7 pages, 4 figures, talk given by BJS at the 30th International School of Nuclear Physics, "Heavy Ion Collisions from the Coulomb Barrier to the Quark Gluon Plasma", Erice, Italy, 16-24 September 2008. To appear in the proceedings
发表信息：
Progress in Particle and Nuclear Physics 62, 381 (2009)
Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.
For the understanding of fluctuation measurements in heavy-ion collisions it is crucial to develop quantitatively reliable dynamical descriptions which take the non-perturbative nature of QCD near the phase transition into account. We discuss a novel QCD-assisted transport approach based on non-equilibrium chiral fluid dynamics and the effective action of low energy QCD. In this framework, we study the time-evolution of fluctuation measures of the critical mode, notably the kurtosis, for a non-expanding system. From this, we can estimate the equilibration times of critical mode fluctuations in…
We study the impact of higher order quark-meson scattering processes on the chiral phase structure of two-flavour QCD at finite temperature and quark density. Thermal, density and quantum fluctuations are included within a functional renormalisation group approach to the quark-meson model. We present results on the chiral phase boundary, the critical endpoint, and the curvature of the phase transition line at vanishing density.
We give an introduction to the phase structure of QCD matter under rotation based on effective four-fermion models. The effects of the magnetic field on the rotating QCD matter are also explored. Recent developments along these directions are overviewed, with special emphasis on the chiral phase transition. The rotational effects on pion condensation and color superconductivity are also discussed.
In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.
We study holographic models of the QCD temperature-chemical potential phase diagram based on the D3/D7 system with chiral symmetry breaking. The baryonic phase may be included through linked D5-D7 systems. In a previous analysis of a model with a running gauge coupling a baryonic phase was shown to exist to arbitrarily large chemical potential. Here we explore this phase in a more generic phenomenological setting with a step function dilaton profile. The change in dilaton generates a linear confining $\bar{q}q$ potential and opposes the screening effect of temperature. We show that the persist…
The transition between the hadronic phase and the quark gluon plasma phase at nonzero temperature and quark chemical potentials is studied within the large-Nc expansion of QCD.
We study the QCD phase diagram at nonzero baryon and isospin chemical potentials using the 1/Nc expansion. We find that there are two phase transitions between the hadronic phase and the quark gluon plasma phase. We discuss the consequences of this result for the universality class of the critical endpoint at nonzero baryon and zero isospin chemical potential.
We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model.
Current status of theoretical researches on the QCD phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include; quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.
We explore the phase diagram of two-flavor QCD at imaginary values of baryon and isospin chemical potentials analyzing the thermodynamic potential of QCD analytically and that of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model numerically. QCD has no pion condensation at imaginary baryon and isospin chemical potentials, and therefore has discrete symmetries that are not present at real baryon and isospin chemical potentials. The PNJL model possesses all the discrete symmetries. The PNJL model can reproduce qualitatively lattice QCD data presented very lately.
We study two phases of supersymmetric QCD associated to the singularities of the renormalization constant of the fermion mass operator. We find a behavior of the potential between two charges for the phases of interest that it is consistent with Seiberg results on these aspects based on a different method.
We give a general overview about the approaches to study the phase diagram of QCD. Thereafter, we examine the evolution of a fireball in a chiral fluid dynamic model including nonequilibrium effects.
Axionlike particle-assisted supercooling chiral phase transition in QCD: Identifying Coleman-Weinberg type-chiral phase transition in QCD-like scenarios
Center for Theoretical Physics and College of Physics, Jilin University（吉林大学理论物理中心和物理学院）；Center for Fundamental Physics, School of Mechanics and Physics, Anhui University of Science and Technology（安徽理工大学力学与物理学院基础物理中心）；Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University（东京女子基督教大学信息数学科学系）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We explore QCD phase diagram by constructing a holographic QCD model using the Einstein-Maxwell-Scalar system. The chiral transition is investigated by adding a probe scalar and confinement transition is studied by adding a probe string into the system. By interpreting the black hole phase transition in the bulk spacetime as the quarkyonic transition in the dual QCD theory and introducing the bypass mechanism for deconfinement transition, we give an explanation why chiral symmetry breaking and deconfinement transition lines coincide with each other despite their different physical origins.
Holography provides a powerful tool to model QCD and other strongly coupled gauge dynamics. As examples of its power to compute in novel environments I review some recent results: these include models of the phase structure of QCD at finite temperature and chemical potential; and computation of time dependent processes at strongly coupled phase transitions.
We study the phase transition between pion condensed phase and normal phase, as well as chiral phase transition in a two flavor($\mathcal{N}_f=2$) IR- improved soft-wall AdS/QCD model at finite isospin chemical potential $μ_I$ and temperature $T$. By self-consistently solving the equations of motion, we obtain the phase diagram in the plane of $μ_I$ and $T$. The pion condensation appears together with a massless Nambu-Goldstone boson $m_{π_1}(T_c, μ_I^c)=0$, which is very likely to be a second-order phase transition with mean-field critical exponents in small $μ_I$ region. When $T=0$, the crit…
We show the universality of phase diagrams in QCD and QCD-like theories through the large-N_c equivalence. The whole phase diagrams are identical between QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. In the chiral limit, they are also identical to that of QCD at finite chiral chemical potential. Outside the pion or diquark condensed phase in these theories, the universality of phase diagrams is applicable to QCD at finite baryon chemical potential. We further argue that the universality may work approximately even for N_c…
I show an updated QCD phase diagram with recent developments from chiral effective theories and phenomenological models. Expected signals of a QCD critical point accessible in heavy-ion collisions are also discussed. In particular, non-monotonic behavior of fluctuations associated with conserved charges is focused on.
The present knowledge of the QCD phase diagram based on simulations of lattice QCD is summarised. The main questions are whether there is a critical point in the QCD phase diagram and whether it is related to a chiral phase transition. It is shown that QCD at imaginary chemical potentials has a rich phase structure, which can be determined in a controlled way without sign problem and which severely constrains the phase structure at real chemical potentials.
We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universal…
We derive exact constraints relating QCD at nonzero baryon chemical potential and temperature to QCD at nonzero isospin chemical potential and temperature, a theory which can be simulated by conventional methods. These results challenge the consistency of dynamical models of superconductivity and superfluidity in QCD.
We investigate the QCD phase diagram of isospin asymmetric matter using the Polyakov loop extended quark meson (PQM) model with vector interaction. The critical point temperature is found to decrease in isospin asymmetric matter and disappear at large isospin chemical potential. We also discuss the QCD phase transition in the neutron star core. From comparison of the QCD phase diagram in PQM and corresponding baryon and isospin chemical potentials of neutron star matter in relativistic mean field models, we show that the order of the chiral phase transition in the neutron star core could be cr…
Recently, deeper understanding of QCD emerges from the study of the AdS/CFT correspondence. New results include the properties of quark-gluon plasma and the confinement/deconfinement phase transition, which are both very important for the scenario of the QCD phase transition in the early universe. In this paper, we study some aspects of how the new results may affect the old calculations of the cosmological QCD phase transition, which are mainly based on the studies of perturbative QCD, lattice QCD and the MIT bag model.
We elucidate that the phase diagram of massless $N$-flavor QCD under $\mathbb{Z}_N$ flavor-twisted boundary condition (massless $\mathbb{Z}_N$-QCD) is constrained by an 't Hooft anomaly involving two-form gauge fields. As a consequence, massless $\mathbb{Z}_N$-QCD turns out to realize persistent order at any temperatures and quark chemical potentials, namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-$(T,μ)$ phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.
We determine the dependence of important parameters for critical fluctuations on temperature and baryon chemical potential in the QCD phase diagram. The analysis is based on an identification of the fluctuations of the order parameter obtained from the Ising model equation of state and the Ginzburg-Landau effective potential approach. The impact of the mapping from Ising model variables to QCD thermodynamics is discussed.
A summary of discussions on selected topics related to QCD phase diagram, phase transition, critical point, fluctuation and correlations at the Quark Matter 2009 conference are presented.
Heavy-ion collisions performed in the beam energy range accessible by the NICA collider facility are expected to produce systems of extreme net-baryon densities and can thus reach yet unexplored regions of the QCD phase diagram. Here, one expects the phase transition between the plasma of deconfined quarks and gluons and the hadronic matter to be of first order. A discovery of the first-order phase transition would as well prove the existence of the QCD critical point, a landmark in the phase diagram. In order to understand possible signals of the first-order phase transition in heavy-ion coll…
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial-vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in th…
We study the characteristics of the QCD phase transitions in dense hadronic matter using the Skyrme model constructed on S^3. We find numerically the localized solutions on $S^3$ using the extended Skyrme model which implements correctly the scale symmetry of QCD. The transition from the localized phase to the delocalized phase is found to be of first order at the critical radius of the hypersphere, $L_c$. The chiral restoration and the gluon decondensation also take place at the same critical size.
We briefly summarize the properties of conserved charge fluctuations as a sensitive probe for the QCD phase transitions. We discuss the density fluctuations which play a significant role to search for the critical end point. The importance of spinodal instabilities to distinguish the first-order phase transition is also indicated.
We study the gravitational wave spectrum from the confinement-deconfinement phase transi-tion in the holographic QCD models for both light quark and heavy quark. We obtain the gravitationalwave spectrum in the deflagration, detonation and runaway cases for different chemical potentials and duration of the phase transition. We find that the gravitational wave spectrum could be observed by EPTA/IPTA and eLISA for large chemical potential and short duartion of phase transtions.
We discuss the phase structure and fluctuations of conserved charges in two flavor QCD. The importance of the density fluctuations to probe the existence of the critical end point is summarized. The role of these fluctuations to identify the first order phase transition in the presence of spinodal phase separation is also discussed.
We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model and interpret our result as the heavy quarks system by comparing the recent lattice QCD simulation. We finally obtain the equations of state in our model.
We discuss the finite-size effects on the chiral phase transition in QCD. We employ the Nambu-Jona-Lasinio model and calculate the thermodynamic potential in the mean-field approximation. Finite-size effects on the thermodynamic potential are taken into account by employing the multiple reflection expansion. The critical temperature is lowered and the order of the phase transition is changed form first to second as the size of the system of interest is reduced.
In this talk I discuss three recent developments in the theoretical understanding of the phase diagram of the strong interaction. The first topic deals with the comparison of model calculations of the quark-hadron transition at vanishing quark chemical potential with state-of-the-art lattice QCD results. In the second relates to the size of a possible 'quarkyonic phase'. The third deals with the occurence of inhomogeneous chiral phases.
The speed of sound in QCD matter at finite temperature and density is investigated within the Polyakov loop improved Nambu--Jona-Lasinio (PNJL) model. The spinodal structure associated with the chiral first-order chiral phase transition is considered to describe the continuous variation of the speed of sound. The behaviors of the squared sound speed in different phases, including the stable, metastable and unstable phases, are derived. The relation between speed of sound and QCD phase transitions is systematically explored. In particular, the boundary of vanishing sound velocity is derived in …
An attempt is made in QCD to explain the growth of total cross-sections with energy, without violating the Froissart bound. This is achieved by computing the phase shifts of elastic scatterings of partons rather than their amplitudes. To render that possible a general formalism of phase-shifts in QCD is developed. Computed to two-loop order, agreements with hadronic and virtual-photon total cross-sections are quite satisfactory. Predications for the slower rate of growth at higher energies are also presented.
QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although sign-free QCD-like theories have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear until recently. In this talk we explain the large-Nc equivalences between QCD and various QCD-like theories, which lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, SO(2Nc) and Sp(2Nc) gauge theories. In particular two-flavor QCD with the baryon che…
We review recent results on the phase structure of QCD and bulk QCD thermodynamics. In particular we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD simulations and how the knowledge on non-universal scaling parameter can be utilized in the exploration of the QCD phase diagram. We also show how various (generalized) susceptibilities can be employed to characterize properties of QCD matter at low and hight temperatures, related to deconfining aspects of the QCD transition. Finally, we address the input these la…
The chiral symmetry breaking ($χ_{SB}$) is one of the most fundamental problems in QCD. In this paper, we calculate quark condensation analytically in a holographic QCD model dual to the Einstein-Maxwell-Dilaton (EMD) system coupled to a probe scalar field. We find that the black hole phase transition in the EMD system seriously affects $χ_{SB}$. At small chemical potential, $χ_{SB}$ behaves as a crossover. For large chemical potential $μ>μ_c$, $χ_{SB}$ becomes first order with exactly the same transition temperature as the black hole phase transition by a bypass mechanism. The phase diagram w…
We study the gravitational waves produced by the collision of the bubbles as a probe for the cosmological first order QCD phase transition, considering heavy static quarks. Using AdS/QCD and the correspondence between a first order Hawking-Page phase transition and confinement-deconfinement phase transition, we find the spectrum and the strain amplitude of the gravitational wave within the hard and soft wall models. We postulate the duration of the phase transition corresponds to the evaporation time of the black hole in the five dimensional dual gravity space, and thereby obtain a bound on th…
Based on lattice QCD-adjusted SU(2) nonlocal Polyakov--Nambu--Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simul…
The Polyakov linear sigma model (PLSM) is used to investigate the respective influence of a finite volume and a magnetic field on the quark-hadron phase boundary in the plane of baryon chemical potential ($μ_{B}$) vs. temperature ($T$) of the QCD phase diagram. The calculated results indicate sizable shifts of the quark-hadron phase boundary to lower values of $(μ_{B}~\text{and}~T)$ for increasing magnetic field strength, and an opposite shift to higher values of $(μ_{B}~\text{and}~T)$ for decreasing system volume. Such shifts could have important implications for extraction of the thermodynam…
Baryon fluctuations exceeding Poisson expectations can signal a nearly first order phase transition at RHIC. We show how these fluctuations can be measured, and apply a dissipative-hydrodynamic formulation used in condensed matter physics to simulate their evolution.
In these lectures we provide an introduction to the phase structure of QCD. We begin with a brief discussion of QCD, the symmetries of QCD, and what we mean by a ``phase of QCD''. In the main part of the lectures we discuss the phase diagram of QCD as a function of the temperature and the baryon density. We focus, in particular, on the high temperature plasma phase, the low temperature and low density nuclear phase, and the high density color superconducting phases.
We study the QCD phase diagram at finite temperature and baryon chemical potential by relating the behavior of the light-quark condensate to the threshold energy for the onset of perturbative QCD. These parameters are connected to the chiral symmetry restoration and the deconfinement phase transition, respectively. This relation is obtained in the framework of finite energy QCD sum rules at finite temperature and density, with input from Schwinger-Dyson methods to determine the light-quark condensate. Results indicate that both critical temperatures are basically the same within some 3% accura…
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
We derive the effective Lagrangian for the low-energy massive meson excitations of the color-flavor-locking (CFL) phase of QCD with 3 flavors of light quarks. We compute the decay constants, the maximum velocities, and the masses of the mesons at large baryon chemical potential mu. The decay constants are linear in mu. The meson maximum velocities are close to that of sound. The meson masses in the CFL phase are significantly smaller than in the normal QCD vacuum and depend only on bare quark masses. The order of the meson masses is, to some extent, reversed compared to that in the QCD vacuum.…
In this talk we present results for the propagators and the phase diagram of QCD, obtained from a truncated set of Dyson-Schwinger equations at finite temperature T and quark chemical potential mu. We include back-coupling effects of the dressed quark and gluon propagators, which also allows us to study the influence of strange quarks. For the phase diagram we find a critical end-point at mu/T = 1.9 and coinciding chiral and deconfinement phase transitions.
We study the QCD phase transition based on the statistical treatment with the bag-model picture of hadrons, and derive a phenomenological relation among the low-lying hadron masses, the hadron sizes and the critical temperature of the QCD phase transition. We apply this phenomenological relation to both full QCD and quenched QCD, and compare these results with the corresponding lattice QCD results. Whereas such a statistical approach works well in full QCD, it results in an extremely large estimate of the critical temperature in quenched QCD, which indicates a serious problem in understanding …
We discuss an exotic phase that adjoint QCD possibly exhibits in the deep infrared (IR). It is a confining phase, with a light spectrum consisting of massless composite fermions. The discrete chiral symmetry is broken, with unbroken continuous chiral symmetry. We argue that it may give a description of the IR of adjoint QCD with three massless Weyl flavors and that it passes all consistency checks known to us.
We map out the phase diagram of QCD$_3$ with a product flavor group of the form $U(f)\times U(F)$. We find interesting structures emerge when $f+F>k$ depending on the relative sizes of $f$,$F$ and $k$. In particular, there exists phase transitions in which a Grassmannian phase will disappear and reappear in a different part of the phase diagram.
