Investigation of high-p_1tnT phenomena within a partonic transport model [Elektronische Ressource] / von Oliver Fochler

Fochler

Sujets

• Physik

Informations

• Publié par: goethe_universitat_frankfurt_am_main
• Publié le: 01 janvier 2011
• Nombre de lectures: 4
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

Investigation of high-pT
phenomena within a partonic
transport model
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften
vorgelegt beim Fachbereich Physik
der Johann Wolfgang Goethe-Universitat¨
in Frankfurt am Main
von
Oliver Fochler
aus Frankfurt am Main
Frankfurt am Main 2011
(D 30)Vom Fachbereich Physik (13) der Johann Wolfgang Goethe-Universitat¨
als Dissertation angenommen.
Dekan: Prof. Dr. Michael Huth
Gutachter: Prof. Dr. Carsten Greiner, Prof. Dr. Marcus Bleicher
Datum der Disputation:Contents
List of Figures v
Deutschsprachige Zusammenfassung vii
1. Overview 1
1.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Structure of this document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Introduction 3
2.1. Quantum chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1. Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2. Asymptotic freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Exploring the phase diagram of nuclear matter . . . . . . . . . . . . . . . . . 6
2.3. Little big bangs in the laboratory . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4. The purpose of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3. The transport model BAMPS 17
3.1. The simulation framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1. Basic concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.2. Collision probabilities, matrix elements and cross sections . . . . . . . 19
3.1.3. Small angle approximation in the 2!3 cross section . . . . . . . . . . 21
3.1.4. Modeling of the LPM effect . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.5. Evaluation of phase space integrals and sampling of momenta . . . . . 31
3.2. The Gunion-Bertsch matrix element . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1. Kinematics and approximations . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2. Computation of the bremsstrahlung Feynman diagrams . . . . . . . . 34
3.2.3. Comparison of Gunion-Bertsch to the exact result . . . . . . . . . . . 39
3.3. Selected results from BAMPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1. Early thermalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.2. Small viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3. Hydrodynamic behavior and shock phenomena . . . . . . . . . . . . . 43
3.3.4. Heavy quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4. The inclusion of light quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1. 2!2 processes containing light quarks . . . . . . . . . . . . . . . . . 45
3.4.2. 2$3 processes containing light quarks . . . . . . . . . . . . . . . . . 46
3.4.3. Numerical test of detailed balance in a static medium . . . . . . . . . 48
4. High energy partons in a static medium 51
4.1. Interaction rates and mean free paths . . . . . . . . . . . . . . . . . . . . . . 51
iii Contents
4.2. Energy loss in a static medium . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1. Energy loss from 2!2 interactions . . . . . . . . . . . . . . . . . . . 56
4.2.2. Energy loss including 2$3 interactions . . . . . . . . . . . . . . . . . 59
4.3. Detailed investigation of energy loss in 2!3 processes . . . . . . . . . . . . . 61
4.3.1. Radiation spectra from the Gunion-Bertsch matrix element . . . . . . 62
4.3.2. Energy loss per 2!3 process versus radiated energy . . . . . . . . . . 64
4.3.3. Typical phase space configurations in 2!3 processes . . . . . . . . . 67
4.4. Conversion of jet partons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5. Momentum broadening of jet partons. . . . . . . . . . . . . . . . . . . . . . . 73
5. Simulations of heavy ion collisions 77
5.1. High-p physics and elliptic flow in ultra-relativistic heavy ion collisions . . . 77T
5.1.1. Jet quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.1.2. Elliptic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2. Setup for simulations of heavy ion collisions with BAMPS . . . . . . . . . . . 81
5.2.1. Initial parton distribution and technical setup . . . . . . . . . . . . . . 81
5.2.2. Simulation strategy for high-p observables . . . . . . . . . . . . . . . 83T
5.2.3. Impact parameters and centrality classes . . . . . . . . . . . . . . . . . 84
5.3. Spectra and fragmentation of high-p partons . . . . . . . . . . . . . . . . . . 85T
5.3.1. Hadronization via fragmentation functions . . . . . . . . . . . . . . . . 85
5.3.2. Fits to parton spectra from BAMPS . . . . . . . . . . . . . . . . . . . 87
5.3.3. Fragmented hadron spectra from BAMPS . . . . . . . . . . . . . . . . 89
5.4. Elliptic flow and thermalization at RHIC from simulations with BAMPS . . . 92
5.4.1. Elliptic flow in a purely gluonic medium . . . . . . . . . . . . . . . . . 92
5.4.2. Thermalization of the medium including light quarks . . . . . . . . . . 94
5.4.3. Elliptic flow including light quarks . . . . . . . . . . . . . . . . . . . . 97
5.5. Jet quenching at RHIC from simulations with BAMPS . . . . . . . . . . . . . 99
5.5.1. Nuclear modification factor of high-p particles . . . . . . . . . . . . . 99T
5.5.2. Origin and interaction history of high-p particles . . . . . . . . . . . 106T
5.6. Sensitivity of the results on the LPM cutoff . . . . . . . . . . . . . . . . . . . 109
5.6.1. Scaling the LPM cutoff . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.6.2. LPM effect via a radiation formation factor . . . . . . . . . . . . . . . 113
5.7. Jet quenching and elliptic flow at LHC from simulations with BAMPS . . . . 114
5.7.1. Thermalization of the medium in Pb+Pb at 2:76ATeV . . . . . . . . 114
5.7.2. Particle spectra and nuclear modification factor . . . . . . . . . . . . . 114
5.7.3. Elliptic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6. Summary and conclusions 121
6.1. Summary of the findings presented in this work . . . . . . . . . . . . . . . . . 121
6.1.1. High energy particles in a static medium . . . . . . . . . . . . . . . . . 122
6.1.2. Simulations of heavy ion collisions . . . . . . . . . . . . . . . . . . . . 123
6.2. Future projects and possible extensions of the model . . . . . . . . . . . . . . 126
6.2.1. Implementation of running coupling . . . . . . . . . . . . . . . . . . . 126
6.2.2. Reassessment of Gunion-Bertsch and the modeling of the LPM effect . 127
6.2.3. Investigation of possible hadronization scenarios . . . . . . . . . . . . 128
6.2.4. Systematic studies of the sensitivity on initial conditions and fluctuations129Contents iii
Appendices 133
A. Notation and conventions 133
A.1. Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.3. On the term “jet” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B. Matrix elements and cross sections 137
B.1. The invariant matrix element . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B.2. The definition of the cross section . . . . . . . . . . . . . . . . . . . . . . . . . 138
B.3. Parton-parton cross sections in small angle approximation . . . . . . . . . . . 139
B.3.1. Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.3.2. The small angle approximation . . . . . . . . . . . . . . . . . . . . . . 140
B.3.3. Binary parton-parton cross sections . . . . . . . . . . . . . . . . . . . 141
B.4. Computation of the differential 2!3 cross section . . . . . . . . . . . . . . . 144
C. Interaction rates and probabilities 147
C.1. Computation of thermal rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C.2. Scaling factors for 2$3 processes including light quarks . . . . . . . . . . . 149
D. Numerical sampling methods 153
D.1. Inverse transform sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D.2. Rejection sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
D.3. Metropolis sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
E. Power law fits to parton spectra 157
Bibliography 162
Danksagung 177
Erkl¨arung 179
Lebenslauf 181List of Figures
2.1. Summary of (Q) measurements . . . . . . . . . . . . . . . . . . . . . . . . . 5s
2.2. Phase diagram of nuclear matter . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3. Energy density from lattice calculations . . . . . . . . . . . . . . . . . . . . . 10
3.1. Mean free path with fixed double counting in 2!3 . . . . . . . . . . . . . . 22
3.2. Illustration of medium induced gluon radiation . . . . . . . . . . . . . . . . . 23
3.3. Illustration of reference frames for the LPM cutoff . . . . . . . . . . . . . . . 25
3.4. Sampling in the y-k phase space . . . . . . . . . . . . . . . . . . . . . . . . . 26?
3.5. Cross sections with the improved LPM cutoff . . . . . . . . . . . . . . . . . . 28
3.6. Boosts and rapidities entering the LPM cutoff . . . . . . . . . . . . . . . . . . 30
3.7. Feynman diagrams for gluon radiation – Overview . . . . . . . . . . . . . . . 33
3.8. Feynman diagram for gl