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 live- time 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 ini- tiates 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, consid- ering 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 mat- ter 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.
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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 particu- lar 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 dur- ing 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 intro- duction 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, chapter 1, lists observational evidence for dark matter, various proposed dark matter candidate models, and discusses different dark matter search strategies. Part I, chapter 2, is a discussion of expected background components for an indirect solar search for WIMP dark matter. The final chapter in part I, chapter 3, is a review of neutrino detection in ice with the IceCube neutrino observatory. Part II, chapters 4 and 5, 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 chapter 6. Chapter 7 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 chapters 4 - 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.
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Author’s contribution
Below, I summarize my contributions to papers I-V, and how these are con- nected 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 mat- ter searches with neutrinos (using IceCube data) to an alternative dark mat- ter 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 re- quired 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 mat- ter 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 neu- trinos 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 correspond- ing 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 ex- plicit 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 de- velopment 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 pub- lished 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 chapters 4-7), 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
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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 summa- rized 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 moti- vated 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 in- side 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 detec- tor 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 understand- ing 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 origi- nating 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,
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including detailed data processing and event selection, while making conser- vative 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 character- istic 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 bottom, models with Ωmh2=0.12 (0.13 and 0.14), all with Ωbh2=0.024. The bottom line shows a pure cold dark matter model (Ωmh2=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 com- ponent present [5, 6].
Baryonic acoustic oscillations (BAO) provide an experimental constraint on the total matter density of the Universe. BAO characterize acoustic den- sity perturbations in the early Universe. Assuming small perturbations in the hot dense plasma of electrons, baryons and photons, pressure waves are cre- ated. During the early expansion of the Universe, photons and baryons initially moved together, until the Universe cooled enough to form hydrogen (recom- bination 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 approximately 100 h−1Mpc. Here, h is the dimensionless Hubble parameter, defined by the Hubble constant (H0), as h≡ H0/100 km s−1Mpc−1. 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 mat- ter, 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< Ωmwould provide strong evidence for dark matter. Such a constraint is given by measurements of light isotopes produced in Big Bang nucleosynthe- sis (BBN) [10]. From observations of very old systems the primordial bary- onic 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 temper- ature variations in the cosmic microwave background (CMB). CMB radia- tion decoupled from matter shortly after recombination and features temper- ature inhomogeneities that reflect the situation at that time [13]. The var- ious angular scales of these temperature inhomogeneities are extracted in multipole expansion analyses. Figure 1.2 shows the most recent measure- ment 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 in- dicates 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 ob- servation 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 electromag- netic 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 ev- idence 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 ob- jects (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 micro- lensing results towards the Magellanic Clouds [19]. Neutrinos fulfill most dark matter criteria. They are stable, massive, non-baryonic particles that do not in- teract 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,
Ωχh2≈ 3 × 10−27cm3s−1/hσ vi, (1.1) wherehσ vi is the thermally averaged product of the total annihilation cross- section and the relative particle velocity. Using the current best measurement of ΩDM from section 1.1 and eq. 1.1, hσ vi is calculated to be near the typi- cal size of weak scale interactionsO(10−25cm3s−1). 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 χ ¯χ→ 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 min- imal 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 ˜qand ˜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 can- didate.
The lightest neutralino
Observational constraints limit the LSP to be neutral, thus carrying no electri- cal 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,
χ≡ ˜χ10= n11B˜+ n12W˜3+ n13H˜10+ n14H˜20, (1.3) is the lightest linear combination of gauginos ( ˜Band ˜W3) and higgsinos ( ˜H10 and ˜H20), which will simply be referred to throughout as χ. The linear coef- ficients 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 ofO(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 lead- ing annihilation channel is into heavy fermion-antifermion pairs like top, bot- tom, and charm quarks and tau leptons as well as heavy gauge boson pairs, like W+W−and Z0Z0pairs. 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 ν ¯ν 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 dimen- sion, the 3+1-dimensional space-time. The first attempts to extend this dimen- sionality 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- tra dimension of size R∼ O(TeV−1) [29]. Within minimal UED theories, the first excitation of the hyper-charge gauge boson, B(1), is generally the light- est 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 conser- vation, 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 detec- tionexperiments 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
SM χ
SM χ
(a) Direct detection
χ χ
SM SM
(b) Indirect detection
SM SM
χ χ
(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
dEr = σnρ0
2mχµnχ2 F2(Er) Z ∞
vmin(Er)
f(~v +~vE(t))
v d3v, (1.4)
where σn is the WIMP-nucleon cross-section, ρ0 the local dark matter den- sity, 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 galac- tic 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- imental material, A, as σSI ∼ A2. The spin-dependent interaction σSD(axial- vector interaction) results from couplings of the WIMP-spin content to the to- tal spin component of the target material. Thus, σSDis 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 depen- dent 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 section in the order of 10−41 cm2 [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 mat- ter. 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
vmin(Er)=
smnEr
2µnχ2 , (1.5)
where mn is the target nucleus mass. From eq. 1.5 we can see that the ex- pected WIMP rate depends on the detectors’ energy threshold and target ma- terial. 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 indi- rect 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 mat- ter 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 can- didates 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 en- ergy 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 atmo- sphere). 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 bod- ies, 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, pre- dict many new particles (e.g. sparticles), which are heavier unstable parti- cles 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 de- tailed 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 de- tectable 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 inde- pendent 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 neu- trino 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 di- rect detection experiments. Here, the target mass (Sun) isO(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
dt = CC−CAN2−CEN, (1.6)
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]. CAdepends on the thermally averaged product of the total annihilation cross-section and the relative particle velocity per vol- ume. 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) de- pends on the halo density and velocity profile of dark matter, mχ, and in- teraction cross-section. We assume a standard dark matter halo model, with the Sun moving at v = 220 km s−1 through a halo with local dark matter density ρ0= 0.3 GeV cm−3 and dark matter velocities following a Maxwell- Boltzmann distribution with average speed ¯v= 270 km s−1. The WIMP model dependent interaction cross-section is composed of the spin-independent com- ponent (σSD) and spin-dependent component (σSI) of the interaction cross sec- tion. 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 it is important to sum over all elements in the Sun (owing to σSI ∼ A2). As a result, σSI depends on detailed information on the solar abundance of ele- ments (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:
ΓA(t) =1
2CAN(t)2 (1.7)
Using eq. 1.6, we derive the annihilation rate at a given time, t, as, ΓA(t) =1
2CCtanh2 t τ
, (1.8)
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
