N-body simulations [8,9] indicate that the observed large-scale structure is only rec- oncilable with simulations, when including dark matter. N-body simulations strongly favor non-relativistic (cold) dark matter over relativistic (hot), and semi-relativistic (warm) dark matter [8]. 1.1 Observational evidence for dark matter 9

Figure 1.2: The temperature angular power spectrum of the primary CMB from Planck, showing a precise measurement of seven acoustic peaks, that are well ﬁt by a six-parameter ΛCDM theoretical model. Figure from [12].

From large-scale structure surveys we see that the total matter content is Ωm 0.29. An independent measurement of the baryonic matter density with ≈ Ωb < Ωm would provide strong evidence for dark matter. Such a constraint is given by measurements of light isotopes produced in Big Bang nucleosynthesis (BBN) [10]. From observations of very old systems the primordial baryonic matter content is measured to Ωb 0.04 [11]. The combination of these two independent observations (BAO and≈ BBN), implies a dark matter content of ΩDM 0.25. Moreover, dark matter is non-baryonic and preferably cold. ≈

Final confirmation of dark matter comes from measurements of temperature variations in the cosmic microwave background (CMB). CMB radiation decoupled from matter shortly after recombination and features temperature inhomogeneities that reflect the situation at that time [13]. The various angular scales of these temperature inhomogeneities are extracted in multipole expansion analyses. Figure 1.2 shows the most recent measurement of the CMB angular power spectrum from Planck [12], together with the ΛCDM model best described by this set of data. The best-fit model indicates a spatially-flat, expanding Universe, which is isotropic and homo- geneous on large scales [12]. The key matter and energy constituents are Ωb = 0.049 0.00073, Ωm = 0.314 0.020, and ΩΛ = 0.686 0.020, result- ± ± ± ing in a dark matter density of ΩDM = 0.265 0.020. Λ is linked with an extra repulsive force, called ‘vacuum’ or ‘dark’± energy, which contributes as a source of gravitation fields even in the absence of matter [14]. The ‘dark’ energy component was first indicated by type Ia supernova observations [15]. The latest Planck measurements indicate a slightly higher fraction of dark matter than previous results [16]. 10 Chapter 1: Dark matter

An alternative approach to solve the galaxy rotation problem are the so- called modiﬁed Newtonian dynamics theories. Instead of explaining the observation with a new kind of matter, Newton’s laws of gravity are modiﬁed at large distances [17]. However, these theories fail to explain all observations, if applied on their own and are therefore disfavored [18].

Overall, the above detailed complementary experimental evidence points to dark matter as being massive (interacts gravitationally), dark (no electromagnetic interactions at rates comparable to ordinary matter) and cold (structure formation). Furthermore, it must be of non-baryonic nature and produced with the right relic abundance of approximately ΩDM = 0.265. As we still see evidence for dark matter today, it appears to be stable on a Cosmological time scale.

1.2 WIMP dark matter Popular candidates to explain dark matter include massive compact halo objects (MACHOs) and standard model (SM) neutrinos. MACHO candidates, such as red or brown dwarfs, consist of baryonic matter. This brings them in conflict with BBN measurements, and effectively rules out MACHOs as the only source of dark matter. This is further confirmed by gravitational microlensing results towards the Magellanic Clouds [19]. Neutrinos fulfill most dark matter criteria. They are stable, massive, non-baryonic particles that do not interact via the electromagnetic force with ordinary matter. On the other hand, neutrino masses are very small (∑mν <0.23 eV from Planck alone [12]) and do not fit the picture of cold dark matter with a limit on the total cosmological abundance of Ω∑ν < 0.024 [16]. The most widely studied cold dark matter (CDM) candidates are WIMPs [14]. They carry no electrical charge and interact only weakly with SM particles, thus imposing no tension with BBN measurements. It is presumed that WIMPs were produced thermally in the early Universe. At that time, particle creation and annihilation rates were in equilibrium (chemical equilibrium). In addition, all particles are assumed to be in thermal equilibrium, which is given when their kinetic energy reflects the temperature of the Universe. As the Universe expands, it cools. A certain particle species freezes out when the rate of expansion exceeds the particle’s production rate. If the particle is stable against decay, its co-moving density will remain constant. As the expansion continues, the mean free path between particle collisions increases, until the particles are no longer in thermal equilibrium. The kinetic energy of the particles is thus set by the temperature at thermal decoupling (see e.g. Refs. [14, 20], for details on the relic density calculation). Detailed calculations [14] yield that the relic density of any particle species (here denoted by χ) in the weak-scale mass range, can be 1.3 The MSSM and the neutralino 11 approximated by,

2 27 3 1 Ωχ h 3 10− cm s− / σ v , (1.1) ≈ × h i where σ v is the thermally averaged product of the total annihilation cross- sectionh andi the relative particle velocity. Using the current best measurement of ΩDM from section 1.1 and eq. 1.1, σ v is calculated to be near the typi- h 25i 3 1 cal size of weak scale interactions O(10− cm s− ). This result demonstrates that we predict the observed relic density (ΩDM) simply by assuming dark matter to be a stable weakly interacting particle. This astonishing match is one of the strongest motivations for WIMPs being CDM and often entitled as ’WIMP miracle’. WIMPs are also of particular experimental interest. By deﬁnition, they are weakly interacting with SM particles, which constitutes a detection channel via WIMP scattering processes on matter (direct detection). Additionally, the non-negligible total annihilation cross-section for processes, like χχ¯ SM-particles, represents viable indirect detection channels. → Suitable WIMP or CDM candidates are not contained within the SM, but are postulated in various extensions. For this work, we focus on the most widely studied WIMP candidates. The neutralino (χ), as introduced in minimal supersymmetric standard models (MSSM) (section 1.3) and the lightest Kaluza-Klein particle (LKP), which is predicted in universal extra dimension (UED) theories (see section 1.4).

Axions, introduced in an attempt to solve the problem of CP violation in strong interactions, represent a possible dark matter candidate, satisfying all observational constraints from section 1.1. However, they are thought to be very light, with cross-sections far below the weak scale [21].

1.3 The MSSM and the neutralino The SM of particle physics makes a fundamental distinction between fermions, half-integer spin particles, and bosons, integer spin particles. Fermions are the constituents of matter, while bosons are the force carriers of interactions. Within the SM, there exists no symmetry to relate the nature of forces and matter. The framework of supersymmetry, SUSY, provides a unified picture between matter and interactions [22]. Additionally, SUSY provides a possible solution to the so-called hierarchy problem, which is linked to the enormous difference between the electroweak and Planck energy scales. Within this thesis, the MSSM is considered. It is minimal in the sense that it has the smallest possible field content necessary to give rise to all SM fields [14]. This introduces a fermionic superpartner for each SM gauge boson and scalar superpartners for all SM fermions. For example, the superpartners of quarks (q) and charged leptons (l) are squarks and sleptons 12 Chapter 1: Dark matter respectively, denoted by q˜ and l˜. The MSSM introduces a new multiplicative quantum number, R ( 1)3B+L+2s , (1.2) ≡ − called R-parity, where B is the baryon number, L the lepton number and s the spin of the particle or superparticle (sparticles). SM particles have R-parity R = 1, while all sparticles have R-parity R = 1. As a consequence of R- parity conservation, sparticles can only decay into− an odd number of lighter sparticles plus SM particles. Therefore, R-parity conservation results in the lightest supersymmetric particle, the LSP, which makes an excellent DM candidate.

The lightest neutralino Observational constraints limit the LSP to be neutral, thus carrying no electrical charge or color. Therefore, within the MSSM, the LSP is either the lightest sneutrino (superpartner of ν) or the lightest neutralino. Sneutrinos as LSPs have been excluded by direct DM detection experiments [23], leaving the lightest neutralino as the most widely studied candidate for the LSP and hence, as DM candidate. The lightest neutralino,

0 0 0 χ χ˜ = n11B˜ + n12W˜ 3 + n13H˜ + n14H˜ , (1.3) ≡ 1 1 2 ˜ ˜ ˜ 0 is the lightest linear combination of gauginos (B and W3) and higgsinos (H1 ˜ 0 and H2 ), which will simply be referred to throughout as χ. The linear coefficients from eq. 1.3 can be summarized in the gaugino fraction, fG = n11 + n12, and the higgsino fraction, fH = n13 + n14. How much ‘gaugino-like’ or ‘higgsino-like’ is χ, or in other words, what determines the characteristics of χ? The exact identity of χ depends on the given supersymmetric scenario. If supersymmetry would not be broken, all superpartners would have the same mass as the corresponding SM particles. This is not observed in Nature and therefore supersymmetry breaking terms are added to the theory. The MSSM, although called minimal, has as many as 124 free parameters [22]. In order make practical phenomenological studies of the MSSM, additional assump- tions are added to limit the number of free parameters. Among the most widely studied scenarios are the four-parameter constrained MSSM (cMSSM) [24], the seven parameter MSSM-7 [25], and the 19 parameter phenomenological MSSM (pMSSM) [26]. Each model results in a characteristic neutralino, with specific mass, cross sections and branching ratios. Under the assumption of the χ being CDM, it is non-relativistic with low velocities of O(100) km/s. Respecting R-parity conservation, the χ can pair-annihilate due to its Majo- rana character into SM particles. At these non-relativistic velocities, the leading annihilation channel is into heavy fermion-antifermion pairs like top, bottom, and charm quarks and tau leptons as well as heavy gauge boson pairs, + 0 0 like W W − and Z Z pairs. Annihilation channels into final states including 1.4 Extra dimensions and Kaluza-Klein dark matter 13

Higgs bosons, are also favored over channels into light fermion-antifermion pairs that are helicity suppressed in the relativistic limit that is easily reached for light ﬁnal states (e.g. direct νν¯ channel). The direct photon channel can only occur at loop level, as χ is electrically neutral and thus does not couple to photons.

1.4 Extra dimensions and Kaluza-Klein dark matter Our world appears to consist of three space dimensions and one time dimension, the 3+1-dimensional space-time. The first attempts to extend this dimensionality were made by Kaluza [27] and Klein [28], who proposed that a unifi- cation of electrodynamics and gravitation might be achievable in a single five dimensional gravitational theory. Based on that concept, various models have been suggested, with possible extra dimensions appearing at higher energy scales. In the simplest framework of UED, there is a single compactified ex- 1 tra dimension of size R O(TeV− )[29]. Within minimal UED theories, the first excitation of the hyper-charge∼ gauge boson, B(1), is generally the lightest Kaluza-Klein (KK) particle (LKP). It is often denoted as the KK-photon, γ(1), because the effective first KK-level Weinberg angle of the mass matrix is very small, and therefore B(1) can also be described as a mass eigenstate [29]. KK-parity conservation, affiliated with extra-dimensional momentum conservation, leads to the stability of the LKP, which makes it a viable DM candidate. There are also other possible natural choices for LKP candidates within UED, such as the KK-graviton, the KK-neutrino or the Z(1)-boson that may consti- tute viable DM candidates. They are not considered here. Instead, we focus on the most promising KK dark matter prospect in terms of indirect detection expectations, the KK-photon. UED models with five space-time dimensions are characterized by two parameters: the LKP mass, mγ(1) , and the mass splitting ∆q(1) (mq(1) mγ(1) )/mγ(1) , where mq(1) is the mass of the first KK-quark excitation,≡ as discussed− in [29, 30, 31, 32].

1.5 Dark matter detection Despite several widely discussed observations which hint at possible dark matter signals, no undisputed experimental evidence for WIMPs exists. Ex- perimental efforts can be divided into three main techniques. Direct detection experiments look for a nuclear recoil signal within the detector volume from weak-scale scattering of WIMPs with target nuclei. Indirect detection experiments aim to detect primary or secondary particles created in WIMP pair-annihilations or decays, such as photons, neutrinos and antimatter. Ac- celerator searches aim to ﬁnd dark matter through its production in particle 14 Chapter 1: Dark matter

χ χ χ SM SM χ

SM SM χ SM SM χ (a) Direct detection (b) Indirect detection (c) Production Figure 1.3: Simplified Feynman graph for WIMP–SM-particle processes, assuming different time orders (time direction from left to right in all graphs). (a) WIMP–SM- particle scattering (direct detection); (b) WIMP pair-annihilation (indirect detection); (c) WIMP pair-production. Interaction details depend on the probed MSSM model and are simplified by drawing a blob (shaded circle). collisions. These search strategies are complementary and can be described by the same simplified process, assuming different time order (figure 1.3).

1.5.1 Direct detection The expected number of dark matter recoils in a detector is very low due to the weak-scale cross-section. As a consequence, direct detection experiments aim to operate at extremely low background. The differential event rate in the laboratory frame for WIMP-nucleon scattering per recoil energy (dEr) is given by ∞ dN σnρ0 2 f (~v +~vE(t)) 3 = 2 F (Er) d v, (1.4) dE 2m µ v v r χ nχ Z min(Er) where σn is the WIMP-nucleon cross-section, ρ0 the local dark matter density, mχ the WIMP mass, F(Er) the nuclear form factor and µnχ the WIMP- nucleus reduced mass [33, 34]. The velocity integral in eq. 1.4 depends on the local dark matter velocity distribution f (~v) and is calculated in the galactic rest frame (v = ~v ). ~vE(t) is the relative velocity of the Earth within this | | rest frame. vmin(Er) is the minimum velocity required for a WIMP to produce a nuclear recoil of energy Er. σn is composed of a spin-dependent and spin- independent interaction component. The spin-independent scattering cross- section σSI (scalar interaction) increases with the atomic number of the exper- 2 imental material, A, as σSI A . The spin-dependent interaction σSD (axial- vector interaction) results from∼ couplings of the WIMP-spin content to the total spin component of the target material. Thus, σSD is proportional to J(J +1), where J is the total nuclear spin of the target nuclei. Different combinations of target materials can be used to optimize direct detection experiments for either σSI or σSD.

Three common techniques are used (individually or in combination) to measure nuclear recoils from dark matter interactions, and to distinguish 1.5 Dark matter detection 15 signal recoil events from such caused by ambient background. One technique is to detect phonon excitations from nuclear recoils. A second approach is to measure ionization of target atoms, which is caused from recoiling nuclei. The third technique aims to capture scintillation radiation from excited target atoms. Detectors, which apply an event-by-event based analysis, commonly use the measured energy-ratio between two such technologies to discriminate electron and nuclear recoils. Liquid noble gas detectors, like XENON100 [35, 36], LUX [37] and DarkSide [38] look for scintillation and ionization signals. Cryogenic detectors, such as CDMS [39], CoGeNT [40], EDELWEISS [41] and CRESST [42], instrument semi-conducting or scintillating crystals to measure phonon energy in combination with ionization or scintillation. A complementary approach is pursued by the COUPP [43] and PICASSO [44] experiments, using superheated liquid detectors. Such detectors are threshold experiments and show great potential due to their unique background rejection capability.

A second strategy is to look for an annual modulation signal of the recoil rate. Such an effect may arise due to the Earth’s annual motion around the Sun within the galactic reference frame. This orbital motion results in a time dependent relative velocity of the Earth~vE(t), and consequently a time dependent event rate (eq. 1.4). The DAMA/LIBRA [45] experiments, measuring scintillation in sodium iodine (NaI), have observed such an annual variation and report that their measured modulation (> 8σ significance) is consistent with detection of WIMPs with approximately 60 GeV mass and a total cross 41 2 section in the order of 10− cm [46]. CoGeNT supports the presence of a modulated component compatible with a galactic halo composed of light- mass WIMPs with a statistical significance for a modulation of 2.8σ [47]. CDMS, XENON100, COUPP and EDELWEISS have explored the DAMA and CoGeNT favored parameter space without finding evidence of dark matter. It was pointed out that a comparison between different detectors and target materials is difficult, as the expected WIMP rate depends on vmin(Er), given by

m E v n r (1.5) min(Er) = 2 , s 2µnχ where mn is the target nucleus mass. From eq. 1.5 we can see that the expected WIMP rate depends on the detectors’ energy threshold and target material. Consequently, it was argued to compare all experiments in the vmin(Er)- space [33]. The authors of Ref. [33] conclude that there is signiﬁcant tension between the DAMA/LIBRA and CoGeNT experiments, most notably it is im- possible to ﬁnd a dark matter velocity distribution that describes the observed modulations and evades the bound from XENON100. The DAMA observation remains a highly controversial claim and would best be put to the test by the proposed DM-ICE detector [48], which plans to use the same detector technology (NaI-crystals) in the opposite Hemisphere 16 Chapter 1: Dark matter at the South Pole. Evidence of the same modulation signal would strongly support a dark matter observation, and effectively rule out background effects correlated with seasonal variations and the surrounding environment as the explanation for the DAMA observation.

1.5.2 Indirect detection A complementary search for the nature of dark matter is through various indirect detection experiments, which aim to detect primary or secondary particles created in WIMP annihilations, such as photons, neutrinos and antimatter. The number of WIMP annihilations is proportional to the square of the dark matter density. As a result, the most promising search targets are regions with an expected high density of dark matter and low, well-understood, astrophysical background. Ordered in increasing distance from the Earth, such target candidates are the Earth, the Sun, the Galactic Center, galactic halo regions, dark matter dominated dwarf galaxies, and nearby galaxy clusters.

High energy gammas are predicted from secondary decays of annihilation products and by internal bremsstrahlung (γ’s emitted from virtual particles in the annihilation process). In addition, monochromatic lines from annihilations into 2γ and γZ are predicted for some WIMP models. Such line signals have very low branching fractions, as the process is loop suppressed [49]. High energy γ signals are searched for by the Fermi satellite [50] and ground based air Cherenkov telescopes e.g., H.E.S.S. [51], VERITAS [52], and the future CTA [53]. The Fermi Collaboration has put tight constraints on dark matter models from searches for γ-rays from Dwarf galaxies [54], the galactic halo and spectral line signals (diffuse) [55]. An indication of a 135 GeV γ-line from dark matter annihilations in an optimized search region at the Galactic Center [56] has recently caused a great deal of excitement. The line signal is conﬁrmed by the Fermi Collaboration [57], but is also seen in the so-called Earth-limb data (γ’s produced in cosmic ray interactions in the Earth atmosphere). Detailed detector response studies and new analyses, including data from a longer data taking period, will help clarify whether the line is caused by a detector systematic, or if it is a true line feature in the γ-spectrum from the Galactic Center. Additionally, the new H.E.S.S.-II telescope may conﬁrm or rule out the presence of this line, given a minimum exposure time of 50 hours of the Galactic Center [58].

Positron and antimatter fluxes from WIMP annihilation have been searched for by the PAMELA satellite [59], the AMS-2 detector [60], and Fermi. PAMELA and Fermi (Fermi uses the Earth’s magnetic field to distinguish positrons and electrons) reported an increased positron flux at high energies above expected background [61]. This observation is consistent with a signal resulting from annihilation of WIMPs in the TeV range [62], but can also convincingly be explained by standard astrophysical phenomena, such as 1.6 Indirect solar search for WIMP dark matter 17 pulsars or supernova remnants [63]. First results from AMS-2 on the positron fraction measurement [64] confirm PAMELA and Fermi observations. This improved measurement provides no further clues on the nature of the increased positron flux at high energies.

A ﬂux of high energy neutrinos from WIMP annihilations may be detected in large neutrino telescopes such as Super-Kamiokande [65], ANTARES [66], and IceCube [67]. IceCube has put constraints on self-annihilating or decay- ing dark matter in the galactic halo [68] and Galactic Center [69]. Neutrino telescopes may also search for neutrino annihilation from large celestial bodies, such as the Sun. This is the dark matter search principle used in this thesis, and is detailed in section 1.6.

1.5.3 Accelerator searches Searches for physics beyond the SM at colliders like the Tevatron and the LHC, are often searches for missing transverse energy signals (ET), because of the potential connection to dark matter. New theories, such as SUSY, predict many new particles (e.g. sparticles), which are heavier unstable particles and may decay into the WIMP itself plus SM particles. Generally, two search techniques are used. First, searches for sparticles (using SUSY as an example) that may decay within the detector sensitive volume into LSPs and SM particles. Analyses are performed looking for missing ET and certain predicted SM particle ﬁnal-states (lepton ﬁnal states or hadronic jets). A detailed summary on ATLAS SUSY search results at the LHC is given in e.g., Ref. [70]. Second, LSPs may be produced directly. This channel may be detectable via some kind of initial state radiation from the incoming quarks or gluons. Analyses are looking for mono-jet and mono-photon signals at hadron colliders [71, 72, 73, 74]. These searches depend strongly on the choice of the underlying effective theory and mediator masses, leading to weaker limits if the mediator is light. All accelerator searches for dark matter have the advantage of being independent of astrophysical uncertainties.

1.6 Indirect solar search for WIMP dark matter WIMPs may be captured in large celestial bodies such as the Sun [75, 76, 77], where self-annihilation to SM particles can result in a ﬂux of high-energy neutrinos. These neutrinos can be searched for as a point-like source by neutrino telescopes, such as IceCube. These indirect searches for dark matter are sensitive to the cross-section for WIMP-proton scattering which initiates the capture process in the Sun. A search for solar WIMP dark matter is different from other indirect searches. We beneﬁt from the self-annihilating nature of 18 Chapter 1: Dark matter

WIMP dark matter to test their scattering cross section with matter, as in direct detection experiments. Here, the target mass (Sun) is O(1028) larger than the target mass of the current leading experiment, XENON100.

Capture and annihilation in the Sun The number of WIMPs in the Sun, N, is governed by the equation

dN 2 = CC CAN CE N, (1.6) dt − − where CC describes WIMP capture, CA annihilation and CE evaporation. CE speciﬁes the loss of initially captured WIMPS due to hard elastic scattering from nuclei in the Sun. Calculations show that WIMP evaporation can be ig- nored for mχ >10 GeV [49]. CA depends on the thermally averaged product of the total annihilation cross-section and the relative particle velocity per volume. The effective core volume for WIMPs inside the Sun is approximated by matching the Sun’s temperature with the gravitational potential energy of a WIMP at the core radius [14]. The WIMP capture calculation (CC) depends on the halo density and velocity proﬁle of dark matter, mχ , and interaction cross-section. We assume a standard dark matter halo model, with 1 the Sun moving at v = 220 km s− through a halo with local dark matter 3 density ρ0 = 0.3 GeV cm− and dark matter velocities following a Maxwell- 1 Boltzmann distribution with average speed v¯ = 270 km s− . The WIMP model dependent interaction cross-section is composed of the spin-independent component (σSD) and spin-dependent component (σSI) of the interaction cross section. WIMP capture in the Sun via the axial-vector interaction (σSD) occurs predominantly on hydrogen. Contributions from heavier elements can be ig- nored [75]. This is different for capture via the scalar interaction (σSI), where 2 it is important to sum over all elements in the Sun (owing to σSI A ). As ∼ a result, σSI depends on detailed information on the solar abundance of elements (see e.g., [78]) and is affected by nuclear form factor suppression [14] (see discussion in section 1.7).

The annihilation rate of WIMP pairs, ΓA, is given by: 1 Γ (t) = C N(t)2 (1.7) A 2 A Using eq. 1.6, we derive the annihilation rate at a given time, t, as, 1 t Γ (t) = C tanh2 , (1.8) A 2 C τ where τ = 1/√CCCA is the capture-annihilation equilibrium time scale. The current WIMP annihilation rate in the Sun is calculated for the age of the solar system (t = t 4.5 billion years). For WIMP models with t /τ 1 ∼ 1.6 Indirect solar search for WIMP dark matter 19

annihilation and capture are in equilibrium, resulting in ΓA(t) = CC/2. Thus, ΓA(t) depends on the total scattering cross-section.

For the results presented and discussed in paper V, we assume equilibrium between ΓA(t) and CC to derive limits on σSI and σSD (valid approximation for most WIMPs within the probed mass range [79]). This approximation is not necessary for the work detailed in papers III and IV, where we calculate ΓA(t) speciﬁcally for each tested MSSM model (equation 1.8).

Neutrino spectra Neutrinos are the only stable SM particles that are able to leave the Sun without being completely absorbed. They are generally produced in decays of short lived particles. Light quarks (u, d, s) have long enough lifetimes to interact with the solar medium and lose most of their energy before decay- ing. The WIMP annihilation products, which produce energetic neutrinos, are b,c and t quarks, τ-leptons, and gauge bosons [49]. Neutrinos from decays of short lived b, c, and t quarks have a soft spectrum (lower energy), as the quarks initially loose energy during hadronization. WIMP annihilations into + W W − result in a hard (higher energy) spectrum through the secondary direct +( ) +( ) decay into charged leptons and neutrinos (W − l − + νl(ν¯l)). Below + → the W mass, the annihilation into τ τ− is assumed as the channel producing the highest energy neutrinos. The ﬂux of high energy neutrinos, created in the core of the Sun, is further reduced through interactions with the solar medium, when propagated out of the Sun. In this context, the Sun becomes more or less opaque to neutrinos with energies above 1 TeV. The escape probability rises signiﬁcantly for lower neutrino energies∼ [79]. Each MSSM model will result in a different set of branching ratios. As it is too time consuming to perform an analysis for every possible annihilation channel and spectrum, two end points of the spectrum are chosen to approximately bracket the range of all models: + + the soft bb and hard W W − (τ τ− below 80.2 GeV) channels (each with 100% branching).

A model-independent analysis, as described above, is performed in chap- ter7 and summarized in paper V. These limits are difficult to translate into actual particle models, where the annihilation cross-section and branching fractions may take on a range of different values for any given WIMP mass and nuclear-scattering cross-section. To properly interpret limits on neutrino fluxes in terms of the parameters of a theory for new physics, we also compare the observed neutrino flux with the predicted neutrino signal for each individual point in the parameter space of the theory (analyses performed in papers III and IV). 20 Chapter 1: Dark matter

Figure 1.4: Velocity modulus distributions for a 2 kpc box at the solar circle for several simulated haloes. At each velocity, a thick red line gives the median for all simulated v-distributions, while a dashed black line gives the median of all the ﬁtted multivariate Gaussians. The dark and light blue contours enclose 68% and 95% of all the simulated distributions at each velocity. Figure from [80].

1.7 Discussion on astrophysical uncertainties Indirect searches for solar WIMP dark matter complement direct detection searches on Earth, as they scale with the dark matter density averaged along the solar circle and are more sensitive to low WIMP velocities [81]. The true WIMP velocity distribution may differ from a Maxwell-Boltzmann distribution, which is generally assumed in standard halo scenarios. Figure 1.4 shows the local velocity distribution, as derived from a high resolution simulation of galaxy haloes from the Aquarius project [80]. These simulations indicate that the local velocity distribution differs significantly from Maxwellian, or from a multivariate Gaussian (shown as best fit model (dashed) in figure 1.4)[80]. Nuclear recoils with the highest velocity WIMPs create the largest recoils in direct detection experiments (‘best’ sensitivity). It is concluded in Ref. [80] that WIMP recoil spectra in direct detection experiments can deviate about 10% from the recoil rate expected from the best-fitting multivariate Gaus- sian model. Similar uncertainties on ΓA(t) arise for indirect solar searches for WIMP dark matter [82].

The WIMP capture rate CC depends linearly on the local dark matter density. In this work, we assume a local dark matter density of 3 ρ0 = 0.3 GeV cm− . This is a conservative choice, as recent measurements favor slightly higher values of ρ0 [83]. Note that this uncertainty affects direct detection experiments in the same way. 1.7 Discussion on astrophysical uncertainties 21

Two additional uncertainties arise in the conversion from limits on the neutrino flux (or muon flux in the ice) from the Sun to limits on the WIMP- nucleon scattering cross-sections: (1) the uncertainty in the nuclear form factor, and (2) the uncertainty in solar composition models. For calculations of σSD the nuclear form factor uncertainty is negligible, because the capture is dominated by protons. For σSI interactions heavy elements are important in the capture process. Assuming various models of the form factor, the uncertainty on the spin-independent WIMP-nucleon scattering cross-section can be as much as 20% [84]. Reference [85] argues that uncertainties due to nuclear form factor models may be reduced for the capture process of WIMPs in the Sun compared to direct detection event rates, because high-energy scatters with large momentum transfer are less important. The dependence of the capture rate on the abundances of elements in the Sun is evaluated by comparing different composition models. Reference [86] calculates an uncertainty of 15% on σSI and 2% on σSD interactions for solar models using DarkSUSY [87]. An uncertainty of at most 4% difference in the annihilation rates between the models based upon the two most recent abundance estimates (AGSS09 and AGSS09ph) is calculated in Ref. [85]. The authors of Ref. [85] conclude that the discrepancy between meteoritic and photospheric measurements is not a significant issue in estimating annihilation rates.

Overall, the above detailed uncertainties on cross-section limits from indirect solar searches for WIMP dark matter are negligible (< 3%) for the dominant term, the σSD interactions. For σSI interactions, we adopt a conservative estimate of 25%.

2 Expected background

The dominant background in this search for dark matter annihilations in the Sun consists of muons and neutrinos created in cosmic ray interactions in the Earth’s atmosphere. This is illustrated in figure 2.1, showing the vertical flux of air shower particles (E >1 GeV) as a function of atmospheric depth [88]. It is evident from the figure that the flux of muons and neutrinos at the Earth’s surface is higher than for other secondaries, and dominates at depths relevant for IceCube. An additional component, which potentially may fake a dark matter signal, arises from cosmic ray interactions in the Solar atmosphere. In this chapter, we discuss all expected background components.

2.1 Atmospheric muon background Cosmic Rays (CRs), consisting predominantly of protons (p+), alpha parti- 2+ cles (α ) and electrons (e−), but also heavier ionized atoms, produce highly energetic, ultra relativistic muons in reactions with molecules in the Earth’s atmosphere. These muons (µatm) can penetrate the Antarctic ice up to several kilometers deep. The dominant production of muons is via the leptonic or semi-leptonic decays of charged pions or kaons, through the following decay chain:

+ 2+ p (α ,etc.) + N π±(K±) + X (2.1) → , µ± + νµ (ν¯µ ) (2.2) → , e± + νe(ν¯e) + ν¯µ (νµ ) (2.3) → N stands for the initial molecule and X for the hadronic remains of the interaction. The average trigger rate of approximately 2.4 kHz for the 79-string detector is entirely dominated by µatm. For muon energies relevant to this analysis, the µatm energy spectrum follows, to ﬁrst order, the initial power law 2.7 spectrum of CRs, which is proportional to E− [89]. The zenith angle range is constrained to 0◦ < Θ < 85◦, as µatm can not traverse the whole Earth.

2.2 Atmospheric neutrino background

CR interactions in the atmosphere also create high energy neutrinos (νatm) in decays of secondary air shower particles like π±(K±) (see eq. 2.2), µ± (see 24 Chapter 2: Expected background

Figure 2.1: Vertical ﬂuxes of cosmic rays in the atmosphere with E >1 GeV. The points show measurements of negative muons (µatm− ) only. Figure from [88].

eq. 2.3) and other mesons. In the GeV-range, their energy spectrum follows the 2.7 CR power law spectrum, proportional to E− . At energies above 1 TeV, the interaction length of the secondary particles becomes shorter than the decay 3.7 length, resulting in increasing steepness of the spectrum (∝ E− )[90] (see figure 2.2). For this work, we use the Honda flux model [90, 91] to describe the conventional νatm component. In addition to the conventional component of the atmospheric neutrino spectrum, defined by eq. 2.2 and 2.1, a prompt component is predicted from the semi-leptonic decay of charmed particles, hadrons with c-quark content [92]. νatm are the dominant background at final level for this analysis. Figure 2.2 shows the latest measurement of the conventional neutrino flux components [93], including a first measurement of the atmospheric νe flux in IceCube and DeepCore [94]. IceCube and DeepCore measurements agree well with complementary measurements from other experiments, and thus with predicted fluxes over the whole energy range. Such a detailed understanding of the main background component of this analysis is beneficial.

2.3 Neutrinos from the solar atmosphere CRs may interact in the Sun’s atmosphere in the same way as when entering Earth’s atmosphere (as described in section 2.1). The produced particles propagate through the Sun until they either decay or produce new particles 2.3 Neutrinos from the solar atmosphere 25 ] −1 10−1 Super−K ν sr µ

−1

s −2 Frejus νµ

−2 10 conventional Frejus ν e −3 conventional AMANDA νµ 10 unfolding forward folding ν

[GeV cm −4 µ ν 10 IceCube νµ

Φ ν unfolding e 2 ν forward folding E 10−5 This Work νe

10−6 prompt −7 ν 10 µ, ν e

10−8

−9 10 −1 0 1 2 3 4 5 6 7 log (E [GeV]) 10 ν Figure 2.2: Neutrino flux measurements from IceCube/DeepCore and other experiments. The νe flux [94] (green open triangles) is shown as well as the unfolded energy spectrum (black filled circles) from [93]. The conventional νe (red line) and νµ (blue line) from Honda [91], and charm-induced neutrinos [92] (magenta band) are shown. Figure from [94]. in secondary interactions (eq. 2.1, 2.2 and 2.3). The main contribution to a detectable neutrino flux component comes from decays of π±, K± and µ±. As the solar atmosphere is less dense at typical interaction heights than the Earth’s atmosphere, a larger fraction of mesons will decay instead of interacting, enhancing the ν-flux component from the solid angle of the solar disc [95]. This ν-flux component describes an indistinguishable background for potential dark matter annihilation ν-signals from the center of the Sun.

The number of events expected from this background at final analysis level is calculated directly from Monte Carlo (MC) simulations, using predicted parameterizations of the solar atmospheric neutrino fluxes [95, 96, 97]. This is shown for the highest flux prediction from Ref. [95] in figure 2.3 for events close to the position of the Sun for all three final event selections, WH, WL and SL (see chapter7 for details on the analysis and event selections). The predicted number of events depends strongly on the chosen event selection. The last bin in figure 2.3 (cos(Ψ) 1) can be directly compared to the bin closest to the Sun’s position in figure∼ 7.18, the unblinded event sample. A direct comparison of the two figures indicates that even for the highest predicted flux model, neutrinos from the solar atmosphere are expected to make up less than 3% of the total expected background. This fraction is further reduced, when considering neutrino oscillations [96, 97]. Due to the small flux expectation, we chose not to include neutrinos from the solar atmosphere in our 26 Chapter 2: Expected background

WH event selection 1 WL event selection SL event selection

10-1

Events 10-2

10-3

0.9 0.92 0.94 0.96 0.98 1 cos(Ψ) Figure 2.3: Cosine of the angle between the reconstructed track and the direction of the Sun, Ψ, for the predicted number of events per bin at ﬁnal level from solar atmospheric neutrinos [95]. Distributions are derived from MC simulations. total MC background prediction. Note, that the background prediction for the ﬁnal directional search is estimated from scrambling experimental data (see chapter6 for details). 3 Neutrino detection and the IceCube neutrino observatory

Neutrinos are weakly interacting fundamental particles with diminutive mass and no electrical charge. Their observation requires extremely large detector volume or very long observation times. High energy neutrinos, such as neutrinos from dark matter annihilation, are best studied with neutrino telescopes. The IceCube neutrino observatory instruments in its 79-string conﬁguration nearly one cubic kilometer of Antarctic ice in an open detector geometry. Ice- Cube detects Cherenkov light radiated by charged particles that are produced in interactions with nuclei inside or close by the detector. This chapter discusses neutrino detection in ice and gives a description of the IceCube detector.

3.1 Neutrino detection in ice 3.1.1 Neutrino-nucleon interactions Neutrinos interact with nuclei in the ice via two different channels, the charged current (CC) interaction via the exchange of charged W bosons, and the neutral current (NC) interaction through the exchange of the neutral Z boson. These are given by: + νl(νl) + N l−(l ) + X (CC) (3.1) → 0 νl(νl) + N ν 0 (ν ) + X (NC) (3.2) → l l Here, N denotes the initial nucleus, X the final hadronic product and l the lepton flavor (e,µ,τ). NC interactions can be regarded as a scattering of the initial neutrino on the nucleus, N. In both processes, the final hadronic product can result in detectable charged leptons at very high energies, but does not contribute at the targeted energies of this work. Both processes are described in the Feynman diagrams (figure 3.1). The main detection signatures are long, straight tracks and approximately spherical cascades. The former are created by neutrino-induced muons, while the latter are neutrino-induced electromagnetic and/or hadronic showers. Muons can travel through the detector medium for up to several kilometers, thus radiating Cherenkov photons (see section 3.1.3). Electrons, roughly 200 times lighter than muons, typically lose their energy in electromagnetic showers within a few meters in ice. Tau leptons have a very short lifetime of less than 1 ps and decay into the following 28 Chapter 3: Neutrino detection and the IceCube neutrino observatory

+ νl(¯νl) νl(¯νl) νl(¯νl) l− (l ) + Z0 W (W−) d (u) d (u) d (u) u (d)

N X N X Figure 3.1: Feynman diagrams contributing to the neutrino interaction with nuclei. The NC interaction (left) and the CC interaction (right). l indicates the lepton ﬂavor, N the initial nucleus and X the resulting hadronic cascade. secondary particles [98]:

+ τ−(τ ) X + ντ (ντ) (3.3) → + ντ (ντ ) + νe(νe) + e−(e ) (3.4) → + ντ (ντ ) + ν µ (νµ ) + µ−(µ ) (3.5) → While muons are produced in the third channel with a branching ratio of 17.36% [99], only a small fraction of the initial kinetic energy of the τ is transferred to the muon produced via equation 3.5.

This analysis is a point source search and aims to detect an excess of neutrinos in the direction from the Sun above atmospheric background. At targeted energies only muon track events created in CC interactions yield enough information (spatial extension of the muon track) to adequately infer the initial neutrino direction and ultimately point to the Sun’s position. Therefore, we consider muons produced through CC interactions the only viable signal detection-channel for this analysis.

Cross sections Neutrino and antineutrino interactions (NC and CC) with nuclei in the ice are deep inelastic scattering processes. Measurements of the CC cross-sections are given in ﬁgure 3.2[99] with a focus on the energy range from 1 to 400 GeV, which is of particular importance when setting limits for low mass WIMP models. For neutrino energies below 106 GeV, the inelastic scattering cross- sections are successfully described in the framework of perturbative QCD. They depend crucially on the parton distribution functions for the quarks (q(x,Q2)) and antiquarks (q¯(x,Q2)), and the kinematic variables x and y [100]. Here, Q2 is linked to the 4-momentum transfer between the incoming neutrino 2 2 and the produced lepton (Q = q ), where Eν and El are their respective en- − 2 ergies. The Bjorken scaling variable x = Q /2mN(Eν El) is the fraction of − the momentum of the nucleus carried by the quark and y = 1 El/Eν is the − 3.1 Neutrino detection in ice 29

1.6 ANL, PRD 19, 2521 (1979) IHEP-ITEP, SJNP 30, 527 (1979) ArgoNeuT, PRL 108, 161802 (2012) IHEP-JINR, ZP C70, 39 (1996) BEBC, ZP C2, 187 (1979) MINOS, PRD 81, 072002 (2010) 1.4 BNL, PRD 25, 617 (1982) NOMAD, PLB 660, 19 (2008) CCFR (1997 Seligman Thesis)

/ GeV) NuTeV, PRD 74, 012008 (2006) 2 1.2 CDHS, ZP C35, 443 (1987) GGM-SPS, PL 104B, 235 (1981) SciBooNE, PRD 83, 012005 (2011) SKAT, PL 81B, 255 (1979) cm 1 GGM-PS, PL 84B (1979) -38 - 0.8 νµ N →µ X (10 ν 0.6 / E

CC 0.4 σ + 0.2 νµ N →µ X

0 1 10 100 150 200 250 300 350 E (GeV) Figure 3.2: Measurements of CC scattering cross-sections divided by neutrino energy as a function of neutrino energy. NC cross sections (not shown) are generally smaller (but non-negligible) compared to their CC counterparts. Figure from [99].

fraction of neutrino energy transferred to the quark. Both scaling variables determine the degree of inelasticity of the interaction. This work uses parameterization of these structure functions according to CTEQ6 [101]. At low energies, where the parton distribution functions are dominated by the valence quarks, the deep inelastic neutrino cross section for scattering on nuclei in ice, is roughly two times larger for the neutrino than for the antineutrino. This is due to helicity suppression of the CC interaction of the antineutrino by a factor (1 y)2 for energies below 10 TeV [20]. At very high energies, the cross section− is no longer dominated∼ by valence quarks but by quarks from the sea, which is q-q¯ symmetric. Consequently, the two cross sections become equal.

The mean scattering angle between the initial neutrino and muon directions 0.7 is approximated as Θνµ 0.7 /(Eν /TeV) [102] and shown for the signal ≈ ◦ energy range in figure 3.3 (left). For Eν > 100 GeV, the directional information of the initial neutrino is well retained. Below 100 GeV, the restriction in angular precision from kinematics is more challenging. At analysis level, quality cuts predominantly select events with large momentum transfer to the created muon. This selection effect reduces the expected mean scattering angle within the final event sample, as illustrated in figure 3.3 for low energy events. Note, the mean scattering angle discussed here does not correspond to the uncertainty in angular reconstruction. 30 Chapter 3: Neutrino detection and the IceCube neutrino observatory ) ° 15

103

102 5 mean muon range (m) mean scattering angle ( 10 10 102 103 10 102 103 Eν (GeV) Eµ (GeV) Figure 3.3: Left: Mean scattering angle between initial neutrino and created muon as a function of Eν (line). Also shown is the mean scattering angle at ﬁnal selection for signal simulations (circles) including the statistical error of each bin. Right: Mean muon range in ice as a function of Eµ as given by eq. 3.7 (line).

3.1.2 Muons in ice Muons loose energy as they propagate through the detector medium. The losses in ice are dominated by four processes. Ionization, as described by the Bethe-Bloch formula, is nearly energy independent at GeV range and above, and occurs continuously along the trajectory of the muon [103]. Energy losses + through bremsstrahlung, pair production of e e− and photo-nuclear interaction, are energy dependent. The average rate of energy loss can be expressed in a single equation: dEµ = a + b Eµ , (3.6) − dx · where the sum of all stochastic contributions is given by b 3.6 10 4mwe 1 ≈ · − − and ionization by a 0.26 GeV mwe 1 [104]. The stochastic losses become ≈ − dominant above a threshold energy of Eth = a/b, and can therefore be used to determine the energy of the muon. The mean muon range, Rµ , found by integration of eq. 3.6, is given by,

1 Eµ Rµ ln + 1 . (3.7) ≈ b E th This leads to a muon range of around 200 m for a 50 GeV muon, which is comparable to the diameter of the ﬁducial volume of the DeepCore sub-array (250 m). Rµ is illustrated in ﬁgure 3.3 (right) for the signal relevant muon energy region. The average energy loss due to Cherenkov radiation (1 keV/m) is not a dominant contribution for muons in ice, but the crucial one from a detection point of view.

3.1.3 Cherenkov radiation Charged particles that travel through a dielectric medium with speed, v, po- larize the surrounding medium. During the successive depolarization of the 3.1 Neutrino detection in ice 31 medium along the particle track, electromagnetic radiation is emitted. The radiation will interfere destructively for charged leptons in general, except for particles with velocities above the speed of light in that particular medium i.e., when v > c/n. Here, n is the index of refraction of the medium. Due to the particle speed being greater than the speed of light, the polarization is anisotropic along the velocity axis. The emitted electromagnetic radiation forms a shock front with a characteristic, photon energy dependent, opening angle (Θc) with respect to the velocity axis [105].

1 cosΘc = (3.8) n(λ) β ·

For muons in ice with β 1, the opening angle is Θc = 41.2 , since to ﬁrst ∼ ◦ order the refractive index is given by n = 1.33 for the visible electromagnetic spectrum. The Cherenkov photon emission is wavelength dependent and increases for shorter wavelengths. The number of photons emitted per unit wavelength and unit length from a particle of charge z e can be calculated with the Frank-Tamm expression [106]: ·

d2N 2π z2α 1 = 1 , (3.9) dx dλ λ 2 − β 2n2(λ) where α = 1/137 is the ﬁne structure constant. A characteristic value for the number of photons emitted by a muon is 330 per cm of track length for the sensitive range of the IceCube optical sensors∼ [ 300nm, 600nm] [107]. ∼ ∼

3.1.4 Propagation of light in the South Pole ice Light propagation in the deep ice at the South Pole is possible over large distances, because the ice is extremely clear and pure. Knowledge of the optical properties of South Pole ice at depths greater than 1400 m, where the ice is signiﬁcantly clearer and contains very few air bubbles, is essential. The ice is modeled using the so-called six-parameter ice model, introduced in Ref. [108]. This model describes the ice by a table of parameters be(400) and adust (400), related to scattering and absorption at 400 nm, and temperature δτ, given for each ice layer (assuming layers of 10-meter depths), and by six parameters that were ﬁtted in Ref. [108] to AMANDA data.

The ice-model currently used in IceCube (the baseline model for this work) is a direct fit approach to fitting the ice properties, called SPICE-MIE, which also includes a new improved parameterization of Mie scattering [110]. A global fit is performed to a set of data with in situ light sources (details section 3.2.3) covering all detector depths, resulting in a single set of scattering and absorption parameters of ice, which best describes these data [109]. Fig- ure 3.4 shows the obtained best fit solution for absorption and scattering length 32 Chapter 3: Neutrino detection and the IceCube neutrino observatory

] SPICE MIE 0.05 20 -1 AHA 25 m [

0.03 33 ] m 0.02 50 [ 70 0.01 100 (400 nm)

125 a λ

0.005 200

absorption a(400 nm) 250

1400 1600 1800 2000 2200 2400 depth [ m ] ] 0.2 5

-1 SPICE MIE

m 7 [ AHA

0.1 10 ] m

14 [

(400 nm) 0.05 20 e 25 0.03 33 (400 nm) e 0.02 50 λ 70

eff. scattering b 0.01 100 1400 1600 1800 2000 2200 2400 depth [ m ] Figure 3.4: Values of be(400) and a(400) vs. depth for converged fit solution for the SPICE-MIE model (solid). The updated model of [108](AHA) is shown by the dashed lines. The scale and numbers to the right of each plot indicate the corresponding effective scattering 1/be and absorption 1/a lengths in m. Figure from [109]. versus depth at the South Pole, compared to the previously used AHA (Addi- tionally Heterogeneous Absorption) ice-model [108]. The AHA model used an analysis based on separate fits to data for individual pairs of emitters and re- ceivers [108] to measure the optical properties of the ice. These fits used data taken at very low light levels. The large peaks in absorption and scattering, and hence the layered structures within the ice, result from the so-called dust layers. The plots indicate extremely clear ice in the bottom of the detector, the DeepCore sub-array region, with an effective absorption length up to 250 m and an effective scattering length up to approximately 70 m. An additional complication in modeling the ice is given by the so-called ‘hole ice’, described in Ref. [111]. This is a column of ice approximately 60 cm in diameter immediately surrounding the IceCube string. It contains residual air bubbles from drilling and deployment processes. This was visu- ally confirmed with a video camera installed below the deepest DOM on one of the IceCube strings during the last deployment season (2010). In ice modeling, the ‘hole ice’ is described by taking into account an increased amount 3.2 IceCube neutrino observatory 33

-1 10

-2 10 relative sensitivity IceCube "hole ice" IceCube nominal -3 10

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos(η) Figure 3.5: Angular sensitivity of an IceCube DOM. η is the photon arrival angle with respect to the PMT axis. The lab measurement (nominal) is normalized to 1 at cosη =1. The integral for both curves is the same. Figure from [109].

of scattering (with effective scattering length of 50 cm) via an empirical mod- iﬁcation to the effective angular sensitivity curve of the receiving DOM [109]. This is illustrated in ﬁgure 3.5 and compared to a nominal angular sensitivity curve.

3.2 IceCube neutrino observatory Completed in December 2010, the IceCube neutrino observatory is a neutrino telescope deployed deep in the East Antarctic Ice Sheet at the geographical South Pole, close to the Amundsen-Scott station (see figure 3.6 for a schematic view). The optical sensors are arranged in a three-dimensional lattice along cables (‘strings’) lowered down vertical wells melted into the ice using a hot water drill. IceCube consists of 5160 digital optical modules (DOMs) installed on 86 strings between 1450 m and 2450 m below the surface [67] with a total instrumented volume of 1 km3. Its design is optimized for the detection of high energy astrophysical neutrinos with energies above 100 GeV, where 78 of the strings have a horizontal spacing of 125 m and a vertical∼ spacing of 17 m. The remaining eight strings are clustered in the center with a horizontal spacing of 72 m. Together with the 12 adjacent standard IceCube strings they make up the DeepCore subarray. DeepCore, discussed in more detail below, provides increased sensitivity at lower energies and reduces the energy threshold. Be- tween May 2010 and May 2011, the detector was operating in its 79-string configuration (see horizontal surface layout and depth profile, figure 3.7). The IceTop surface air shower array consists of pairs of tanks placed at the top of 81 of the 86 ‘in-ice’ strings, separated from each other by 10 m. Each 34 Chapter 3: Neutrino detection and the IceCube neutrino observatory

Figure 3.6: Three dimensional overview of the 79-string IceCube 2010 detector with the location of the DeepCore array marked in the center, bottom of the detector. IceTop stations are at the surface at each string location. The seven missing strings are marked in orange.

tank is instrumented with two DOMs frozen into the top of the ice inside the tanks, which contains a reﬂective coating to improve Cherenkov light capture. IceTop is predominantly used in CR composition studies, but also acts as a surface veto for the ‘in-ice’ detector for extremely bright down-going CR shower events.

The 79-string detector Within the IceCube 79-string detector, 73 strings are ‘standard’ IceCube strings and six strings are DeepCore strings, explained below. The IceCube coordinate system is deﬁned in a right-handed coordinate system by the (x,y,z)-axis (ﬁgure 3.7). The y-axis is grid North, aligned with the prime meridian. The x-axis is grid East, pointing 90 degrees clock-wise from y. The z-axis is normal to the Earth’s surface pointing up. The origin corresponds to a below-surface depth of 1948 m.

DeepCore The DeepCore sub array is a dense array of six strings (IceCube-79) surrounding the IceCube center string (string 36). The distance to neighboring strings is less than 75 m. There is 7 m between break-outs on each string below the 3.2 IceCube neutrino observatory 35

X (grid East (m)) -600 -400 -200 0 200 400 600 600

400

200

0 Y (grid North (m)) -200

-400 IceCube-79 -600 IceCube-86 cCb string IceCube string DeepCore -1400

-1600 Depth (m)

-1800

DC-veto -2000 dust layer

-2200

-2400 dust concentration DC-fiducial Figure 3.7: Top and side view of the IceCube detector. Strings deployed within the IceCube 79-string detector (solid) and strings deployed during the 2010-2011 season (circles) are indicated. DeepCore string and/or DOM positions are shown in blue. Also shown is the main dust layer within the detector and a dust concentration proﬁle as measured with the dust logger [112].

dust layer and 10 m above. This array forms a dense core of DOMs within the clearest part of the ice with a five times higher effective photo-cathode density than IceCube. In addition, the standard IceCube photo multiplier tube (PMT), discussed in section 3.2.1, is exchanged for high quantum, HQ, efficiency PMTs with a 40% higher quantum efficiency. Spacing and positioning of the DeepCore DOMs and strings relative to ‘standard’ IceCube strings is shown in figure 3.7. Within the 79-string configuration, the ‘in-fill’ strings 79 and 80 that form an even more compact array within the six DeepCore strings are not yet deployed (marked by blue circles in figure 3.7). 36 Chapter 3: Neutrino detection and the IceCube neutrino observatory

Cable penetrator assembly HV-generator

Flasher board LED Main board

DOM harness Delay board

Magnetic shield cage

PMT Glass pressure sphere

Figure 3.8: Photograph of a DOM with key components indicated. Figure is adapted from [67].

3.2.1 IceCube digital optical module The optical modules consist of a 13 mm thick glass sphere containing a down- wards orientated photo multiplier tube (PMT), a 2 kV high voltage power supply for the PMT and a DOM Main Board (MB). The PMT (Hamamatsu R7081-02) is 25 cm in diameter and in contact with the glass via a transparent silicone gel [107]. The PMT has 10 dynodes with a total amplification of about 107, allowing accurate single photon detection. The glass sphere is transparent to wavelengths between 300 nm and 600 nm and has a transmission maximum at 410 nm [67, 113]. The MB additionally contains an LED flasher board for in situ calibration, discussed in section 3.2.3. Key components of a DOM are shown in figure 3.8.

In contrast to OMs used in IceCube’s predecessor AMANDA, the IceCube DOMs operate as completely autonomous data acquisition modules by digi- tizing the pulse information within the module (in-ice digitization). All modules are remotely controlled, independent of each other, and synchronized by a master clock system to a GPS disciplined reference to establish a common time-base for all created pulses in data [114]. Accordingly, DOMs timestamp each pulse with the actual ‘in-ice’ time information. The pulse information sent to the surface is not susceptible to cross talk or dispersion like previous analog AMANDA signal. IceCube PMTs detect Cherenkov photons by creating analog charge signals, which are digitized if the PMT signal exceeds the discriminator threshold of 0.25 photo electrons (PE). The digitizers are a fast Analog-to-Digital converter (fADC) and a set of two advanced transient waveform digitizers (ATWDs) on the MB. The ATWDs contain three chan- 1 nels with gains of 4 , 2 and 16 [67]. The ATWDs sample 128 bins of 3.3 ns width, whereas the fADC samples at a rate of 40 MHz for a time window 3.2 IceCube neutrino observatory 37

Figure 3.9: Average waveforms observed in a PMT for 3 ns laser light pulses with pro- gressively higher intensity. (a) Main peak; (b) secondary peak due to unusual electron trajectories, such as inelastic scattering on dynodes (late pulses); (c) pre-pulse; and (d) after-pulse. Figure from [107].

of 6.4 µs. In order to minimize dead time, one ATWD is available to capture signal, while the other is processing previously recorded charge signals. Raw IceCube data contain timestamped and digitized waveforms of the measured charge pulses. The average PMT waveform (e.g. in figure 3.9) is composed from individual waveforms that are caused by different processes within the PMT. The pre- pulse is ascribed to PEs ejected from the first dynode and thereby missing the first amplification step, thus, occurring some tens of ns earlier than the main peak. Pre-pulses are seen in less than 1% of the single-photo electron (SPE) rate [107]. This prompt response to a light pulse has a tail extending to about 100 ns after the initial rise of the main pulse (figure 3.9). After-pulses are seen in the range of 300 ns to 11 µs. Such pulses are attributed to ionization of residual gases by electrons accelerated in the space between dynodes [107]. Ions created in this way can be accelerated back to the photo-cathode, causing ejection of electrons which are subsequently amplified like the original PEs. In addition to these PMT effects, thermal electrons evaporate from the photo cathode and dynodes causing the dark noise of the PMT. Radioactive decays within the glass sphere are an additive component to the dark noise. The total noise rate of ‘standard’ IceCube DOMs is 650 Hz and for the HQ-DOMs in DeepCore it is 900 Hz. These noise pulses can not be distinguished from pulses caused by Cherenkov photons. As noise pulses occur randomly, coincidence conditions between adjacent optical modules help to reject noise pulses in data taking. 38 Chapter 3: Neutrino detection and the IceCube neutrino observatory

A DOM that records a hit sends a signal to the neighboring DOMs. This enables each DOM to check individually whether the detected hit fulfills the local coincidence (LC) condition, or if it is an isolated hit. For the generally used LC span 2 setting, it is required that there is an additional DOM hit within two neighboring DOMs of the initially responding DOM inside a maximum time window of 1000 ns. DOMs fulfilling this LC condition are tagged with a so-called hard local coincidence, HLC. DOMs that record a hit without being in LC to the next closest DOM, are isolated hits. These hits are often referred to as soft LC, SLC, hits, although they are in no ‘true’ coincidence. An SLC readout is reduced to only 3 samples of the first 25 samples of the fADC (the highest amplitude bin and its two neighbors), instead of the full fADC and ATWD information, as in the case of an HLC readout.

3.2.2 Data acquisition The IceCube trigger system is software based, because the DOM signals are already digitized. All DOM hits, as described in section 3.2.1, are sent to digital string processors (DSPs), one per detector string. The DSPs report all hits to a central trigger processor. If there is a minimum of 8 hit DOMs within 5 µs that fulfill the LC condition, IceCube is triggered. This basic trigger is called simple majority trigger (SMT-8). Once a trigger is found, the full waveforms from the digitizers are sent to the surface for all hit DOMs. Within the Deep- Core fiducial volume, consisting of the bottom 50 DOMs on all six Deep- Core strings plus the bottom 22 DOMs on the 7 surrounding IceCube strings (strings 26, 27, 35, 36, 37, 45, 46), a low threshold SMT trigger is applied for selecting low energy events. This SMT-3 trigger is based on HLC hits in the above defined DOM subset, requiring 3 hit DOMs within a 2.5 µs time window. A third trigger algorithm, the string trigger, is designed to increase the sensitivity for vertically up-going low energy events. It is also based on HLC hits and requires 5 hit DOMs among 7 adjacent ones on the same string, within a time window of 1 µs. If one or multiple triggers are recorded, a global trigger is formed, containing all relevant information of the sub-triggers within a trigger hierarchy e.g., trigger type, trigger time and trigger duration.

Data filtering and processing The DAQ trigger rate for the 79-string configuration is about 2.4 kHz. All triggering events are passed to the online processing and filtering (PnF) farm in the IceCube laboratory at the South Pole. During the PnF steps, all events undergo calibration, pulse extraction and basic event reconstruction, which in turn is used in a series of physics filters to select interesting events for analysis. The PnF rate totaled 160 Hz for IceCube-79, corresponding to a data volume of 70 GB per day. 3.2 IceCube neutrino observatory 39

Figure 3.10: Moon shadow analysis. (left) Contour plot of the value of ns for the on-source region. (right) Contour plot for the position of the minimum of the Moon shadow in data. The reconstructed position for the Moon shadow from the maximum likelihood analysis is shown as a black point, while the position of the Moon after accounting for magnetic deﬂection is shown as a white circle. Figure from [115].

3.2.3 Calibration The in-ice IceCube detector components are repeatedly checked in a series of quantitative measurements and their performance determined. This not only veriﬁes a stable detector performance, but improves the understanding of individual components in an attempt to further reduce systematic uncertainties.

The LED ﬂasher board is used for in situ time, charge and position calibrations of the DOMs within the detector array and measurements of the optical properties of the ice. The LEDs emit a calibrated light pulse that can be detected with receiving DOMs surrounding the emitter. The wavelength corresponds to the DOMs optical transition maximum. For a more detailed understanding of the wavelength dependence of the optical properties, a number of so-called color DOMs (cDOMs) were installed. Each cDOM is equipped with LEDs of four different wavelengths, corresponding to 340 nm, 370 nm, 450 nm and 505 nm. Cascade energy and vertex reconstruction is calibrated with in-ice laser modules (337 nm), using absolutely calibrated light output. Its well-known location and per-pulse energy is used to calibrate the detector and verify MC simulation.

The high statistics sample of observed minimum-ionizing CR induced muons are used to study relative DOM efﬁciency. This is done by looking at a sample of well reconstructed muons with energies below Eth passing close to a DOM, and using the average number of photons detected per track as a measure of the relative DOM efﬁciency [116]. This in situ method has the advantage that only very local ice properties, in particular those of the hole ice, affect the measurements. 40 Chapter 3: Neutrino detection and the IceCube neutrino observatory

This work relies heavily on the directional reconstruction capabilities of IceCube. In the absence of a ‘true’ astrophysical calibration source, the presence of a relative deficit in the flux of cosmic rays coming from the direction of the Moon may be used as a way of calibrating the angular resolution and the pointing accuracy. This effect, due to the absorption of cosmic rays by the Moon, was first predicted by Clark in 1957 [117] and was measured for the 59-string configuration [115]. The observed position of the shadow minimum shows good agreement with expectation, given the statistical uncertainties. Figure 3.10 (left) shows the fitted value of the number of shadowed events, ns, in a coordinate system that is characterized by a right ascension difference ∆α = (αµ αmoon)cos(δµ ) and a declination difference ∆δ = δµ δmoon with respect to the− nominal Moon position [115]. An important implication− of this observation is that any systematic effects introduced by the detector geometry and event reconstruction on the absolute pointing capabilities of IceCube are smaller than about 0.2 degrees, as indicated in the right figure 3.10. Part II: Search for dark matter annihilations in the Sun with the 79-string IceCube detector

4 Event simulation

In an effort to reduce the dependence on simulation and associated systematic errors, this work employs off-source data to estimate the background at all analysis levels. Background simulation is ‘merely’ used to verify accurate understanding of the detector. In this context, a good description of background components, verified against experimental data, affirms confidence in Monte Carlo (MC) signal simulations. The IceCube software framework (IceTray) contains modules for simulation, reconstruction, and analysis applications. All applications work as independent code units that can be individually improved, changed or developed. The simulation chain1 is divided into three main parts. First, particles are randomly generated according to a specific flux expectation and injected in the proximity of the detector. Second, created primary and secondary particles, including photons, are propagated through the detector medium accounting for all energy losses and particle interactions. Third, the detector response is simulated.

4.1 Event generators 4.1.1 Atmospheric background The dominant downgoing muon component is simulated using CORSIKA [118], including simulations of single and coincident air showers. The cosmic ray spectrum is generated following the poly-gonato model by Hörandel [119] with a primary energy spectrum roughly proportional 2.7 to E− . The simulation includes hadronic interactions in the Earth’s atmosphere, decays of unstable particles and secondary processes, such as ionization and scattering losses. Muons that do not reach the sensitive cylindrical volume of the detector are neglected.

The atmospheric neutrino background is generated with neutrino-generator, which is based on the ANIS event generator [120]. Simulations used in this work include all neutrino ﬂavors with 2 an energy spectrum proportional to Eν− . Events are propagated through Earth to the detector and interactions are simulated. The νµ and νe components of the atmospheric spectrum are weighted following the Honda ﬂux model [91].

1Simulation release V02-06-03 is used for all simulations 44 Chapter 4: Event simulation

Table 4.1: Details for atmospheric background simulation datasets.

dataset primary energy livetime dataset Nﬁle ice photon range (GeV) number model prop. 9 atm.νµ Eν [10,10 ] 50 y 6359 15 k SPICE-MIE ppc ∈ 9 ∼ atm.νe Eν [10,10 ] 150 y 7439 10 k SPICE-MIE ppc ∈ 11 ∼ atm.µ Epr [600,10 ] 11.6 d 6568 100 k SPICE-MIE ppc . ∈

For veriﬁcation and cross-checks, a dedicated simulation of atmospheric νs below 200 GeV was performed with GENIE [121]. Table 4.1 lists all atmospheric background datasets used in this analysis.

4.1.2 WIMP signal All signal simulations are made with WimpSim [122], which uses DarkSUSY [87] for the solar model, and Pythia [123]. The simulation describes the capture and annihilation of WIMPs inside the Sun and the consequent production, interaction, and propagation of neutrinos from the core of the Sun to the detector, including three-ﬂavor oscillations and matter effects. Neutrino oscillation parameters used for simulation are listed in table 4.2. The primary WIMP annihilation spectrum is very model dependent, owing to different branching ratios into SM particles. We approximately bracket the range of possible models by assuming 100% branching into two channels with very different characteristics. The ‘hard’ + + channel, χχ W W (τ τ below mχ = 80.4 GeV) and the ‘soft’ channel → − − χχ bb¯. For this work, WIMP masses ranging from 20 GeV to 5 TeV are simulated→ (table 4.3). Additionally, table 4.4 lists all systematic signal datasets, used in chapter 7.11. LKP annihilations in the Sun are simulated for LKP masses ranging from 250 GeV to 3 TeV. Neutrino-hadron interactions are simulated with nusigma [124], which uses the CTEQ6 [101] parton distributions for the CC and NC interactions for neutrinos and antineutrinos.

Table 4.2: Neutrino oscillation parameters for WIMP simulation.

Parameter Value

θ12 34.43◦ θ13 7.39◦ θ23 45.0◦ δ 0 ∆m2 7.59 10 5 (eV2) 12 × − ∆m2 2.43 10 3 (eV2) 13 × − 4.1 Event generators 45

Table 4.3: Signal simulation dataset details, listed by annihilation channel and WIMP mass (mWIMP). The number of generated files (Nfile) and number of generated annihilations per file (Ngen) are shown, along with simulation propagator details.

mWIMP Channel Nﬁle Ngen ice-model photon (GeV) (1 106) prop. + × 20 τ τ− 100 1 SPICE-MIE clsim + 35 τ τ−, bb¯ 100, 200 1 SPICE-MIE clsim + 50 τ τ−, bb¯ 100, 200 1 SPICE-MIE clsim + 100 W W −, bb¯ 50, 200 1 SPICE-MIE clsim + 250 W W −, bb¯ 20, 100 1 SPICE-MIE clsim + 500 W W −, bb¯ 20, 100 1 SPICE-MIE clsim + 1000 W W −, bb¯ 20, 50 1 SPICE-MIE clsim + 3000 W W −, bb¯ 20, 20 1 SPICE-MIE clsim + 5000 W W −, bb¯ 20, 20 1 SPICE-MIE clsim 250 LKP 20 1 SPICE-MIE clsim 500 LKP 20 1 SPICE-MIE clsim 700 LKP 20 1 SPICE-MIE clsim 900 LKP 20 1 SPICE-MIE clsim 1100 LKP 20 1 SPICE-MIE clsim 1500 LKP 20 1 SPICE-MIE clsim 3000 LKP 20 1 SPICE-MIE clsim

The WimpSim output is a physical event corresponding to one annihilation process that results in a neutrino. It contains directional and energy information for the incoming neutrino, the created lepton and the resulting hadronic shower. The interaction vertices of all events are randomly placed inside an energy dependent cylindrical Volume (Vi), where the size is determined by the muon range. The number of corresponding physical events, Nphys, from Ngen Ngen generated annihilations, is given by Nphys = ∑i Viwi, where wi is the energy dependent simulation weight, given per annihilation and unit volume.

In order to determine detection efficiencies, we can calculate the effective volume, Veff, corresponding to an equivalent volume of 100% detection efficiency, which is defined for WIMP signal simulation using:

Ngen ∑i wiViδi 0 event not observed Veff = , where δi = (4.1) Ngen ∑i wi ( 1 event observed 46 Chapter 4: Event simulation

Table 4.4: Signal simulation dataset details, listed by systematic uncertainty, annihilation channel and WIMP mass (mWIMP). The number of generated files (Nfile) and the number of generated annihilations per file (Ngen) are shown, along with simulation propagator details. For more details on systematic uncertainties, see chapter 7.11.

systematic mχ Channel Nﬁle ice-model photon uncertainty (GeV) prop. Photon 20, 50 τ+τ , τ+τ 50, 50 − − WHAM! clsim + propagation 100, 1000 bb,¯ W W − 50, 10 spread in rel. 20, 50 τ+τ , τ+τ 50, 50 − − SPICE-MIE clsim + DOM sens. 100, 1000 bb,¯ W W − 50, 10 Absolut DOM 20, 50 τ+τ , τ+τ 50, 50 − − SPICE-MIE clsim + efﬁciency 100, 1000 bb,¯ W W − 50, 10

Likewise, the effective area (Aeff) corresponds to the equivalent area of a detector with 100% neutrino detection efﬁciency and can be calculated as,

Ngen ∑i wiViδi Aeff = n . (4.2) · Ngen i ∑i wi/σ(Eν ) i Here, n is the target number density of ice and σ(Eν ) the neutrino to muon cross-section, given by nusigma [124]. It is important to discriminate between neutrino and antineutrino when applying eq. 4.2, as the respective cross- sections differ substantially.

4.2 Particle propagators Propagation of charged particles through ice is simulated using Muon Monte Carlo (MMC) [104], accounting for stochastic and continuous energy losses (see section 3.1.2). Inside the detector sensitive volume, secondary particles of energies higher than 0.5 GeV are treated as individual particles.

The transport of photons emitted from these particles to the DOMs is performed using direct photon tracking [125], taking into account measured ice properties [108, 109]. Two ice models (SPICE-MIE and WHAM!) are considered, which differ in parameterization technique (more details in section 3.1.4). Traditionally, tracking of the photons in IceCube is performed with photonics [111]. Here, probability distribution functions for photons within the detector are created from large simulations for all initial and ﬁnal photon coordinates and directions, and for all possible arrival times. These are tabulated and then used during the simulation or reconstruction to estimate the mean number of photons arriving at given times. The actual number of photons is sampled from Poisson distributions with those means. 4.3 Detector response 47

0.25 MMC + PPC MMC + Clsim 0.2 GEANT4 + Clsim 0.15 MMC + Photonics

0.1

0.05 entries per event

0 200 400 600 800 1000 1.3 hit residuals (ns) 1.2 1.1 1 Ratio 0.9 0.8 0 200 400 600 800 1000 hit residuals (ns) Figure 4.1: Residual hit time distribution (see chapter 5.1 for deﬁnition) for untrig- + gered signal MC simulation (20 GeV τ τ−). The residual times are calculated with respect to the true muon track. (top) Comparison of four combinations of particle and photon propagator. (bottom) Hit residual ratio with respect to the combination (MMC+ppc), used as default within the Collaboration-wide background simulation datasets.

This simulation suffers from a wide range of binning artifacts, which become more or less pronounced for different particle energy. The linear interpolation between bins leads systematically to an overestimation of the number of emitted photons, except for light emitters very close to the receiving DOM (first 1-2 bins). For this low energy analysis, photonics overestimates the light yield, emitted from short muon tracks, and consequently leads to an overestimated signal efficiency. This is illustrated in figure 4.1, where + simulated time residuals from a 20 GeV τ τ− signal is compared for four different combinations of particle and photon propagator. Both available direct photon propagation codes, ppc and clsim, perform identically (figure 4.1). Thus, all signal simulation within this analysis are done using clsim, due to the superior input configuration, especially for systematic studies. The simulation cross check with GEANT4 [126] verifies particle propagation with MMC down to the lowest targeted energies.

4.3 Detector response The ﬁrst detector response simulation step constructs hits from photons that were propagated by clsim. Pulses associated with the propagated particle are created, as well as pulses for dark noise, pre-pulses and after-pulses. The number of pulses depend on the quantum efﬁciency and the effective DOM 48 Chapter 4: Event simulation area. In the next step, the response of the PMT and DOM mainboard electron- ics, including digitization steps, is simulated. Last, the IceCube trigger logic is applied and an IceCube event is created, which contains the same type of information as experimental data. 5 Event reconstruction and event observables

In order to use the recorded raw IceCube data for analysis, the photon arrival times and intensities at the DOMs are calculated and then fitted with various particle hypotheses. This allows one to derive event observables from the extracted time, intensity and particle-fit information, that in turn can be used to distinguish between signal and background. In this chapter, we first discuss how recorded DOM waveform features are extracted, and subsequently how this information is used to reconstruct the event. Lastly, the list of event observables used within the data analysis of chapter7 is defined.

5.1 Waveform calibration & feature extraction The raw DOM information contains time stamped and digitized waveforms of the measured PMT charge pulses (DOMLaunch). This information is given in ADC counts per digitizer bin. The calibration software (DOMCalibrator) performs baseline subtraction, ‘droop’ correction and translates ADC counts into the voltage equivalent. Each DOM has a unique baseline measured from in-situ DOM calibration data. The so-called ‘droop’ originates from a trans- former between HV supply and PMT, and causes the tails of the waveform to undershoot. The waveform features are extracted from the calibrated waveforms through an iterative unfolding method. In this step the full waveform is deconvoluted into single pulses, which resemble an SPE pulse shape. The pulse amplitude corresponds to the number of recorded photons and the leading edge time of the pulse is estimated as the initial photon arrival time. The leading edge is found by fitting a straight line through the segment of fastest ascent of the extracted pulse. The intersection point of this fitted line with the DOM baseline defines the leading edge time of the pulse. An example of such a feature extraction process is illustrated for one recorded IceCube waveform in figure 5.1. Feature extraction of SLC waveforms, which contain only three fADC bins (see section 3.2.1), is performed identically.

During the IceCube 79-string data taking period pulse information from all DOMs in HLC and SLC condition was available for event reconstruction. We refer to a single pulse with an associated extracted photon arrival time and 50 Chapter 5: Event reconstruction and event observables

220 Raw DOMLaunch 14 Calibrated Waveform 200 12 10 180 8 6 160

ADC counts 4

140 ADC voltage (-mV) 2 0 0 20 40 60 80 100 120 1100 1200 1300 1400 1500 bin number time (ns) (a) Decoding (b) Calibration

0.4 extracted pulses

0.3

0.2 charge (pe) 0.1

0 1120 1140 1160 1180 1200 1220 time (ns) (c) Feature extraction Figure 5.1: Example of a feature extraction process in IceCube data for one recorded waveform (ATWD example). (a) Decoding of the raw DOMLaunch, given in ADC counts per ATWD bin. The DOM baseline is indicated by the dashed line (b) The calibrated waveform after baseline subtraction is given in negative ADC voltage per time. (c) Full waveform (dashed) is deconvoluted into single pulses (color), which resemble an SPE pulse shape. The last deconvoluted pulse at 1340 ns is not shown. The leading edge of the ﬁrst extracted pulse (red) is indicated by the gray straight line. integrated charge, as a hit. Each DOM can record multiple hits in an event. A so-called channel is a DOM with hits in an event.

Noise cleaning It is fair to assume that HLC pulses are generally associated with a true physics event, due to the strict LC condition. This is in contrast to SLC pulses, which are dominated by noise. Extensive noise-cleaning studies have shown that one can gain up to 20% additional physics hits by including SLC pulses. 5.1 Waveform calibration & feature extraction 51

This additional information aids the directional reconstruction of signal and background, which in turn increases background rejection capabilities and improves the signal point spread function (PSF) overall. We use in this analysis two noise-cleaned pulse series. First, a pulse series based on classic radial- time (RT) pulse-cleaning. Here, a pulse is kept if there is another pulse within a specific time and distance in space, while isolated pulses are rejected. This pulse series is mainly used for veto decisions. Second, we use a more ag- gressive noise-cleaning, the so-called seeded-radial-time (SRT) cleaning. The SRT algorithm is based on the classic RT-cut, but not all pulses are checked for the RT-condition. Instead, one starts from a clean subset of pulses (a ‘seed’), namely HLC pulses. All ‘seed’-pulses are looped over and if an SLC pulse is found, that fulfills the RT-condition, it is added to the kept set of pulses. This is repeated iteratively until no more pulses are added. In this way SLC- pulses that are RT-compatible with the ‘seed’ are available for track fitting, whereas random noise pulses can be rejected. Studies show that this pulse series contains less than 2% of noise. The SRT-cleaned pulse series is used for directional reconstructions and forms the basis for most event observables, detailed in section 5.3. Additionally, a static time-window cut is applied on both cleaned pulse- series, rejecting pulses more than 4µs earlier or 10µs later than the event triggering time.

The hit time distribution Cherenkov photons, emitted along a particle trajectory, are subject to scattering in the ice. A residual time (tres) can be defined by the time difference between photons with no scattering and absorption, and the observed hit time (thit) as, n tres = thit tgeo = thit t0 + rgeo . (5.1) − − c tgeo is the expected arrival time of a photon, calculated along the geometrical path without scattering. The time residual is illustrated in figure 5.2. The Pan- del distribution [127] defines the probability density of observing a hit with tres at a closest distance, d, between track and hit DOM. The distribution ac- counts for scattering and absorption of photons in ice, and is parametrized as,

d (d/λs 1) ( /λs) t − τ − res (tres/τ +ctres/nλa+d/λa) p(tres,d) = · e− , (5.2) Γ(d/λs) · with the scattering time, τ = 557 ns, the absorption length, λa = 98 m, and the scattering length, λs = 33.3 m [127]. One shortcoming of equation 5.2 is that it only considers bulk ice properties, with constant λa and λs over depth. 52 Chapter 5: Event reconstruction and event observables

Emission point t 0 ,r 0 , E 0

c r geo

t hit t ,r , E  d i i i Photon path

Cherenkov light



Figure 5.2: Illustration of residual time (tres). Photons are emitted at emission point (t0,~r0,E0) and detected at thit (ti,~ri,Ei). The time difference between the actual indicated photon path (including scattering) and the straight line distance rgeo is deﬁned as tres.

5.2 Reconstruction algorithm line-fit The line-fit [128] first guess method estimates an initial track on the basis of hit times, ti. It ignores specific optical properties of the medium, as well as the geometry of the Cherenkov cone, and assumes photons to travel along a 1-dimensional line with constant speed v [129]. A χ2 variable can be defined by summing over all observed channels, N, N 2 2 χ = ∑(~ri ~r ~v ti) . (5.3) i − − · By minimizing χ2 the fit parameters~v and~r are obtained.

Likelihood track reconstruction The likelihood (llh) reconstruction algorithm determines a set of unknown track parameters, ~a, for a certain track hypothesis from a set of observed experimental values,~x, by minimizing the negative log-likelihood, logL (~x ~a), deﬁned as − | N L (~x ~a) = ∏ p(xi ~a) . (5.4) | i | p(xi ~a) is the probability density function of the independently measured com- | 1 ponents, xi, in units of ns− [129]. The track parameters ~a are

~a = (~r0, pˆ,t0,E0) with ~r0 = (x0,y0,z0) and pˆ = (θ,ϑ). (5.5) 5.2 Reconstruction algorithm 53

Table 5.1: Hit classes, deﬁned by the time residual.

class time interval in ns a [ 15;25] − b [ 15;75] − c [ 15;150] − d > 15 − e < 15 −

Here,~r0 is an arbitrary point along the track, t0 is the time at~r0, E0 is the event energy at~r0, and pˆ is the track direction (figure 5.2). Generally, we do not fit directly for the energy, E0, reducing the number of free parameters for track reconstruction to six. The Pandel distribution does not include electronic jitter, PMT noise and may also diverge at small tres when d < λs. This is corrected in the so-called patched Pandel distribution, where p(tres,d) is patched with a Gaussian function with a width σjit of the Gaussian set to match the jitter time of the PMT. Noise is accounted for with a constant probability to the distribution. The best fit track hypothesis with ~a parameters, given the set of N launches with tres,i and closest distance di with respect to ~a, is found by minimizing N ~ logL (~tres, d ~a) = ∑log p(tres,i,di ~a) . (5.6) − | − i |

The observed residual times, tres, of DOM hits can be used to estimate the goodness of the obtained llh-track, since the distribution of tres of photons emitted at a distance from the DOM is well known. The different classes of hits are summarized in table 5.1 and are (e.g.) referred to as direct hits of class b, etc.

Paraboloid fit The paraboloid reconstruction method [130] is additionally performed, to estimate the angular uncertainty of each event. Paraboloid fits a paraboloid to the likelihood function in the neighborhood of the best fit. The resulting one sigma confidence ellipse is represented by the axes σ1 and σ2. The llh-track 2 2 uncertainty, σpara, is calculated as σpara = (σ1 + σ2 )/2. Good track fits generally result in a narrow peak of the fittedq paraboloid and therefore have a small σpara.

Bayesian atmospheric muon fit The Bayesian llh-fit reconstruction uses the fact, that data are dominated by down-going atmospheric muons, as prior knowledge. It is based on the like- 54 Chapter 5: Event reconstruction and event observables lihood definition of the ‘standard’ llh-track reconstruction, as defined above. The Bayesian posterior becomes the product of the llh and a zenith angle dependent prior for a down-going atmospheric muon hypothesis, g(θ).

Finite track fit Finite Reco is a likelihood algorithm developed to analyze event topologies [131]. It aims to identify events with a neutrino interaction vertex within the detector. The likelihood of a muon to produce or not produce hits in the DOMs along the reconstructed track up-stream of an assumed starting point is determined. Maximizing this likelihood gives the location of the interaction vertex. Similar, one can find the location of the stopping point. For muon tracks there are four different shapes to be distinguished: Through going events (infinite tracks), starting or stopping events inside the detector, and fully contained events. The interaction vertex information and the likelihood ratio of a starting track relative to a through-going track hypothesis are used as classifiers to distinguish starting signal-like neutrino events from penetrating atmospheric muon background. This reconstruction performs best on the pulse series with classic RT noise cleaning.

5.2.1 Coincident event splitting In a detector with an instrumented volume of nearly 1 km3 multiple events may arrive in coincidence. Such coincidences may be composed of multiple background events, or signal neutrinos that arrive in coincidence with atmospheric background. In order to improve background rejection and retain these signal events, a set of topological criteria are applied to ‘split’ combined hit patterns into distinct sub-events. Pulses are considered to be topologically connected if the distance in the xy-plane is less than 300 m, the gap between pulses on one string is less than 15 DOMs wide, and the maximum deviation from the muon crossing time between the pulses is less than 1µs. Pulses that fail these criteria can be associated with sub-events. Sub-events are required to have a minimum multiplicity of ﬁve hit DOMs. If only one split pulse series is found, a check is made to see if it is the same ‘event’ as the full pulse series. The directions of the full and ‘split’ reconstructions are compared and the sub-event is discarded and the full event recovered, if the space angle is smaller than ten degrees. If two or more sub-events are found, they are processed in the same way as single events, and undergo all event reconstruction and selection steps in their own right. 5.3 Event observables 55

5.3 Event observables We use information from extracted and cleaned pulse series together with details from the reconstructed track fits to define the event observables, which are used within the data analysis of chapter7. The value logL (~tres, d~ ~a) (eq. 5.6) of the best fit will simply be referred to throughout− as llh-value. |

Nchan Number of hit DOMs (channels). Nchanfid Number of hit DOMs in fiducial region (all Deep- Core DOMs and IceCube DOMs> 19 on strings 26, 27, 35, 36, 37, 45, 46). Nchanveto Number of hit DOMs in detector outside of fiducial region (Nchan - Nchanfid). fid NchanDC Number of hit DOMs in fiducial DeepCore region (DeepCore DOMs> 10 and IceCube DOMs> 38 on strings 26, 27, 35, 36, 37, 45, 46). Nstr Number of hit strings. time-extension Time between first and last hit DOM of an event. z-extension The maximum separation in z coordinate of channels. z-travel Average drift of hits in z-direction from the first Nchan quartile of channels; ∑ (zi < z1quart >)/Nchan. i − finiteReco z Finite Reco reconstructed vertex position z coordinate. finiteReco xy The radial distance from string 36 of the Finite Reco reconstructed vertex position in xy plane. finiteReco-llh(start-inf) llh-value difference of best fit for a starting track vs. infinite track hypothesis. finiteReco-llh/Nchan llh-value of best fit for an infinite track hypothesis divided by degrees of freedom. rllh llh-value of best fit divided by degrees of freedom. Θzen Reconstructed zenith angle. Φazi Reconstructed azimuth angle. COGx(y,z) x, y or z-coordinate of the center of gravity of event. σpara Width of llh best fit found from a paraboloid estimation by the paraboloid reconstruction method. Ψreco(llh, linefit) Space angle between llh-fit and first guess algorithm; Consistency check between llh-fit and its seed. Θzen(COG, vertex) Zenith angle of the line between fitted llh-track vertex and center of gravity. σ(COGz) Spread of hit DOMs in z-coordinate.

Ndir,a(b,c,d) Number of hits in time residual class a (or b, c, d). Ldir,a(b,c,d) Largest distance along the track between direct hits of class a (or b, c, d). str Ndir,a(b,c,d) Number of strings with direct hits of time residual class a (or b, c, d). 56 Chapter 5: Event reconstruction and event observables

accumulation time Time at which 75% of total charge is accumulated. linefit-velocetyz Linefit (first guess) velocity component in z-coordinate. Bayes-llh llh-value of best fit weighted with a Bayesian prior for a down-going muon track hypothesis. ρav Average perpendicular distance from llh-track to hit DOMs. 6 Analysis method

This chapter discusses the analysis method that is used to estimate the number of dark matter induced signal events, µs, within the experimental data set. We will use hypothesis testing based on the space angle Ψ, the angle between the reconstructed track and the direction to the Sun. This method was successfully applied in previous IceCube analyses [1, 132] to derive limits on µs. Owing to the complexity of the method, systematic errors are not incorporated and are evaluated separately (see section 7.11 for details). Here, the method is described in the context of this solar dark matter search (chapter7), but it can be used for any set of signal and background probability distributions.

6.1 Probability densities

The probability distribution fs(Ψ) for signal is determined from each set of signal simulation. It is the distribution of the space angle between initial neutrino direction and reconstructed track direction, as simulated signal neutrinos always point to the exact Sun position. The probability distribution for background, fbg(Ψ), is found by computing Ψ between the reconstructed direction of recorded events and a scrambled Sun direction. The scrambled Sun position is found by sampling fake event times uniformly from the data-taking period, hereby keeping the true Sun direction blind. The time-scramble is repeated within the event sample in order to achieve a smooth background distribution. Figure 6.1 shows fs(Ψ) and fbg(Ψ) for all four ﬁnal event selections of this analysis (details in chapter 7.9). The general peaks in the background distributions around 20 and 140 degrees are phase space effects due to the zenith angle selection criteria.

6.2 Shape analysis Likelihood deﬁnition Using the above deﬁned probability distributions in signal and background, an expression for the combined probability density to observe Ψ for a single event when µ signal events are present within the total number of observed data events, Nobs, is given by, µ µ f (Ψ µ) = fs(Ψ) + (1 ) fbg(Ψ). (6.1) | Nobs − Nobs 58 Chapter 6: Analysis method

dataset WH dataset SL 0.008 0.007 signal scaled by 0.028 signal scaled by 0.196 0.007 0.006

0.006 0.005

Ψ 0.005 Ψ 0.004 0.004 0.003

pdf in 0.003 pdf in 0.002 0.002

0.001 0.001

0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Ψ (deg) Ψ (deg) dataset WL dataset WL(b) 0.008 signal scaled by 0.132 0.008 signal scaled by 0.224 0.007 0.007

0.006 0.006

0.005 Ψ Ψ 0.005

0.004 0.004

pdf in 0.003 pdf in 0.003

0.002 0.002

0.001 0.001

0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Ψ (deg) Ψ (deg) Figure 6.1: Distributions in Ψ for signal (color) and background (gray) for all four ﬁnal datasets WH, SL, WL and WL(b) (details in chapter 7.9). Example signal distributions are 1 TeV hard for dataset WH, 50 GeV hard for datasets WL and SL, 35 GeV hard for datasets WL(b) and scaled by the indicated factors to be better comparable to fbg(Ψ).

The likelihood of observing Nobs events at space angles Ψi is consequently given as the product of all individual event probabilities,

Nobs L (µ) = ∏ f (Ψi µ). (6.2) i |

Test statistic The test statistic chosen is the likelihood ratio (rank), L (µ) R(µ) = , (6.3) L (µˆ ) as proposed by Feldman and Cousins [133]. µˆ is the best ﬁt of µ to the observed distribution of angles Ψi, maximizing the likelihood. This results in L (µ) L (µˆ ) and also R(µ) 1 for all µ in the region of physical signal ≤ ≤ values of µ [0,Nobs]. ∈

Frequentist confidence intervals & critical region We want to define the confidence interval on the signal content µ at a confidence level (CL) 1 α as [ µα , µα ]. This interval is defined by Rα (µ) < − lower upper 6.2 Shape analysis 59

0 µ = 0 µ = 40 true true

-1 -ln(R90%(µ)) )) µ

-2 - ln(R(

-3

0 10 20 30 µ40 50 60 70 80 s Figure 6.2: The critical value ln(Rα (µ)) at the 90% CL derived from 10000 pseudo experiments for each value of µ (thin black line). The χ2 approximation is shown in dashed. Markers indicate ln(R(µ)) for two pseudo experiments; one background-only experiment with µtrue = 0 (solid) and one example including 40 signal events (circles).

R(µ). In order to infer the chosen conﬁdence interval, Npseudo pseudo experiments are performed for each value of µ. Within each pseudo experiment Nobs events are randomly drawn from the distribution of observed space angles f (Ψ µ) and the rank (R(µ)) is calculated. The lower α quantile of the | resulting distribution in R(µ) for every tested µ forms the critical region. Cal- culations are performed in terms of ln(R(µ)) and can be veriﬁed against a χ2 distribution with 1 degree of freedom using the lower α quantile,

2ln(Rα (µ)) = χ2(α,1). (6.4) −

Equation 6.4 is only valid in the Gaussian regime (Nobs ∞) and within the → asymptotic regions, i.e. well away from the physical boundaries of µ at 0 and Nobs. The 10% quantile of ln(R(µ)) at the 90% CL is shown in ﬁgure 6.2 together with the χ2 approximation.

Sensitivity Having constructed the critical region with α significance level, we can perform again a number of pseudo experiments, Nsens, to determine the median upper limit (sensitivity) at the 1-α CL on the number of signal events, µCL, under the assumption of no signal. We follow the same procedure as for finding the critical distribution Rα (µ). This time, events are sampled from the background-only distribution, f (Ψ 0). 10000 such pseudo experiments are | α performed, where the median value of the resulting µupper distribution defines 60 Chapter 6: Analysis method

µ90% Lower limits s -1σ +1σ Upper limits 103

102 sens N

1 0 10 20 30 µ 40 50 60 s α α Figure 6.3: Distributions of µlower and µupper of the conﬁdence interval at 90% CL for the example of 5000 background-only pseudo experiments. The median upper limit µ90% is marked by the vertical solid line. The 1σ statistical spread of µ90% is marked by the dashed vertical lines.

the sensitivity on µ. Figure 6.2 illustrates ln(R(µ)) for one such pseudo experiment with µtrue = 0 (solid markers) at the 90% CL. In addition, figure 6.2 shows the example of µtrue = 40 signal events (circles). In these examples, the 90% confidence interval is the region where ln(R(µ)) is above the critical value. The lower and upper bound of the confidence regions are given by the points of intersection of the two curves. Figure 6.3 is an example of a distri- α α bution of µupper (µlower) for dataset WH for a 1 TeV hard signal that is used to determine µCL for the background-only case. Also shown is the 1σ statistical spread on µCL.

Combined likelihood analysis for all event samples It is straight-forward to formulate a combined hypothesis test for all three final event samples of chapter 7.9, where it is essential that all three event selections are non overlapping and independent. This requirement is fulfilled in this work between winter and summer selections, and also between the final winter selections WH and WL (alternatively WL(b)). Each dataset j is characterized by, the effective volume, V j ; • eff the number of observed final events, N j ; • obs the detector livetime T j ; • live 6.3 Calculation of WIMP signal quantities 61

j the observed distribution of space angle, Ψi ; • j j and signal and background probability distributions, fs (Ψ) and f (Ψ). • bg The combined likelihood function is deﬁned as:

L (µ) = L1(µ1)L2(µ2)L3(µ3) 1 2 3 (6.5) Nobs 1 Nobs 2 Nobs 3 = ∏ f1(Ψ µ1)∏ f2(Ψ µ2)∏ f3(Ψ µ3) i i | i i | i i |

The individual µ j are deﬁned in equation 6.6 and are weighted by corresponding livetime and effective volume to fulﬁll the criterion µ = µ1 + µ2 + µ3.

T j V j µ = µ live eff (6.6) j 3 k k ∑ TliveVeff k=0 Using this expression for the likelihood function, we perform the same procedure as outlined in the sections above, to determine the sensitivity on µCL of the combined dataset.

6.3 Calculation of WIMP signal quantities Using the above described analysis method, lower and upper limits on the number of signal can be derived at α confidence. Here, we denote the up- CL CL per limit on the number of signal events by µs . This limit on µs is then converted to a limit on the observed volumetric flux of signal muons, the conversion rate, given for the combination of all three event selections in this work by, µCL ΓCL = s . (6.7) ν µ 3 → k k ∑ TliveVeff k=0 CL Γν µ can be related through DarkSUSY [122, 87], to a limit on the WIMP → CL annihilation rate in the Sun, ΓA . For better comparison to other experiments, limits on the neutrino flux (Φν+ν ) from the Sun, and the corresponding induced muon flux in the ice ( + ), both integrated above 1 GeV, are com- Φµ +µ− puted at the CL 1-α. Under the assumption of equilibrium between WIMP capture and CL annihilation in the Sun, limits on ΓA are converted into limits on the spin-dependent, σSD,p, and spin-independent, σSI,p, WIMP-proton scattering cross-sections, using the method from Ref. [134]. These limits are conservative as they are obtained by assuming the capture is dominated by either σSD,p or σSI,p. For all calculations a standard dark matter halo with a local density of 0.3 GeV/cm3 [99] and a Maxwellian WIMP velocity distribution with an RMS velocity of 270 km/s is assumed. Detailed effects of 62 Chapter 6: Analysis method diffusion and planets upon the capture rate are not factored in, as the simple free-space approximation [75] included in DarkSUSY has been shown to be accurate [135].

Limit calculation cross-check with Aeff

A full cross check of the above detailed limit calculation chain via Veff can be made, by using the averaged Aeff(mχ ) per signal simulation directly, to calculate the limit on the neutrino ﬂux Φν+ν from the Sun. The Φν+ν limit is given by, µCL ΦCL = s . (6.8) ν+ν 3 k k ∑ TliveAeff(mχ ) k=0

In equation 6.8 Aeff(mχ ) is given as the ﬂux averaged neutrino effective area of ν and ν. Φν and Φν can also be explicitly calculated. We use this second calculation to independently cross-check the obtained limits via equation 6.7. 7 IceCube 79-string data analysis

This analysis searches for muon neutrinos from dark matter annihilation in the center of the Sun with the 79-string conﬁguration of the IceCube neutrino telescope. Results from this work are presented and discussed in paper V. This analysis incorporates two signiﬁcant additions compared to previous work. Firstly, the search is extended to the southern hemisphere. This doubles the livetime of the analysis, but presents new challenges to reduce the down-going atmospheric muon background. Secondly, this analysis searches for neutrinos from WIMPs with masses (mχ ) as low as 20 GeV whereas past IceCube searches have only been sensitive from 50 GeV. In this context all analysis details are outlined to allow for this work to be reproduced in the future. Such detailed analysis information1 is crucial when combining this experimental dataset with future years of data in order to derive multi-year limits.

Analysis Strategy As illustrated in Fig. 7.1, the IceCube 79-string detector records O(1011) events per year from downward propagating muons, O(106) events per year from atmospheric neutrinos, and O(10) events per year or less from WIMP signal neutrino fluxes given the limits obtained in this work. The dominant background in this search consists of muons created in cosmic ray interactions in the Earth’s atmosphere. Based on distributions of event multiplicities and observables from signal simulations and experimental data, cuts are placed to reduce the content of atmospheric muon events. This is repeated within several analysis cut levels until the event selection is dominated by signal-like atmospheric neutrino events. Each level is designed to exploit characteristic differences between signal and background. The final step is a directional search comparing the observed number of events from the direction of the Sun with the background-only hypothesis. This analysis searches for signal neutrinos originating from potential WIMP masses (mχ ), ranging from 20 GeV to 5 TeV. Within this mχ -range, signal events can have very different event topologies in the detector. To accommo- date all expected event topologies within one single analysis, the full dataset is split into three independent non-overlapping event selections; first into two

1Additional technical details and information, e.g. data processing scripts and analysis code, is available for IceCube Collaboration members on the password protected IceCube wiki (https://wiki.icecube.wisc.edu/index.php/IC79_solarWIMP_analysis). 64 Chapter 7: IceCube 79-string data analysis

1 online-filter atm. µ total MC background 10-1

-2 data 10 MC-true Θ reconstructed Θ 10-3

atm. νµ+νµ 10-4 Rate in Hz

10-5 final sample 10-6 WIMP-limit flux 10-7 W +W - τ+τ- (1TeV) (50GeV) 10-8 -1 -0.5 0 0.5 1 cos(Θ) Figure 7.1: Zenith angle (cos(Θ)) distributions for data and simulation at several analysis levels in Hz. Reconstructed (solid) and MC-true (fine dashed) zenith angle distributions are shown for atmospheric muon (red) and neutrino (green) background at online-filter level and final event selection. Also shown is online-filter level data (solid markers) and the combined final data selection of WH, SL and WL data (circles). The total signal rate at final level (blue-solid) is scaled to match the limit on the number 90% of signal events (µs ). Signal within the up-going region (cos(Θ) < 0) corresponds to a 1 TeV hard WIMP. In the down-doing region (cos(Θ) > 0) a 50 GeV hard WIMP is shown. The difference between final and online-filter level for signal is determined by the selection efficiency of the analysis with respect to the chosen signal models. The particular zenith distribution shape of data at final level is due to the combination of all three independent event samples, which differ in energy and consequently in rate.

seasonal data streams, ‘summer’ and ‘winter’, when the Sun is above and below the horizon, respectively. The ‘winter’ dataset comprises two samples. The first sample (‘winter high-energy’ event selection, WH) has no particular track-containment requirement and aims to select upward-going muon tracks. The second sample (‘winter low-energy’ event selection, WL) is a low energy sample, with focus on starting or fully contained neutrino-induced muon tracks inside DeepCore. The ‘summer’ sample (‘summer low-energy’ event selection, SL) is a dedicated low energy event sample that uses the surrounding IceCube strings as an instrumented muon veto in order to select starting 7.1 Experimental dataset 65 neutrino-induced events within DeepCore. The event selection is carried out separately for each independent sample and the final search is conducted using the combined likelihood function defined in equation 6.5. Figure 7.3 illustrates this analysis strategy.

Blindness In order to avoid potential bias, a strict blindness criterion is imposed by scrambling the azimuthal position of the Sun in data. The true direction is unknown until the ﬁnal step, and the information is not used in any way in the event selection.

7.1 Experimental dataset This analysis uses 317 live-days of data taken between May 2010 and May 2011. During this period, the detector was operating in its 79-string configuration. The full dataset is split into two seasonal streams, where September 22nd 2010 and March 22nd 2011 mark the beginning and end of the summer dataset (details in table 7.1). We select first all ‘good’ data runs. A run is defined ‘good’ for which data was acquired in a standard physics data run configuration (not a test or calibration run) with the nominal or partial detector being active, provided the run satisfies a minimum length requirement. Large parts of this analysis rely on veto methods to reject down-going background. Inactive strings or segments of strings within the veto regions of the detector can result in a lower background rejection efficiency and consequently in an increased data rate. To ensure no such data runs are used in this work, the rate stability is tested for each run at early analysis levels L2 and L3. For runs to be included in the winter dataset (for which down-going veto is less crucial) the L3 rate is not allowed to deviate by more than 10% from the previous run within each selected filter stream. The summer dataset comprises the Deep- Core filter stream only. This filter depends strongly on the down-going veto efficiency and the L3 rate of runs is demanded to differ by less than 5% between runs. All data runs that satisfy the above criteria are shown at filter levels L2 and L3 in Fig. 7.2. A list of runs, which are removed due to the rate

Table 7.1: List of key dates and corresponding live-days for the experimental dataset.

season start date end date livetime winter 31/05/10, 23/03/11 21/09/10, 13/05/11 151.4 d summer 22/09/10 22/03/11 165.9 d total 31/05/10 13/05/11 317.3 d 66 Chapter 7: IceCube 79-string data analysis stability requirement, is given in table 7.2. The complete list of selected data runs is given in table 7.3.

35 DC filter (w) lowUp filter (w) 30 muon filter (w) all filter (w) 25 DC filter (s) 20 L2 filter rate (Hz)

3 15 ×10 116 116.5 117 117.5 118 2 Run number

1.5

0.5 L3 filter rate (Hz) 116000 116500 117000 117500 118000 run number Figure 7.2: Rate stability checks at analysis ﬁlter level L2 and L3.

Table 7.2: List of data runs removed because of rate instabilities.

season data run number winter 116332, 116353, 116354, 116376, 116378, 116394, 116396,118031, 118080, 118106, 118168 summer 116692, 116915, 116916, 117247, 117436, 117450, 117458,117632, 117690, 117751, 117754, 117769, 117886, 117912,117914

7.2 Online filter level Events triggering the IceCube detector (see section 3.2.2) are processed and subjected to online filters at the South Pole IceCube lab. First, all events undergo calibration, pulse extraction and noise-hit cleaning. Photon arrival times and intensities at the DOMs are calculated and then fitted with a muon track hypothesis (see chapter5). Only events that pass at least one physics filter are transmitted via satellite and available for further analysis. Filters are developed in advance for each physics data year and applied to enhance the content of signal-like muon events above the dominant atmospheric muon background. Within the online filter level, events are required to have passed at least one or more of the filters relevant for this analysis: the muon-filter, the 7.2 Online filter level 67

Table 7.3: Complete list of data run numbers used in analysis.

115986-115996 116608-116610 117250 117719 116011-116012 116660-116670 117258-117260 117721-117723 116020-116037 116672-116679 117262-117265 117744-117746 116039-116051 116681-116682 117268-117270 117748-117750 116054-116059 116693-116722 117273-117275 117753 116064-116092 116724-116730 117280-117292 117755-117762 116095-116108 116751-116766 117303-117309 117764-117767 116110-116129 116778-116779 117311-117323 117770-117771 116131-116132 116781 117331-117332 117773-117774 116136-116137 116794 117351-117356 117776-117786 116142-116148 116796-116800 117359 117788 116155 116802-116804 117370-117373 117790 116160-116169 116806-116831 117382 117793-117800 116172-116176 116836-116843 117399-117403 117802-117811 116178-116180 116846 117407 117813-117816 116192-116196 116848-116858 117409 117818-117819 116198-116200 116874 117412-117417 117824 116210-116211 116876-116877 117435 117827-117828 116214-116223 116882-116895 117437 117830-117864 116232 116897-116898 117438 117866-117867 116239 116916-116920 117441-117442 117870-117885 116243-116246 116956 117446 117888-117891 116258-116287 116964-116965 117448-117449 117894-117902 116289-116294 116967-116972 117451 117907 116296-116297 117006-117008 117457 117909 116302-116305 117014-117015 117459 117911 116307-116314 117019 117461 117915-117916 116333 117024-117028 117472-117476 117925 116338 117030-117031 117480 117927-117942 116340 117035 117482-117483 117944-117951 116342-116352 117037-117043 117487 117956-117967 116355-116362 117046-117049 117490 117972-117978 116368-116369 117052-117060 117503 117992-118000 116371-116375 117072-117086 117525-117526 118002-118004 116379-116393 117094-117096 117545 118011-118013 116397 117098-117103 117568-117569 118018-118023 116400-116401 117105 117576-117578 118029-118030 116451-116472 117107 117593-117595 118040-118042 116481-116487 117108 117602 118049-118059 116489-116495 117113-117122 117610-117612 118062-118067 116498-116500 117127-117128 117630-117631 118072-118074 116502-116512 117154 117635 118082-118083 116516 117209-117211 117637-117639 118089-118101 116518-116534 117214-117215 117664-117672 118113 116536-116556 117234-117235 117678 118115-118120 116558-116583 117237-117246 117680-117682 118130-118167 116603-116606 117248 117691-117714 118169-118173 68 Chapter 7: IceCube 79-string data analysis

Table 7.4: Summary of all selected online ﬁlters. Acceptance criteria and considered triggers are detailed.

ﬁlter selection criteria considered trigger

muon Nchan > 8, Θzen > 78.5◦ SMT-8 llh/(Nchan 2) 8.1 − ≤ LowUp Nchan 4, Θzen > 80 SMT-3, SMT-8, String ≥ ◦ z-extension < 600 m, z-travel > 10 m time-extension < 4000 ns DeepCore veto all ‘particle’ speeds [0.25;0.4] (m/ns) SMT-3

LowUp-filter and the DeepCore-filter. These three filters are described in the following sections.

Muon filter The muon-filter is developed with the aim of providing a sample of muons useful for analyses over the whole sky. The sky is divided in two different zenith regions, a down-going and up-going region. For this analysis only the up-going stream of this filter is relevant. This stream exclusively considers events triggering SMT-8 and has additional acceptance criteria, summarized in table 7.4.

Low energy up-going event filter (LowUp) This filter is designed particularly for this analysis, selecting all low energy muon track-like events with an up-going track reconstruction within IceCube. It is the only selected filter that accepts events triggering all three operational trigger algorithms. In addition to the filter criteria listed in table 7.4, the filter imposes two mild vetoes. A top veto, allowing no hit DOMs within the upper-most five DOM layers on standard IceCube strings, and an inner-string criterion, which requires at least one inner-string to be part of the event. Inner- strings are defined as all strings that are not contained within the single outermost string layer.

DeepCore filter The filter algorithm applies a simple veto to reject down-going cosmic ray muon background. The algorithm looks at hit DOMs inside and outside Deep- Core separately. The center of gravity (COG) of hit DOMs inside DeepCore is determined and compared to each surrounding hit DOM (IceCube), assuming the hypothesis that the outside hit is caused by direct, unscattered photons from a particle passing through the DOM. This is used to calculate the speed 7.3 Filter level L2 69 at which the particle would need to travel to reach the COG from the DOM given the relative SMT-3 trigger time. ‘Particle’ speeds greater than zero are associated with DOMs that occur prior to the time determined for the COG and are an indication of a muon passing through the detector when the ‘particle’ speed is near the speed of light. A ‘particle’ speed cut window is defined that removes all events that have one or more hit DOMs with related velocities between 0.25 and 0.40 m/ns.

7.3 Filter level L2 Level L2 corresponds to the collaboration-wide mass off-line processing carried out on all transmitted data. No cuts are applied beyond filter level. Data are again calibrated, raw waveforms are feature-extracted and obtained pulses are subjected to noise cleaning (see chapter5). The cleaned pulse-series is then fitted with a line-fit, which is used as a track seed for the llh-fit. No further analysis cuts are applied at this level and all pulse-series and track fitting information is stored for higher analysis cut levels. 2

7.4 Analysis specific data processing The L2 data processing for the 79-string dataset contains no effective treat- ment of signal neutrinos that arrive in coincidence with atmospheric background. In order to retain these signal events, a set of topological criteria are applied to ‘split’ combined hit-DOM patterns into distinct sub-events, as discussed in section 5.2.1. This sub-event splitting step is applied twice within the data processing chain. First, as an additional L2 processing step, in order to retain all possible signal content at this early analysis step. Second, together with higher level reconstructions within the WIMP analysis stream specific L3 data processing. Double processing was necessary as a minor bug within the SRT logic had been found within L2 after the completion of the collaboration- wide processing. Additionally, new more accurate geometry calibration data were available for L3. Cut efficiencies for the analysis were checked for data based on L2 and a ‘corrected L2’ processing. The difference was found to be negligible and we decided to proceed with existing L2 data. All events passing L3 cuts undergo updated calibration and corrected noise-cleaning. In addition to fits contained in L2, two high-level reconstructions are applied. A paraboloid fit to all llh track-fits and a llh-fit with a Bayesian prior for a down-going muon track hypothesis. The latter is performed for all events with a reconstructed zenith angle greater than 90 degrees.

2This low energy analysis uses the original L2 processing and it was decided against using the reprocessed data set (L2’). The reprocessing was motivated by discrepancies in high energy events which are alleviated by using more sophisticated calibration techniques. 70 Chapter 7: IceCube 79-string data analysis

IceCube 79 Level 2 data ~ 160 Hz

additional L2 processing

Summer data, SL (L3 cuts) Winter data (L3 cuts) ~ 1.4 Hz ~ 1.73 Hz

L3 processing L3 processing (higher level reconstructions) (higher level reconstructions)

SL L4 cuts WL L4 cuts WH L4 cuts ~ 160 mHz ~ 80 mHz ~ 110 mHz

SL L5 cuts WL(b) & WL L5 cuts WH L5 cuts ~ 0.26 mHz ~ 0.16 / 0.11 mHz ~ 1.48 mHz

Combined likelihood analysis of SL, WL and WH data selections

Figure 7.3: Analysis ﬂowchart into SL, WH and WL data streams. Note, that within the WL selection at L5 a second alternative event selection, WL(b), is also applied. This sample has an even stronger focus on the lowest mχ -signal models. For a given signal model WL or WL(b) have to be chosen within the ﬁnal combined likelihood analysis.

7.5 Filter level L3 At analysis level L3 the full data set is split into two non-overlapping seasonal event selections. The ‘summer’ event sample corresponds to the time when the Sun is above the Horizon at the South Pole and the ‘winter’ sample to the time when it is below. All data runs between run number 1176562 (September 22) and 117930 (March 22) make up the ‘summer’ event selection. Within each seasonal stream, L3 specific acceptance criteria are applied and outlined below. The main focus at this filter level is a data reduction of order 100 from L2, while maximizing the signal efficiency. Starting with L3, coincident events are topologically split into sub-events (see section 7.4) and individually tested against the acceptance criteria. If one or possibly more split events pass the acceptance criteria, the event passes. In the case of non-split events, cuts are directly applied.

7.5.1 L3, summer event selection For the L3 summer sample, we consider events passing the DeepCore ﬁlter stream only. Cuts are placed on hit multiplicity and the vertical extension of the event. Information on the reconstructed vertex position from Finite Reco is used to identify neutrino induced starting muon events inside the detector. 7.6 Filter level L4 71

Table 7.5: Summary of L3 acceptance criteria.

event selection selection criteria ‘summer’ Nchan > 5, Nstr > 1, z-extension < 400 m, z-travel > 50 m, ﬁniteReco z < 200 m, − − ﬁniteReco xy < 400 m − str ‘winter’ Nchan > 6, Nstr > 1, Ndirc > 0, Ndirc > 1, z-travel > 25 m, rllh < 22, − 85◦ < Θzen < 120◦

(DeepCore) 85◦ < Θzen < 160◦, keep events with [ Nchanfid >= 8 DC ∨ Nchanfid /(Nchan - Nchanfid )> 4 z-travel> 40 m ] DC DC ∨ −

Cuts applied in L3 are detailed in table 7.5. In addition, a top veto is imposed, demanding no hit DOMs in the upper 14 DOM layers on standard IceCube strings.

7.5.2 L3, winter event selection Events are selected from all three online ﬁlters listed in table 7.4 and required to have a successful track llh reconstruction with an upward going zenith angle, minimum hit multiplicity for good llh-ﬁts, and cuts on several event observables listed in table 7.5. These criteria are relaxed for DeepCore events with more than 8 hit DOMs inside DeepCore and a ratio of DeepCore hits compared to non-DeepCore hits larger than 4, to also accept events with a zenith angle up to 160◦.

7.6 Filter level L4 Signal-efﬁcient event selection for low-mass WIMP signals and high-mass WIMP signals is only feasible by imposing different selection criteria. As a result, cut-level L4 splits the ‘winter’ dataset into WH and WL event selections. For events to be included in event selection WL, we demand that the number of hit DOMs inside DeepCore be larger than outside. Additionally, the number of outside hits must be less than seven. This ensures that events with a long lever arm and therefore good angular resolution are assigned to the complement sample. The step is well motivated when looking at the event topology of the two classes of muon events that are selected for each event sample. Selection WH, deﬁned as the complement of WL, contains high energy events with no containment requirement. Associated muon tracks have accurate track reconstructions and good associated quality parameters. This is used to separate true up-going muon-like events from mis-reconstructed 72 Chapter 7: IceCube 79-string data analysis

WH WL 10-4

10-5 Rate in Hz

10-6

1 2 3 4 5 log10( Eν / GeV )

Figure 7.4: True neutrino energy (Eν ) distributions from simulation for the atmospheric neutrino ﬂux at L4 in Hz. WL and WH event selections show a clear separation in Eν . atmospheric muons, which will exhibit lower quality parameter values. The DeepCore dominated WL selection consists of shorter track-like events, with in general lower track reconstruction quality, but extremely good containment. In this context this dataset split is an obvious choice for a hybrid detector con- ﬁguration to create two independent data samples. Figure 7.4 shows the clear separation into a low and high energy event sample for the example of atmospheric neutrinos at L4 after applying the split criteria. The L4 selection imposes further requirements for each of the three datasets, SL, WH and WL, that are outlined in the following sections and listed in table 7.6.

7.6.1 L4, SL event selection For events in the SL selection, L4 criteria exclude events with very ‘poor’ quality parameters, as such events are not suitable for point-source analyses. We remove events reconstructed outside an extended on-source zenith region. The cut on the estimated angular uncertainty reflects the broadened signal point spread function at low energies. In addition to the cuts listed in table 7.6, a tight hit-time containment criterion to reject down-going events is imposed. The hit-time criterion is that the first hit in the veto region must be later than the fourth hit within the fiducial region.

7.6.2 L4, WH event selection Events that fulﬁll the WH selection criteria undergo a series of additional, stricter cuts on the same variables as in the initial ‘winter’ L3 selection. Here, we demand higher hit DOM and string multiplicities for the selected events 7.7 Multivariate event classiﬁcation 73

Table 7.6: Summary of L4 acceptance criteria.

event selection selection criteria

SL Nchan > 9, Nstr > 2, σpara < 25◦,

65◦ < Θzen < 100◦

WH Nstr > 2, rllh < 13, σpara < 10◦, z-travel > 15 m, rllh < 22, Ψreco(llh,lineﬁt) < 45 , − ◦ 88◦ < Θzen < 120◦, COGz< 425 m, (WH-veto) (COGx< 400 m COGx> 500 m) COGz< 420 m − ∧ ∨ − (WH-veto) (COGy< 400 m COGy> 400 m) COGz< 420 m − ∧ ∨ − WL 88◦ < Θzen < 130◦, z-travel > 20 m, σpara < 25 − ◦

as expected for TeV-energy muon tracks. In this context events are removed if they have poor estimated angular uncertainty or show inconsistent fit results between the reconstructed direction of the llh-fit and first guess fit. This fit stability between llh-seed and llh-fit is tested with the space-angle distribution between the two reconstructions, Ψreco(llh,linefit). A careful study of data events in the event viewer indicates that a large fraction of background events are in the outermost row of strings and at the bottom edges of the detector array. Three moderate containment criteria are applied in L4: First, the inner-string-criteria as defined in the LowUp-filter (see section 7.2). Second, a shallow top veto and, third, a bottom-edge detector veto (table 7.6).

7.6.3 L4, WL event selection The data rate in the WL event selection is already strongly reduced, as the ‘dataset split’ criteria imply very strong containment requirements. For consistency with the summer low energy selection, events not suitable for point- source analyses are removed (table 7.6). As the WL selection focuses on events contained in DeepCore, no hit DOMs are accepted in the ten upper- most layers of DOMs on the regular (non-DeepCore) strings.

7.7 Multivariate event classification The final background reduction utilizes one Boosted Decision Tree (BDT) for each dataset. Decision trees are a series of linear cuts on selected variables (one at a time), until a stop criterion is fulfilled. In this process, the multidi- mensional phase space spanned by the variables, is split into many regions that are classified as signal or background-like, depending on the majority of training events that end up in a final leaf node. In a BDT, this concept is ex- 74 Chapter 7: IceCube 79-string data analysis

Table 7.7: Datasets used in TMVA training and testing.

event statistics event selection dataset details total (training) SL (Bg) August data runs 372077 (330000) + + (Sig) W W −& bb(100 GeV), τ τ−(50 GeV) 32527 (25000) WH (Bg) October data runs 304971 (250000) + (Sig) W W − 1000 GeV 28712 (25000) WL (Bg) October data runs 217676 (200000) + + (Sig) W W −& bb(100 GeV), τ τ−(50 GeV) 34330 (30000) tended from a single tree to a series of trees (forest). Each tree is derived from the same training event ensemble by reweighting events based on their previous classification. The final output, BDT score, is an average of all individual decision trees and ranges from values 1 to 1 for most background-like to signal-like, respectively. For training and− testing an independent, high statistics set of signal simulations is used, and discarded afterwards. This multivariate analysis is data driven for background and uses one month of experimental data recorded when the Sun was not within the analysis region. Details about the datasets used in the BDT training step are listed in table 7.7. The BDT algorithm implemented within the Toolkit for Multivariate Data Analysis [136] (TMVA) within the data analysis framework ROOT [137] is used. Through an iterative process, individual variables are removed and added and the BDT’s performance evaluated, until we arrive at a final set of 14 variables in selection WH and ten in selections WL and SL. In this process, the signal cut efficiency at a specific set background level (99% data reduction) is used as a criterion to measure the quality of the tested combination of variables. The dimensionality of the BDT is kept as low as possible. All input distributions for simulated background and data are required to have adequate agreement and are discussed and shown in the sections below. Correlated input variables reduce the final signal cut efficiency strongly. In this context training the BDTs with decorrelated input variables is investigated. Variable decorrelation is equivalent to a coordinate transformation (rotation). Further BDT parameter optimization is performed on the total number of trees and the level of pruning. Pruning is the process of cutting back a tree from the bottom up to remove statistically insignificant nodes and thus reduce the overtraining of the tree.

7.7.1 SL event selection In the low energy selection SL a BDT is trained to differentiate neutrino induced starting tracks within DeepCore from down-going muon background penetrating the detector. The summed spectra for three low WIMP masses is 7.7 Multivariate event classification 75 chosen to adequately represent signal in the BDT training. The ten variables chosen to characterize signal and background are shown in figures 7.5 and 7.6. They describe direction, hit multiplicity of direct hits, the degree of containment and the vertical and lateral extension of the event within the detector. The Finite Reco track reconstruction variable is a llh-value difference of the best fit for a starting track compared with an infinite track hypothesis. The SL BDT output distribution is shown in figure 7.12 (top). This dataset has very good agreement between data and MC within the whole parameter range. A clear identification of neutrino candidate events within the signal-like region is more challenging within this down-going event sample.

10-2 10-2

10-3 10-3

10-4 10-4 Rate in Hz Rate in Hz

-5 10-5 10

10-6 10-6 0 20 40 60 80 0 1000 2000 3000 4000 Ndir, b accumulation time (ns) (a) Number of hits in time residual class b. (b) Time till 75% of total charge is accumulated.

-2 10-2 10

-3 10-3 10

-4 10-4 10 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 -0.2 -0.1 0 0.1 0.2 -100 -50 0 50 100 linefit-velocetyz Z-travel (m) (c) Lineﬁt (ﬁrst guess) velocity component (d) Average drift of hits in z-direction. in z-coordinate. Figure 7.5: Distribution of observables for event selection SL used as input for training the BDT at L4. A 50 GeV hard signal (solid-blue) is chosen for signal simulation. Experimental data (points), µatm (dotted-red), νatm (dashed-green) and total MC background (band-gray) are shown. The thickness of the gray band represents the statistical uncertainty in the MC simulation only. 76 Chapter 7: IceCube 79-string data analysis

-2 10 10-2

-3 10 10-3

10-4 10-4 Rate in Hz Rate in Hz 10-5 10-5

10-6 10-6 0 50 100 150 0 50 100 Θ σ zen(COG, vertex) (deg) (COG z) (m) (a) Zenith angle of the line between ﬁtted (b) Spread of hits in z-coordinate. llh-track-vertex and center of gravity.

10-2 10-2

10-3 10-3

-4 10 10-4 Rate in Hz Rate in Hz -5 10 10-5

10-6 10-6 60 80 100 0 50 100 Θ zen (deg) finiteReco-llh(start-infinite) (c) Reconstructed zenith angle. (d) llh-value difference of best ﬁt for a starting track vs. inﬁnite track hypothesis.

10-2 10-2

10-3 10-3

10-4 10-4 Rate in Hz Rate in Hz

-5 10 10-5

10-6 10-6 0 2000 4000 6000 0 200 400 600 800 time extension (ns) Ldir, c (m) (e) Time between ﬁrst and last hit of an (f) Largest distance along the track between event. direct hits of class c.

Figure 7.6: As ﬁgure 7.5, for the remaining four variables. 7.7 Multivariate event classiﬁcation 77

7.7.2 WH event selection This event selection consists of the highest energy events within this analysis. Signal candidate events have values of quality parameters indicating successful reconstruction. These are used to separate up-going muon-like events from mis-reconstructed atmospheric muons. 14 variables are selected that have strong separation power between signal and background (A simulated 1 TeV signal is used for training). They describe direction, track quality and hit multiplicity of direct pulses. In addition a llh-value from the Bayesian fit reconstruction and a Finite Reco track reconstruction variable are added. This Finite Reco track variable is defined by the llh-value of the best fit for an infinite track hypothesis divided by the number of degrees of freedom. The value is calculated from the individual probability densities of all hit DOMs as well as non-hit DOMs within a cylinder around the reconstructed track. For mis-reconstructed events, this cylinder will not enclose all hit DOMs associated with the event. Consequently, the llh-value will be larger than for well reconstructed events. The COGx- and COGy-coordinates are also included, as signal events have values closer to the origin, whereas background events are more concentrated at the outer detector region. All distributions have very good shape agreement between data and µatm background simulation, but show a constant rate offset of a factor 1.5 (figures 7.7, 7.8 and 7.9). This is also reflected in the BDT output distribution in figure 7.12. This offset is attributed to mis-reconstructed events, which are difficult to simulate. At high BDT score values (very signal-like events) atmospheric neutrino events dominate. Here, not only the shape between data and simulation is in good agreement, but also the total rate.

10-2

10-2 10-3

10-3

10-4 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 0 20 40 60 80 0 50 100 150 Θ Ndir, b zen(COG, vertex) (deg) (a) Number of hits in time residual class b. (b) Zenith angle of the line between ﬁtted llh-track-vertex and center of gravity. Figure 7.7: Distribution of observables for event selection WH used as input for training the BDT at L4. A 1 TeV hard signal (solid-blue) is chosen for signal simulation. Experimental data (points), µatm (dotted-red), νatm (dashed-green) and total MC background (band-gray) are shown. The thickness of the gray band represents the statistical uncertainty in the MC simulation only. 78 Chapter 7: IceCube 79-string data analysis

-3 10 10-3

10-4 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 -500 0 500 -500 0 500 COG x (m) COG y (m) (a) x-coordinate of center of gravity. (b) y-coordinate of center of gravity.

-2 10 10-2

-3 10 10-3

10-4 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 0 1000 2000 3000 4000 0 50 100 150 200 accumulation time (ns) Z-travel (m) (c) Time at which 75% of total charge is ac- (d) Average drift of hits in z-direction. cumulated.

10-2 10-3

10-3

10-4 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 0 10 20 30 40 90 100 110 120 str Θ Ndir, a+b+c zen (deg) (e) Number of strings with direct hits of (f) Reconstructed zenith angle. classes (a+b+c).

Figure 7.8: As ﬁgure 7.7, for six additional variables. 7.7 Multivariate event classiﬁcation 79

-2 10-2 10

-3 10-3 10

-4 10-4 10 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 0 10 20 30 40 50 6 8 10 12 14 Ψ reco(Llh, linefit) (deg) rllh (a) Space angle between llh-fit and first (b) llh-value of best fit divided by degrees of guess algorithm. Check of consistency be- freedom. tween llh-fit and its directional seed.

-2 10-2 10

-3 10-3 10

10-4 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 -25 -20 -15 -10 -5 0 5 10 σ finiteReco-llh/Nchan para (deg) (c) llh-value of best fit for an infinite track (d) Width of llh best fit found from a hypothesis divided by degrees of freedom. paraboloid estimation.

-2 10 10-2

-3 10 10-3

-4 10 10-4 Rate in Hz Rate in Hz

10-5 10-5

10-6 10-6 0 200 400 600 800 1000 0 500 1000 Bayes-llh Ldir, c (m) (e) llh-value of best ﬁt weighted with a (f) Largest distance along the track between Bayesian prior for a down-going muon track direct hits of class c. hypothesis. Figure 7.9: As ﬁgure 7.7, for six additional variables. 80 Chapter 7: IceCube 79-string data analysis

7.7.3 WL event selection The WL BDT is trained on the same combination of three low mass WIMP signals as the SL event selection. The ten variables chosen to characterize signal and background are shown in ﬁgures 7.10 and 7.11. They are similar to the WH selection variables and describe direction, track quality and hit multiplicity of direct pulses, but also the vertical and lateral extension of the event within the detector. All input distributions are in very good agreement between data and MC. This agreement is seen within the BDT output distribution in the bottom plot of ﬁgure 7.12. The transition from atmospheric muon background to atmospheric neutrinos in data is clearly visible for high BDT scores.

10-2 10-2

-3 10-3 10

-4 10-4 10 Rate in Hz Rate in Hz

-5 10-5 10

10-6 10-6 0 20 40 60 0 5 10 15 20 25 str Ndir, b Ndir, a+b+c (a) Number of hits in time residual class b. (b) Number of strings with direct hits of classes (a+b+c).

10-2

10-3 10-3

10-4 10-4 Rate in Hz Rate in Hz 10-5 10-5

-6 10-6 10 0 100 200 300 0 50 100 ρ (m) av Z-travel (m) (c) Average perpendicular distance from llh- (d) Average drift of hits in z-direction. track to hit DOMs. Figure 7.10: Distribution of observables for event selection WL used as input for training the BDT at L4. A 50 GeV hard signal (solid-blue) is chosen for signal simulation. Experimental data (points), µatm (dotted-red), νatm (dashed-green) and total MC background (band-gray) are shown. The thickness of the gray band represents the statistical uncertainty in the MC simulation only. 7.7 Multivariate event classiﬁcation 81

-3 10 10-3

-4 10 10-4 Rate in Hz Rate in Hz 10-5 10-5

10-6 10-6 0 50 100 150 0 50 100 Θ σ zen(COG, vertex) (deg) (COG z) (m) (a) Zenith angle of the line between ﬁtted (b) Spread of hits in z-coordinate. llh-track-vertex and center of gravity.

10-3 10-3

10-4 10-4

Rate in Hz -5 Rate in Hz 10 10-5

10-6 10-6 90 100 110 120 130 0 10 20 Θ σ zen (deg) para (deg) (c) Reconstructed zenith angle. (d) Width of llh best ﬁt found from a paraboloid estimation.

10-2 10-2

10-3 10-3

10-4 10-4 Rate in Hz Rate in Hz 10-5 10-5

10-6 10-6 0 200 400 600 0 200 400 600 Bayes-llh Ldir, c (m) (e) llh-value of best ﬁt weighted with a (f) Largest distance along the track between Bayesian prior for a down-going muon track direct hits of class c. hypothesis.

Figure 7.11: As ﬁgure 7.10, for six additional variables. 82 Chapter 7: IceCube 79-string data analysis

event selection SL (summer, low energy) 10•2

10•3

10•4

10•5 Rate in Hz

10•6

10•7 2 •0.8 •0.6 •0.4 •0.2 0 0.2

(data / MC) •0.8 •0.6 •0.4 •0.2 0 0.2 BDT output score event selection WH (winter, high energy) 10•2

10•3

10•4 Rate in Hz 10•5

10•6 2•0.6 •0.5 •0.4 •0.3 •0.2 •0.1 0 0.1 0.2

(data / MC) •0.6 •0.5 •0.4 •0.3 •0.2 •0.1 0 0.1 0.2 BDT output score event selection WL (winter, low energy) 10•2

10•3

10•4

10•5 Rate in Hz

10•6

10•7 2 •0.6 •0.4 •0.2 0 0.2

(data / MC) •0.6 •0.4 •0.2 0 0.2 BDT output score

Legend: measured data sum of atm. backgrounds

atm. νµ+νµ background (Honda 2006) atm. µ background WIMP signal (scaled to data rate) Figure 7.12: BDT output distributions for the summer (top), the winter ‘high energy’ (middle) and the winter ‘low energy’ (bottom) selections. For illustration a 1 TeV hard WIMP signal is shown for WH and a 50 GeV hard WIMP signal for WL and SL. 7.8 Filter level L5 83

7.8 Filter level L5 The cut on the BDT score is optimized for each event selection separately in the final likelihood analysis (described in detail in chapter6). The latter is based on the space angle Ψ between the reconstructed tracks and the position of the Sun. The distribution of Ψ observed in the final event samples is used to define a likelihood-ratio test statistics, using the Feldman-Cousins unified approach [133]. This results in confidence intervals for the number of signal events, µs . The required probability densities for signal are computed from simulations, while for background they are based on real data events at the final selection level, with scrambled azimuth direction. Under the assumption of no signal, the sensitivity of each data sample for different BDT score cut- values is derived. This is repeated for several signal hypothesis, defined by a combination of annihilation channel and mχ . In order to optimize this cut, we calculate the following quantities: The number of events in the final sample, Nobs, the resulting effective Volume, Veff, the median 90% upper limit on the 90% number of signal events with Nobs events, µs , the model rejection factor, MRF [138], and the model discovery potential, MDP, as defined in [139]. For a large number of pseudo experiments, in the absence of signal, the cut minimizing the MRF, defined as 90% µs MRF = , where ns ∝ Veff Tlive, (7.1) ns · gives the best average limit. The MDP as given in reference [139] is an analyti- cal parametrization for the sensitivity of the experiment for a chosen discovery level at a given confidence level. This figure-of-merit is defined in equation 7.2 and chosen to represent the signal flux needed for a 5σ significance discovery (a=5) at the 90% confidence level (b=1.28). Here, the best cut is given by the cut maximizing the MDP, where εs represents the signal efficiency. ε MDP = s (7.2) a2 9b2 b 2 8 + 13 + a√Nobs + 2 b + 4a√Nobs + 4Nobs Figure 7.13 shows all five derived quantitiesp for the WH event selection and + a 1 TeV (W W −) signal hypothesis. For this analysis the option of one single BDT score cut per event selection for all signal hypotheses is investigated. This approach is a more robust and simple choice, than creating individual final event samples that are optimized for each signal hypothesis. The latter yields the danger of an over-optimized analysis and would lead to non-trivial correlations in the final result between each tested signal hypothesis. Instead, for each event selection, the BDT cut (BDTfinal) which minimizes the MRF for one representative signal model is chosen. The final acceptance criteria are listed in table 7.8 and motivated in the sections below. The plots in Fig. 7.14 show for selected signal models for each event selection the ratio between the final flux sensitivity and the potentially best flux sensitivity for this particular model. This illustrates clearly that for most signal models we do not 84 Chapter 7: IceCube 79-string data analysis

30000

obs 20000 N 10000

-0.05 0 0.05 0.1 0.15 0.2 BDT cut value 0.15 eff

V 0.1 0.05 20-0.05 0 0.05 0.1 0.15 BDT cut value 15 90% s

µ 10 ×10-6 -0.05 0 0.05 0.1 0.15 0.15 BDT cut value

MRF 0.1

×10-3 -0.05 0 0.05 0.1 0.15 0.7 BDT cut value 0.6

MDP 0.5

-0.05 0 0.05 0.1 0.15 BDT cut value Figure 7.13: Cut optimization quantities for various BDT score cut values. The opti- + mization is shown for the example of the WH event selection and a 1 TeV (W W −) signal. From top to bottom: The number of events within the final sample (Nobs), the 90% effective Volume (Veff), µs , MRF and MDP. expect more than a 10% deviation from the ‘best’ signal flux case with a sin- 3 gle BDTfinal cut . Note, in Fig. 7.13 the MDP is very close to its maximum at the chosen cut value. This is true for most models and event selections, except for the SL selection. Here, the MDP is maximal for a lower BDTfinal cut, corresponding to a higher background level within the final sample, that is dominated by atmospheric muon background. In this context, the optimization for the MRF is the more conservative analysis choice, which results in a final sample with less Nobs and a more pure sample of neutrino candidate events.

7.8.1 L5, SL event selection

The cut on the BDT score for the SL event selection, BDTscore,SL, is optimized for a 250 GeV (bb) signal. After the ﬁnal BDTscore,SL cut, the events and variable distributions in the SL sample are closely analyzed. It becomes clear that the veto requirements applied to this point are not stringent enough to sufﬁ-

3This is not true for the very low mass signal models within the WL selection, which will be discussed under L5-WL event selection of section 7.8.3. 7.8 Filter level L5 85

dataset SL dataset WH dataset WL & WL(b) )

final 1 1 1 (BDT

µ 0.9 0.9 0.9 Φ ) / 0.8 0.8 0.8 best

(BDT 0.7 0.7 0.7 µ Φ 0.6 0.6 0.6 35(h) 50(h) 100(h) 250(s) 100(h) 250(h) 500(s) 1000(h) 20(h) 35(h) 50(h) 100(h)250(s) signal model Figure 7.14: The expected ratio between the final flux sensitivity (for the optimized BDTfinal cut) and the potentially best flux sensitivity for this particular model (BDTbest cut) is shown for selected signal models. From left to right; SL, WH and WL selections. Two signal models in WL have additional entries marked by triangles. These models are found to be not sufficiently optimized by the BDTscore,WL cut, and are consequently re-optimized for the WL(b) event selection (see text for details).

ciently remove the down-going muon background. As a result, the hit-time criterion (introduced in section 7.6.1) is tightened, and an additional, special- ized ‘cone’ cut is applied to reject faint muons with very few hit DOMs outside the DeepCore fiducial volume. In this algorithm, a cone is defined around the reconstructed track direction and searched for the presence of hit DOMs at earlier times. The presence of too many hits inside the cone is evidence of a faint muon, and these events are rejected. Additionally, most events classified as ‘split’-events in the final SL sample consist of falsely split down-going muon events entering the main IceCube dust layer around 2050 m depth at shallow zenith angles. This class of events is well represented in MC simulation. Consequently, all events in the final SL event sample are demanded to be non-split events. The BDT output distribution of the SL event selection is shown after final cut in figure 7.15 and shows good agreement between data and the total sum of all expected MC background simulations. Simulations indicate a fraction of 30% atmospheric neutrino candidate events within the final sample. The number of events expected from atmospheric νe-flux is shown to be negligible within this dataset.

7.8.2 L5, WH event selection

The cut on the BDT score for the WH event selection, BDTscore,WH, is opti- + mized for a 1 TeV (W W −) signal. This chosen cut value is nearly optimal for all WH selection relevant signal models, as shown in the middle plot of figure 7.14. The BDT output distribution of the WH event selection is shown after final cut in figure 7.15 and shows excellent agreement between data and MC background simulations. The remaining sample is dominated by at- 86 Chapter 7: IceCube 79-string data analysis

Table 7.8: Summary of ﬁnal acceptance criteria.

event selection selection criteria

SL BDTscore,SL > 0.0 hit-time containment cut (see text),

remove ‘split’-events, ConeCut(45◦) < 3

WH BDTscore,WH > 0.025

WL BDTscore,WL > 0.14 ﬁd WL(b) BDTscore,WL(b) > 0.05, NchanDC < 30, hit-time containment cut (see text) mospheric neutrino events including a minor contribution from atmospheric muon background ( 7%). ∼

7.8.3 L5, WL event selection

The choice of a single BDTscore,WL cut for all WL relevant signal models works well for most signal models in figure 7.14 with deviations of less than 10% of the expected ‘best’ flux sensitivity for each model. The plot also indicates that for the two lowest mχ signal models a single BDTscore,WL cut is not optimal anymore. For this reason, the general BDTscore,WL cut is optimized + for a 50 GeV (τ τ−) signal and a second, less stringent cut (see table 7.8) is + optimized for the lowest mχ signal model, 20 GeV (τ τ−). This is marked by the triangles in figure 7.14. This super-set of events is denoted by WL(b) + and is picked for the four lowest mχ signal models, 20 GeV (τ τ−), 35 GeV + (τ τ−), 35 GeV (bb) and 50 GeV (bb). The resulting BDT output distribution of the WL event selection is shown in figure 7.15. Bins exclusive to WL(b) are indicated by triangles. Overall, this event sample shows good agreement between data and the total sum of all expected MC background simulations. The WL sample is largely dominated by atmospheric neutrino events, whereas the more loose BDTscore,WL(b) cut results in an increase of atmospheric muon background. Close analysis of the remaining WL(b) data and low mχ signal expectations indicates that the remaining signal content is concentrated within the bottom DeepCore region, whereas the DeepCore top region is dominated by background. For this reason, a hit-time criterion similar to the one applied within SL is imposed, where the fiducial region contains only bottom Deep- Core. Additionally, we restrict the number of hit DOMs within the fiducial region reflecting the low mχ signal expectation. Details are listed in table 7.8. 7.8 Filter level L5 87

dataset SL (summer, low-energy)

10-5

10-6 Rate in Hz

10-7

4 0 0.05 0.1 0.15TMVA output 2 0 (data/MC) 0 0.05 0.1 0.15 BDT output score

dataset WH (winter, high-energy) 10-4

10-5 Rate in Hz

10-6

1.5 0.05 0.1 0.15 0.2TMVA output 1 0.5

(data/MC) 0.05 0.1 0.15 0.2 BDT output score

dataset WL & WL(b) (winter, low-energy) 10-4

10-5

10-6 Rate in Hz

10-7

2 0.1 0.2 0.3TMVA output 1 0

(data/MC) 0.1 0.2 0.3 BDT output score Figure 7.15: BDT output distributions at ﬁnal level for the summer (top), the winter ‘high energy’ (middle) and the winter ‘low energy’ (bottom) selections. Experimental data (points), µatm (dotted-red), νatm (dashed-green) and total MC background (band- gray) are shown (νatm-electron background is shown in the top plot in ﬁne-dotted green). The WL(b) data-subset is shown in the bottom plot (triangles). The thickness of the gray band represents the statistical uncertainty in the MC simulation only. 88 Chapter 7: IceCube 79-string data analysis

-36 Expected individual sensitivities: winter high energy (bb) ♦ winter high energy (W+W-)

winter low energy (bb) ♦ winter low energy (W+W-)

summer (bb) ♦ -37 summer (W+W-) ) 2 / cm -38 SD,p σ

-39 log10 (

♦ τ+τ- ( for mχ < mW = 80.4GeV) IceCube 2011 (8y. data) (bb) -40 ♦ IceCube 2011 (8y. data) (W+W-) expected IceCube 2012 (bb) ♦ expected IceCube 2012 (W+W-) 1 2 3 4 log10 ( mχ / GeV )

Figure 7.16: 90% CL sensitivities (median upper limits) on σSD,p for hard and soft annihilation channels over a range of WIMP masses. Systematic uncertainties are not included. Individual sensitivities from event selections WH, WL, SL and the combined multi-dataset sensitivity is compared with the 2011 multi-year IceCube limits [132].

7.9 Sensitivity The likelihood ratio test, used to optimize L5 and detailed in chapter6, resulting in a confidence interval for a possible excess of events from the Sun. Under the assumption of no signal, we derive the sensitivities for all three data samples SL, WH and WL. Note, for the four lowest mχ signal models the WL(b) event sample is chosen instead of WL. A single result is calculated from all three data samples with a combined likelihood, constructed from the set of three independent distributions of signal and background, weighting each by the respective livetime and effective volume. The sensitivities are evaluated by performing 10000 pseudo- experiments for the background-only case, where each pseudo-experiment is a random selection of Nobs Ψ-values sampled from the background distribution. 90 The median of the resulting µs -distribution from all pseudo experiments de- 90 90 fines the sensitivity on the number of signal events, µs . The limit on µs can be converted to limits on other WIMP signal related physical quantities, like the induced muon flux in the ice, Φµ , and the WIMP-proton scattering cross- sections (spin-independent, σSI,p, and spin-dependent, σSD,p), as discussed in chapter 6.3. Figure 7.16 shows the resulting sensitivities of this work to the spin-dependent WIMP-proton scattering cross-section, σSD,p, for the combined data set and the three individual subsets. It is evident from the figure that in some regions a single event sample is dominant, whereas in others multiple data sets contribute to the final sensitivity. The combined 7.10 Results 89

10-1 10-2 ) 2 10 10-3 (m ) eff ° -4 ( A 10 Θ 10-5 10-6

-7 1 10 10 102 103 10 102 103 Eν (GeV) Eν (GeV)

Figure 7.17: The median angular error, Θ, and the total neutrino effective area (νµ + ν µ ) for all final event selections are shown as a function of neutrino energy. Aeff is an average over the austral winter. WH selection is shown in black (solid), SL in blue (solid), WL in green (solid) and WL(b) in green (dashed, circle). sensitivity is compared with the IceCube multi-year limit from 2011 [132], corresponding to eight years of data taking with AMANDA, the IceCube 22-string configuration, and the 40-string configuration. The effective area (Aeff) and median angular resolution (Θ) for all final event selections is shown as a function of neutrino energy in figure 7.17. The expected muon flux limit is listed for each signal model in table 7.9. Also given for each signal model is Veff, the accumulative signal cut efficiency, εcut, the resulting median muon energy, Eµ , and Θ, see table 7.10.

7.10 Results After unblinding the direction of the events in the ﬁnal data samples, the observed distributions are compared to the expected background distributions from atmospheric muons and neutrinos, shown in Fig. 7.18 for each event selection. The observed number of events from the direction of the Sun are consistent with the background-only hypothesis. Upper 90% CL limits on µs are calculated and listed for each signal hypothesis in Table 7.9. The resulting lower 90% CL limit on µs is 0.0 for all models. For an additional illustration of the ﬁnal results, Figure 7.19 shows the weighted sum of unblinded events (Nw) for all event selections for two signal models. Here, Nw are events weighted by the signal purity of each individual selection (expression of Nw given in Fig. 7.19). 90 Chapter 7: IceCube 79-string data analysis

80 dataset WH (winter, high-energy) 60 40 20

0.99 0.992 0.994 0.996 0.998 1 8 dataset WL (winter, low-energy) 6

4 2 Events 0.99 0.992 0.994 0.996 0.998 1 8 dataset WL(b) (winter, lowest-energy) 6 4 2

0.99 0.992 0.994 0.996 0.998 1 dataset SL (summer, low-energy) 10

0 0.99 0.992 0.994 0.996 0.998 cos(Ψ) 1 Figure 7.18: Cosine of the angle between the reconstructed track and the direction of the Sun, Ψ, for observed events (squares) with one standard deviation error bars, and the background expectation from atmospheric muons and neutrinos (dashed line). Also shown is a simulated signal (1 TeV hard for dataset WH, 50 GeV hard for datasets 90 WL and SL, 35 GeV hard for datasets WL(b)) scaled to µs (details in Table 7.9). 7.10 Results 91

N events N events

w 100 w 20 40 60 80 10 20 30 0.4 0 0.4 N w = ∑ i=1 3 N 0.5 obs i 0.5

Σ signal+background background signal scaled to data j=1 3 V V eff i eff j T live i T live j (N 0.6 0.6 (N obs i obs j ) -1 µ ) s 90 -1 0.7 0.7 signal channel(50GeV, signal signal channel(500GeV, b signal 0.8 0.8 0.9 0.9 τ + cos( τ - b ) ) Ψ cos( ) Ψ 1 ) 1

Figure 7.19: cos(Ψ) distribution for weighted events, Nw, (squares) with one standard deviation error bars and weighted background expectation from atmospheric muons and neutrinos (solid line). Nw is deﬁned as the averaged sum of signal purities over all three independent event selections (see formula in top plot). Also shown is simu- 90 lated signal (50 GeV hard (top) and 500 GeV soft (bottom)) scaled to µs , accordingly. Note, the cos(Ψ) distribution of Nw events is different for each signal model, as it de- i pends on Veff, where i( j) denotes the three ﬁnal event selections. 92 Chapter 7: IceCube 79-string data analysis

Table 7.9: Results from the combination of the three independent datasets. Upper 90 limits on the number of signal events µs , the WIMP annihilation rate in the Sun ΓA, the muon flux Φµ and neutrino flux Φν (both integrated above 1 GeV), at the 90% confidence level including systematic errors. The sensitivity Φµ (see text) is shown for comparison.

90 mχ Channel µs ΓA Φµ Φµ Φν 1 2 1 2 1 2 1 (GeV) (s− ) (km− y− ) (km− y− ) (km− y− ) 20 τ+τ 162 2.46 1025 5.26 104 9.27 104 2.35 1015 − × × × × 35 τ+τ 70.2 1.03 1024 1.03 104 1.21 104 1.02 1014 − × × × × 35 bb 128 1.99 1026 5.63 104 1.04 105 6.29 1015 × × × × 50 τ+τ 19.6 1.20 1023 4.82 103 2.84 103 1.17 1013 − × × × × 50 bb 55.2 1.75 1025 2.06 104 1.80 104 5.64 1014 × × × × 100 W +W 16.8 3.35 1022 1.49 103 1.19 103 1.23 1012 − × × × × 100 bb 28.9 1.82 1024 7.57 103 5.91 103 6.34 1013 × × × × 250 W +W 29.9 2.85 1021 3.04 102 4.15 102 9.72 1010 − × × × × 250 bb 19.8 1.27 1023 1.85 103 1.45 103 4.59 1012 × × × × 500 W +W 25.2 8.57 1020 1.46 102 2.23 102 2.61 1010 − × × × × 500 bb 30.6 4.12 1022 8.53 102 1.02 103 1.52 1012 × × × × 1000 W +W 23.4 6.13 1020 1.19 102 1.85 102 1.62 1010 − × × × × 1000 bb 30.4 1.39 1022 4.33 102 5.99 102 5.23 1011 × × × × 3000 W +W 22.2 7.79 1020 1.09 102 1.66 102 1.65 1010 − × × × × 3000 bb 26.1 4.88 1021 2.52 102 3.47 102 1.89 1011 × × × × 5000 W +W 22.8 8.79 1020 1.01 102 1.58 102 1.77 1010 − × × × × 5000 bb 26.4 6.50 1020 2.21 102 3.26 102 1.63 1011 × × × × 7.10 Results 93

Table 7.10: Results from the combination of the three independent datasets. The effective Volume Veff, the accumulated signal cut efficiency with respect to online-filter level εcut, the median muon energy at final selection Eµ and the median angular error Θ are listed. Also shown are the upper limits on the WIMP-proton scattering cross- sections (spin-independent, σSI,p, and spin-dependent, σSD,p), at the 90% confidence level including systematic errors.

mχ Channel Veff εcut Eµ Θ σSI,p σSD,p 3 2 2 (GeV) (km ) (%) (GeV) (◦) (cm ) (cm ) 20 τ+τ 1.5 10 4 1.1 10.4 36.4 1.1 10 40 1.3 10 38 − × − × − × − 35 τ+τ 7.1 10 4 5.0 16.9 23.0 6.6 10 42 1.3 10 39 − × − × − × − 35 bb 7.5 10 5 0.8 8.4 44.1 1.3 10 39 2.5 10 37 × − × − × − 50 τ+τ 1.1 10 3 5.2 23.7 14.1 1.0 10 42 2.7 10 40 − × − × − × − 50 bb 2.0 10 4 1.5 12.4 34.6 1.5 10 40 4.0 10 38 × − × − × − 100 W +W 4.6 10 3 9.0 42.5 7.8 6.0 10 43 2.7 10 40 − × − × − × − 100 bb 5.8 10 4 2.2 21.1 17.3 3.3 10 41 1.5 10 38 × − × − × − 250 W +W 5.7 10 2 26.2 130.3 2.9 1.7 10 43 1.3 10 40 − × − × − × − 250 bb 3.1 10 3 8.9 47.1 8.2 7.4 10 42 5.9 10 39 × − × − × − 500 W +W 1.4 10 1 36.3 181.5 2.3 1.5 10 43 1.6 10 40 − × − × − × − 500 bb 1.1 10 2 15.9 84.8 4.5 7.0 10 42 7.6 10 39 × − × − × − 1000 W +W 2.0 10 1 39.4 201.5 2.2 3.5 10 43 4.5 10 40 − × − × − × − 1000 bb 2.5 10 2 22.5 112.8 3.4 7.8 10 42 1.0 10 38 × − × − × − 3000 W +W 2.1 10 1 38.3 206.8 2.1 3.4 10 42 5.0 10 39 − × − × − × − 3000 bb 4.9 10 2 28.9 139.8 2.9 2.2 10 41 3.2 10 38 × − × − × − 5000 W +W 2.2 10 1 40.3 211.6 2.1 1.1 10 41 1.6 10 38 − × − × − × − 5000 bb 5.6 10 2 29.7 142.5 2.7 4.9 10 41 7.3 10 38 × − × − × − 94 Chapter 7: IceCube 79-string data analysis

7.11 Systematic uncertainties The effect of different sources of systematic uncertainties on signal flux expectations is calculated for three signal energy regions, defined in Table 7.11 by corresponding benchmark WIMP masses. Sources of uncertainties are divided into two classes; measurement and parameterization errors on cross sections and neutrino properties on the one hand and limitations in the detector simulation and uncertainties in detector calibrations on the other hand. The first class, Class-I, affects signal normalization only, whereas the latter (Class-II) alters signal acceptance and introduces changes in the point spread function that is the basis for the likelihood analysis. Class-II uncertainties are evaluated using alternative signal simulations with varied calibration parameters, processed through the same analysis chain, and evaluated with the full multi-dataset combined likelihood. This procedure explicitly determines the systematic effect on µs.

Class I uncertainties Uncertainties in neutrino-nucleon cross-sections arise in the parameterization of the CTEQ6-DIS parton distribution functions as used in nusigma [124]. In addition to this theoretical uncertainty on σν , the energy dependent error on the experimental σν -measurement [99] is included. The uncertainty in neutrino oscillation parameters used in signal ﬂux calculations is investigated through variations of mixing parameters within the quoted 1σ regions [99]. Here, the dominant effect results from the least constrained mixing angle, θ23, maximizing tau (dis)appearance within the expected ﬂux expectation. The uncertainty on muon propagation in ice is estimated from the uncertainties on the simulated muon track length in ice, and is based on Ref. [104]. The effect from uncertainties in position calibration is calculated from a set of signal simulation with a previous DOM geometry calibration. The effect of time calibration is estimated from a previous analysis [1] and added to the uncertainty on the position calibration.

Class II uncertainties The second class of uncertainties includes absolute calibration and DOM to DOM variation of sensitivity, optical properties of the glacial ice, and photon propagation to the detector. The systematic uncertainties on absolute DOM sensitivity are evaluated with sets of signal simulations with an overall shift of 10% in DOM efficiency. As baseline simulations do not account for varying relative DOM efficiency, dedicated signal simulations were performed with individual DOM efficiencies from a Gaussian fitted to the in-situ measured spread (σ = 0.087) and centered around the nominal value. Optical properties of the glacial ice are measured [108] and characterized in models that are parameterizations of the absorption and scattering coefficients as a function 7.12 Final results and discussion 95

*IceCube PRELIMINARY* •36 Expected (b )b Expected (W+W•)♦ Observed (b )b •37 Observed (W+W•)♦ ± 1 σ expected ± 2 σ expected ) 2 •38 / cm SD,p σ

•39 log10 (

•40

+ • ♦ (τ τ for mχ < mW = 80.4GeV) •41 1.5 2 2.5 3 3.5 log10 ( m / GeV ) χ

Figure 7.20: Final sensitivity on σSD,p for hard and soft annihilation channels over a range of WIMP masses (mχ ). The total expected systematic uncertainty and statistical ﬂuctuation is shown at the one (green band) and two sigma (yellow band) level and compared to the ﬁnal unblinded result at the 90% CL. of depth and position in the detector. Two such models [108, 109], differing in parameterization techniques, are considered to bracket the uncertainty in light yield resulting from the ice description.

Individual uncertainties, listed in Table 7.11, are added in quadrature to ob- tain the total systematic uncertainty for each benchmark mass region. Fig- ure 7.20 shows for the example of σSD,p, the resulting median sensitivity, the total expected systematic uncertainty and statistical ﬂuctuation (see chap- 90 ter 6.2) on µs at one and two sigma level compared to the ﬁnal unblinded result. All results are well within the expected range at the one sigma level.

Additional uncertainties, which arise in the conversion from limits on Φµ from the Sun to limits on the WIMP-nucleon scattering cross-sections, due to the uncertainty in the nuclear form factor, and the uncertainty in solar composition models are discussed in chapter 1.7. These uncertainties are negligible for the calculation of limits on σSD,p, and comparable or less than the total detector systematic uncertainty for σSI,p. These uncertainties are not included in the ﬁnal results for the WIMP-proton scattering cross-sections.

7.12 Final results and discussion Final results are calculated as outlined in section 6.3 including systematic uncertainties and are listed in tables 7.9 and 7.10. The limits on σSI,p and σSD,p are shown in Fig. 7.21 together with other experimental limits [140, 141, 142, 96 Chapter 7: IceCube 79-string data analysis

Table 7.11: Systematic errors on signal ﬂux expectations in percent. Class-II uncertainties marked ∗

Source mass ranges (GeV) < 35 35 -100 > 100 ν oscillations 6 6 6 ν-nucleon cross-section 7 5.5 3.5 µ-propagation in ice <1 <1 <1 Time, position calibration 5 5 5

DOM sensitivity spread∗ 6 3 10

Photon propagation in ice∗ 15 10 5

Absolute DOM efﬁciency∗ 50 20 15 Total uncertainty 54 25 21

143, 144, 145, 40, 146, 46, 147]. Limits on the WIMP-nucleon scattering cross section can also be deduced from limits on mono-jet and mono-photon signals at hadron colliders, but these depend strongly on the choice of the underlying effective theory and mediator masses [71, 72, 73]. The latest limit from CMS [74] for an optimistic choice of mediator is included in Fig. 7.21.

In conclusion, the results of this work are the most stringent limits to date on the spin-dependent WIMP-proton cross-section for WIMPs with masses + + above 35 GeV, annihilating into W W − or τ τ−. With this dataset, we have demonstrated for the first time the ability of IceCube to probe WIMP masses below 50 GeV. This has been accomplished through effective use of the Deep- Core sub-array. Furthermore, the southern sky has been accessed for the first time by incorporating strong vetos against the large atmospheric muon backgrounds. The added livetime has been shown to improve the presented limits. IceCube has now achieved limits that strongly constrain viable dark matter models and that will impact global fits of the allowed dark matter parameter space.

A detailed description of such an integration of IceCube event level data in global fits for theories of new physics is given in paper III. In this work we describe how IceCube data can be used to constrain SUSY dark matter models in general. The analysis is based on explicit exploration of theoretical SUSY parameter spaces, including a model-by-model comparison with fluxes observed by IceCube. This approach allows models to also be tested against a range of complementary data, including accelerator constraints, direct dark matter search constraints, the relic density of dark matter, limits on rare processes in B-physics and the anomalous magnetic moment of the muon. This is performed in two different analyses. The first is a model exclusion exercise. Here, individual SUSY models are tested for consistency (at some set confi- 7.12 Final results and discussion 97

-38 MSSM incl. XENON (2012) ATLAS + CMS (2012) DAMA no channeling (2008) -39 CDMS (2010) CDMS 2keV reanalyzed (2011) CoGENT (2010) -40 XENON100 (2012) ) 2 -41 / cm

SI,p -42 σ

-43 log10 (

-44

IceCube 2012 (bb) -45 ♦ IceCube 2012 (W+W-) ♦ τ+τ- 2 ( for mχ

MSSM incl. XENON (2012) ATLAS + CMS (2012) -35 DAMA no channeling (2008) COUPP (2012) Simple (2011) PICASSO (2012) CMS monojet (2012) -36 SUPER-K (2011) (bb) SUPER-K (2011) (W+W-) ) 2

-37 / cm SD,p σ -38 log10 (

-39 IceCube 2012 (bb) ♦ IceCube 2012 (W+W-) ♦ τ+τ- 2 ( for mχ

1 2 3 4 -2 log10 ( mχ / GeV c )

Figure 7.21: 90% CL upper limits on σSI,p (top figure) and σSD,p (bottom figure) for hard and soft annihilation channels over a range of WIMP masses. Systematic uncertainties are included. The shaded region represents an allowed MSSM parameter space (MSSM-25 model scan from paper V) taking into account recent accelerator [148, 149, 150], cosmological and direct dark matter search constraints. Results from Super-K [140], COUPP(exponential model) [141] , PICASSO [142], CDMS [143, 144], XENON100 (limits above 1 TeV/c2 from XENON100 Coll. pri- vate communication) [145], CoGeNT [40], Simple [146] and DAMA [46, 147] are shown for comparison. Also shown a recent CMS mono-jet result [74]. 98 Chapter 7: IceCube 79-string data analysis dence level) with IceCube data and other existing constraints, and identified as allowed or excluded (see paper IV). Results of this work underline nicely the complementarity of this indirect dark matter search with direct detection and collider search efforts. The second more ambitious analysis constitutes a parameter estimation exercise within a given SUSY framework. This analysis involves a global fit to all existing constraints, with the inclusion of IceCube data. In this analysis, the full likelihood of each experimental result, including IceCube, is combined to give frequentist confidence intervals and Bayesian credible intervals on SUSY parameters (see paper III).

Lessons learned - future improvements This analysis added several new aspects to the already well established Ice- Cube solar dark matter search. Many novel analysis concepts were incorporated, but some key lessons were only realized in hindsight of unblinding the final data sample. Other factors became clear during the late stages of this work and could not be fully incorporated due to time constraints. Here, we list a series of lessons learned: Coincidence event identification: Better identification of coincidence events within the detector will not affect signal efficiency by a large fraction, as signal coincidences are with 10% not a leading contribution. In addition, most of the signal coincidences∼ are identified correctly. Con- versely, an improvement in background coincidence identification will noticeably improve the fraction of ‘easy’ to remove muon background.

Extended analysis method: The current maximum likelihood method can be improved in several ways. Firstly, instead of a ﬁnal cut on the BDT- output distribution, it is preferable to add the BDT score as an additional term (dimension) directly to the analysis likelihood method. Secondly, the current probability distributions in Ψ represent an average over the whole data taking period. Better discrimination between background and signal may be achieved by accounting for different zenith regions during this period. Thirdly, the analysis method can be further improved by the addition of a spectral (energy) term, as shown successfully in paper III.

Philosophical change in analysis method for low mχ : This work utilizes surrounding IceCube strings to develop strong veto criteria for low energy DeepCore event analysis. Nevertheless, the full potential of demanding a virtually ‘quiet’ veto region to identify neutrino induced muon events inside DeepCore was only realized in hindsight of this work. Subsequently, this comprehension lead to three new, successful veto techniques to reject atmospheric background with high signal retention (>95%). Such a background rejection of three orders of 7.13 Search for Kaluza Klein dark matter 99

magnitude without exploiting analysis variables to distinguish between signal and background yields great potential for future work in the low WIMP mass region (mχ <100 GeV).

7.13 Search for Kaluza Klein dark matter In this section the analysis is extended to an alternative dark matter candidate, Kaluza-Klein (KK) particles, arising from theories with extra spacetime dimensions. Paper I describes with the example of the IceCube 22-string solar WIMP analysis [1] that it is justiﬁed to use the same analysis cuts as for neutralino DM searches. This is due to the signature of the expected signal at the detector being very similar for the LKP and neutralinos, considering the hard + annihilation channel into W W −. The neutrino spectrum from annihilations of a LKP of a given mass in the center of the Sun is considerably harder than that of a neutralino of the same mass. However, oscillations and energy losses of the neutrinos on their way out of the Sun, like neutral current (NC) scattering, absorption and ντ -regeneration, softens out the energy spectra in a way that makes them comparable at Earth. Accelerator measurements imply a lower bound for the mass of the LKP at roughly 500 GeV [151]. Consequently, this analysis uses exclusively the WH event selection. LKP annihilations in the Sun are simulated using WimpSim [122] for LKP masses (mLKP) ranging from 250 to 3000 GeV. Upper limits on µs are calculated and listed for each signal hypothesis in Table 7.12. The resulting lower limit on µs is 0.0 for all models. Final results are calculated as outlined in section 6.3, including systematic uncertainties, and are listed in tables 7.12 and 7.13.

Table 7.12: Results from the WH event selection on LKP models. Upper limits at the 90 90% CL on the number of signal events µs , the WIMP annihilation rate in the Sun ΓA, the muon ﬂux Φµ and neutrino ﬂux Φν , including systematic errors.

90 mLKP µs ΓA Φµ Φν 1 2 1 2 1 (GeV) (s− ) (km− y− ) (km− y− ) 250 27.4 3.89 1021 4.29 102 1.19 1011 × × × 500 24.6 1.16 1021 2.39 102 3.31 1010 × × × 700 22.9 8.38 1020 1.99 102 2.34 1010 × × × 900 22.3 7.30 1020 1.87 102 2.02 1010 × × × 1100 22.3 6.96 1020 1.84 102 1.89 1010 × × × 1500 22.3 6.85 1020 1.80 102 1.81 1010 × × × 3000 21.9 7.56 1020 1.65 102 1.88 1010 × × × 100 Chapter 7: IceCube 79-string data analysis

Table 7.13: Results from the WH event selection on LKP models. The effective Vol- ume Veff, the accumulated signal cut efficiency with respect to online-filter level εcut, the median muon energy at final selection E¯ µ and the median angular error Θ¯ are listed. Also shown are the upper limits on the WIMP-proton scattering cross-sections (spin-independent, σSI,p, and spin-dependent, σSD,p), at the 90% confidence level including systematic errors.

mLKP Veff εcut E¯ µ Θ¯ σSI,p σSD,p 3 2 2 (GeV) (km ) (%) (GeV) (◦) (cm ) (cm ) 250 4.8 10 2 23.8 138.8 2.5 2.3 10 43 1.8 10 40 × − × − × − 500 1.2 10 1 33.8 174.1 2.3 1.9 10 43 2.1 10 40 × − × − × − 700 1.5 10 1 35.9 188.7 2.1 2.5 10 43 3.0 10 40 × − × − × − 900 1.7 10 1 37.2 196.0 2.1 3.4 10 43 4.3 10 40 × − × − × − 1100 1.8 10 1 37.6 201.6 2.1 4.7 10 43 6.1 10 40 × − × − × − 1500 1.9 10 1 38.3 208.3 2.1 8.1 10 43 1.1 10 39 × − × − × − 3000 2.1 10 1 38.8 212.6 2.1 3.4 10 42 4.9 10 39 × − × − × − Sammanfattning på svenska

IceCube är en kubikkilometerstor neutrinodetektor som byggts djupt i in- landsisen vid sydpolen och som här använts för att söka efter neutriner från egenannihilationer av mörk materia inuti astronomiska objekt med stor massa. Tydligheten i den förväntade signaturen av ett neutrinoflöde från centrum av ett känt objekt gör detta till en mycket lovande indirekt kanal i sökandet efter mörk materia. Denna avhandling presenterar resultaten från ett antal analyser av experimentella data från IceCube som har sökt efter mörk materia som an- nihilerat i solens inre och gett upphov till ett koncentrerat neutrinoflöde från solens riktning. Den huvudsakliga fysikanalysen som beskrivs i avhandlingen sökte efter en neutrinosignal från mörk materia i form av svagt växelverkande massiva partiklar (så kallade WIMP:ar) med data från den IceCube-konfiguration som tog data under 2010 och som då omfattade 79 av de slutgiltiga 86 detek- torsträngarna. Detta var den första mörk materia-analysen som använde sig av data från DeepCore, en deldetektor i IceCubes mitt med tätare instrumenter- ing och därmed lägre energitröskel. Dessutom inkluderades för första gången data från sommarhalvåret då solen befann sig över horisonten och jorden inte kunde användas för att filtrera bort myoner från sönderfall av hadroner som skapats i växelverkningar av kosmisk strålning i atmosfären, så kallade at- mosfäriska myoner. Fördelningen av rekonstruerade riktningar för de ungefär 25.000 lovande händelser som sållats fram ur data motsvarande 317 dagars exponeringstid var statistiskt förenlig med en fördelning som förväntas från atmosfäriska myoner och neutriner, men övre gränser sattes på den mörka materiens förintelsetakt och räknades om till gränser på tvärsnittet för WIMP- proton-spridning, vilken är den process som leder till att WIMP:arna fångas i solen där de annihilerar. Dessa gränser för spinn-beroende WIMP-proton- tvärsnitt är för de flesta WIMP-modelllerna de hittills lägsta experimentellt bestämda gränserna för en WIMP-massa över 35 GeV. Avhandlingen beskriver också en likelihood-metod som utvecklats för att snabbt och direkt kunna jämföra misstänkta neutrinohändelser rekonstruerade från IceCube-data med godtyckliga annihilationsspektra i en skann över modellparametrar, i vilken inte endast det totala antalet händelser utan även neutrinernas rekonstruerade riktingar och energier används. Denna formalism tillämpades i två analyser och visade sig vara användbar både till att utes- 102 Chapter 7: IceCube 79-string data analysis luta modeller genom bestämning av parametergränser och till att bestämma parametervärden i supersymmetriska utvidgningar av standardmodellen för elementarpartiklar. IceCubes indirekta sökmetoder efter neutriner från mörk materia utvidgades dessutom för första gången till att omfatta en alternativ kandidat för mörk materia, så kallade Kaluza-Klein-partiklar vilka förutspås av teorier med extra rumtidsdimensioner. De metoder som utvecklats för att söka efter neutriner från mörk materia som annihilerar i solen användes slutligen även till att söka efter neutriner från Krabbnebulosan vilka avgetts då den sken upp med en ’flare’ under 2010. 8 Bibliography

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