Quark-Gluon plasma : from big bang to little bang / Kohsuke Yagi, Tetsuo Hatsuda, Yasuo Miake.

Format:

Book

Author/Creator:

Yagi, K. (Kohsuke), 1934-2014.

Contributor:

Hatsuda, Tetsuo.

Miake, Yasuo

Craig M. Merrihue Memorial Fund.

Series:

Cambridge monographs on particle physics, nuclear physics, and cosmology ; 23.

Cambridge monographs on particle physics, nuclear physics, and cosmology ; 23

Language:

English

Subjects (All):

Quark-gluon plasma.

Physical Description:

xviii, 446 pages : illustrations ; 26 cm.

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Summary:

Quark-Gluon Plasma introduces the subject matter (QGP) as a primordial matter composed of two types of elementary particles, quarks and gluons, created at the Big Bang. During the evolution of the universe, QGP undergoes a transition to hadronic matter governed by the law of strong interactions, quantum chromodynamics. After an introduction to gauge theories, various aspects of quantum chromodynamic phase transitions are illustrated in a self-contained manner. The cosmological approach and renormalization group are discussed, as well as the cosmological and astrophysical implications of QGP, on the basis of Einstein's equations. Recent developments towards the formation of QGP in ultrarelativistic heavy ion collisions are also presented in detail.

This text is suitable as an introduction for graduate students, as well as providing a valuable reference for researchers already working in this and related fields. It includes eight appendices and over a hundred exercises.

Contents:

1 What is the quark-gluon plasma? 1

1.1 Asymptotic freedom and confinement in QCD 1

1.2 Chiral symmetry breaking in QCD 4

1.3 Recipes for quark-gluon plasma 5

1.4 Where can we find QGP? 6

1.5 Signatures of QGP in relativistic heavy ion collisions 9

1.6 Perspectives on relativistic heavy ion experiments 12

1.7 Natural units and particle data 14

Part I Basic Concept of Quark-Gluon Plasma 15

2 Introduction to QCD 17

2.1 Classical QCD action 17

2.2 Quantizing QCD 19

2.3 Renormalizing QCD 22

2.3.1 Running coupling constants 24

2.3.2 More on asymptotic freedom 27

2.4 Global symmetries in QCD 28

2.4.1 Chiral symmetry 28

2.4.2 Dilatational symmetry 29

2.5 QCD vacuum structure 30

2.6 Various approaches to non-perturbative QCD 32

3 Physics of the quark-hadron phase transition 39

3.1 Basic thermodynamics 39

3.2 System with non-interacting particles 43

3.3 Hadronic string and deconfinement 44

3.4 Percolation of hadrons 45

3.5 Bag equation of state 46

3.6 Hagedorn's limiting temperature 50

3.7 Parametrized equation of state 51

3.8 Lattice equation of state 53

4 Field theory at finite temperature 57

4.1 Path integral representation of Z 57

4.2 Black body radiation 60

4.3 Perturbation theory at finite T and [mu] 62

4.3.1 Free propagators 63

4.3.2 Vertices 64

4.3.3 Feynman rules 65

4.4 Real-time Green's functions 66

4.5 Gluon propagator at high T and zero [mu] 69

4.6 Quark propagator at high T and zero [mu] 75

4.7 HTL resummation 77

4.8 Perturbative expansion of the pressure up to O(g[superscript 5]) 78

4.9 Infrared problem of O(g[superscript 6]) and beyond 81

4.10 Debye screening in QED plasma 82

4.11 Vlasov equations for QED plasma 84

4.12 Vlasov equations for QCD plasma 87

5 Lattice gauge approach to QCD phase transitions 92

5.1 Basics of lattice QCD 92

5.1.1 The Wilson line 92

5.1.2 Gluons on the lattice 94

5.1.3 Fermions on the lattice 95

5.1.4 Partition function on the lattice 98

5.2 The Wilson loop 99

5.3 Strong coupling expansion and confinement 101

5.4 Weak coupling expansion and continuum limit 102

5.5 Monte Carlo simulations 105

5.6 Lattice QCD at finite T 109

5.7 Confinement-deconfinement transition in N[subscript f] = 0 QCD 111

5.8 Order of the phase transition for N[subscript f] = 0 115

5.9 Effect of dynamical quarks 116

5.10 Effect of finite chemical potential 117

6 Chiral phase transition 122

6.1 <qq> in hot/dense matter 122

6.1.1 High-temperature expansion 123

6.1.2 Low-temperature expansion 123

6.2 The NJL model 124

6.2.1 Dynamical symmetry breaking at T = 0 126

6.2.2 Symmetry restoration at T [not equal] 0 127

6.3 Mean-field theory and the Landau function 129

6.3.1 Order of the phase transition 129

6.3.2 Second order phase transition 131

6.3.3 First order transition driven by cubic interaction 134

6.3.4 Tricritical behavior with sextet interaction 135

6.4 Spatial non-uniformity and correlations 137

6.5 Critical fluctuation and the Ginzburg region 139

6.6 Renormalization group and [epsilon]-expansion 141

6.6.1 Renormalization in 4 - [epsilon] dimensions 141

6.6.2 Running couplings 143

6.6.3 Vertex functions 144

6.6.4 RG equation for vertex function 145

6.7 Perturbative evaluation of [beta subscript 1] 146

6.8 Renormalization group equation and fixed point 147

6.8.1 Dimensional analysis and solution of RG equation 147

6.8.2 Renormalization group flow 149

6.9 Scaling and universality 152

6.9.1 Scaling at the critical point 152

6.9.2 Scaling near the critical point 153

6.10 Magnetic equation of state 154

6.11 Stability of the fixed point 156

6.12 Critical exponents for the O(N)-symmetric [phi] model 156

6.13 Chiral phase transition of QCD at finite T 158

6.13.1 Landau functional of QCD 159

6.13.2 Massless QCD without axial anomaly 160

6.13.3 Massless QCD with axial anomaly 161

6.13.4 Effect of light quark masses 163

6.13.5 Effect of finite chemical potential 165

7 Hadronic states in a hot environment 170

7.1 Heavy quarkonia in hot plasma 170

7.1.1 QQ spectra at T = 0 170

7.1.2 QQ at T [not equal] 0 172

7.1.3 Charmonium suppression at high T 174

7.1.4 Correlation of Polyakov lines in lattice QCD 174

7.2 Light quarkonia in a hot medium 176

7.2.1 qq spectra at T = 0 176

7.2.2 Nambu-Goldstone theorem at finite T 178

7.2.3 Virial expansion and the quark condensate 179

7.2.4 Pions at low T 180

7.2.5 Vector mesons at low T 182

7.3 In-medium hadrons from lattice QCD 183

7.4 Photons and dileptons from hot/dense matter 185

7.4.1 Photon production rate 186

7.4.2 Dilepton production rate 187

Part II Quark-Gluon Plasma in Astrophysics 191

8 QGP in the early Universe 193

8.1 Observational evidence for the Big Bang 193

8.2 Homogeneous and isotropic space 197

8.2.1 Robertson-Walker metric 197

8.2.2 Hubble's law and red shift 198

8.2.3 Horizon distance 199

8.3 Expansion law of the Universe 200

8.3.1 The Einstein equation 200

8.3.2 Critical density 201

8.3.3 Solution of the Friedmann equation 202

8.3.4 Entropy conservation 204

8.3.5 Age of the Universe 204

8.4 Thermal history of the Universe: from QGP to CMB 206

8.5 Primordial nucleosynthesis 209

8.6 More on the QCD phase transition in the early Universe 211

8.6.1 t < t[subscript 1] (T > T[subscript c]) 213

8.6.2 t[subscript 1] < t < t[subscript F] (T = T[subscript c]) 214

8.6.3 t > t[subscript F] (T < T[subscript c]) 214

9 Compact stars 217

9.1 Characteristic features of neutron stars 218

9.2 Newtonian compact stars 220

9.2.1 White dwarfs 221

9.2.2 Neutron stars 223

9.3 General relativistic stars 224

9.3.1 Maximum mass of compact stars 224

9.3.2 Oppenheimer-Volkoff equation 226

9.3.3 Schwarzschild's uniform density star 229

9.4 Chemical composition of compact stars 229

9.4.1 Neutron star matter and hyperon matter 229

9.4.2 u, d quark matter 232

9.4.3 u, d, s quark matter 233

9.5 Quark-hadron phase transition 233

9.5.1 Equation of state for nuclear and neutron matter 234

9.5.2 Equation of state for quark matter 236

9.5.3 Stable strange matter 239

9.6 Phase transition to quark matter 239

9.7 Structure of neutron stars and quark stars 240

9.7.1 Mass-radius relation of neutron stars 240

9.7.2 Strange quark stars 242

9.8 Various phases in high-density matter 243

Part III Quark-Gluon Plasma in Relativistic Heavy Ion Collisions 245

10 Introduction to relativistic heavy ion collisions 247

10.1 Nuclear stopping power and nuclear transparency 247

10.2 Space-time picture of collisions 250

10.3 Central plateau and fragmentation region 253

10.4 Time history of ultra-relativistic AA collisions 254

10.5 Geometry of heavy ion collisions 256

10.6 Past, current and future accelerators 259

11 Relativistic hydrodynamics for heavy ion collisions 261

11.1 Fermi and Landau pictures of multi-particle production 261

11.2 Relativistic hydrodynamics 265

11.2.1 Perfect fluid 265

11.2.2 Dissipative fluid 267

11.3 Bjorken's scaling solution 269

11.3.1 Perfect fluid 270

11.3.2 Effect of dissipation 273

11.4 Relation to the observables 274

12 Transport theory for the pre-equilibrium process 278

12.1 Classical Boltzmann equation 278

12.2 Boltzmann's H-theorem 282

12.3 Covariant form of the classical transport equation 283

12.3.1 Conservation laws 284

12.3.2 Local H-theorem and local equilibrium 285

12.4 Quantum transport theory 286

12.4.1 The density matrix 287

12.4.2 The Dirac equation 287

12.4.3 The Wigner function 288

12.4.4 Equation of motion for W(x, p) 290

12.4.5 Semi-classical approximation 291

12.4.6 Non-Abelian generalization 293

12.5 Phenomenological transport equation in QCD 294

13 Formation and evolution of QGP 297

13.1 The initial condition 298

13.1.1 Color-string breaking model 298

13.1.2 Color glass condensate 299

13.1.3 Perturbative QCD models 300

13.2 Minijet production 302

13.3 Longitudinal plasma expansion with QCD phase transition 305

13.4 Transverse plasma expansion 307

13.5 Transverse momentum spectrum and transverse flow 309

14 Fundamentals of QGP diagnostics 314

14.1 QGP diagnostics using hadrons 314

14.1.1 Probing the phase transition 314

14.1.2 Ratios of particle yields and chemical equilibrium 315

14.1.3 Transverse momentum distributions and hydrodynamical flow 316

14.1.4 Anisotropic flow and the equation of state 317

14.1.5 Interferometry and space-time evolution 320

14.1.6 Event-by-event fluctuations 323

14.1.7 Hadron production by quark recombination 325

14.2 QGP diagnostics using hard probes: jet tomography 327

14.3 QGP diagnostics using leptons and photons 330

14.3.1 Drell-Yan production of dileptons 330

14.3.2 J/[psi] suppression and Debye screening in QGP 332

14.3.3 Thermal photons and dileptons 334

15 Results from CERN-SPS experiments 338

15.1 Relativistic heavy ion accelerators 339

15.2 Basic features of AA collisions 339

15.2.1 Single-particle spectra 340

15.2.2 Collective expansion 343

15.2.3 HBT two-particle correlation 343

15.3 Strangeness production and chemical equilibrium 345

15.4 J/[psi] suppression 347

15.5 Enhancement of low-mass dileptons 349

15.6 Observation of direct photons 351

16 First results from the Relativistic Heavy Ion Collider (RHIC) 353

16.1 Heavy ion acceleration and collisions in the RHIC 353

16.2 Particle production 357

16.3 Transverse momentum distributions 361

16.4 HBT correlations 363

16.5 Thermalization 364

16.6 Azimuthal anisotropy 366

16.7 Suppression of high-p[subscript T] hadrons 369

16.8 Modification of the jet structure 371

16.9 Quark-number scaling 373

17 Detectors in relativistic heavy ion experiments 375

17.1 Features of relativistic heavy ion collisions 375

17.2 Transverse energy, E[subscript T] 377

17.3 Event characterization detectors 378

17.4 Hadron spectrometer 378

17.4.1 Particle identification using dE/dx measurements 381

17.4.2 Particle identification using time of flight measurements 381

17.4.3 Particle identification using Cherenkov detectors 384

17.5 Lepton pair spectrometer 386

17.6 Photon spectrometer 387

17.7 PHENIX: a large hybrid detector 390

Appendix A Constants and natural units 393

Appendix B Dirac matrices, Dirac spinors and SU(N) algebra 396

Appendix C Functional, Gaussian and Grassmann integrals 400

Appendix D Curved space-time and the Einstein equation 404

Appendix E Relativistic kinematics and variables 412

Appendix F Scattering amplitude, optical theorem and elementary parton scatterings 418

Appendix G Sound waves and transverse expansion 424

Appendix H Tables of particles 429.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

0521561086

OCLC:

60560089

Publisher Number:

9780521561082