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Qcd Matter Under Extreme Conditions Heavy Ion Technische Universitat¨ Munchen¨ Physik Department Institut fur¨ Theoretische Physik T39 Univ.-Prof. Dr. W. Weise QCD MATTER UNDER EXTREME CONDITIONS — HEAVY ION COLLISIONS Dipl.-Phys. (Univ.) Thorsten Renk Vollstandiger¨ Abdruck der von der Fakultat¨ fur¨ Physik der Technischen Universitat¨ Munchen¨ zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. Reiner Kruc¨ ken Pruf¨ er der Dissertation: 1. Univ.-Prof. Dr. Wolfram Weise 2. Univ.-Prof. Dr. Manfred Lindner Die Dissertation wurde am 22.10.2002 bei der Technischen Universitat¨ Munchen¨ eingereicht und durch die Fakultat¨ fur¨ Physik am 3.12.2002 angenommen. ii CONTENTS 1 Introduction 1 2 Basics of thermal field theory 5 2.1 Basic relations . 5 2.2 Perturbative techniques . 6 2.2.1 The imaginary time formalism . 7 2.2.2 The real-time formalism . 8 2.3 Thermal self-energies . 10 2.4 Hard Thermal Loop Resummation . 11 2.5 Lattice techniques . 12 2.5.1 Gauge fields . 13 2.5.2 Fermion fields . 13 3 Properties of the Quark Gluon Plasma 15 3.1 Thermodynamics of the QGP . 16 3.1.1 The ideal quark-gluon gas . 16 3.1.2 Perturbative QCD thermodynamics . 17 3.1.3 Lattice simulations . 19 3.2 Deconfinement . 21 3.3 Chiral symmetry restoration . 22 3.4 A quasiparticle picture of the QGP . 24 3.4.1 Introduction . 24 3.4.2 The quasiparticle picture . 24 3.5 The Equation of State . 26 4 Heavy Ion Collision Dynamics 29 4.1 Introduction . 29 4.2 Kinematics and Geometry . 30 4.2.1 Kinematic variables . 30 4.2.2 Spacetime picture . 31 4.3 Initial conditions . 33 4.3.1 Overlap geometry . 33 4.3.2 Longitudinal dynamics . 34 iii iv CONTENTS 4.4 Thermalization . 34 4.4.1 The ’Bottom Up’ scenario . 34 4.4.2 Elliptic flow — an experimental signal of thermalization . 36 4.5 The partonic phase . 36 4.5.1 Theoretical considerations . 37 4.5.2 Experimental signals . 41 4.6 The phase transition . 41 4.7 The hadronic phase . 42 4.7.1 Theoretical considerations . 43 4.7.2 Experimental signals . 44 4.8 Freeze-out . 44 5 Hadronic Observables — a Basis for Models 47 5.1 Introduction . 47 5.1.1 Event generators . 47 5.1.2 Hydrodynamics . 48 5.1.3 Thermodynamics . 49 5.2 Hadronic Observables . 49 5.2.1 dN=dy Spectra . 50 5.2.2 mt Spectra . 51 5.2.3 HBT correlation measurements . 53 5.2.4 Elliptic Flow and early thermalization . 56 5.2.5 An intermediate summary . 58 5.2.6 A global analysis of the freeze-out state . 59 5.3 A model based on thermodynamics . 59 5.3.1 The spacetime picture of a homogeneous fireball . 60 5.3.2 Rapidity distributions . 61 5.3.3 Evolution dynamics . 62 5.3.4 Thermodynamics . 63 5.3.5 Longitudinal acceleration . 65 5.4 Extending the scenario . 66 5.4.1 Variations in centrality . 66 5.4.2 Results for different centrality . 67 5.4.3 Variations in beam energy . 68 5.4.4 Results for different beam energy . 70 6 Hadrochemistry and chemical equilibrium 73 6.1 Chemical equilibrium and statistical hadronization . 73 6.1.1 Introduction . 73 6.1.2 Successes and caveats . 74 6.2 The model . 76 6.2.1 Basic equations . 76 6.2.2 Resonance decays . 77 6.3 Results . 77 6.3.1 Standard scenario . 77 6.3.2 Late chemical freeze-out . 78 6.3.3 In-medium modifications . 79 6.4 Hadron ratios at RHIC . 83 7 Dileptons - a view into the fireball core 85 7.1 Dileptons from a fireball . 85 7.2 Calculation of the photon spectral function . 87 CONTENTS v 7.2.1 The quark-gluon phase . 87 7.2.2 The hadronic phase . 90 7.2.3 After freeze-out contributions . 92 7.2.4 Drell-Yan and charm contributions . 93 7.3 Dilepton invariant mass spectra . 94 7.3.1 SPS data at 40 and 158 AGeV . 94 7.3.2 RHIC at ps = 200 AGeV . 98 7.3.3 Sensitivity to model parameters . 100 7.4 Conclusions . 102 8 Thermal Photon Emission 103 8.1 Introduction . 103 8.2 The Photon Emission Rate . 104 8.2.1 The QGP phase . 104 8.2.2 The hadronic phase . 106 8.2.3 The integrated rate . 106 8.2.4 Prompt photons . 106 8.3 Results . 107 8.4 Conclusions . 109 9 Charmonium Dissociation 111 9.1 Introduction . 111 9.2 Charmonium suppression in different pictures . 112 9.3 The fate of charmonia . 114 9.3.1 Charm production . 114 9.3.2 Charmonium production . 115 9.3.3 Nuclear absorption . 116 9.3.4 The charmonium dissociation cross section . 116 9.3.5 Kinetic description of charmonium evolution . 117 9.4 Results . 119 9.5 Conclusions . 120 10 Summary and Conclusions 123 10.1 Summary . 123 10.2 Conclusions . 126 10.3 Outlook . 128 A Properties of QCD 131 A.1 The Lagrangian . 131 A.2 Symmetries and Condensates . 133 B Bottom-up thermalization 135 B.1 Parton saturation . 135 B.2 Shattering the Color-Glass Condensate . 136 B.3 Creation of soft gluons . 137 B.4 Soft gluons take over . 137 B.5 Thermalized soft sector . 138 C The dilepton rate from a hot source 139 Thanks 155 vi CONTENTS Summary The main goal of this work is a comprehensive description of the fireball created in current ultrarelativistic heavy-ion collisions. This has to be a three-step process: In the first step, properties of hot and dense hadronic matter are investigated, culminating in the introduction of a phenomenological quasiparticle model for the description of the.
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