Understanding the Origin of Matter: Perspectives in Quantum Chromodynamics

Preface
Acknowledgments
Contents
Contributors
Acronyms
Introduction
Group Photo from the 53rd Karpacz Winter School on Theoretical Physics
Part I Ultrarelativistic Heavy-Ion Collisions
1 Probing the QCD Phase Diagram with Heavy-Ion Collision Experiments
1.1 Introduction
1.2 QCD Phase Diagram
1.3 BES at RHIC
1.4 STAR Experiment at RHIC
1.5 Results
1.5.1 Global Properties of Created Nuclear Matter
1.5.2 Onset of the QGP—Disappearance of Characteristic Signals of the Plasma Phase
1.5.3 Critical Point Search
1.5.4 Search for the First-Order Phase Transition
1.5.5 A Short Summary of What Have We Learned from BES I
1.6 Fixed-Target Mode
1.7 Beam Energy Scan Phase II (BES II)
1.8 In to the Future ...
References
2 The Early Stage of Heavy-Ion Collisions
2.1 Introduction
2.2 Hadron Wave Function
2.2.1 Deep Inelastic Scattering
2.2.2 DGLAP Evolution Equation
2.2.3 Collinear Factorization
2.2.4 BFKL Evolution Equation
2.2.5 Saturation Momentum
2.3 Propagation of Fast Partons in Dense QCD Matter
2.3.1 Eikonal Approximation, Wilson Lines
2.3.2 Deep Inelastic Scattering in Dipole Frame
2.3.3 The Dipole–Nucleon S-Matrix
2.3.4 Multiple Scattering, Momentum Broadening,Saturation
2.3.5 Phenomenological Dipole Model
2.4 Propagation in Random Fields
2.4.1 McLerran–Venugopalan Model
2.5 Non-linear Evolution Equations
2.5.1 Dipole Operator in a Fixed Background
2.5.2 Balitsky–Kovchegov Equation
2.6 Conclusions
References
3 Hydrodynamic Description of Ultrarelativistic Heavy-IonCollisions
3.1 Introduction
3.1.1 Standard Model of Heavy-Ion Collisions
3.1.2 Basic Hydrodynamic Concepts
3.1.3 From Global to Local Equilibrium
3.1.3.1 Landau and Bjorken Models
3.1.4 Navier–Stokes Hydrodynamics
3.1.5 Insights from AdS/CFT
3.1.6 RTA Kinetic Equation
3.2 Basic Dictionary for Phenomenology
3.2.1 Glauber Model
3.2.2 Harmonic Flows
3.3 Viscous Fluid Dynamics
3.3.1 Müller–Israel–Stewart Theory
3.3.2 DNMR Theory
3.3.3 BRSSS Theory
3.3.4 Anisotropic Hydrodynamics
3.4 Gradient Expansion
3.4.1 Formal Aspects
3.4.2 RTA Kinetic Model with Bjorken Geometry
3.5 Closing Remarks
References
Part II Aspects of Quantum Chromodynamics
4 Three Lectures on QCD Phase Transitions
4.1 Chiral Symmetry and Phase Transitions in QCD
4.1.1 Flavor and Chiral Symmetries
4.1.1.1 Flavor Symmetries
4.1.1.2 Chiral Symmetry
4.1.2 Second-Order Transitions for Two Flavors
4.1.2.1 Chiral Phase Transition for Massless Pions
4.1.2.2 Chiral Phase Transition with Massive Pions
4.1.2.3 Complete Theory for Two Flavors
4.1.2.4 Axial Anomaly for Two Flavors
4.1.2.5 Chiral Symmetry for Three Flavors
4.1.2.6 Sigma Models for χ Symmetry
4.1.3 Three Flavors: Cubic Terms Rule the Roost
4.1.3.1 Chiral Transition for Three Flavors
4.1.3.2 QCD and 2+1 Flavors
4.1.3.3 Background Field: Big or Small?
4.1.3.4 Critical Endpoint?
4.1.3.5 Swept Under the Rug
4.1.4 Tetraquarks and the Chiral Transition
4.1.4.1 Diquarks and Tetraquarks for Two Flavors
4.1.4.2 Sigma Models and Tetraquarks for Two Flavors
4.1.4.3 Tetraquarks for Three Flavors
4.1.4.4 Mirror Model at T=0
4.1.4.5 Two Chiral Transitions with Tetraquarks?
4.1.4.6 Columbia Phase Diagram for Light Quarks. Tetraquarks in the Plane of (T, μ)
4.2 Deconfining Phase Transition in Pure Gauge Theories
4.2.1 Polyakov Loop and Hidden Global Symmetries
4.2.1.1 Hidden Symmetry
4.2.1.2 Global Z(3) Symmetry
4.2.1.3 Lines and Loops
4.2.1.4 Confinement as Z(3) Domains. Deconfinement at Non-zero Temperature
4.2.2 Z(3) Interface Tension, Potential for A0
4.2.2.1 Z(3) Degenerate Vacua
4.2.2.2 Tricks to Compute
4.2.2.3 Lifting the Degeneracy
4.2.2.4 Z(3) Interface Tension. A Tunneling Problem
4.2.2.5 Lattice: Z(N) Interfaces = 't Hooft Loop
4.2.3 Results from the Lattice, Pure Glue and Not
4.2.3.1 Lattice: Renormalized Loop, No Quarks
4.2.3.2 Lattice: Renormalized Loop, with Quarks
4.2.4 Matrix Model for Pure Glue Theories
4.2.4.1 Path to
4.2.4.2 Matrix Model for Pure Glue
4.2.4.3 Gross–Witten–Wadia Transition and Matrix Models at Infinite N
4.3 Chiral Matrix Models for QCD
4.3.1 The Quark–Gluon Plasma Near the CriticalTemperature
4.3.2 Effective Lagrangians for Chiral Symmetry
4.3.3 Solution at T=0
4.3.4 Solution at T≠0
4.3.5 Equations of State and Order Parameters
4.3.6 Baryon Susceptibilities
4.3.7 Suppression of Color in the Semi-QGP
4.3.8 Dilepton Rates
4.3.9 Real Photon Production
Appendix: Exercises
Exercise 1
Exercise 2
Exercise 3
Solution 1
Solution 2
Solution 3
References
5 Effective Approaches to QCD
5.1 QCD and Phases of Strongly Interacting Matter
5.1.1 Pictures of Confinement
5.1.2 Color Charge and Static Quark Potential
5.1.3 Quark Masses
5.1.4 Chiral Symmetry
5.1.5 Order Parameters in QCD
5.1.5.1 Quark Condensate
5.1.5.2 Wilson Loop
5.1.5.3 Temporal Wilson Loop
5.1.5.4 Spatial Wilson Loop
5.1.5.5 Polyakov Loop Correlator
5.1.5.6 Polyakov Loop
5.1.5.7 Spatial 't Hooft Loop
5.2 Magnetic Monopole Picture of Confinement
5.2.1 Meissner Effect in Superconductors
5.2.2 Emergence of Magnetic Monopoles in QCD
5.2.3 Induced Magnetic Monopole
5.2.4 Dual Superconductor Models of QCD
5.3 Center Vortex Picture of Confinement
5.3.1 Introduction
5.3.2 Lattice Gauge Theory
5.3.3 Center Projection
5.3.4 The Random Vortex Model
5.3.5 Topology of Center vortices and Chiral Symmetry Breaking
5.3.6 Center Vortex Dominance
5.3.7 Conclusions
5.4 Hamiltonian Approach to QCD in Coulomb Gauge
5.4.1 Introduction
5.4.2 Canonical Quantization of Yang–Mills Theory
5.4.3 Variational Solution for the Yang–Mills Vacuum Wave Functional
5.4.4 Hamiltonian Formulation of QCD in Coulomb Gauge
5.4.5 Alternative Hamiltonian Approach to Finite-Temperature QFT
5.4.6 Conclusions
Appendix: Exercises
References
6 Heavy Flavors and Exotic Hadrons
6.1 Introduction
6.1.1 What Are Exotic Hadrons?
6.1.2 Importance of Studying Exotic Hadrons
6.1.3 Main Subject of This Lecture: Charm and Bottom Exotic Hadrons
6.1.4 Introduction of Review Articles on X, Y, Z Hadrons
6.2 Theoretical Framework for Heavy Hadrons
6.2.1 Heavy Quark Spin Symmetry
6.2.1.1 Heavy Quark Effective Theory
6.2.1.2 Heavy Quark Spin Symmetry
6.2.1.3 1/mQ Corrections
6.2.2 Heavy Hadron Effective Theory
6.3 Heavy Exotic Hadrons -X, Y, Z Hadrons-
6.3.1 Quarkonia
6.3.2 X(3872)
6.3.3 Y(4260)
6.3.4 Zc(4430)+ and Zc(3900)+
6.3.5 Yb(10888)
6.3.6 Zb(10610)+ and Zb(10650)+
6.3.7 Pc(4380) and Pc(4450): Charm Pentaquark
6.3.8 Miscellaneous Exotic Hadrons
6.3.9 Tcc —New Possible Exotic Hadrons—
6.4 Heavy Hadrons in Nuclear Matter
6.4.1 Flavor Nuclei: From Strangeness to Charm and Bottom
6.4.2 Topics on Anti-heavy–Light (q) Meson in Nuclear Matter
6.4.2.1 Interaction
6.4.2.2 Properties in Nuclear Matter
6.4.2.3 Kondo Effect
6.5 Summary
Appendix: Exercises
Exercise 1: Feshbach Resonance in One-Dimensional System
Basics
Feshbach Resonance
Exercise 2: Simple Model of the Kondo Effect
Exercise 3: Resonance States in One-Dimensional System
References
Part III Simulations of QCD and Heavy-Ion Collisions
7 Flavored Aspects of QCD Thermodynamics from Lattice QCD
7.1 Introduction
7.2 QCD Thermodynamics and Strangeness
7.2.1 Tc and the Equation of State
7.2.2 HRG and Missing Strange Baryons
7.2.3 Strangeness Freeze-Out
7.2.4 Taylor Expansion in Chemical Potential
7.2.5 Equation of State in a Strangeness Neutral System
7.2.6 Melting and Abundance of Open Charm Hadrons
7.2.7 Conclusions
7.3 Basics of Lattice Gauge Theory
7.3.1 Discretization of Space-Time Points
7.3.2 Gauge Transformation and Gauge Action
7.3.3 Renormalization and Continuum Limit
7.4 Basics of Monte Carlo Integration
7.4.1 Importance Sampling
7.4.2 Markov Chain
Appendix: Exercises
Exercise 1
Exercise 2
Exercise 3
References
8 Spectral and Transport Properties from Lattice QCD
8.1 Motivation
8.2 Hadronic Correlation Functions
8.3 Inversion Methods
8.4 Thermal Dilepton Rate and Electrical Conductivity
8.4.1 Continuum Extrapolated Vector Meson Correlation Functions
8.4.2 Lattice Estimate on the Thermal Dilepton Rate and Electrical Conductivity
8.5 Lattice Estimate of Thermal Photon Rate
8.6 Charmonia and Bottomonia Spectral Function from LatticeQCD
8.6.1 Free Spectral Function
8.6.2 Spectral Functions of Charmonia and Bottomonia in the Pseudo-Scalar Channel
8.6.3 Spectral Functions of Charmonia and Bottomonia in the Vector Channel
8.7 Heavy Quark Momentum Diffusion Coefficient
8.8 Conclusions
Exercises
Exercise 1
Exercise 2
Exercise 3
Exercise 4
References
9 Monte-Carlo Statistical Hadronization in Relativistic Heavy-Ion Collisions
9.1 Relativistic Heavy-Ion Collisions
9.2 Relativistic Perfect Fluid Dynamics
9.3 Fluid Dynamics from Kinetic Theory
9.4 Event-Averaged Initial Conditions for Fluid Dynamics
9.5 Particle Decoupling
9.6 Single-Freeze-Out Scenario
9.7 Freeze-Out Hypersurface Extraction
9.8 Cooper-Frye Formalism
9.9 Hadron Abundances
9.10 Decays of Resonances
9.11 Hydro-Inspired Parameterizations of Freeze-Out
9.12 Monte-Carlo Statistical Hadronization
9.13 Performing Analysis with THERMINATOR2
9.13.1 Single-Particle Spectra
9.13.2 Impact of Resonance Decays
9.13.3 Experimental Feed-Down Corrections
9.13.4 Ratios of Particle Yields
Appendix: Exercises
Exercise 1: Compiling the Code
Exercise 2: Default Run
Exercise 3: Performing the Analysis
Exercise 4: Improving Statistics
Exercise 5: Studying the Impact of Resonance Decays
Exercise 6: Applying the Experimental Feed-Down Corrections
Exercise 7: Calculating Particle Yields
Exercise 8: Including Heavy States
References
Index