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.     

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.     

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<T_c, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below T<T_c and diverges like in the chiral limit.     

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.     

Quark matter nucleation in hot hadronic matter

We study the quark deconfinement phase transition in hot β-stable hadronic matter. Assuming a first order phase transition, we calculate the enthalpy per baryon of the hadron–quark phase transition. We calculate and compare the nucleation rate and the nucleation time due to thermal and quantum nucleation mechanisms. We compute the crossover temperature above which thermal nucleation dominates the finite temperature quantum nucleation mechanism. We next discuss the consequences for the physics of proto-neutron stars. We introduce the concept of limiting conversion temperature and critical mass M_cr for proto-hadronic stars, and we show that proto-hadronic stars with a mass M<M_cr could survive the early stages of their evolution without decaying to a quark star.     

Quasiparticle picture of quarks near chiral phase transition

We study how the quasiparticle picture of the quark can be modified near but above the critical temperature (T _c) of the chiral phase transition; we incorporate into the quark self-energy the effects of the precursory soft modes of the phase transition, i.e. ‘para-σ(π) meson’. It is found that the quark spectrum has a three-peak structure near T _c: We show that the additional new spectra originate from the mixing between a quark (antiquark) and an antiquark-hole (quark-hole) caused by a “resonant scattering” of the quasi-fermions with the thermally-excited soft modes.     

Hadronic spectral function and charm meson production

At the chiral restoration/deconfinement transition, most hadrons undergo a Mott transition from being bound states in the confined phase to resonances in the deconfined phase. We investigate the consequences of this qualitative change in the hadron spectrum on final state interactions of charmonium in hot and dense matter, and show that the Mott effect for D-mesons leads to a critical enhancement of the J/ψ dissociation rate. Anomalous J/ψ suppression in the NA50 experiment is discussed as well as the role of the Mott effect for the heavy-flavor kinetics in future experiments at the LHC. The status of our calculations of hadron–hadron cross sections using the quark interchange and chiral Lagrangian approaches is reviewed, and an ansatz for a unification of these schemes is given.     

Phase transition to color-flavor-locked matter and condensation of Goldstone bosons in neutron star matter

Deconfinement phase transition and condensation of Goldstone bosons in neutron star matter are investigated in a chiral hadronic model (also referred as to the FST model) for the hadronic phase (HP) and in the color-flavor-locked (CFL) quark model for the deconfined quark phase. It is shown that the hadronic-CFL mixed phase (MP) exists in the center of neutron stars with a small bag constant, while the CFL quark matter cannot appear in neutron stars when a large bag constant is taken. Color superconductivity softens the equation of state (EOS) and decreases the maximum mass of neutron stars compared with the unpaired quark matter. The K⁰ condensation in the CFL phase has no remarkable contribution to the EOS and properties of neutron star matter. The EOS and the properties of neutron star matter are sensitive to the bag constant B, the strange quark mass m_s and the color superconducting gap Δ. Increasing B and m_s or decreasing Δ can stiffen the EOS which results in the larger maximum masses of neutron stars.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

Discontinuity of the Wilson string tension in the 4-dimensional lattice pure gauge Potts model

We consider the 4-dimensionalq-state pure gauge Potts model. Forq large enough, we give a new proof of the existence of a unique coupling constant β _t , where a first order phase transition occurs. Moreover we prove the following new results: The string tension is discontinuous at β _t , the Wilson parameter exhibits at β _t a direct transition from an area law decay (quark confinement) to a perimeter law decay (quark deconfinement).     

Neutrino emissivities in 2SC color-superconducting quark matter

The phase structure and equation of state for two-flavor quark matter under compact star constraints is studied within a nonlocal chiral quark model. Chiral symmetry breaking leads to rather large, density dependent quark masses at the phase transition to quark matter. The influence of diquark pairing gaps and quark masses on density dependent emissivities for the direct URCA is discussed. Since m _u > m _d , the direct URCA process due to quark masses cannot occur. We present cooling curves for model quark stars and discuss their relation to observational data. The text was submitted by the author in English.     

Mott effect and J/\psi dissociation at the quark-hadron phase transition

We investigate the in-medium modification of pseudoscalar and vector mesons in a QCD-motivated chiral quark model by solving the Dyson-Schwinger equations for quarks and mesons at finite temperature for a wide mass range of meson masses, from light ( , ) to open-charm (D, D ^*) states. At the chiral/deconfinement phase transition, the quark-antiquark bound states enter the continuum of unbound states and become broad resonances (hadronic Mott effect). We calculate the in-medium cross-sections for charmonium dissociation due to collisions with light hadrons in a chiral Lagrangian approach, and show that the D- and D ^*-meson spectral broadening lowers the threshold for charmonium dissociation by - and -mesons. This leads to a step-like enhancement in the reaction rate. We suggest that this mechanism for enhanced charmonium dissociation may be the physical mechanism underlying the anomalous suppression observed by NA50.Received: 30 September 2002, Published online: 22 October 2003PACS: 05.20.Dd Kinetic theory - 12.38.Mh Quark-gluon plasma - 14.40.-n Mesons - 25.75.Nq Quark deconfinement, quark-gluon plasma production, and phase transitions     

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence, from lattice simulations of QCD with three degenerate quark species, for two tricritical points in the (T, m) phase diagram at fixed imaginary chemical potential μ/T = iπ/3 mod2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary μ, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to nondegenerate and light quark masses is discussed.     

Effects of mesonic correlations in the QCD phase transition

The finite-temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T _c the pressure is well described by the mean-field-approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed. The text was submitted by the authors in English.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

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.     

Mass and chemical asymmetry in QCD matter

We consider two-flavor asymmetric QCD combined with a low-energy effective model inspired by chiral perturbation theory and lattice data to investigate the effects of masses, isospin and baryon number on the pressure and the deconfinement phase transition. Remarkable agreement with lattice results is found for the critical temperature behavior. Further analyses of the cold, dense case and the influence of quark mass asymmetry are also presented.     

Chiral-symmetry restoration in the linear sigma model at nonzero temperature and baryon density

We study the chiral phase transition in the linear sigma model with 2 quark flavors and N _c colors. One-loop calculations predict a first-order phase transition at both μ = 0 and μ ≠ 0. We also discuss the phase diagram and make a comparison with a thermal parametrization of existing heavy-ion experimental data.