Chiral phase transition and Anderson localization in the instanton liquid model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an instanton liquid model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.     

Higher-order ratios of baryon number cumulants

The relevance of higher order cumulants of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy-ion collisions at LHC and RHIC is addressed. The sign structure of the higher order cumulants in the vicinity of the chiral crossover temperature might be a sensitive probe and may allow to elucidate their relation to the QCD phase transition. We calculate ratios of generalized quarknumber susceptibilities to high orders in three flavor QCD-like models and investigate their sign structure close to the chiral crossover line.     

Density-Dependence of Nuclear Symmetry Energy: Role of QCD Chiral Phase Transition

The density-dependence of symmetry energy is of particular importance to many problems in nuclear physics and astrophysics. By using the functional path integral method, we show explicitly the relation between nuclear symmetry energy and isospin susceptibility. The latter one is found to be a probe to the QCD chiral phase transition. We further found in the Nambu-Jona-Lasinio model calculations that, the nuclear symmetry energy has an abrupt change at the critical nuclear density where the chiral symmetry restores partially.     

利用格点量子色动力学研究手征平滑过渡温度和手征相变温度

回顾了最近关于手征平滑过渡温度和手征相变温度的研究结果。首先给出了在零重子化学势能下的手征平滑过渡温度为156.5(1.5) MeV，其次，给出了在非零重子化学势能下手征相转变曲线的二阶及四阶曲率分别为0.012(4)和0.000(4)。接着讨论了在格点QCD中第一次得到的量子色动力学的手征相变温度。在热力学极限、连续极限及手征极限下，我们得到手征相变温度为132$^{+3}_{-6}$ MeV。     

Finite-size behavior near the critical point of QCD phase-transition

It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.     

Chiral symmetry breaking and pion properties at finite temperatures

Spontaneous and explicit chiral symmetry breaking is analyzed in Coulomb gauge QCD at finite temperatures, using an instantaneous approximation for the quark interaction and incorporating confinement through a running coupling constant. The thermodynamics of the quarks is treated approximatively by assuming that the momentum-dependent constituent quark mass sets the scale for thermodynamic fluctuations of colour singlet excitations. We investigate the class of a temperature independent and a temperature dependent interaction between quarks. In the chiral limit both temperature independent and a smooth temperature dependent interaction yields a second order chiral phase transition with critical exponents close to the values for a BCS super-conductor. For explicit chiral symmetry breaking we find a nearly constant pion mass below the transition temperature, but a strongly overdamped mode above. For a first order deconfining transition in the gluonic sector also the quark sector shows a first order chiral phase transition. The relevance of our results for relativistic heavy ion collisions is briefly discussed.     

Disoriented chiral condensate: Theory and experiment

It is thought that a region of pseudo-vacuum, where the chiral order parameter is misaligned from its vacuum orientation in isospin space, might occasionally form in high-energy hadronic or nuclear collisions. The possible detection of such disoriented chiral condensate (DCC) would provide useful information about the chiral structure of the QCD vacuum and/or the chiral phase transition of strong interactions at high temperature. We review the theoretical developments concerning the possible DCC formation in high-energy collisions as well as the various experimental searches that have been performed so far. We discuss future prospects for upcoming DCC searches e.g. in high-energy heavy-ion collision experiments at RHIC and LHC.     

Chiral electric field in relativistic heavy-ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

It has been proposed that electric fields may lead to chiral separation in quark-gluon plasma(QGP).This is called the chiral electric separation effect.The strong electromagnetic field and the QCD vacuum can both be completely produced in off-central nuclear-nuclear collision.We use the Woods-Saxon nucleon distribution to calculate the electric field distributions of off-central collisions.The chiral electric field spatial distribution at Relativistic Heavy-Ion Collider(RHIC) and Large Hadron Collider(LHC) energy regions are systematically studied in this paper.The dependence of the electric field produced by the thermal quark in the central position with different impact parameters on the proper time with different collision energies in the RHIC and LHC energy regions are studied in this paper.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Probing the color structure of the perfect QCD fluids via soft-hard-event-by-event azimuthal correlations

We develop a comprehensive dynamical framework, CIBJET, to calculate on an event-by-event basis the dependence of correlations between soft(p_T2 GeV) and hard(p_T10 GeV) azimuthal flow angle harmonics on the color composition of near-perfect QCD fluids produced in high energy nuclear collisions at RHIC and LHC. CIBJET combines consistently predictions of event-by-event VISHNU2+1 viscous hydrodynamic fluid fields with CUJET3.1 predictions of event-by-event jet quenching. We find that recent correlation data favor a temperature dependent color composition including bleached chromo-electric q(T) + g(T) components and an emergent chromo-magnetic degrees of freedom m(T) consistent with non-perturbative lattice QCD information in the confinement/deconfinement temperature range.     

Disappearance of Chiral Soliton Solutions and Chiral Phase Transition at High Temperature

The behavior of the chiral soliton model at high temperature is investigated.as well as the influence of thermal effects on the chiral soliton solutions and the fermion condensation is analysed.One possible physical mechanism is established,which is responsible for why there exists a difference between the critical temperature in deconfinement phase transition and that in chiral restoration phase transition.     

相对论重离子碰撞手征电荷分离效应的研究

相对论重离子碰撞的拓扑荷作用破坏作用平面两侧不同手征性的夸克数目的平衡,从而引起P和CP破坏特征。本工作主要分析RHIC和LHC能区的手征电荷分离作用,分析手征电荷分离随碰撞中心度、碰撞能量和核屏蔽等依赖关系。并未发现手征电荷分离效应与碰撞能量大小有非常紧密的依赖关系,但发现核屏蔽效应对手征电荷分离有重要的影响,与不考虑屏蔽效应相比,考虑屏蔽效应会使手征分离效应明显压低,由于屏蔽效应出现,使得a₊₊（a_--）的分布与a_+-（a_-+）分布并不对称。并且还发现手征分离效应主要发生在碰撞参量较大的周边碰撞,越接近中心碰撞,手征分离效应几乎可以忽略。The topological charge interactions in relativistic heavy ion collisions cause quark chirality imbalance, resulting in charge separation under the strong magnetic field and local P and CP violation. In this paper, the chiral charge separation at RHIC and LHC energies is systematically analyzed as functions of the collision centrality, the collision energy and the nuclear shielding factor. It is found that there is not a very close dependence of the chiral charge separation effect on the collision energies, but that has an important dependence on nuclear shielding factor. Compared with the non-shielding effect, the shielding effect can reduce the chiral separation effect obviously. Due to the shielding effect, the distribution of a₊₊(a_--) and the distribution of a_+-(a_-+) are asymmetric. One also finds that chiral separation effect, which is almost negligible when more close to the central collision, occurs mainly in the peripheral collision for larger impact parameter.     

Fluctuations as probe of the QCD phase transition and freeze-out in heavy ion collisions at LHC and RHIC

We discuss the relevance of higher order cumulants of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. Using properties of O(4) scaling functions, we discuss the generic structure of these higher cumulants at vanishing baryon chemical potential and apply chiral model calculations to explore their properties at non-zero baryon chemical potential. We show that the ratios of the sixth to second and eighth to second order cumulants of the net baryon number fluctuations change rapidly in the transition region of the QCD phase diagram. Already at vanishing baryon chemical potential they deviate considerably from the predictions of the hadron resonance gas model which reproduce the second and fourth order cumulants of the net proton number fluctuations at RHIC. We point out that the sixth order cumulants of baryon number and electric charge fluctuations remain negative at the chiral transition temperature. Thus, they offer the possibility to probe the proximity of the chemical freeze-out to the crossover line.     

Strongly interacting low-viscosity matter created in relativistic nuclear collisions

Substantial collective flow is observed in collisions between large nuclei at BNL RHIC (Relativistic Heavy Ion Collider) as evidenced by single-particle transverse momentum distributions and by azimuthal correlations among the produced particles. The data are well reproduced by perfect fluid dynamics. A calculation of the dimensionless ratio of shear viscosity eta to entropy density s by Kovtun, Son, and Starinets within anti-de Sitter space/conformal field theory yields eta/s=variant Planck's over 2pi/4pikB, which has been conjectured to be a lower bound for any physical system. Motivated by these results, we show that the transition from hadrons to quarks and gluons has behavior similar to helium, nitrogen, and water at and near their phase transitions in the ratio eta/s. We suggest that experimental measurements can pinpoint the location of this transition or rapid crossover in QCD.     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.     

Chiral effective Lagrangian for excited heavy-light mesons from QCD

We derive the chiral effective Lagrangian for excited heavy-light mesons from QCD under proper approximations. We focus on the chiral partners with j_l~P=3+/2 and j_l~P=3~-/2 which amounts to(1~+, 2~+) and(1~-, 2~-) states respectively. The low energy constants including the masses of the chiral partners are calculated. The calculated spectrum for the excited mesons are found roughly consistent with experimental data. In addition, our results indicate that quantum numbers of B_J(5970) can be identified with 1~-or 2~-.     

Meson Effects on the Chiral Condensate at Finite Density

Meson corrections on the chiral condensate up to next-to-leading order in a 1/N_c expansion at finite density are investigated in the NJL model with explicit chiral symmetry breaking. Compared with mean-field results, the chiral phase transition is still of the first order while the properties near the critical density for chiral phase transition are found to change significantly.     

QCD vacuum as a disordered medium: a simplified model for the QCD dirac operator

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the dimensionless Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scaling in the RBM remains the same as in the bulk which agrees with chiral perturbation theory but not with the ILM. Finally we discuss how this RBM should be modified in order to describe the spectral correlations of the QCD Dirac operator at the finite temperature chiral restoration transition.     

Heavy ions: Report from Relativistic Heavy Ion Collider

We review selected highlights?from the experiments at the Relativistic Heavy Ion Collider (RHIC) exploring the QCD phase diagram. A wealth of new results appeared recently from RHIC due to major recent upgrades, like for example the ?? suppression in central nucleus?Cnucleus collisions which has been discovered recently in both RHIC and LHC. Furthermore, we discuss RHIC results from the beam energy scan (BES) program aiming to search for a possible critical point and to map out the QCD phase diagram.