Dark Matter Lecture

Dark matter lecture

Teresa Marrod´anUndagoitia Max-Planck-Institut f¨urKernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany E-mail: [email protected]

Abstract. This document is a brief summary of the topics discussed during the experimental part of the the dark matter lecture held together with Tilman Plehn in the winter term of 2015 at the University of Heidelberg. CONTENTS

Contents

1 Dark matter indications4 1.1 Dispersion velocities of galaxies in clusters...... 4 1.2 Rotation curves...... 4 1.3 Gravitational lensing...... 4 1.4 Galaxy-cluster collisions...... 6 1.5 Cosmic microwave background...... 7 1.6 Large structure formation...... 9 1.7 Big Bang nucleosynthesis...... 10

2 Explanations and particle candidates 12 2.1 Explanations...... 12 2.1.1 Modification of gravitational laws...... 12 2.1.2 MACHOS and micro-lensing measurements...... 13 2.2 Particle properties to be the dark matter...... 13 2.3 Standard model particles...... 13 2.4 Beyond the standard model...... 13 2.5 WIMPs and their production mechanism...... 14 2.6 Supersymmetry (SUSY)...... 15 2.7 Extra dimensions...... 15 2.8 Superheavy WIMPs...... 16 2.9 Sterile neutrinos...... 16 2.10 Axions...... 17

3 Dark matter distribution 19 3.1 Motivation...... 19 3.2 Objects of interest...... 19 3.2.1 Structure of the Milky Way...... 19 3.2.2 Milky Way satellite galaxies (dwarf spheroidals)...... 20 3.2.3 Other objects...... 20 3.3 Simulations of dark matter halos...... 21 3.3.1 Historical developments...... 21 3.3.2 Density profile and substructure...... 22 3.3.3 Velocity distribution...... 23 3.4 Uncertainties in indirect detection...... 23 3.5 The standard halo model (SHM)...... 24 3.6 Uncertainties in the determination of halo parameters...... 24

4 Indirect detection 25 4.1 Locations of indirect signals...... 25 4.2 Possible processes and signal rates...... 25 4.3 Particle propagation and detection...... 25

2 CONTENTS

4.4 Searches using neutrinos...... 25 4.5 Gamma detection in Cherenkov telescopes...... 28 4.6 Gamma detection by satellites...... 31 4.7 X-rays: XMM-Newton & Chandra signal and interpretations...... 33 4.8 Charged particles...... 35

5 Direct detection 37 5.1 Principles...... 37 5.2 Backgrounds...... 43 5.2.1 External backgrounds: gammas, neutrons and neutrinos..... 43 5.2.2 Internal and surface backgrounds...... 46 5.3 Statistical treatment of data...... 47 5.4 Detector calibration...... 48 5.5 Experiments and results...... 51 5.5.1 Scintillator crystals...... 51 5.5.2 Germanium detectors...... 52 5.5.3 Cryogenic bolometers...... 52 5.5.4 Liquid noble-gas detectors...... 52 5.5.5 Superheated fluids...... 52 5.5.6 Directional searches...... 53

6 Dark matter searches at particle accelerators 53 6.1 Introduction...... 53 6.2 Signatures and features...... 53 6.3 Searches at LEP...... 53 6.4 Searches at LHC...... 53 6.5 Comparison to direct/indirect detection results...... 53

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1. Dark matter indications

Introduction: observing matter by gravity. Analogy with the discovery of Neptune.

1.1. Dispersion velocities of galaxies in clusters • First historical indication for dark matter (1933) • Virial theorem: relation between kinetic and potential energy • Derivation of Coma cluster mass following F. Zwicky paper [1]. The derived mass is 400 times larger than the observed mass

1.2. Rotation curves • Measurement of rotation velocity from the Doppler shift of the 21 cm hydrogen line • Expectation: decreasing velocities for increasing distance to the galactic centre q (outside the main visible mass distribution ∝ 1/r) • Measurement: rotation curves are approximately flat for large radii • Early measurement in 1978 by V. Rubin [2], see figure1 (left) • A halo of additional ’dark’ matter with density ρ ∝ 1/r2 can explain the data at large radii • Recent detailed fitting of visible mass components and dark matter, see figure1 (right) and [3]

Figure 1. Examples of rotation curve measurements. (Left) Figure from V. Rubin et al., 1978 [2]. (Right) Figure from E. E. Richards et al., arXiv:1503.05981 [3]).

1.3. Gravitational lensing • Deflection of light by a massive object (lens) as it travels from the source to the observer

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• By analysing deflection patterns, the matter distribution of the lens can be reconstructed • Effect proposed by Einstein in 1936 [4] • Types of lensing [5]: strong, flexion, weak and microlensing. See figure2 for the classification of images from the first three lensing types

Figure 2. Various regimes of gravitational lensing image distortion. A circular source is distorted into an ellipse by weak lensing being the typical resulting axis ratio ∼ 2 % (exaggerated for illustration). For most curved space-time (most massive objects), strong gravitational lensing produces multiple imaging and giant arcs. Figure from R. Massey et al. (2010), arXiv:1001.1739 [5].

• Strong lensing for dense concentrations of mass. If source is behind, Einstein rings can appear, otherwise multiple images result. See figure3 for observed examples

Figure 3. (Left) Strong lensing: Einstein ring. Figure from ESA/Hubble & NASA. (Right) Weak lensing in Abell 2218. Figure from NASA.

• Weak lensing appears when the lines of sight pass through more extended objects. By analysing a large number of object behind the lens, a statistical analysis can be performed to extract a mass distribution map. See figure4 • Flexion is an intermediate effect between strong and weak lensing • Microlensing: small increase in observed luminosity when a small object crosses the line of sight of a star. Used to search for Jupiter-like objects, see also section 2.1.2

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Figure 4. Weak lensing. (Left) Physical gravitational lensing produce E-modes, tangential to mass over densities. Other spurious artefacts can mimic E-modes. The curl-like B-mode is used to verify the E-mode resulting potential. (Right) Observed ellipticity of half a million galaxies within 2 square degree Hubble COSMOS survey. Lines represent the mean ellipticity. From R. Massey et al. (2010), arXiv:1001.1739 [5].

1.4. Galaxy-cluster collisions • Galaxy clusters are composed by stars in galaxies, gas clouds and dark matter • Rare events: collision of two such objects (tangential to observers on Earth) • X-ray measurements determine the collision of the gas clouds which are the main visible-mass constituent of the galaxy cluster • Telescope in the ’visible’ range determine the position of galaxies • Weak gravitational lensing used to determine the total mass distribution • Few examples of such event are shown in figure5, see also reference [6]

Figure 5. Galaxy-cluster collisions: bullet cluster, Abell 520 and DLSCL J0916.2+2951, respectively. Figures from astro-ph/0608407 [6], X-ray: NASA / CXC/ U. Victoria/ A. Mahdavi et al. and arXiv:1110.4391.

• Recent study of 72 cluster collisions [7] used to determine the average displacement of dark matter center to the baryonic matter centre, see figure6 6 1 DARK MATTER INDICATIONS

• Limits on the dark matter self-interaction can be placed [7]

Figure 6. Galaxy-cluster collisions: (Right) Diagram of the displacement between gas (red), dark matter (blue) and the stars (green). (Left) Displacement results for 72 collisions. Figure from D. Harvey et al. Science 347 (2015) 1462, arXiv:1503.07675 [7].

1.5. Cosmic microwave background • CMB: thermal photon radiation emitted at the end of recombination era • Isotropic emission with a temperature of T = 2.7 K • Predicted by Gamov ∼ 1950 • First measurement by Penzias and Wilson, accidentally, in 1964 using horn antennas for telecommunications • CMB anisotropies: fist measured by the COBE satellite in 1992. Also confirmed the black-body shape of the spectrum

Figure 7. Cosmic microwave background maps. (left) Figure Planck Collaboration, arXiv:1507.02704 [8]. (Right) CMB resolution for different satellite measurements.

• WMAP and Planck satellites measured the anisotropies (10−5 K) in great detail. See figure7 for a current map [8] (left) and the comparison of the resolutions (right)

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• Most recent measurements by the Planck satellite operated from 2009 to 2013 • Two instruments (low and high frequency) to cover different frequency regions • The backgrounds of the measurement affect differently the various frequencies, see in figure8 (left) the different backgrounds to the measurement and the frequencies measured by Planck (grey vertical bands)

Figure 8. (left) CMB foregrounds as modelled by the Planck experiment. Figure from Planck Collaboration, arXiv:1502.01588 [9]. (Right) Temperature angular power spectrum of the primary CMB map by Planck. Figure Planck Collaboration, arXiv:1502.01589 [10].

• CMB power spectrum derived from the correlation of temperatures with respect to an angular scale • Power spectrum as measured by Planck in figure8 (right) • At low `, the measurement is affected by low statistics (cosmic variance) • At high `, the resolution of the satellite determines how well structures are measured • Main spectral feature: ripples in the spectrum originating from baryon acoustic oscillations • Position of the first peak determines the curvature of the Universe • Other features in the spectrum are related to how photons were emitted and effects (like lensing) during the propagation • Spectrum is fit with a 6 parameter model: ΛCDM (Λ cold dark matter) indicating that dark matter is a fundamental ingredient. The Λ refers to the cosmological constant necessary to explain the accelerated expansion of the Universe • From CMB we know that 27% of the total energy content in the Universe is dark matter

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1.6. Large structure formation • Measurements of matter distribution from CMB maps, spectroscopic surveys, gravitational lensing and Lyman-α line of quasars • Simulations provide the link from CMB map to matter distributions today, see figure9 for an example from the Millennium simulation [11] • Figure9: dark matter on the left panels and galaxies on the right

Figure 9. Projected dark matter distributions from Millennium N-body simulations. The epochs displayed correspond to times of 600 million, 1 billion, 4.7 billion and 13.6 billion years after the Big Bang, respectively. The dark matter evolves from a smooth, nearly uniform distribution into a highly clustered state, quite unlike the galaxies, which are strongly clustered from the start. From Springel, Frenk & White, Nature 440 (2006) [11].

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• Spectroscopic galaxy survey data can be compared to simulations, see figure 10 • Very good agreement between simulated distributions and measurements

Figure 10. Comparison of clustering in observations of galaxy surveys (in blue) and in dark matter simulations (red). From Springel, Frenk & White, Nature 440 (2006) [11].

• Simulations were until recently ’dark-matter-only’. Dark matter is necessary to form structures • If dark matter is a particle and it is relativistic at the time of structure formations, the relative size of structures would be smeared out → dark matter can not be ’hot dark matter’ • Challenges of ΛCDM: number of small-scale structures within haloes and cusp-core problem in the halo density profile. Prospects: baryonic feedback might solve some of theses discrepancies

1.7. Big Bang nucleosynthesis • Big Bang nucleosynthesis (BBN) happens as the Universe is expanding and cooling down (∼ 3 min after BB) • Light nuclei are created: H, D, 4He, 3He and small amount of 7Li • 3H and 7Be are also created but are unstable and decay

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• Heavier elements are only created by stellar nucleosynthesis • BBN predicts the abundances of elements as function of temperature, nucleon density, expansion rate and neutrino properties, see prediction bands in figure 11 • The baryon to photon ratio η is a key parameter as high energy photons can disrupt deuterium changing the production rate of some isotopes • Figure 11 shows the predicted abundances as a function of η [12]

Figure 11. Abundances of 4He, D, 3He and 7Li predicted by the standard model of Big Bang nucleosysthesis. Boxes indicate observations and the vertical narrow band indicates CMB measure of cosmic baryon density. Figure from B. Fields and S. Sarkar, J. Phys. G33 (2006) 1 [12].

• By comparing the baryon density obtained by theses measurements and the one of CMB, we learn that dark matter can not be baryonic

11 2 EXPLANATIONS AND PARTICLE CANDIDATES

2. Explanations and particle candidates

2.1. Explanations In this lecture, we discuss how to explain the cosmological and astronomical indications that were summarised in the last lecture.

2.1.1. Modification of gravitational laws • Modification of gravitational laws, first proposed in 1983 (MOND [13]) to explain rotation curves (phenomenological approach) • With this modification the rotation curve is asymtotically flat • Observational support: Tully-Fisher correlation and ’cusp’ density profiles predicted by simulations • Fits of the MOND model to rotation curves data with only one free parameter (figure 12 (left)) • Problems: no explanation for lensing, cluster collision, CMB or structure formation • Relativistic extension TeVeS [14]. Explains lensing but not structure formation and CMB description is not very satisfactory

Figure 12. (Left) Fits of the MOND model (continuous line) to rotation curves data in Ursa Major galaxies. The dashed line represents the luminous disk and the dotted line the gaseous disk. Figure from Sanders & Verheijen, ApJ 503 (1998) 97. (Right) Examples of microlensing observations in the Large Magellanic Cloud. From C. Alcock et al. [MACHO Collaboration] Astrop. J. 542 (2000) 281 [15].

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2.1.2. MACHOS and micro-lensing measurements • MACHOS: Massive compact halo objects. These would be objects that produce very little to no light: black-holes, neutron stars, brown dwarfs .. • Microlensing suggested by Paczynski in 1986 [16]: observed brightness increases when a MACHO is aligned with the observed object • Very rare phenomena, surveys monitor typically O(107) stars • MACHO collaboration observed 12 million stars in the Large Magellanic Cloud and detected (13−17) microlensing events, few see examples [15] can be seen in figure 12 (right) • A 100% MACHO-composition of the Milky Way is ruled out at 95% C.L. [15]

2.2. Particle properties to be the dark matter Ordinary matter is made out of particles. Therefore, it is natural to make the hypothesis that dark matter is also made out of elementary particles. Theses particles have to fulfil: • Massive → to explain gravitational effects • Neutral particle → no EM interaction • Stable or long-lived such that they didn’t decay until today • At most weak interaction • No strong interaction • Cold or warm (Cold are particles moving non-relativistically at the time when galaxies started forming, hot particles are relativistically moving at that time and warm is in-between)

2.3. Standard model particles • Out of the standard model only the neutrino fulfils most of the properties above • But it would be a hot dark matter candidate [17] • Phase-space arguments: due to the fermionic character of neutrinos, their occupation number is constrained by the Fermi-Boltzmann distribution, thus, they can not account for the observed dark-matter density in halos [18]

2.4. Beyond the standard model The standard model is very successful in describing particles and their interactions but:

• Does not include neutrino masses • No explanation for the matter-antimatter asymmetry in the Universe • Has no explanation for the 3 generations of particles • Has no unification of forces

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• Does not include gravitation • Does not explain the ’strong CP-problem’ (see section 2.10) • And does not provide a dark-matter candidate

Therefore, we need new models ’beyond the standard model’ which ideally provide a new particle to account for dark matter

2.5. WIMPs and their production mechanism • WIMPs (weakly interacting massive particles) are favoured candidates because they naturally have the right abundance to account for the dark matter • For high temperatures in the early Universe, WIMPs were in equilibrium with the thermal plasma • When the Universe expands, the temperature of the plasma decreases and the number density of created WIMPs also decreases. At some point the comoving number density stays constant, freeze-out [19] • The freezing out of the number density depends on the interaction cross-section

< σav >. For the typical strength of the weak interaction, the proper relic density results → remarkable coincidence! • Figure 13 shows the WIMPs together with other particle candidates in the cross- section versus particle mass parameter space [20]

Figure 13. Dark matter particle candidates. Figure from L. Roszkowski arXiv:hep- ph/0404052 [20].

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2.6. Supersymmetry (SUSY) • SUSY [21] was proposed by Wess and Zumino in 1973 • Relates bosons (spin integer) to fermions (half-integer). Each particle of the SM has a super partner which differs in the spin by 1/2 • Motivation: unification of EM, weak and strong interaction (see figure 14) and solving the hierarchy problem

Figure 14. Unification of forces in Supersymmetry. Figure from CERN.

• R-parity prevents the proton to decay and makes the lightest SUSY particle (LSP) stable → ideal DM candidate • Three possible DM candidates in this model: sneutrino, neutralino and gravitino • Sneutrino ruled out long ago because it couples to Z and direct detection experiments would have measured it already • Neutralino is the most favoured candidate. It is a superposition of the partners of the gauge bosons. Several orders of magnitude for cross-section and mass allowed • Gravitino appears in SUSY theories involving gravitation. Produced non-thermally in the early Universe via decay of another particle. No direct detection possible since it does not couple weakly

2.7. Extra dimensions • This is one of many different alternatives to the SUSY WIMP • Extra-dimensions models postulated around 1920 to unify EM and gravity • New particles appear: KK-particles (from Kaluza and Klein) 15 2 EXPLANATIONS AND PARTICLE CANDIDATES

• KK-parity protect the lightest particle to decay to SM particle, DM is stable • Interaction strength of the weak scale → WIMP

2.8. Superheavy WIMPs • Dark matter masses m ∼ (1012 − 1016) GeV, see figure 13 • Motivation: observation of ultra-high energy cosmic rays with energies above 1019 eV (above GZK cut-off) [22]

2.9. Sterile neutrinos • Neutral leptons with no ordinary interactions besides mixing (right-handed ν). Present in many extensions of the SM. In principle, almost any mass allowed • Originally proposed to explain the smallness of neutrino masses (See-saw mechanism). It also can explain the matter-antimatter asymmetry. Typical masses m ∼ (105 − 1012) GeV • Also light sterile neutrinos with ∼ keV masses are widely discussed nowadays [23] • Need to be sufficiently stable, be produced in the right abundance and fulfil the experimental constrains from the non-observation of an X-ray signal from the radiative channel N → νγ, see figure 15. The white region represents the region still allowed and the coloured regions are excluded.

Figure 15. Constrains for sterile neutrino dark-matter. Figure from Alexey Boyarsky et al., Physics of the Dark Universe 1 (2012) 136.

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2.10. Axions • In QCD there is no reason to conserve CP but experimental bounds on the neutron electric dipole moment indicate very small CP violation • In 1977 Peccei and Quinn postulated a new symmetry to solve this issue • The axion particle appears when the symmetry is spontaneously broken at the scale

fa, axion mass and couplings are: ma, gaii ∝ 1/fa

• Couplings of axions to matter: gaNN , gaγγ and gaee and processes like Compton, Primakoff and Bremstrahlung • Early constrains from accelerator experiments → ’invisible axion’ • Astrophysics constrains using an energy-loss argument: properties of stars would change if they lose too much energy via axion production [24], see figure 16. The lighter the regions, the more model dependent are the constrains. Regions uncovered by bulks are still allowed axion masses.

Figure 16. Summary of astrophysical and cosmological axion limits. The black sensitivity bars indicate the search ranges of the CAST solar axion search and the ADMX search for galactic dark matter axions. Light-grey exclusion bars are very model dependent. Figure from G. Raffelt, Astrophysical axion bounds, Lect. Notes Phys. 741 (2008) 51 [24].

• Telescope limits → from absence of signal of axion decay a → γγ, see figure 17

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Figure 17. Constrains of axion/axion-like particles (ALPs) coupling to photons as function of their mass. The yellow band represents favoured regions for ’invisible axions’. Other coloured regions represent excluded regions while white regions are still allowed. Figure from Letter of Intent to the CERN SPSC. The International Axion Observatory IAXO (2013).

• Axion search experiments: – Solar axion searches using helioscopes: CAST or Tokyo axion telescope. – Search for cosmic axions using microwave cavity haloscopes: ADMX and CARRACK – Laser searches for ALPs∗ using polarised laser beams or ’light-shinning through the wall’ experiments • ∗ ALPs: Axion-like particles, similar type of particle but does not solve necessarily the strong CP problem • Axion production in the early Universe. Thermal would give hot dark matter. Non thermal production: vacuum realignment, string decay and wall decay. The latter mechanisms make possible to produce very cold axions

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3. Dark matter distribution

3.1. Motivation • If dark matter is a particle, there are three main strategies to confirm this hypothesis: indirect-, direct detection and production at accelerators

Figure 18. Representation of ways to test the hypothetical particle nature of dark matter. Figure from J. Phys. G: 43 (2016) 1 [25].

• For indirect- and direct detection, information on the density profile and velocity distribution is required • Indirect detection: the annihilation flux depends on the density squared (J-factor). For the particle decay, the flux of particles depends linearly on density • Direct detection: linear with the DM density and contains the integral over the velocity distribution

3.2. Objects of interest • Indirect detection: galactic center/halo, Milky Way satellite galaxies and close galaxies/ galaxy-clusters • Direct detection: Milky Way at the position of the Sun • Units: 1pc ≈ 2.06 × 105 AU ≈ 3.3 light years. • Origin of units: A parsec is the distance such that one astronomical unit subtends an angle of an arcsecond. An astronomical unit (AU) is the distance from Earth to the Sun.

3.2.1. Structure of the Milky Way • Complex system of stars, gas, dust and dark matter • Best studied of all galaxies but measurements challenging because observations are performed ’from inside’

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• Figure 19 shows a schematic view of the Milky Way (MW) including typical sizes in kpc

Figure 19. Scheme of the Milky Way.

3.2.2. Milky Way satellite galaxies (dwarf spheroidals) • Galaxies orbiting the Milky Way at distances (15−250) kpc from the galactic centre • Best known: Large and Small Magellanic clouds (discovered in 1591) • Few other discovered from 1938-1994 and several after 2005 with the Sloan Digital Sky Survey (SDSS) telescope • Most important for dark matter: very large mass-to-light ratios, 100 or greater. Therefore, it is unlikely that luminous components have altered the DM distribution in theses systems. These arguments make the dwarf spheroidals a very favoured target for dark matter searches

3.2.3. Other objects • Andromeda galaxy (780 kpc from Earth). Largest galaxy in the local group • Virgo cluster (∼ 20 Mpc from the MW) which belongs to the Virgo supercluster • Coma cluster (∼ 100 Mpc from the MW) which belongs to the Coma supercluster • Figure 20 shows the distribution of objects in the local group and the virgo supercluster

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Figure 20. Left: local galactic group. Right: Virgo supercluster. Figures from wikipedia.

3.3. Simulations of dark matter halos

3.3.1. Historical developments •∼ 1960: early simulations of the gravitational collapse of a collision less system (formation of elliptical galaxies) • 1980: large cubes of the Universe simulated (understanding of hierarchical clustering, to match large-scale structures) • 1990: resolution allows to resolve individual objects (galaxies) from large simulations • 1996: Navarro, Frenk & White (NFW) simulated haloes with 4 orders of magnitude different in mass. A profile steeper than the isothermal one is obtained in the central structure of the haloes (see figure 21). The profile is ’universal’, i.e. same shape for all simulated halo masses [26]. •∼ 2006: Full cosmological simulations starting from CMB anisotropies (Millennium simulation [11]). These are dark-matter only simulations. Baryonic matter is added to subsamples of the simulation using semi-analytic techniques to study galaxy formation • 2008: Detailed simulations of MW-like galaxies from parts of the cosmological simulations: Acquarius[27], GHALO[28] and Via Lactea[29] • 2013: Illustris simulation + various other studies show the effects of baryonic matter on the dark matter profile. Illustris includes baryons in the simulation including cooling mechanisms, stellar evolution and feedback, chemical enrichment, supermassive black-hole growth and feedback from AGNs. See simulation output in figure 23

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Figure 21. Comparison of different dark matter density profiles for the Galactic halo. Figure from A. Albert et al., JCAP 10 (2014) 023 or arXiv:1406.3430.

3.3.2. Density profile and substructure • Dark matter simulations show universal profiles, see figure 22 (left) → fractal nature of dark matter clustering

Figure 22. Via Lactea II. Left: density profiles of main halo and subhaloes. Profile of a Milky Way-sized galaxy (black line) and eight large sub haloes (thin lines). Right: projected dark matter density map of a galaxy with the mass of the Milky Way. Figures from J. Diemand et al. [29].

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• All dark matter only simulations favour steeper profiles (CUSP) while observations favour flatter ones (CORE). The CUSP/CORE problem has been during long time seen as a challenge for the cold dark matter model. The recent simulations including baryonic matter show that baryonic matter can account or the profile differences • Missing satellite problem: in simulations a large amount of substructure is found, see figure 22 (right). However, the number of satellites observed is far lower. Recent measurements have found already more satellites and future measurements in the next years might solve completely this ’problem’ • Figure 23 (left) shows also the appearance of substructure in the Aquarius simulation. The tail to large ρ is due to subhaloes. The probability density function is in the region (6 − 12) kpc corresponding approx. to the location of the Sun in the Milky Way. The chance that the Sun lies in a subhalo is 10−4.

Figure 23. (Left) Density probability distribution function for six simulated haloes. Figure from M. Vogelsberger et al. [30]. (Right) Output from the illustris simulation showing for different z the distribution of dark matter, gas density, gas temperature and gas metalicity. Figure from http://www.illustris-project.org.

3.3.3. Velocity distribution • Simulations find triaxial velocity distributions. Example from Aquarius [30] in fig 24 • High velocity tails have a large impact on direct detection experiments

3.4. Uncertainties in indirect detection • J-Factors differ for the different DM profiles • The amount of substructure considered lead to significant changes in sensitivity (see section4)

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Figure 24. (Left) Velocity distributions in a 2 kpc box at a position similar to our Sun. v1, v2 and v3 are the velocity components parallel to the major, intermediate and minor axes of the velocity ellipsoid. (Right) Velocity modulus distribution for four simulated haloes at high resolution. All distributions are smooth and show characteristic broad bumps, present in all boxes for a given halo. Figures from M. Vogelsberger et al. [30].

3.5. The standard halo model (SHM) • Used in direct detection to derive results with the same local density and velocity distribution for all experiments • SHM: isotropic and isothermal with ρ ∝ 1/r2 • The solution of the collision less Boltzmann equation is a Maxwellian velocity distribution. This function is usually truncated to be 0 at the escape velocity (for which particles are not bound in the gravitational potential anymore) • Standard parameters of the Milky Way SHM [31]: – Local dark matter density: 0.3 GeV/cm3 – Circular speed: (220 ± 20) km/s and escape velocity: 544 km/s • Direct detection experiments use the SHM but the results are not astrophysics independent

3.6. Uncertainties in the determination of halo parameters • Dark matter density: calculated via mass modelling of the Milky Way (simulations with cored or cusped profiles and models using equations). Standard value uses parameters in agreement with observational data. Depending on the profile model used for the halo, a density range from (0.2−0.6) GeV/cm3 can be derived (see [32]) • Circular velocity: velocities ranging from (200 ± 20) km/s to (279 ± 33) km/s are found [31] (also dependent on the MW profile used). 24 4 INDIRECT DETECTION

• Escape velocity: the commonly used value of 544 km/s is the likelihood median calculated using data from the RAVE survey [33]. The 90% confidence interval contains velocities from 498 km/s to 608 km/s.

4. Indirect detection

4.1. Locations of indirect signals At objects with large DM density + reasonably large solid angle (close distance)

• Milky Way galactic center and halo • Satellite galaxies: dwarf spheroidals • Sun and Earth • Andromeda (nearest galaxy) and ’close’ galaxy clusters (Coma, Virgo, ..)

4.2. Possible processes and signal rates • Annihilation: various channels χχ → γγ, γZ, γH, qq, W +W − .. • Particle decay: if the dark matter particle is unstable (gravitino, sterile neutrino, axion ..). Signal would be more spatially extended than the annihilation one as the particle flux scales linearly with density and not quadratically • Capture in the Sun + annihilation into neutrinos: set constrains to the DM-nucleus cross section (as in direct detection)

4.3. Particle propagation and detection • Neutral particles point to the source where they were produced → pointing. While neutrinos have a negligible absorption during propagation, for gammas the propagation has to be considered only for very high energies or very large distances • Charged particles (e−, e+, p, p) are deflected in interstellar magnetic fields • Detector technologies: – High energy neutrinos (from ∼ GeV to 100 TeV) → large ν-detectors

– High energy (Eγ > 100 GeV) gamma-rays → Cherenkov imaging telescopes – Low energy (20 MeV < Eγ < 100 GeV) → ballon or satellites, e.g. Fermi – X-rays → X-ray satellites as XMM-Newton or Chandra – Charged particles → at satellites, e.g. Pamela, Fermi, AMS

4.4. Searches using neutrinos • Use the same target and detection medium (water or ice) • Neutrino reactions with target particles/nuclei • Cherenkov photons emitted by charged particles are recorded with photosensors

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• Ice-Cube detector at the south pole (see figure 26 left), Eν ∼ (0.1 − 100) TeV • Background sources: (1) Muons which are suppressed by looking at particle traces ’from below’ and (2) Atmospheric neutrinos, irreducible but the spectrum is well known and decreases with increasing energy • Experimental uncertainty mainly from optical-modules efficiency and photon propagation in ice • Discussion of PRD 88 (2013) 122001: upper limits on thermally averaged cross section for searches at dwarf spheroidals, Andromeda and galaxy clusters • Figure 25 shows the results of this publication, showing explicitly the dependence on the source, the annihilation channel, the astrophysical uncertainties and the effect of considering boost factors due to substructures, i.e. sub haloes.

Figure 25. Ice Cube searches for self-annihilating dark matter in nearby galaxies and galaxy clusters. Top left: upper limits for annihilation into W +W − in dwarf galaxies. Top right: upper limits for the Virgo cluster for annihilation into bb, W +W −, τ +τ −, µ+µ−, and νν. Bottom left: upper limit for Segue 1 for annihilation into W +W − including astrophysical uncertainties. Bottom right: upper limits (W +W − annihilation) assuming a pure NFW profile (dashed) and taking into account substructures within halos (solid). Figures from IceCube collaboration, Phys. Rev. 88 (2013) 122001 [34].

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Figure 26. (Right) Schematics of the IceCube detector. Figure from Into the Ice: Completing the IceCube Neutrino Observatory, Berkeley Lab. (Left) Schematics of the SuperKamiokande detector. Figure from SuperKamiokande homepage.

• Super-Kamiokande detector (see figure 26 right), water Cherenkov detector in Japan. It can measure events with visible energy > 30 MeV. • Searches for DM annihilation producing neutrinos after the capture of the DM particles in the Sun [35] • Figure 27 shows types of events in the Super-Kamokande detector. Fully-contained (middle and left for different energies), partially contained (PC, top right) and through going muons (bottom right). The data is compared to the MC simulation of a DM annihilation signal for 6 GeV/c2 and 200 GeV/c2 WIMP masses

Figure 27. Angular and reconstructed momentum in GeV/c distributions (data in black), atmospheric ν-background (solid blue) and WIMP neutrino signal for 6 GeV/c2 and 200 GeV/c2 magnified 30 times for visibility. Figure from Super-Kamiokande Coll., Phys. Rev. Lett. 114 (2015) 141301 [35].

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• As no excess is observed in figure 27, upper limits on the neutrino flux can be converted into upper limits on WIMP-nucleon cross section. Figure 28 shows in red the SuperKamiokande upper limits on the WIMP-nucleon and spin-dependent WIMP-proton cross sections in comparison with the direct detection results. The shadowed regions around the limits represent the uncertainties which are mainly from the metal composition of the Sun 25% (45%) for SI (SD) and the velocity distribution of DM particles: 40% (25%) for SI (SD)

Figure 28. Results from Super-Kamiokande searches for captured low-mass dark matter in the Sun, spin-independent (left) and spin-dependent (right). Figure from Super-Kamiokande Coll., Phys. Rev. Lett. 114 (2015) 141301 [35].

4.5. Gamma detection in Cherenkov telescopes • Detection of high energy gamma-rays with energies ∼ (0.05 − 50) TeV • The atmosphere is the target and calorimeter at the same time • Cherenkov light from particle-showers (figure 30, top left) • Imaging technique: image reconstructed in the camera (see examples in figure 29). A muon-like event is a ring, a hadron-like shower is an irregular bump and a gamma- like shower is a ’more regular’ ellipse.

• Background is mainly from protons. 99% of the cosmic rays are protons. The shower shape is used to reduce this background • Electrons from cosmic rays make ∼ 10% of the gamma-like events → irreducible

• Direct signal production χχ → γγ, γZ, Bremstrahlung of charged particles and decay of hadrons, Bremstrahlung of one of the internal particles in the annihilation diagram and decay (for example χ → γX)

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Figure 29. Examples of signals in one of the MAGIC Chrenkov telescopes. Figures from the MAGIC Collaboration (homepage).

• Secondary radiation by e−e+ produced in the annihilation: Inverse Compton scattering onto CMB, star light and Infrared light, Bremstrahlung and synchrotron emission • Instruments: – Veritas in southern Arizona (US), 4×12 m optical reflectors, 2 600 m above see – MAGIC in La Palma (Spain), 2 × 17 m reflectors, 2 400 m above see – HESS in Namibia, 4 × 13 m and one 28 m reflectors, 1 800 m above see

• Discussion of the publication: HESS PRL 114 (2015) 081301: observation of the central region of the Milky Way • Bottom panels of figure 30 show the signal and background regions when using the ON/OFF technique (left) and the models used to describe the dark matter distribution (right). A conservative approach is used in which the density is assumed constant for radius smaller than 500 pc. • The upper right panel of figure 30 shows the upper limit resulting from this analysis depending on the dark matter distribution model used.

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Figure 30. (Top left) Schematics of a imaging Cherenkov telescope. Figure from HESS homepage. Search for dark matter annihilation in the galactic centre by HESS: (Top left) Upper limits on the velocity-averaged cross section for different halo profiles. (Bottom left) Signal and background regions. (Bottom right) Profiles used for the analysis. Figures from HESS Collaboration, PRL114 (2015) 081301, arXiv:1502.03244 [36].

• Discussion of the publication: HESS PRD 90 (2014) 112012: results of the observation of dwarf spheroidals using 140 hours total observation time • No significant signal → limits derived for the thermally averaged annihilation cross section. Figures 31 show the dependence of the 95% C.L. exclusion limits on the object (left) and on the annihilation channel (right). The relative differences on the limits for different annihilation channels are related to the energy spectrum of the produced gamma rays.

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Figure 31. Exclusion limit at 95% C.L. on the velocity averaged cross section of WIMP annihilation in the W +W − and ZZ final states using the NFW halo profile for different dwarf spheroidals (left). Same figure but for different annihilation channels (right). Figures from HESS Collaboration, Phys. Rev. D90 (2014) 112012 [37].

4.6. Gamma detection by satellites • The measurement of gamma rays at satellites is sensitive to lower γ-energies that are not absorbed by the atmosphere. However, in general those detectors have an smaller volume and therefore are also limited on measuring high γ-ray energies. • Fermi-LAT detector (see figure 32), an imaging high-energy γ-telescope in orbit since 2008 (1 orbit in 96 min)

• The energy range covers from Eγ ∼ (10 MeV − 300 GeV)

Figure 32. Scheme of the the FermiLAT instrument. Figure from Fermi homepage.

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• Detector construction: – Anticoincidence detector (to select neutral particles) – Tungsten conversion foil (target for γs) – Silicon strips (for tracking) – CsI calorimeter (measurement of energy) • The device is able to measure both energy and the direction of the γ-ray particle • Volume of 0.72 m × 1.8 m2, 2.8 tons and 650 W power consumption • Calibrated at particle beams (CERN, SLAC and GSI)

• Fermi collaboration has set limits on < σAv > from searches in the galactic halo (continuum and line-like), galaxy clusters and dwarf spheroidals. • Galactic center signal indication: – First seen in 2011: Hooper & Goodenough PLB 697 (2011) 412. Excess around the galactic centre (∼ 10◦) at (1 − 10) GeV – Reanalysis (Daylan 2014 and Calore 2015) confirm signal and study systematics

Figure 33. Constrains on the dark matter annihilation cross section at the 95% C.L. for the bb and ττ channels from the combined analysis of 15 dwarf spheroidals. (Top) The bands represent the expected sensitivity. (Bottom) Comparison with of these results with other experimental results. Figure from Fermi-LAT Collaboration, Phys. Rev. Lett. 115 (2015) 231301 [38].

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– Fermi analysis → unclear significance and large uncertainties due to unknown background modelling – Other explanations: Protons from supernova remnants, electrons or ms pulsars • Discussion of publication: Fermi PRL 115 (2015) 231301. Dark matter search at

dwarf spheroidals → limits on < σAv > (see figure 33). Limit in tension with the galactic centre excess (bottom panels of the figure).

4.7. X-rays: XMM-Newton & Chandra signal and interpretations • Goals of X-ray satellites: study star-forming regions, formation and evolution of galaxy clusters, study of supermassive black holes & searches for dark matter • Detection energy range ∼ (0.1 − 10) keV • Measurements at satellites because the atmosphere would absorb this radiation • Instruments: XMM-Newton, Chandra • Detection principle: Wolter grazing mirrors (lenses or parabolic mirrors do not work to focus X-rays). The focussing happens only if the incident angle is very small (up to 2 degrees). Designed by Wolter in 1952, see figure 34.

Figure 34. Schematic of grazing X-ray telescope. This cross section through four nested pairs of mirrors illustrating the principle of grazing incidence reflection and focussing of X-rays. Figure from Chandra homepage.

• Wolter telescopes can be used to search for DM signals in the ∼ keV energy range • Background from ’known’ plasma emission lines (Al, Si, Fe, Ca, Ar, ..) • The 3.5 keV line: – 2014: weak unidentified emission line at ∼ 3.5 keV in the XMM-Newton and Chandra data of galaxy clusters (independently by E. Bulbul et al. 2014 and A. Boyarsky et al. 2014), see figure 35 (left) – Explanations: unknown plasma emission line (Jeltema & Profumo 2014 and recent paper: arXiv:1511.06557), sterile neutrino decay or axion decay

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– Morphology study shows that the line is distributed following the plasma distribution and not a dark matter profile (see figure 35 (right)) but the background below the line might be responsible for the distribution as the significance of the signal is low – Figure 36 shows the available parameter space for sterile neutrino decay and the favoured point (blue dot) derived from the 3.5 keV signal

Figure 35. (Left) XMM-Newton data in the region (3−4) keV stacking several galaxy clusters. Spectrum rebind to make the excess at ∼ 3.57 keV more apparent. Figure from E. Bulbul et al., ApJ 789 (2014) 13. (Right) Morphology of 8 plasma emission lines including the ∼ 3.57 keV band surrounding the galactic centre. Figure from E. Carlson et al. JCAP 1502 (2015) 02, 009 and arXiv:1411.1758.

Figure 36. Favoured point (blue dot) when interpreting the 3.5 keV line as a signature from sterile neutrino decay. Other constrains are shown in coloured regions. Figure from A. Boyarsky et al., PRL 113 (2014) 251301.

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4.8. Charged particles • Mainly measuring e−/e+ and p/p. No directionality, particles deflected in magnetic fields • Instruments: satellites as HEAT, CAPRICE, PAMELA, Fermi, AMS • Since 2008, ”positive results” in few experiments pointing to an excess at ∼ TeV scale in the positron fraction e+/(e+ + e−)

• AMS detector (see figure 4.8): Alpha Magnetic Spectrometer • At the international space station (ISS) since 2011 with 8.5 tons 2 500 W power consumption • Scientific goals: measurement of antimatter & dark matter

Figure 37. Schematics of the AMS detector. Figure from the homepage.

• Detector design: HE-physics type of detector (tested at CERN) – silicon tracker (9 planes) – transition radiation detector (particle identification) – Time of flight (4 planes) – Magnet – Anticoincidence counter (to reject particles entering from the sides) – Cherenkov detector

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– Electromagnetic calorimeter (energy measurement) • AMS has provided measurements of charged particles in the range – (10 − 290) GeV/c for e+e− – (180 − 400) GeV/c for protons • also provides the most precise measurements of the positron fraction (see figure 38 (left))

Figure 38. Compilation of data in charged cosmic rays: positron fraction (left) and sum of electrons and positrons (right). Figure from M. Cirelli (2015) arXiv:1511.02031.

• Discussion of the publication AMS, PRL 113 (2014) 121101 • Below 8 GeV, the positron fraction decreases with increasing energy. This is expected from the diffuse production of positrons. • Above 8 GeV, the fraction increases and this measurement is consistent with the observations of other experiments (besides normalization). This fraction is isotropic in the arrival direction. • Explanations: – e+ from pulsers → show show a slow decrease of the rate with increasing energies and a dipole asisotropy – DM annihilation: should show a rapid decreasing of the rate with increasing energy (the steepness depends however on the annihilation channel). This DM hypothesis requires, however, a large annihilation rate into leptonic final channels. Constrains from the non-observation of other signals.

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• Figure 39 shows a summary of the current (summer 2015) most stringent bounds on dark matter annihilation in different channels and from different searches.

Figure 39. Summary figure of the current most stringent bounds on dark matter annihilation in different channels and from different searches. The data originates from AMS-02, Fermi, CMB, HESS, ANTARES and IceCube. Figure from M. Cirelli (2015) arXiv:1511.02031.

5. Direct detection

5.1. Principles • For a ∼ (10 − 1000) GeV/c2 WIMP mass with the velocities of the standard halo model, nuclear recoils with target nuclei in ∼ (1 − 100) keV result • A nucleus moving through a medium can create ionisation, excitation and heat • Separation of recoils from different particles (electronic and nuclear recoils) is possible by combining different signals. This is called ’discrimination’ • Due to the low cross section of particles being tested, only a single interaction is expected. The probability for multiple interactions is negligible • WIMP interactions are expected to be homogeneously distributed in the detector volume while several of the background interact at the outermost layers of the target material. By using a fiducial volume cut to the data, the signal/noise ratio is improved

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• Signatures: – Spectral shape: most common approach in direct detection experiments is the attempt to measure the energy dependence of dark matter interactions (see figure 42). Differential energy spectrum of nuclear recoils from WIMP interactions can be approximated by dR dR !  E  (E) ≈ F 2(E) exp − , (1) dE dE 0 Ec  dR  where denotes the event rate at zero momentum transfer and Ec is dE 0 a constant parameterizing a characteristic energy scale which depends on the dark matter mass and target nucleus [39]. The signal is dominated at low recoil energies by the exponential function. F 2(E) is the form-factor correction which will be described later. dR ρ Z dσ (E, t) = 0 · v · f(v, t) · (E, v) d3v (2) dE mχ · mA dE

– Annual modulation: as a consequence of the Earth rotation around the Sun, the speed of the dark matter particles in the Milky Way halo relative to the Earth is largest around June 2nd and smallest in December. Consequently, the amount of particles able to produce nuclear recoils above the detectors’ energy threshold is also largest in June [40].

Figure 40. Scheme of the kinematic that give an annual modulation of the dark matter rate.

The temporal variation of the differential event rate can be written following [41] as dR 2π(t − t )! (E, t) ≈ S (E) + S (E) · cos 0 , (3) dE 0 m T

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where t0 is the phase which is expected at about 150 days and T is the expected period of one year. The time-averaged event rate is denoted by S0, whereas

the modulation amplitude is given by Sm. – Directional dependence of the signal: as the direction of the nuclear recoils resulting from WIMP interactions has a strong angular dependence [42]. This dependence can be seen in the differential rate equation when it is explicitly written as a function of the angle γ, defined by the direction of the nuclear recoil relative to the mean direction of the solar motion

" 2 # dR −[(vE + v ) cos γ − vmin] ∝ exp 2 . (4) dE d cos γ vc

In equation4, vE represents the Earth’s motion, v the velocity of the Sun around the galactic centre, vmin the minimum WIMP velocity that can produce q a nuclear recoil of an energy E and vc the halo circular velocity vc = 3/2v . The rate of events scattering in the forward direction will, therefore, exceed the rate for backwards scattering events. A detector able to determine the direction of the WIMP-induced nuclear recoil would provide a powerful tool to confirm the measurement of these particles.

Figure 41. Directionality signature: (top) WIMP flux in the case of an isothermal spherical halo, (middle) WIMP-induced recoil distribution and (bottom) a typical simulated measurement: 100 WIMP recoils and 100 background events (low angular resolution). Figure from J. Billard et al. 2010.

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Figure 42. (Left) Event rates as function of nuclear recoil energy for different target materials assuming a 100 GeV/c2 WIMP mass and an interaction cross section of 10−45 cm2 (solid lines). (Right) Event rates for argon and tungsten. Dotted line: no form factor correction. Dashed line: for a 25 GeV/c2 WIMP mass. Figures from arXiv:1509.08767.

• Cross sections and form factors: – Typically two cases are considered. Spin-dependent: in this case it is assumed that the protons and neutrons contribute equally (isospin conservation). Spin- dependent: Nuclei with an odd number of protons/neutrons contribute. The cross section σ is then related to the quark spin content of the nucleon – For momentum transfer q, such that the wavelength is small compared to the nuclear radius, σ decreases with q. The form factor account for this effect: 2 σ ∝ σ0 · F , (5)

where σ0 is the cross-section at zero momentum transfer. Figure 42 shows the effect of the form factor for different target nuclei. For heavy nuclei, the rate of nuclear recoils at large recoil energies is strongly suppressed. – The differential WIMP-nucleus cross section, dσ/dE shown in equation2, can be written as the sum of a spin-independent (SI) contribution and a spin- dependent (SD) one,

dσ mA SI 2 SD 2 = 2 2 · (σ0 · FSI(E) + σ0 · FSD(E)). (6) dE 2µAv The WIMP-nucleus reduced mass is described by µA. – For spin independent interactions, the cross-section at zero momentum transfer can be expressed as 2 SI µA p n 2 σ0 = σp · 2 · [Z · f + (A − Z) · f ] (7) µp 40 5 DIRECT DETECTION

where f p,n are the contributions of protons and neutrons to the total coupling

strength, respectively, and µp is the WIMP-nucleon reduced mass. Usually, f p = f n is assumed and the dependence of the cross-section with the number of nucleons A takes an A2 form.

– FSI is calculated assuming that the distribution of scattering centres is similar to the charge distribution obtained in electron scattering experiments. Helm form factor is typically used – For spin dependent in the dark matter field, it is common to display the cross- section for the interaction with protons and with neutrons 32 J + 1 σSD = µ2 · G2 · [a · hSpi + a · hSni]2 · (8) 0 π A F p n J 2 where GF is the Fermi coupling constant, J the total nuclear spin and ap,n the effective proton (neutron) couplings. The expectation value of the nuclear spin content due to the proton (neutron) group is denoted by hSp,ni. • Generalized approach: effective field theory – Instead of SI/SD, use of generalised operators using six possible nuclear response functions ~q ⊥ ~ ~ – The EFT operators are constructed by four three-vectors i ,~v , SN , Sχ which mN describe the momentum transfer q scaled with the nucleon mass mN , the ⊥ ~ WIMP-nucleon relative velocity ~v , the spin of the nucleus SN and the possible ~ spin of the dark matter particle Sχ, respectively. See figure 43.

Figure 43. Relative strength of event rates for a 50 GeV/c2 spin-1/2 WIMP in xenon for different non-relativistic operators. Figure from Dent et al., PRD 92 (2015) 6, 063515, arXiv:1505.03117.

– This approach will become more relevant in the case of a dark matter signal • Other signatures/physics channels: – Inelastic scattering: target nucleus left in an excited state which de-excite simultaneously to the NR [43]

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– Inelastic scattering: dark matter transitioning to an state δ above the ground state [44] – Dark matter coupling to electrons: axial-vector coupling [45] or axion interactions[46] (axioelectric effect) • Generic result of a direct dark matter experiment – The outcome of an experiment is an event rate with a certain spectral shape. Results are then commonly displayed in a parameter space of the dark matter- nucleon cross-section and the dark matter mass. – First question: is there statistical significance of signal over background? – If answer YES: Signal contours at a certain confidence level (2 σ are typical) – If answer NO: The left plot in figure 44 shows a generic limit (open black curve) on the dark matter cross-section with respect to the dark matter mass. At low WIMP masses the sensitivity is reduced mainly due to the low-energy threshold of the detector, whereas the minimum of the exclusion curve is given by the kinematics of the scattering process which depends on the target nucleus. At

larger WIMP masses, the event rate is overall suppressed by 1/mχ. Given that the local dark-matter density is a constant of 0.3 GeV/cm3, the heavier the individual particles, the less particles are available for scattering.

Figure 44. Sensitivity of direct detection experiments for different detector parameters. Figures from arXiv:1509.08767.

– Evolution of the sensitivity versus the exposure: The right plot in figure 44 illustrates the evolution of the sensitivity to the cross-section with respect to the exposure. For a given detector mass, the increase in exposure is caused by the accumulation of measuring time.

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5.2. Backgrounds 5.2.1. External backgrounds: gammas, neutrons and neutrinos • Gamma radiation: dominant radiation from gamma-decays originates from the decays in the natural uranium and thorium chains, as well as from decays of common isotopes e.g. 40K, 60Co and 137Cs present in the surrounding materials. Energies from tens of keV up to 2.6 MeV (highest γ-energy from the thorium chain). • The interactions of γ-rays with matter include the photoelectric effect, Compton scattering and e− e+ pair production [47]. Photoelectric effect has the highest cross-section at energies up to few hundred keV and pair production dominates above several MeV. Compton scattering is the most probable process for energies in between. All these processes result in the emission of an electron (or electron and positron for the pair production) which can deposit its energy in the target medium contributing to the experiment’s background. • Reduction by selecting materials with low radioactive traces. Gamma-spectrometry using high-purity germanium detectors is a common technique to screen and select radio-pure materials (see figure 46 left). Other techniques: mass spectrometry or neutron activation analysis [48]. • Shielding against γ’s: by surrounding the detector by a material with a high atomic number and a high density, i.e. good stopping power, and low internal contamination. Lead is a common material (see figure 47) but also large water tanks are employed: homogeneous shielding and low background. See figure 47.

Figure 45. Left: Background spectra of a Ge detector without shield (top), with 15 cm lead shield (middle), and with shield and at 500 m.w.e. (bottom). Right: flux of cosmic ray secondaries and tertiary-produced neutrons in a typical Pb shield as function of shielding depth. Figures from G. Heusser, Annu. Rev. Nucl. Part. Sci. 45 (1995) 543 [48].

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• Neutron radiation: Neutrons can interact with nuclei in the detector target via elastic scattering producing nuclear recoils. Dangerous background: this type of signal is identical to the one of the WIMPs. Also inelastic scattering where the nuclear recoil is typically accompanied by a gamma emission. • Cosmogenic neutrons: spallation reactions of muons on nuclei in the experimental setup or surrounding rock. Neutron energies up to several GeV [49] which are moderated by the detector surrounding materials resulting to MeV energies which can produce nuclear recoils in the energy regime relevant for dark matter searches. • Radiogenic neutrons: emitted in (α, n)- and spontaneous fission reactions from natural radioactivity. These neutrons have energies of around a few MeV. • Shielding: experiments are typically placed at underground laboratories in order to minimise the contribution of muon-induced neutrons. The deeper the location, the lower the muon flux. Figure 46 right shows the muon flux as a function of depth (km water equivalent, has to multiplied by the density of the rock to obtain the value in km) for different underground laboratories.

Figure 46. (Left) Schematic of the GIOVE Ge-detector at MPIK. Figure from G. Heusser et al. Eur. Phys. J. C75 (2015) 11, 531. (Right) Total muon flux measured for the various underground sites as function of the equivalent vertical depth relative to flat overburden. Figure from arXiv:1509.08767.

• Neutron background reduction: via material selection. Detector materials with low uranium and thorium content give lower α- and spontaneous fission rates. • Neutron shielding: water or polyethylene layers installed around the detectors to moderate the neutrons effectively [50] (see figure 47). Active vetoes are designed 44 5 DIRECT DETECTION

to record interactions of muons. The data acquired in the inner detector simultaneously to the muon event is discarded in order to reduce the muon- induced neutron background. Plastic scintillator plates are, for example, used for this purpose [51][52]. Also water Cherenkov detectors [53][54]: higher muon tagging efficiency (full coverage), efficient in stopping neutrons and, for sufficiently large thickness, the external gamma activity is also reduced. To tag directly the interactions of neutrons, liquid scintillator shielding can be used [55].

Figure 47. Examples of detector shielding using layers of lead, copper and polyethylene: DAMA detector (left) and XENON100 detector (right).

• Analysis techniques for background reduction: Given the low probability of dark matter particles to interact, the removal of multiple simultaneous hits in the target volume can be, for instance, used for background-event suppression. Tagging time-coincident hits in different crystals or identifying multiple scatters in homogeneous detectors. • For detectors with sensitivity to the position of the interaction, an innermost volume can be selected for the analysis (fiducial volume). Penetration range of radiation has an exponential dependence on the distance: most interactions take place close to the surface → background suppressed. The fiducial volume selection very effective for γ-radiation, slight smaller effect in the reduction of background for neutrons because of the larger mean free path of neutrons. • Detectors able to distinguish electronic recoils from nuclear recoils can reduce the background by exploiting the corresponding separation parameter.

• Neutrino background: With increasing target masses (hundreds of kilograms to tons) dark-matter detectors start being sensitive to neutrino interactions → significant background contributing both to electronic and nuclear-recoils.

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• Solar neutrinos can scatter elastically with electrons in the target via charged and

neutral current interactions for νe and only neutral current for the other neutrino flavours [56]. pp- and 7Be-neutrinos (large fluxes) would be the first neutrinos which could be detected. The resulting signal is a recoiling electron: neutrino- electron scattering is an important background for experiments which are not able to distinguish between nuclear and electronic recoils. See figure 48; the neutrino background from solar neutrinos is shown by the green curve. • Coherent neutrino-nucleus elastic scattering also possible producing nuclear recoils with energies up to few keV [57]. Process not measured yet. Coherent scattering of solar neutrinos would limit the sensitivity of dark matter experiment for low WIMP masses (few GeV) for cross-sections around ∼ 10−45 cm2. For higher masses, the coherent scattering of atmospheric neutrinos would limit dark matter searches at ∼ 10−49 cm2 [58][59][60]. Figure 48 (right) shows the contributions of coherent scattering of different neutrinos for the XENON1T experiment. The XENON1T experiment expects 5.4 events from coherent neutrino scattering in 2 t·y exposure.

Figure 48. Neutrino background, example for liquid xenon detectors. (Left) Contribution of ER from solar neutrinos (green) in comparison with other backgrounds. (Right) Spectral shape of coherent neutrino scattering in xenon. Figures from XENON Coll., arXiv:1512.07501.

5.2.2. Internal and surface backgrounds • Crystalline detectors: contamination of the crystal matrix negligible. Germanium or scintillators are grown from high purity powders or melts: during the growth process remaining impurities are effectively rejected. • Most important are surface contaminations with radon decay products. Either α-, β-decays or the nuclear recoils associated to the latter can enter the crystal depositing part of its energy. New detector designs have been developed over the last years to mitigate this background.

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• Cosmic activation of the target or detector surrounding materials during the time before the detector is placed underground. Most important processes: spallation of nuclei by high energy protons and neutrons producing long-lived isotopes. Neutrons dominate the activation at the Earth’s surface for energies below GeV [61]. Precautions: minimising time at surface and avoiding transportation via airplane

• Noble gas detectors: internal background originating from cosmogenic-activated radioactive isotopes contained in the target nuclei. • Argon: 39Ar with an endpoint energy at 565 keV at a level of 1 Bq/kg in natural argon. Reduction by using underground argon. • Xenon: cosmic activation produces rather short-lived isotopes: 127Xe has the longest lifetime of 36 d. Xenon also contains a double beta decaying isotope: 136Xe. Its lifetime is so large, 2.2 × 1021 y [62], that it doesn’t contribute to the background for detectors up to few tons mass. • Contamination of the target with krypton and the radon emanation from the detector materials contribute to the internal background. 85Kr: β-decaying isotope produced in nuclear fission. It is released to the atmosphere by nuclear-fuel reprocessing plants and in nuclear weapons tests. Krypton can be removed from xenon either by cryogenic distillation [63] or using chromatographic separation [53]. See blur curve in figure 48 (left). • Radon is emanated from all detector materials containing traces of uranium or thorium and it is dissolved in the liquid target. An approach to reduce radon is to use materials with low radon emanation [64][65]. Furthermore, methods to continuously remove the emanated radon are being investigated [66][67][68].

• Surface: both for solids and liquids surface deserves special attention. Treatment with acid cleaning and electropolishing have been proven to be effective in removing radioactive contaminants at the surfaces [69].

5.3. Statistical treatment of data • Result of a dark matter experiment: (eventually) a small number of signal event + a number of background events • Question: is there statistical significance of a signal over the expected background? • Counting method: Need to take into account signal, background and their corresponding fluctuations (typically Poisson fluctuations). Feldman and Cousins method [70] is used to derive both two-sided confidence intervals and upper confidence limits. Disadvantage: this method doesn’t take into account the spectral shape of the measured events. See confidence-belt construction in figure 49.

• Maximum gap or optimum interval method (also called Yellin’s method [71]): takes into account the shape of the expected signal but does not make any assumption

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Figure 49. Statistical methods to derive upper limits or two-sided confidence intervals. (Left) Feldman and Cousins generic confidence-belt construction. Figure from G. J. Feldman and R. D. Cousins, arXiv:physics/9711021 [70]. (Right) Yellin’s illustration of the maximum gap method. Figure from S. Yellin, Phys. Rev. D66 (2002) 032005 [71].

on the background. It is used when there is no knowledge (or poor knowledge) about the background. Disadvantage: can be used only to set upper limits. See illustration of the maximum gap method in figure 49. • Maximum likelihood methods: used when it is possible to determine the pdf of both signal and background • Two hypotheses tested: background only and background + signal hypothesis • For non-discriminating experiments: 1-dimensional pdf (energy dependence) of signal and background. For experiments that can separate electronic recoils (background) from nuclear recoil (signal), a 2-dimensional pdf (energy and discrimination parameters) are considered. • Profile likelihood method: incorporates uncertainties to the result calculation [72] • Figure 50 shows an illustration of different methods mentioned above

5.4. Detector calibration • The goals of calibration are: characterise the energy scale, determine signal and background regions and monitor the response and stability of the detector. • Calibration of recoil energies: conversion from phonons, photons or charge to a

recoil energy (keVnr) • Methods to determine the conversion to recoil energy: neutron scattering experiments, MC/data comparisons and modelling of underlying processes • Neutron scattering experiments performed for several detection media. Use mono energetic neutron source, a detector with the medium of interest and a coincidence

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Figure 50. Illustration of different statistical methods used to derive results from direct detection experiments. Figure from arXiv:1509.08767 [25].

Neutron detector























































Shield n

Scattering angle



n







Neutron source Target

Figure 51. Schematic of a neutron scattering experiment. Figure from arXiv:1509.08767 [25].

detector (see figure 51). For fixed kinematics, the nuclear recoil energy is also fixed. By changing the angle, the energy dependence of the response can be studied.

• Figure 52 summarises the results from neutron scattering experiments. The panels show the relative ionisation yield for Ge and the relative scintillation yields for Na, LAr and LXe. • Those are non linear energy scale and the related uncertainty is relevant specially in order to determine the energy threshold of the experiment

• Determination of signal and background regions: The signal and background regions are typically defined via dedicated calibration campaigns in between the science data taking. • The distribution of nuclear recoils (signal region) can be studied selecting interactions of neutron sources as 241AmBe or 252Cf. • The modelling of the background composition of each experiment is required to calibrate the various components adequately. Most of the background from electronic recoils from γ-interactions in the target → the background region can be determined by exposing the detector to gamma sources at different positions.

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0.6 0.6 Spooner 1994 Grebier 1999 Chagani 2008 Sattler 1966 Messous 1995 --- Bernabei 1996 Simon 2003 Collar 2013 Chasman 1968 Baudis 1998 0.5 Tovey 1998 Jagemann 2006 Xu 2015 0.5 Jones 1971 Simon 2003 Shutt 1992 CDMS 2011 0.4 0.4

0.3 0.3

0.2 Ge relative ionisation yield 0.2 Na relative scintillation yield

0.1 0.1 0 3 0 10 102 10 1 10 102 Recoil energy [keV ] Recoil energy [keV ] nr nr 0.6 0.6 Brunetti 2005 Cao 2014 Arneodo 2000 Chepel 2006 Gastler 2012 Creus 2015 Bernabei 2001 Aprile 2009 0.5 Regenfuss 2012 0.5 Akimov 2002 Manzur 2010 Aprile 2005 Plante 2011 0.4 0.4

0.3 0.3

0.2 0.2 LAr relative scintillation yield LXe relative scintillation yield

0.1 0.1

0 0 10 102 1 2 3 4 5 6 10 20 30 100 Recoil energy [keV ] Recoil energy [keV ] nr nr

Figure 52. Nuclear-recoil energy scale for different target materials relevant for dark matter detection. Figures from arXiv:1509.08767 [25].

Commonly, radioactive sources like 133Ba, 137Cs, 60Co or 232Th are used. For liquid noble-gas detectors also internal background contributes and internal sources can be used to characterise them (e.g. a tritiated source used by LUX or 220Rn by XENON). • Figure 53 shows schematically how signal (in blue) and background (in red) events are distributed for some detector technologies: on the left the ionisation yield of a germanium bolometer is represented; the middle panel shows the separation of signal and background for a liquid xenon detector using the ratio of charge to light signals; and finally the right panel shows, for a certain energy interval, the combination of two discrimination parameters (charge to light signal-ratio and pulse shape) as it can be done in liquid argon time-projection-chamber (TPC).

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Figure 53. Schematic representation of signal (blue) and background (red) regions for a bolometer like a germanium detector (left), a liquid xenon TPC (middle) and a liquid argon TPC (right).

5.5. Experiments and results In this section, the main detector technologies are summarised. For each of them an example of a detector, its results and most important implications are presented. Note that not all experiments are mentioned.

5.5.1. Scintillator crystals • Scintillation: energy deposition by particles produce excitation of the medium which de-excites via photon emission • Mostly NaI (Tl) and CsI (Tl) are used in DM searches. Advantages are the high density and large light output. • It is a ’simple’ technology (good for long term stability), low backgrounds can be achieved (very pure crystals) • Disadvantages: Crystals of several cm3 → arrays of crystals are necessary to achieve large target masses. Most important: no electronic/nuclear recoil discrimination. • Annual modulation signature is used

• DAMA experiment at LNGS laboratory in Italy • Annual modulating signal present in the data (14 annual cycles), 9.3 σ significance, exposure of 1.33 ton.y (see figure 54) • Signal in the (2 − 6) keV energy range with maximum compatible with expectation within 2 σ (see figure 55)

• The DAMA signal has been interpreted in different dark matter scenarios: SI, SD, axion signal, inelastic dark matter .. • But many other experiments cannot confirm (i.e. have excluded) most of these interpretations. Therefore the origin of the signal remains unclear/controversial

51 5 DIRECT DETECTION

Figure 54. Residual rate of single-hit scintillation events by the DAMA/LIBRA experiment in the (2−6) keV energy region as a function of time. A sinusoidal function fitting the data is also shown. Figure from DAMA Coll., Eur. Phys. J. C 56 (2008) 333.

Figure 55. Energy distribution of the modulated component (Sm) for 1.33 ton×y exposure. Figure from DAMA Coll., Eur. Phys. J. C 73 (2013) 2648 [73].

• Other non-dark matter related explanations of the DAMA signal are being discussed. The signal could be related to atmospheric muons (annually modulated due to temperature variations in the stratosphere [74]), or to combinations of muons and modulated neutrinos (caused by the varying Sun-Earth distance [75]). Furthermore, also varying rates of background neutrons have been considered [76] (see also [77] for a discussion).

5.5.2. Germanium detectors

5.5.3. Cryogenic bolometers

5.5.4. Liquid noble-gas detectors

5.5.5. Superheated fluids

52 6 DARK MATTER SEARCHES AT PARTICLE ACCELERATORS

5.5.6. Directional searches

6. Dark matter searches at particle accelerators

6.1. Introduction 6.2. Signatures and features 6.3. Searches at LEP 6.4. Searches at LHC 6.5. Comparison to direct/indirect detection results References

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