Complex heavy-quark potential at finite temperature from lattice QCD

We calculate for the first time the complex potential between a heavy quark and antiquark at finite temperature across the deconfinement transition in lattice QCD. The real and imaginary part of the potential at each separation distance r is obtained from the spectral function of the thermal Wilson loop. We confirm the existence of an imaginary part above the critical temperature T(C), which grows as a function of r and underscores the importance of collisions with the gluonic environment for the melting of heavy quarkonia in the quark-gluon plasma.     

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, μEP/TEP≈3. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

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.     

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

Quasipartiele model for the quark-gluon plasma: Equation of state near Tc

We test the quark mass dependence implemented in the quasiparticle dispersion relations of our quasiparticle model for the QCD equation of state by comparing with recently available lattice QCD data employing almost physical quark masses. In addition, we emphasize the capability of our model to successfully describe lattice QCD results (or imaginary chemical potential and to analytically continue the latter to real chemical potential.     

Deconfinement and chiral restoration in non-local PNJL models at zero and imaginary chemical potential

We study the deconfinement and chiral restoration transitions in the context of non-local PNJL models, considering the impact of the presence of dynamical quarks on the scale parameter appearing in the Polyakov potential. We show that the corresponding critical temperatures are naturally entangled for both zero and imaginary chemical potential, in good agreement with lattice QCD results. We also analyze the Roberge-Weiss transition, which is found to be first order at the associated endpoint.     

On the QCD phase structure from effective models

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.     

Critical behaviour in baryonic matter

First we consider the phenomenology of deconfinement and chiral symmetry restoration for strongly interacting matter at non-vanishing baryon number density. Subsequently, we present numerical results obtained by a Monte Carlo evaluation of statistical QCD on an 8³×3 lattice, using Wilson fermions withN _f =2, in fourth order hopping parameter expansion, and suppressing the imaginary part of the fermion action. We consider baryonic chemical potentials up to μa=0.6μa=0.6 (μ/Λ _L ?200); in this range, the critical parameters for deconfinement and chiral symmetry restoration are found to coincide.     

Polyakov-loop拓展的夸克介子模型中的Roberge-Weiss相变研究

${\mathbb{Z}}_3$-QCD是具有严格中心对称性的类QCD理论,研究其在特殊条件下的性质有助于理解QCD退禁闭相变。本文应用三种味道的Polyakov-loop拓展的夸克介子模型作为${\mathbb{Z}}_3$-QCD的低能有效理论,研究了不同中心对称性破缺模式下的Roberge-Weiss(RW)相变。为保证RW周期性,本文采用味道依赖的虚化学势$(\mu_{\rm{u}},\mu_{\rm{d}},\mu_{\rm{s}})={\rm{i}}T(\theta-2C\pi/3,\theta,\theta+2C\pi/3)$,其中${\mathbb{Z}}_3$-QCD是具有严格中心对称性的类QCD理论,研究其在特殊条件下的性质有助于理解QCD退禁闭相变。本文应用三种味道的Polyakov-loop拓展的夸克介子模型作为${\mathbb{Z}}_3$-QCD的低能有效理论,研究了不同中心对称性破缺模式下的Roberge-Weiss(RW)相变。为保证RW周期性,本文采用味道依赖的虚化学势$(\mu_{\rm{u}},\mu_{\rm{d}},\mu_{\rm{s}})={\rm{i}}T(\theta-2C\pi/3,\theta,\theta+2C\pi/3)$,其中$0\!\leqslant\!{C}\!\leqslant1$。传统的和夸克反馈效应改进的两种不同Polyakov-loop势被分别用于相应的计算。研究表明,当$N_{\rm{f}}\!=\!3$,$C\!\ne\!1$时,RW相变出现在$\theta=\pi/3$(mod $2\pi/3$)处,其强度随$C$值的减小而加强;当$C\!=\!1$,$N_{\rm{f}}\!=\!2\!+\!1$时,RW相变位置出现反常,变为$\theta=2\pi/3$(mod $2\pi/3$);而当$C\!=\!1$,$N_{\rm{f}}\!=\!1\!+\!2$时,RW相变点又返回$\theta\!=\!\pi/3$(mod $2\pi/3$)。上述几种情形的RW相变端点均为三相点。研究发现,夸克反馈效应使得RW相变强度减弱,退禁闭相变温度变低,但并未改变前述的定性结论。     

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.     

Chemical Potential Dependence of the Dressed—Quark Propagator from an Effective Quark—Quark Interaction

We exhibit a method for obtaining the low chemical potential dependence of the dressed quark propagator from the dressed-quark propagator,which provides a means of determining the behavior of the chiral and deconfinement order parameters.A comparison with the results of previous researches is given.     

改进的PNJL模型下QCD的相图

Polyakov-Nambu-Jona-Lasinio（PNJL）模型是研究强相互作用物质性质的使用最为广泛的有效模型之一。在PNJL模型的基础上考虑了手征凝聚和Polyakov圈之间的纠缠作用,并且引入了化学势修正的Polyakov有效势,由此得到了化学势依赖的entangled PNJL（μEPNJL）模型。在平均场框架下的计算结果表明:相较于原始的PNJL模型,由μEPNJL模型计算得到的临界点（CEP）朝着温度更高、化学势更小处移动,并且手征对称性恢复相变和退禁闭相变在较大的化学势范围内都重合得很好。通过与STAR合作组在相对论重离子对撞机（RHIC）上进行的净质子数分布的测量结果相比,可以发现,通过适当的参数调节,由μEPNJL模型计算得到的CEP更加靠近实验预言的CEP可能存在的区域。Polyakov-Nambu-Jona-Lasinio (PNJL) model is one of the most popular effective quark models to investigate the properties of strongly interacting matter. Based on the PNJL model, we consider the entanglement interactions between the chiral condensate and Polyakov-loop, as well as the chemical potential modification of Polyakov-loop potential simultaneously, which is named μEPNJL model. Compared with the original PNJL model, the calculations in the mean field approximation show that the critical end point (CEP) given in the μEPNJL model moves towards higher temperature and smaller chemical potential in the T-μ phase diagram. Besides, the chiral symmetry restoration and deconfinement phase transition coincide well in a wide range of chemical potential. Comparing our calculations with the measurement of the moments of net-proton multiplicity distributions at Relativistic Heavy-Ion Collider (RHIC) by STAR Collaboration, we find that the CEP given by μEPNJL model can be closer to the range predicted by the experiment through appropriate parameter adjustment.     

Nonperturbative dynamics in the color-magnetic QCD vacuum

In the deconfinement phase of QCD, quarks and gluons interact with the dense stochastic color-magnetic vacuum. We consider the dynamics of quarks in this deconfinement phase using the field correlators method and derive an effective nonperturbative interquark potential, in addition to the usual perturbative short-range interaction. We find the resulting angular-momentum-dependent interaction to be attractive enough to maintain bound states and, for light quarks (and gluons), to cause emission of quark and gluon pairs. Possible consequences for the strong-interacting quark-gluon plasma are briefly discussed. The text was submitted by the authors in English.     

Physics around the QCD (tri)critical endpoint and new challenges for femtoscopy

On the basis of exactly solvable models with the tricritical and critical endpoints I discuss the physical mechanism of endpoints formation which is similar to the usual liquids. It is demonstrated that the necessary condition for the transformation of the 1-st order deconfinement phase transition into the 2-nd order phase transition at the (tri)critical endpoint is the vanishing of surface tension coefficient of large/heavy QGP bags. Using the novel model of the confinement phenomenon I argue that the physical reason for the cross-over appearance at low baryonic densities is the negative value of QGP bag surface tension coefficient. This implies the existence of highly non-spherical or, probably, even fractal surfaces of large and heavy bags at and above the cross-over, which, perhaps, can be observed via some correlations. The model with the tricritical endpoint predicts that at the deconfinement transition line the volume (mass) distribution of large (heavy) QGP bags acquires the power law form at the endpoint only, while in the model with the critical endpoint such a power law exists inside the mixed phase. The role of finite width of QGP bags is also discussed.     

Novel approach to deriving the canonical generating functional in lattice QCD at a finite chemical potential

A novel approach to the problem of deriving the generating functional for the canonical ensemble in lattice QCD at a nonzero chemical potential is proposed. The derivation proceeds in several steps. First, the baryon density for imaginary values of the chemical potential is obtained. Then, again for imaginary values of the chemical potential, the generating functional of the grand canonical ensemble is derived. In this analysis, a fit of baryon density is employed toward simplifying the procedure of numerical integration. Finally, the generating potential for the canonical ensemble is derived using a high-precision numerical Fourier transform. The generating functional for the canonical ensemble is also derived using the known hopping-parameter expansion, and the results obtained with the two methods are compared for the deconfinement phase in the lattice QCD with two flavors.     

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyze the dependence on temperature T and chemical potential p of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the p-T criticality curve for symmetry restoration. We find out that the critical temperature T_c = 2υ for μ = 0 and the critical chemical potential μ_c = 2 π υ / √3 for T = 0. When μ = 0, the top-quark mass near T_c has the leading (T_c² - T²)^1/2 behavior with an extra factor dependent on temperature T and the momentum cutoff Λ. However, it is generally argued that the symmetry restoration at T ≥ T_c is still a second-order phase transition.