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Dark Matter Vienna University of Technology V2.1 Jochen Schieck and Holger Kluck Institut f¨urHochenergiephysik Nikolsdorfer Gasse 18 1050 Wien Atominstitut derTechnischen Universit¨atWien Stadionallee 2 1020 Wien Wintersemester 2017/18 18.12.2017 2 Contents 1 Introduction 7 1.1 What is "Dark Matter" . .7 1.1.1 Dark . .7 1.1.2 Matter . .7 1.1.3 Cosmology . .7 1.1.4 Massive particles as origin of "Dark Matter" . .7 1.1.5 "Dark Matter" as contribution to the energy density of the universe in Cosmology . .7 1.2 First Indication of observing "Dark Matter" . 13 1.3 Brief Introduction to Cosmology . 15 1.3.1 Special Relativity . 16 1.3.2 Differential geometry . 16 1.3.3 General Relativity . 16 1.3.4 Cosmology . 17 1.3.5 Decoupling of matter and radiation . 18 1.4 The Standard Model of Particle Physics . 19 1.4.1 The matter content of the Standard Model . 19 1.4.2 Forces within the Standard Model . 19 1.4.3 Shortcoming of the Standard Model . 20 1.4.4 Microscopic Behaviour of Gravity . 21 2 Evidence 23 2.1 Dynamics of Galaxies . 23 2.2 Gravitational Lensing . 24 2.2.1 Bullet Cluster . 31 2.3 Cosmic Microwave Background . 33 2.4 Primordial Nucleosynthesis (Big Bang Nucleosynthesis - BBN) . 35 3 Structure Evolution 39 3.1 Structure Formation . 39 3.1.1 The Classic Picture . 39 3.1.2 Structure Formation and Cosmology . 41 3.2 Model of the Dark Matter Halo in our Galaxy . 45 3 4 Unsolved Questions and Open Issues 49 4.1 Core-Cusp Problem . 50 4.2 Missing Satellite Problem . 50 4.3 "Too big to fail" Problem . 51 5 Particle Character of "Dark Matter" 55 5.1 Baryonic Dark Matter . 55 5.2 Weakly Interacting Particle (WIMP) . 56 5.2.1 The WIMP miracle . 56 5.2.2 Supersymmetry (SUSY) . 58 5.3 Sterile Neutrinos . 61 5.4 Asymmetric Dark Matter (ADM) . 63 5.5 Axions . 64 5.6 Alternative Theories . 65 5.6.1 Modified Newtonian Dynamics - MOND . 65 6 Orthogonal Approaches for "Dark Matter" searches 69 6.1 The Feynman Diagram from different directions . 69 6.2 Strength and Weakness of the various Approaches . 70 7 Indirect "Dark Matter" detection 75 7.1 Search Strategy . 75 7.1.1 Expected Signal . 75 7.2 Instruments and Methods . 77 7.3 Experimental Search for "Dark Matter" annihilation . 78 7.3.1 Gamma Flux from Dwarf Galaxies . 78 7.3.2 Neutrino flux from the Galactic Center . 79 7.3.3 Claims for Detection of "Dark Matter" annihilation . 80 7.3.4 "Dark Matter" Signal at 130 GeV from Galactic Center . 80 7.3.5 Excess of Positron fraction in Cosmic Rays . 81 8 Direct "Dark Matter" detection 87 8.1 Astrophysical parameters . 88 8.2 Signals . 89 8.3 WIMP-nucleus cross section . 90 8.3.1 Spin-independent interactions . 91 8.3.2 Spin-dependent interactions . 93 8.4 Experiments . 94 8.4.1 DAMA/LIBRA . 97 8.4.2 LUX . 98 8.4.3 CRESST . 98 9 "Dark Matter" Production 101 9.1 Production of "Dark Matter" in particle colliders . 101 9.1.1 Model dependent searches . 101 9.1.2 Search Strategy . 102 9.1.3 Effective Field Theory (EFT) . 103 4 9.1.4 Relation to Direct and Indirect Dark Matter Detection Experiments 105 9.1.5 Results of Searches at LHC . 105 9.1.6 Relation between "Dark Matter" Production and Relic Density . 106 9.1.7 Validity of EFT Approach . 106 9.1.8 "Dark Matter" searches with Higgs as a mediator . 107 5 6 Chapter 1 Introduction 1.1 What is "Dark Matter" 1.1.1 Dark non-luminous, i.e. electrically neutral • weak, or even less interacting with ordinary matter • stable with respect to the lifetime of the universe • 1.1.2 Matter non-baryonic • massive particle - acts gravitationally • 1.1.3 Cosmology the abundance or relic density must match the measured "Dark Matter" density • 1.1.4 Massive particles as origin of "Dark Matter" no evidence for the particle character of "Dark Matter", however, well motivated • from the particle physic point of view all observation of "Dark Matter" are based on gravitational interactions • alternative approach: deviations from the 1/r distance relations at all scales (ie. • "Modified Newtonian Dynamics" (MOND), not consistent with all observations) 1.1.5 "Dark Matter" as contribution to the energy density of the universe in Cosmology (Here we just mention the basic energy and matter ingredients of our universe. A more detailed introduction to cosmology will follow later in this chapter). The information sketched below are taken from [1]. 7 the Friedmann-equation describes expansion of the Universe: • a_ 2 8 π G kc2 H2 = = ρ (1.1) a 3 − a2 with H the Hubble parameter, a being scale factor of the universe reflecting a co- moving universe, G being the Newtonian gravitational constant, ρ the mass density and k a constant which can be identified as the curvature of the universe (k=-1,0,1). the Friedmann-equation allows to add a constant term Λ, the so called cosmological • constant, a repulsive force: a_ 2 8 π G kc2 Λ H2 = = ρ + (1.2) a 3 − a2 3 8 Fig. 1.1: Sketch of a 2-dim curved plane with different values for the curvature k=1,-1,0 (Ω0 > 1, Ω0 < 1 and Ω0 = 1)in space. The triangle on the plane indicates the change of angles within a triangle (picture taken from Wikipedia). 9 using the measured Hubble parameter H we define the critical density • 2 3H 26 kg MeV 2 3 3 ρ = 10− 5200 11h H Atoms m− 5 H Atoms m− (1.3) c 8πG ≈ m3 ≈ m3 ≈ 0 − ≈ − H (with H being the Hubble Constant, h = 1 1 = 0:673(12) [2] and G being • 100kms− Mpc− the Newtonian gravitational constant.) using the critical density ρ Eq. 1.2 can be rewritten as • c 3kc2 Λ ρ = ρ + (1.4) c 8πGa2 − 8πG or Λ 3kc2 ρ ρ = (1.5) c − − 8πG −8πGa2 the various parts of the energy density can be normalised to the critical energy • ρ Λ 3kc2 density ρ : Ω = ,Ω = and Ω = 2 c ρc Λ 8πG ρc k 8πGa ρc 1 Ω Ω = Ω (1.6) − − Λ − k with Ω0 = Ω + ΩΛ Ω0 = 1 + Ωk (1.7) the curvature is consistent with a flat universe k = 0 • the different contributions to Ω are Ω = Ω +Ω +Ω and the density contribution • r lum b from the cosmological constant ΩΛ, 5 the contributions are measured to be Ωr 5 10− , the energy density contribu- tion from radiation (can be neglected), Ω≈ × 0:01, the energy contribution from lum ≈ luminous matter, and the contribution from baryonic luminous matter, Ωb 0:05. The energy density from the cosmological constant is determined to be Ω ≈ 0:7: Λ ≈ 1 = Ωr + Ωlum + Ωb + ΩΛ = 0:06 + 0:7 < 1 (1.8) i) the sum of the measured contributions is not adding up to one ii) the missing contribution acts gravitationally (not like a cosmological constant) iii) the missing gravitational part acts like non-luminous matter Dark Matter ! 10 Fig. 1.2: Measurements of the energy density from the cosmological constant (ΩΛ) as a function of the total matter energy density (Ωm = Ωlum + Ωb + Ωdm). The diagonal line indicates the expectation for a flat universe with k = 0 [2]. Fig. 1.3: The size of the microwave background fluctuation at the surface of last scat- tering. Theory (ΛCDM) predicts the size of the fluctuation to be about θ 1◦. ' Depending on the geometry this fluctuation is smaller (k < 1 and θ < 1◦), indi- cating that Ω < 1, larger (k > 1 and θ > 1◦), indicating that Ω > 1 or iden- tical to one (k = 0 and θ 1◦), indicating that Ω = 1 (Picture taken from http://map.gsfc.nasa.gov/media/030639/index.html' ). 11 Fig. 1.4: Energy matter density content of our current universe. 12 1.2 First Indication of observing "Dark Matter" circular movement of a star around the galactic centre, the velocity can be calculated • by requiring the gravitational and the centrifugal force to be equal: G m M m v2 F = = = F (1.9) G r2 r Z GM v(r) = (1.10) r r with M being the mass within the orbit, G the gravitational constant and r as the radius example for the velocity distribution of the planes within our solar system (see • Fig. 1.5), with the mass M being the mass of the sun (Jupiter, the heaviest planet, has about 1/1000 of the solar mass) no sign for deviation from 1=r behaviour • Velocity of Planets 50 Mercury velocity in m/s 40 Venus Earth 30 Mars 20 Jupiter 10 Saturn Uranus Neptune 0 5 10 15 20 25 30 distance in AU Fig. 1.5: Velocity distribution of the planets within our solar system with the nice v 1=r distribution. / p assuming a spherical distribution of matter with a constant density ρ, M = ρ V = • · 4 3 G ρ 4=3 π r3 ρ 3 π r , leads to v(r) = r = r G ρ 4=3 π q p 13 the measurement of spiral galaxies returns the relation v(r) constant for a test • mass m being within the spherical distribution of density ρ / a measurement of the circular speed as a function of radius for the barred spiral • galaxy NGC 3198 is shown in Fig. 1.6 For large r > 10 kpc the velocity is almost constant (1 pc = 3.26 light years) • additional non-luminous gravitational matter Dark Matter • ! 1985ApJ...295..305V Fig.
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