QCD at finite temperature and chemical potential from Dyson-Schwinger equations

Abstract

We review results for the phase diagram of QCD, the properties of quarks and gluons and the resulting properties of strongly interacting matter at finite temperature and chemical potential. The interplay of two different but related transitions in QCD, chiral symmetry restoration and deconfinement, leads to a rich phenomenology when external parameters such as quark masses, volume, temperature and chemical potential are varied. We discuss the progress in this field from a theoretical perspective, focusing on non-perturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We aim at a pedagogical overview on the physics associated with the structure of this framework and explain connections to other approaches, in particular with the functional renormalization group and lattice QCD. We discuss various aspects associated with the variation of the quark masses, assess recent results for the QCD phase diagram including the location of a putative critical end-point for $N_f=2+1$ and $N_f=2+1+1$, discuss results for quark spectral functions and summarise aspects of QCD thermodynamics and fluctuations.

80 pages; invited review article, v2: typos corrected, figures updated, comments added; version accepted by PPNP

References in corpus (114)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Exact evolution equation for the effective potential
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Color superconductivity in dense quark matter
• The equation of state in (2+1)-flavor QCD
• The QCD equation of state with dynamical quarks
• The QCD transition temperature: results with physical masses in the continuum limit II.
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• The Phase Structure of the Polyakov--Quark-Meson Model
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Infrared Properties of QCD from Dyson-Schwinger equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Pinch Technique: Theory and Applications
• Probing freeze-out conditions in heavy ion collisions with moments of charge fluctuations
• Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Inhomogeneous chiral condensates
• The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential
• The QCD phase diagram at nonzero quark density
• Freeze-out conditions from net-proton and net-charge fluctuations at RHIC
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Phase structure of three and four flavor QCD
• Phase diagram and critical endpoint for strongly-interacting quarks
• Susceptibilities near the QCD (tri)critical point
• Distribution Functions of the Nucleon and Pion in the Valence Region
• Dressed-quark anomalous magnetic moments
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Propagators and phase structure of Nf=2 and Nf=2+1 QCD
• Renormalization Group Approach towards the QCD Phase Diagram
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Chiral magnetic effect in lattice QCD with a chiral chemical potential
• Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Mixing of scalar tetraquark and quarkonia states in a chiral approach
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• Dual quark condensate and dressed Polyakov loops
• Chiral and deconfinement transition from Dyson-Schwinger equations
• Linking confinement to spectral properties of the Dirac operator
• Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
• Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential
• Hadronic unquenching effects in the quark propagator
• Beyond the rainbow: effects from pion back-coupling
• Baryon number fluctuations at finite temperature and density
• On light baryons and their excitations
• QCD phase transitions via a refined truncation of Dyson-Schwinger equations
• Superconductivity from Repulsive Interactions in Rhombohedral Trilayer Graphene: a Kohn-Luttinger-Like Mechanism
• The chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations
• The infrared behavior of Landau gauge Yang-Mills theory in d=2, 3 and 4 dimensions
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Discretization effects on renormalized gauge-field Green's functions, scale setting and gluon mass
• Quark Confinement: The Hard Problem of Hadron Physics
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Dynamical chiral symmetry breaking and a critical mass
• The QCD phase diagram: Results and challenges
• On the critical line of 2+1 flavor QCD
• Massless Mode and Positivity Violation in Hot QCD
• Quark Number Fluctuations at Finite Temperature and Finite Chemical Potential via the Dyson-Schwinger Equation Approach
• Color-superconductivity in the strong-coupling regime of Landau gauge QCD
• The critical surface of the SU(3)_L x SU(3)_R chiral quark model at non-zero baryon density
• Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study
• Functional renormalization group studies of nuclear and neutron matter
• The Critical End Point of Quantum Chromodynamics Detected by Chirally Imbalanced Quark Matter
• Quark spectral density and a strongly-coupled QGP
• Spectral sums of the Dirac-Wilson Operator and their relation to the Polyakov loop
• $\bar{q}q$ condensate for light quarks beyond the chiral limit
• Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach
• Quark spectral properties above Tc from Dyson-Schwinger equations
• Interface Effect in QCD Phase Transitions via Dyson-Schwinger Equation Approach
• The phase structure of QCD for heavy quarks
• Status of Lattice Studies of the QCD Phase Diagram
• Complete spectra of the Dirac operator and their relation to confinement
• Critical endpoint of finite temperature phase transition for three flavor QCD
• Hadron yields, the chemical freeze-out and the QCD phase diagram
• Relation between chiral symmetry breaking and confinement in YM-theories
• A covariant study of tensor mesons
• On the unlocking of color and flavor in color-superconducting quark matter
• Extraction of Spectral Functions from Dyson-Schwinger Studies via the Maximum Entropy Method
• A confinement criterion for gauge theories with matter fields
• Heavy dense QCD and nuclear matter from an effective lattice theory
• On non-primitively divergent vertices of Yang-Mills theory
• Evidence for O(2) universality at the finite temperature transition for lattice QCD with 2 flavours of massless staggered quarks
• Width of the QCD transition in a Polyakov-loop DSE model
• Confinement in Polyakov Gauge
• The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation
• Spectral properties of quarks above T_c in quenched lattice QCD
• The influence of chiral chemical potential, parallel electric and magnetic fields on the critical temperature of QCD
• Polyakov loop fluctuations and deconfinement in the limit of heavy quarks
• Color-spin locking in a self-consistent Dyson-Schwinger approach
• Strangeness Neutrality and QCD Thermodynamics
• Spurious divergences in Dyson-Schwinger equations
• Strangeness neutrality and baryon-strangeness correlations
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach at finite temperature
• Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories
• Landau Gauge QCD: Functional Methods versus Lattice Simulations
• On bounds and boundary conditions in the continuum Landau gauge
• Running coupling in the conformal window of large-Nf QCD
• Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension
• Quasi-quark spectrum in the chiral symmetric phase from the Schwinger-Dyson equation
• Neutrality of the color-flavor-locked phase in a Dyson-Schwinger approach
• Pseudoscalar Meson Nonet at Zero and Finite Temperature
• A model study of quark number susceptibility at finite temperature beyond rainbow-ladder approximation
• Covariant variational approach to Yang-Mills Theory: Thermodynamics
• Update on Nf=3 finite temperature QCD phase structure with Wilson-Clover fermion action
• Center phase transition from matter propagators in (scalar) QCD
• Quark back reaction to deconfinement transition via gluon propagators
• Disappearance of quasi-fermions in the strongly coupled plasma from the Schwinger-Dyson equation with in-medium gauge boson propagator

Cited by in corpus (174)

• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at energies available at the BNL Relativistic Heavy Ion Collider
• Diquark Correlations in Hadron Physics: Origin, Impact and Evidence
• QCD phase structure from functional methods
• Chiral phase structure and critical end point in QCD
• Locating the critical endpoint of QCD: mesonic backcoupling effects
• Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations
• Fully coupled functional equations for the quark sector of QCD
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Hyper-order baryon number fluctuations at finite temperature and density
• Exploring the partonic phase at finite chemical potential within an extended off-shell transport approach
• Empirical Consequences of Emergent Mass
• QCD at finite temperature and density within the fRG approach: An overview
• Correlation functions of Landau gauge Yang-Mills theory
• Exploring QCD matter in extreme conditions with Machine Learning
• Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment
• Selected Science Opportunities for the EicC
• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Chiral Susceptibility in (2+1)-flavour QCD
• A Study of the Properties of the QCD Phase Diagram in High-Energy Nuclear Collisions
• The Present and Future of QCD
• Impressions of the Continuum Bound State Problem in QCD
• QCD Running Couplings and Effective Charges
• Universal location of the Yang-Lee edge singularity in O(N) theories
• Vector-meson production and vector meson dominance
• Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
• Beam Energy Dependence of Triton Production and Yield Ratio (${\mathrm{N}}_t\times {\mathrm{N}}_p/{\mathrm{N}}_d^2$) in Au+Au Collisions at RHIC
• Concerning pion parton distributions
• Contact interaction analysis of pion GTMDs
• Spectrum of scalar and pseudoscalar glueballs from functional methods
• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• Nucleon elastic form factors at accessible large spacelike momenta
• Emergence of pion parton distributions
• Measures of pion and kaon structure from generalised parton distributions
• Lattice study of thermodynamic properties of dense QC${}_2$D
• Regulator dependence of inhomogeneous phases in the 2+1-dimensional Gross-Neveu model
• Finite-density gauge correlation functions in QC2D
• Chiral spin symmetry and the QCD phase diagram
• Shocks and quark-meson scatterings at large density
• Inhomogeneous chiral condensates in three-flavor quark matter
• Nucleon axial-vector and pseudoscalar form factors, and PCAC relations
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• Vector and Axial-Vector Mesons in Nuclear Matter
• Cosmology meets functional QCD: First-order cosmic QCD transition induced by large lepton asymmetries
• Spectrum and structure of octet and decuplet baryons and their positive-parity excitations
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
• Dynamical exploring the QCD matter at finite temperatures and densities-a short review
• Finite-density QCD transition in magnetic field background
• Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field
• QCD in the heavy dense regime for general $N_c$: On the existence of quarkyonic matter
• Dilepton Radiation from Strongly Interacting Systems
• Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model
• Emergent Hadrons and Diquarks
• Dense two-color QCD from Dyson-Schwinger equations
• Topological susceptibility of pure gauge theory using Density of States
• Inhomogeneous phases in the quark-meson model with explicit chiral-symmetry breaking
• Form Factors of the Nucleon Axial Current
• Particle Interferometry in a Moat Regime
• Ripples of the QCD Critical Point
• Practical scheme from QCD to phenomena via Dyson-Schwinger equations
• Centrality selection effect on higher-order cumulants of net-proton multiplicity distributions in relativistic heavy-ion collisions
• The Myriad Uses of Instantons
• Spontaneous chiral symmetry breaking in the massive Landau gauge: realistic running coupling
• Quark propagator in Minkowski space
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Phase structure of 2+1-flavour QCD and the magnetic equation of state
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Quarks and light (pseudo-)scalar mesons at finite chemical potential
• Thermal properties of light mesons from holography
• Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram
• Chiral spin symmetry and hot/dense QCD
• Localized rainbows in the QCD phase diagram
• Nucleon axial form factor at large momentum transfers
• On the quark spectral function in QCD
• Semileptonic $B_c\to {\eta }_c,J/\psi$ transitions
• Mesonic dynamics and QCD phase transition
• Quark anomalous magnetic moment and its effects on the $\rho$ meson properties
• Constraining the gauge-fixed Lagrangian in minimal Landau gauge
• A symmetry preserving contact interaction treatment of the kaon
• Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography
• Four-quark scatterings in QCD I
• Thermodynamics from the quark condensate
• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• On the critical end point in a two-flavor linear sigma model coupled to quarks
• Pion scalar, vector and tensor form factors from a contact interaction
• Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
• Regularization effects in the Nambu-Jona-Lasinio model: Strong scheme dependence of inhomogeneous phases and persistence of the moat regime
• Probing criticality with deep learning in relativistic heavy-ion collisions
• Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2+1) Polyakov-Nambu-Jona-Lasinio Model
• Search for the QCD Critical Point by Transverse Velocity Dependence of Anti-deuteron to Deuteron Ratio
• Heavy+light pseudoscalar meson semileptonic transitions
• Constraining the QCD phase diagram at finite temperature and density
• Structure formation during phase transitions in strongly interacting matter
• Effects of hadronic repulsive interactions on the fluctuations of conserved charges
• Evaluation of pion-nucleon sigma term in Dyson-Schwinger equation approach of QCD
• Chiral crossover transition from the Dyson-Schwinger equations in a sphere
• Regulator scheme dependence of the chiral phase transition at high densities
• Masses and decay constants of (axial-)vector mesons at finite chemical potential
• QCD pressure: renormalization group optimized perturbation theory confronts lattice
• From imaginary to real chemical potential QCD with functional methods
• Thermal properties of $\pi$ and $\rho$ meson
• Finite-volume effects in baryon number fluctuations around the QCD critical endpoint
• The strange critical endpoint and isentropic trajectories in an Extended PNJL Model with Eight Quark Interactions
• Comprehensive simulation of heavy-ion collisions at non-zero baryon chemical potential
• Pauli radius of the proton
• Color, Flavor, Temperature and Magnetic Field Dependence of QCD Phase Diagram: Magnetic Catalysis and its Inverse
• QCD equation of state and the structure of neutron stars in NJL model
• Correlations of conserved charges and QCD phase structure
• Pileup Correction on Higher-order Cumulants with Unfolding Approach
• Chiral symmetry restoration and properties of Goldstone bosons at finite temperature
• Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry
• Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Spatially oscillating correlation functions in $\left(2+1\right)$-dimensional four-fermion models: The mixing of scalar and vector modes at finite density
• Hadron-quark phase transition in neutron star by combining the relativistic Brueckner-Hartree-Fock theory and Dyson-Schwinger equation approach
• $\Delta$-baryon axialvector and pseudoscalar form factors, and associated PCAC relations
• A contact interaction model for the $\eta$ and ${\eta }^{\prime }$ mesons in a SDE-BSE approach to QCD: masses, decay widths and transition form factors
• New insight on the quark condensate beyond chiral limit
• QCD phase transition and equation of state of stellar strong interaction matter via Dyson-Schwinger equation approach
• Chiral symmetry breaking in accelerating and rotating frames
• A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth-Uhlenbeck approach
• Renormalization group improved pressure for hot and dense quark matter
• Jet evolution in a dense QCD medium
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• Effects of centrality fluctuation and deuteron formation on proton number cumulant in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV from JAM model
• Centrality determination with a forward detector in the RHIC Beam Energy Scan
• A comprehensive approach to the physics of mesons
• Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram
• Towards a unified hadron-quark equation of state for neutron stars within the relativistic mean-field model
• Quantum fluctuation in an inhomogeneous background and its influence on the phase transition in a finite volume system
• Effect of momentum anisotropy on quark matter in the quark-meson model
• Mesons at finite chemical potential and the Silver-Blaze property of QCD
• QCD phase diagram from the gluon propagator at finite temperature and density
• Vector interaction bounds in NJL-like models from LQCD estimated curvature of the chiral crossover line
• QCD chiral condensate and pseudoscalar-meson properties in the nuclear medium at finite temperature
• Constraining the Hadron-Quark Phase Transition Chemical Potential via Astronomical Observation
• Mass-dependence of pseudocritical temperature in mean field approximation
• A window on infrared QCD with small expansion parameters
• Covariant formulation of spinodal decomposition in rapidly expanding quark gluon plasma
• Revealing pion and kaon structure via generalised parton distributions
• The cosmic QCD transition for large lepton flavour asymmetries
• Partial wave analysis for the in-hadron condensate
• Cosmic QCD transition-from quark to strangeon and nucleon
• Implementation of Cluster expansion for hot QCD matter
• Dynamical and finite-size effects on the criterion of first-order phase transition
• Chiral-vacuum excited replicae in QCD modeling
• Dynamics of the conserved net-baryon density near QCD critical point within inhomogeneous quark-gluon plasma profile
• Locating fixed points in the phase plane
• Renormalizing the Quark-Meson-Diquark Model
• The chiral phase transition and equation of state in the chiral imbalance
• Quark cluster expansion model for interpreting finite-T lattice QCD thermodynamics
• Transport properties and equation-of-state of hot and dense QGP matter near the critical end-point in the phenomenological dynamical quasi-particle model
• Influence of light quark loops on the Wigner phase with Dyson-Schwinger equations approach
• An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers
• Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
• Unified Functional-Holographic Theory of the QCD Critical End Point
• Generalized susceptibilities of net-baryon number based on the 3-dimensional Ising universality class
• Application of radial basis functions neutral networks in spectral functions
• Critical endpoint of QCD in a finite volume
• Pion superfluid phase transition at finite isospin chemical potential
• Unified analysis of screening masses for vector and axial-vector mesons and their diquark partners in the Contact Interaction model
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings from Dyson-Schwinger equations framework
• Dyson-Schwinger approach to baryon number fluctuations
• Pion GPDs: A path toward phenomenology
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model
• Linking continuum and lattice quark mass functions via an effective charge
• Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach
• nonlocal quark condensate from Dyson-Schwinger Equation and its contributions to the gluon vacuum polarization based on OPE approach
• Fermionic domain-wall Skyrmions of QCD in a magnetic field
• On the nature of the QCD chiral phase transition with imaginary chemical potential
• The effect of charm quark on the QCD chiral phase diagram