The Deconfinement Transition of QCD: Theory Meets Experiment (Lecture Notes in Physics, 981)

In the last few years, numerical simulations of QCD on the lattice have reached a new level of accuracy. A wide range of thermodynamic quantities is now available in the continuum limit and for physical quark masses. This allows a comparison with measurements from heavy ion collisions for the first time. Furthermore, calculations of dynamical quantities are also becoming available. The combined effort from first principles and experiment allows to gain an unprecedented understanding of the properties of quark-gluon plasma. This concise text, geared towards postgraduate students and newcomers to the field, carefully introduces and reviews the state-of-the-art techniques and results from lattice simulations and connects them to the experimental information from RHIC and the LHC. ​ Preface Acknowledgments Contents About the Authors Acronyms Part I Bulk Properties of Strongly Interacting Matter 1 Introduction to Lattice QCD 1.1 QED Action, QCD Action and Gauge Invariance 1.2 Action Discretization and Lattice Gauge Theory 1.2.1 Pure Gauge Theory 1.2.2 Fermions on the Lattice 1.2.3 Fermion Doubling and Staggered Fermions 1.3 Monte Carlo Methods 1.3.1 The Metropolis Algorithm 1.3.2 The Hybrid Monte Carlo (HMC) Algorithm References 2 Phase Transitions in QCD 2.1 QCD Partition Function on the Lattice 2.2 Phase Transitions 2.3 Polyakov Loop 2.3.1 Physical Interpretation of the Polyakov Loop 2.3.2 Polyakov Loop on the Lattice 2.4 Chiral Symmetry 2.4.1 Experimental Observation 2.5 Chiral Phase Transition 2.5.1 Chiral Limit and Transition Temperature 2.5.2 Lattice QCD Predictions on Parity Doubling and Chiral Symmetry Restoration 2.6 QCD in an External Magnetic Field 2.6.1 Magnetic Catalysis References 3 Equation of State of QCD at Finite Temperature and μB=0 3.1 Equation of State of QCD at μB=0 3.1.1 Differential Method 3.1.2 Integral Method 3.1.3 High Temperature, Ideal Gas Limit 3.1.4 Results References 4 QCD at Finite Chemical Potential 4.1 Sign Problem 4.2 Equation of State of QCD at Finite Chemical Potential 4.2.1 Taylor Expansion 4.2.2 Simulations at Imaginary Chemical Potential 4.2.2.1 Simulation Setup 4.2.3 Results 4.3 QCD Phase Diagram at Imaginary Chemical Potential 4.4 QCD Phase Diagram at Real Chemical Potential 4.4.1 Limits on the Critical Point Location 4.5 Other Approaches at High Chemical Potential 4.5.1 Dyson-Schwinger Equation 4.5.2 Critical Point in the Black Hole Engineering Approach 4.5.3 Lattice-Based Approach with a 3D-Ising Model Critical Point 4.6 QCD at Finite Isospin Chemical Potential References 5 Fluctuations of Conserved Charges 5.1 Introduction and Definition 5.2 Probability Functions 5.3 Chemical Freeze-Out Parameters 5.3.1 Canonical vs Grand Canonical Ensemble 5.3.2 Lattice QCD Observables 5.4 Critical Fluctuations 5.4.1 Model Predictions for a Critical Point in the QCD Phase Diagram 5.4.2 Model Predictions on Chiral Criticality 5.5 Results from Lattice QCD References 6 The Hadron Resonance Gas Model 6.1 Introduction 6.2 Boltzmann Approximation 6.3 Comparison to Lattice QCD Results 6.3.1 Early Days: Distorted Hadronic Spectrum 6.3.2 Investigation of a Possible Flavor Hierarchy 6.3.3 The Resonance Spectrum 6.3.4 Off-Diagonal Correlators 6.4 HRG Model Fits to Particle Yields 6.5 Interacting Hadron Resonance Gas Model 6.5.1 Excluded Volume HRG Model 6.5.2 Van der Waals HRG Model 6.5.3 S-Matrix Formulation References 7 Experimental Verification of Lattice QCD Predictions 7.1 Introduction 7.2 Experimental Methods 7.2.1 Relation Between Moments, Cumulants and Susceptibilities 7.2.2 Caveats in the Comparison Between Theory and Experiment and How to Solve Them 7.2.3 The Statistical Baseline and the Impact of Conservation Laws 7.2.4 Experimental Procedures to Determine Particle-Identified Event by Event Multiplicity Distributions 7.3 Results 7.3.1 Results on Searches for a Critical Point 7.3.1.1 Event-by-Event Net-Particle Multiplicities as a Proxy for Conserved Quantum Numbers 7.3.1.2 Net-Proton Measurements 7.3.1.3 Other Net-Particle Measurements 7.3.2 Results on Searches for Chiral Criticality 7.3.3 Results on Chemical Freeze-Out Predictions 7.3.4 Expectations for Near Term Future Measurements References Part II Transport Properties of Strongly Interacting Matter 8 Transport Properties of QCD Matter 8.1 Introduction 8.2 Reconstruction Methods 8.2.1 Physics-Based Ansätze 8.2.2 Maximum Entropy Method 8.2.3 Bayesian Approaches 8.2.4 Stochastic Approaches 8.2.5 Backus-Gilbert Method 8.2.6 Tikhonov Regularization 8.3 Charge Diffusion and Electromagnetic Probes 8.4 Heavy Quark Diffusion Coefficient 8.5 Viscosity References 9 Heavy Flavors and Quarkonia 9.1 Introduction 9.2 In-Medium q Potential 9.3 Quark-Antiquark Free Energy 9.4 Euclidean Temporal Correlators and Spectral Functions 9.5 Spatial Correlation Functions 9.6 Effective Theories for Heavy Quarkonium 9.6.1 Non-relativistic QCD 9.6.2 Potential Non-relativistic QCD 9.7 Other Approaches References Index