The chiral and deconfinement phase transitions

By introducing the dressed Polayakov loop or dual chiral condensate as a candidate order parameter to describe the deconfinement phase transition for light flavors, we discuss the interplay between the chiral and deconfinement phase transitions, and propose the possible QCD phase diagram at finite temperature and density. We also introduce a dynamical gluodynamic model with dimension-2 gluon condensate, which can describe the color electric deconfinement as well as the color magnetic confinement.     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Monte Carlo study of long-range chiral structure in QCD

Results of a Monte Carlo study of long-range chiral structure is massless 4-dimensional QCD are presented. The algorithm employed integrates fermion degrees of freedom exactly. The behavior of chiral correlations in both abelian and SU(2) color theories is compared. We find strong evidence for chiral breakdown, with a solution of the U(1) problem, in lattice QCD at large β.     

Do instantons like a colorful background?

We investigate chiral symmetry breaking and color symmetry breaking in QCD. The effective potential of the corresponding scalar condensates is discussed in the presence of non-perturbative contributions from the semiclassical one-instanton sector. We concentrate on a color singlet scalar background which can describe chiral condensation, as well as a color octet scalar background which can generate mass for the gluons. Whereas a non-vanishing singlet chiral field is favored by the instantons, we have found no indication for a preference of color octet backgrounds.     

Coexistence of color superconductivity and chiral symmetry breaking within the NJL model

The phase diagram for quark matter is investigated within a simple Nambu-Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature-density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where, within the first one, a first-order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T _t = 55 MeV occurs, whereas for the second one a second-order phase transition for temperatures below T _t = 7 MeV is found. In the latter case, there is also a coexistence phase of broken chiral symmetry with color superconductivity, which is a new finding within this class of models. Possible consequences for the phenomenology of the QCD phase transition at high baryon densities are discussed. Received: 3 January 2003 / Accepted: 21 February 2003 / Published online: 24 April 2003     

Lattice results on QCD at high temperature and non-zero baryon number density

Studies of QCD thermodynamics on the lattice now can be performed with an almost realistic quark mass spectrum and on quite large lattices. This will soon allow a controlled extrapolation to the continuum limit. We present recent results on the QCD equation of state, discuss deconfining and chiral symmetry restoring aspects of the QCD transition at vanishing chemical potential and show results on baryon number, electric charge and strangeness fluctuations. We briefly discuss the generic structure of Taylor expansion coefficients in the vicinity of the chiral phase transition and comment on the determination of the anticipated chiral critical point within the framework of Taylor expansions of the QCD partition function.     

Modelling the QCD phase transition with an effective Lagrangian of light and massive hadrons

The temperature dependence of quark and gluon condensates in QCD as precursor of the chiral and deconfining phase transition is modelled with a conformally extended nonlinear σ-model including broken chiral and scale invariance. The model is further enlarged by including (free) heavier hadrons. Within this frame we then study the interplay of QCD scale breaking effects and heavier hadrons in chiral symmetry restoration.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

Confining but chirally symmetric dense and cold matter

The possibility for existence of cold, dense chirally symmetric matter with confinement is reviewed. The answer to this question crucially depends on the mechanism of mass generation in QCD and interconnection of confinement and chiral symmetry breaking. This question can be clarified from spectroscopy of hadrons and their axial properties. Almost systematical parity doubling of highly excited hadrons suggests that their mass is not related to chiral symmetry breaking in the vacuum and is approximately chirally symmetric. Then there is a possibility for existence of confining but chirally symmetric matter. We clarify a possible mechanism underlying such a phase at low temperatures and large density. Namely, at large density the Pauli blocking prevents the gap equation to generate a solution with broken chiral symmetry. However, the chirally symmetric part of the quark Green function as well as all color non-singlet quantities are still infrared divergent, meaning that the system is with confinement. A possible phase transition to such a matter is most probably of the first order. This is because there are no chiral partners to the lowest lying hadrons.     

Mixed quark–gluon condensate at finite temperature and density in the global color symmetry model

We study the properties of mixed quark–gluon condensate at finite temperature and chemical potential in the framework of global color symmetry model. In comparing with the quark condensate, we confirm that both of these condensates give the same information about chiral phase transition. We also find that the ratio of these two condensates is insensitive to the temperature T and the chemical potential μ, which supports the conclusion obtained recently by the authors using quenched lattice QCD.     

Effects of the anomaly on the two-flavor QCD chiral phase transition

We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the chiral phase transition in two-flavor massless QCD. Our model allows us to vary the QCD anomaly and thus study its effects on the transition. Our study confirms the widely accepted viewpoint that the chiral phase transition is first order in the absence of the anomaly. Turning on the anomaly weakens the transition and turns it second order at a critical anomaly strength. The anomaly strength at the tricritical point is characterized using r=(M(eta')-M(pi))/rho(eta'), where M(eta'), M(pi) are the screening masses of the anomalous and regular pions and rho(eta') is the mass scale that governs the low energy fluctuations of the anomalous symmetry. We estimate that r ~ 7 in our model. This suggests that a strong anomaly at the two-flavor QCD chiral phase transition is necessary to wash out the first order transition.     

Chiral Magnetic Effect and Chiral Phase Transition

We study the influence of the chiral phase transition on the chiral magnetic effect. The azimuthal charge-particle correlations as functions of the temperature are calculated. It is found that there is a pronounced cusp in the correlations as the temperature reaches its critical value for the QCD phase transition. It is predicted that there will be a drastic suppression of the charge-particle correlations as the collision energy in RHIC decreases to below a critical value. We show then the azimuthal charge-particle correlations can be the signal to identify the occurrence of the QCD phase transitions in RHIC energy scan experiments.     

Manohar-Georgi 模型的QCD分析及核子的一种有效手征夸克模型

Manohar 和Georgi 提出了一种基于QCD的有效组份夸克模型(MG 模型),用于解释唯象夸克模型成功的原因。最近Weinberg 指出,该模型在大Nc (夸克颜色数目) 极限下是可重整化的。从QCD 配分泛函出发,对MG模型的有效理论进行了分析,并通过将胶子-夸克耦合做唯象的Skyrme 作用近似,提出了核子的一种有效手征夸克模型,它包括了夸克和pion 云以及pion 云的非线性自耦合。利用有效手征夸克模型计算的核子静态性质的结果与实验值相符很好。Manohar-Georgi proposed an effective constituent quark model(MG model) based on QCD, explaining the success of quark models. Recently, Weinberg has shown that the MG model is renormalizable in the large Nc limit of the color number. In this paper, we present a functional QCD analysis of the MG model and propose an effective chiral quark model of the nucleons, which includes the nonlinear interaction between quark-pions and pions among themselves byapproximating the quark-gluon coupling with the phenomenological Skyrme interaction. The calculation for the nucleon static properties is in good agreement with experimental data.     

Equation of state and chiral transition in soft-wall AdS/QCD with a more realistic gravitational background

We construct an improved soft-wall AdS/QCD model with a cubic coupling term of the dilaton and the bulk scalar field. The background fields in this model are solved by the Einstein-dilaton system with a nontrivial dilaton potential, which has been shown to reproduce the equation of state from the lattice QCD with two flavors. The chiral transition behaviors are investigated in the improved soft-wall AdS/QCD model with the solved gravitational background, and the crossover transition can be realized. Our study provides the possibility to address the deconfining and chiral phase transitions simultaneously in the bottom-up holographic framework.     

Phase structure of two-flavor QCD at finite chemical potential

We study the phase diagram of two-flavor QCD at imaginary chemical potentials in the chiral limit. To this end we compute order parameters for chiral symmetry breaking and quark confinement. The interrelation of quark confinement and chiral symmetry breaking is analyzed with a new order parameter for the confinement phase transition. We show that it is directly related to both the quark density as well as the Polyakov loop expectation value. Our analytical and numerical results suggest a close relation between the chiral and the confinement phase transition.     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Dynamical mass function of quark and effective potential in QCD

Direct variational method is applied to the problem of the dynamical breaking of chiral symmetry in QCD. The minimum of the effective potential corresponding to the phase with spontaneous chiral symmetry breaking is found.     

Universal results from an alternate random-matrix model for QCD with a baryon chemical potential

We introduce a new non-Hermitian random-matrix model for QCD with a baryon chemical potential. This model is a direct chiral extension of a previously studied model that interpolates between the Wigner-Dyson and Ginibre ensembles. We present exact results for all eigenvalue correlations for any number of quark flavors using the orthogonal polynomial method. We also find that the parameters of the model can be scaled to remove the effects of the chemical potential from all thermodynamic quantities until the finite density phase transition is reached. This makes the model and its extensions well suited for studying the phase diagram of QCD.