Direct photons in heavy ion collisions [Elektronische Ressource] / von Björn Bäuchle

Baeuchle

Sujets

• Physik

Informations

• Publié par: goethe_universitat_frankfurt_am_main
• Publié le: 01 janvier 2010
• Nombre de lectures: 21
• Langue: Deutsch
• Poids de l'ouvrage: 4 Mo

Extrait

Direct Photons in Heavy-Ion Collisions
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften
vorgelegt beim Fachbereich Physik
der Johann Wolfgang Goethe -Universit¨at
in Frankfurt am Main
von
Bj¨orn B¨auchle
aus Frankfurt am Main
Frankfurt 2010
D 30Direct Photons in Heavy-Ion Collisions
vom Fachbereich Physik der
Johann Wolfgang Goethe-Universita¨t
als Dissertation angenommen.
Dekan: Michael Huth
Gutachter: Marcus Bleicher, Horst Sto¨cker
Datum der Disputation: 13. Dezember 2010
iiDiese Arbeit beruht auf folgenden Publikationen:
• “Hybrid model calculations of direct photons in high-energy nuclear colli-
sions” [B¨au10]
√
• “Direct photon calculations in heavy-ion collisions at s = 62.4 - 200NN
GeV in a (3+1) dimensional hybrid approach” [B¨au10a]
• “Transport and hydrodynamic calculations of direct photons at FAIR”
[B¨au10b]
• “Directphotonemissionfromhadronicsources: Hydrodynamicsvs.Trans-
port theory” [B¨au09]
• “Direct photon emission in Heavy Ion Collisions from Microscopic Trans-
port Theory and Fluid Dynamics” [B¨au10c]
√
• “Calculations of direct photon emission in heavy ion collisions at s =NN
200 GeV” [B¨au10d]
• “Direct Photons from a Hybrid Approach – Exploring the parameter
space” [B¨au10e]
iiiDirect Photons in Heavy-Ion Collisions
ivContents
1 Introduction 1
2 Direct Photons 11
2.1 Direct photon experiments . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Photon emission sources . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Photon measurement . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Direct photon extraction . . . . . . . . . . . . . . . . . . . 13
2.4 Calculations of direct photons . . . . . . . . . . . . . . . . . . . . 15
3 Model 17
3.1 Transport Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 UrQMD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Hydrodynamic Models . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 SHASTA . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Hybrid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Early Stage . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 Intermediate Stage . . . . . . . . . . . . . . . . . . . . . . 25
3.3.3 Late Stage . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Photon emission sources . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.1 Photon emission from the Transport Phase . . . . . . . . 36
3.5.2 Photon emission from the Hydrodynamic Phase. . . . . . 43
3.5.3 Photon emission from primordial pQCD scatterings . . . 45
4 Numerical Tests and Investigations 49
4.1 Rates from transport and hydrodynamics . . . . . . . . . . . . . 49
4.2 String ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 ρ-meson width . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Comparison to previous works with UrQMD . . . . . . . . . . . . 52
4.5 Exploring the parameter space . . . . . . . . . . . . . . . . . . . 54
4.5.1 Transport→ hydrodynamics . . . . . . . . . . . . . . . . 55
4.5.2 Hydrodynamics→ transport . . . . . . . . . . . . . . . . 55
vDirect Photons in Heavy-Ion Collisions
5 Results 61
5.1 Photons at FAIR: CBM . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Photons at SPS: WA98 . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Photons at RHIC: PHENIX . . . . . . . . . . . . . . . . . . . . . 68
5.4 Collective Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6 Channel decomposition 81
6.1 Hadronic channels . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Partonic contribution. . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Time emission patterns 89
7.1 Emission stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2 High-p emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 96⊥
7.3 Emission times . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8 Baryon number density 113
9 Summary 119
A Kinetic variables in 2↔2 scatterings 123
A.1 Mandelstam variables . . . . . . . . . . . . . . . . . . . . . . . . 123
A.2 Lorentz-Transformations . . . . . . . . . . . . . . . . . . . . . . . 125
B Photons from Hydrodynamics 129
C Conventions and Units 135
C.1 Natural Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
C.2 Einstein notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
C.3 Coordinate systems and indices . . . . . . . . . . . . . . . . . . . 136
C.4 Accelerator parameters . . . . . . . . . . . . . . . . . . . . . . . . 137
D Bibliography 139
E Acknowledgements 153
F Zusammenfassung 155
F.1 Einfu¨hrung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
F.2 Das Modell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
F.3 Ergebnisse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
F.4 Schlussfolgerungen . . . . . . . . . . . . . . . . . . . . . . . . . . 159
G Index 161
H Lebenslauf 163
H.1 Meine Akademischen Lehrer . . . . . . . . . . . . . . . . . . . . . 163
H.2 Lebenslauf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
viList of Figures
1.1 Particles in Standard Model . . . . . . . . . . . . . . . . . . . . . 2
1.2 Phase Diagram of Strongly Interacting Matter . . . . . . . . . . 4
2.1 Photon sources in Heavy-Ion collisions . . . . . . . . . . . . . . . 12
3.1 Cross-sections π+π in UrQMD (resonance / string / PYTHIA) 19
3.2 Spectra in UrQMD with and without PYTHIA . . . . . . . . . . 20
3.3 Speed of sound in HG-EoS . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Degree of deconfinement in χ-EoS . . . . . . . . . . . . . . . . . 28
3.5 Speed of sound in χ-EoS . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Degree of deconfinement in BM-EoS . . . . . . . . . . . . . . . . 30
3.7 Speed of sound in BM-EoS . . . . . . . . . . . . . . . . . . . . . 31
3.8 Initial temperature profiles . . . . . . . . . . . . . . . . . . . . . 32
3.9 Distribution of transition points with gradual transition . . . . . 33
3.10 Distribution of QGP-content of the hydrodynamic system . . . . 34
3.11 Distribution of temperatures in hydrodynamic calculations . . . . 35
3.12 Photon production Feynman-diagrams . . . . . . . . . . . . . . . 37
3.13 Photon production cross-sections . . . . . . . . . . . . . . . . . . 42
3.14 Thermal rates with and without form factor at T =170 MeV . . 46
3.15 Comparison of hadronic vs. partonic thermal rates . . . . . . . . 47
3.16 Integrated thermal rates vs. temperature . . . . . . . . . . . . . . 47
4.1 Comparison of UrQMD box calculations to thermal rates . . . . 50
4.2 Comparison of UrQMD and HG-EoS hybrid (common channels
only) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Comparison of calculations with and without string contribution 51
4.4 Impact of taking into account the ρ-spectal function . . . . . . . 53
4.5 Comparison to calculations by Dumitru et al. . . . . . . . . . . . 54
4.6 Effect of changing start time for hydrodynamics t . . . . . . . 56start
4.7 Effect of changing the critical energy density for the transition to
transport calculation ε . . . . . . . . . . . . . . . . . . . . . . 58crit
4.8 Effect of transferring the whole system at the same time . . . . . 59
5.1 Direct photon spectra in U+U at E =35 AGeV . . . . . . . . 62lab
viiDirect Photons in Heavy-Ion Collisions
5.2 Photon emission from the intermediate stage at E =35 AGeV 63lab
5.3 Direct photon spectra in central Pb+Pb at E =158 AGeV . . 65lab
5.4 Direct photon spectra at E = 158 AGeV including promptlab
photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.5 Direct photons in peripheral Pb+Pb-collisions at E =158 AGeV 67lab
5.6 Direct photons from pQCD, cascade and BM-EoS calculations at
√
s =200 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . 69NN √
5.7 Direct photons from central Au+Au at s =200 GeV . . . . 70NN√
5.8 Direct photons in Au+Au and Cu+Cu at s = 62.4 GeV,NN√ √
s =130 GeV and s =200 GeV . . . . . . . . . . . . . . 72NN NN
5.9 v (p ) at E =35 AGeV . . . . . . . . . . . . . . . . . . . . . . 752 ⊥ lab
5.10 v (p ) at E =158 AGeV . . . . . . . . . . . . . . . . . . . . . 762 ⊥ lab√
5.11 v (p ) at s =62.4 GeV . . . . . . . . . . . . . . . . . . . . . 782 ⊥ NN√
5.12 v (p ) at s =130 GeV . . . . . . . . . . . . . . . . . . . . . 792 ⊥ NN√
5.13 v (p ) at s =200 GeV . . . . . . . . . . . . . . . . . . . . . 802 ⊥ NN
6.1 Channel decomposition in transport calculations . . . . . . . . . 82
6.2 Relative contributions of hadronic channels: HG-EoS . . . . . . . 83
6.3 Relative contributions of hadronic channels: χ-EoS . . . . . . . . 84
6.4 Relative contributions of hadronic channels: BM-EoS . . . . . . . 85
6.5 Contributions of QGP and pQCD to photon spectra with χ-EoS 87
6.6 Contributions of QGP and pQCD to photon spectra with BM-EoS 88
7.1 Contribution of the different stages at E =35 AGeV . . . . . . 90lab
7.2 Contribution of the different stages at E =158 AGeV . . . . . 92lab
7.3 Contribution of the different stages at E = 158 AGeV withlab
isochronous tra