Behavior of the topological susceptibility at finite T and <Emphasis Type="Italic">μ</Emphasis> and signs of restoration of chiral symmetries

We investigate the possible restoration of chiral and axial symmetries across the phase transition at finite temperature and chemical potential, by analyzing the behavior of several physics quantities, such as the quark condensates and the topological susceptibility, the respective derivatives with respect to the chemical potential, and the masses of meson chiral partners. We discuss whether only chiral symmetry or both chiral and axial symmetries are restored and what the role of the strange quark is. The results are compared with recent lattice results.     

Spatial and temporal hadron correlators below and above the chiral phase transition

Hadronic correlation functions at finite temperature in QCD, with four flavours of dynamical quarks, have been analyzed both above and below the chiral symmetry restoration temperature. We have used both point and extended sources for spatial as well as temporal correlators. The effect of periodic temporal boundary conditions for the valence quarks on the spatial meson correlators has also been investigated. All our results are consistent with the existence of individual quarks at high temperatures. A measurement of the residual interaction between the quarks is presented.     

Effects of Composite Pions on the Chiral Condensate within the PNJL Model at Finite Temperature

We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth–Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. This in turn also entails a modification of the Polyakov-loop so that the SU(3) center symmetry gets broken at finite temperature and dynamical quarks (and gluons) appear in the system, taking over the role of the dominant degrees of freedom from the pions. At low temperatures our model reproduces the chiral perturbation theory result for the chiral condensate while at high temperatures the PNJL model result is recovered. The new aspect of the current work is a consistent treatment of the chiral restoration transition region within the Beth–Uhlenbeck approach on the basis of mesonic phase shifts for the treatment of the correlations.     

q-deformed supersymmetric Newton oscillators

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at is shown to be supported by finite temperature lattice calculations. Received: 27 September 2000 / Published online: 8 December 2000     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

UL(N) x UR(N)-Invariant Four-Fermion Interactions and Nambu-Goldstone Mechanism at Finite Temperature

In a chiral U_L(N) x U_R(N) fermion model of NJL-form, we prove that, if all the fermions are assumed to have equal masses and equal chemical potentials, then at the finite temperature T below the symmetry restoration temperature T_c, there will be N² massive scalar composite particles and N² massless pseudoscalar composite particles (Nambu-Goldstone bosons). This shows that the Goldstone theorem at finite temperature for spontaneous symmetry breaking U_L(N) x U_R(N) → U_L+R(N) is valid and consistent with the real-time formalism of thermal field theory in this model.     

Chiral symmetry breaking at finite temperature in Coulomb gauge QCD

Chiral symmetry breaking at finite temperature is analysed in Coulomb gauge QCD, using a suitably renormalised gap equation. In Coulomb gauge the gap equation is derived using the Ward identities and the Dyson equations for the vector and axial-vector vertices. Making the ladder approximation to the Bethe-Salpeter kernel relates the chiral symmetry breaking parameters to the static quark potential. It is thus possible to use a confining potential in the analysis of chiral symmetry breaking. We extend this to finite temperature. For a confining potential there is no chiral symmetry restoration at any finite temperature.     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Real-time approach to quark confined systems at finite temperatures

A real-time formalism is proposed to incorporate finite temperatures into confined quark systems at the example of the Generalised Nambu-Jona-Lasinio model for QCD. This approach allows one to study various properties of the system at T > 0, such as chiral symmetry breaking and restoration, properties of the bound-state spectrum, and so on.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.     

Taste symmetry breaking at finite temperature

The breaking of the taste symmetry is studied in the temperature range between 140 MeV to 550 MeV. In order to investigate this violation we have calculated the screening masses of the various taste states fitting the exponential decay of the spatial correlators. The computation has been performed using dynamical N _f =2+1 gauge field configurations generated with the p4 staggered action along the Line of Constant Physics (LCP) defined by a pion mass m _π of approximately 220 MeV and the kaon mass m _K equals 500 MeV. For temperatures below the transition an agreement with the predictions of the staggered chiral perturbation theory has been found and no temperature effect can be observed on the taste violation. Above the transition the taste splitting still shows an $\mathcal{O}(a^{2})$ behavior but with a temperature-dependent slope. In addition to the analysis done for the pion multiplet we have performed an analogous computation for the light–strange and strange mesons and also looked at the scalar, vector and axial-vector channels to understand how the multiplets split at finite temperature. Finally the temperature dependence of the pion decay constant f _π is investigated to get further information regarding the chiral symmetry restoration.     

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.     

Chiral crossover transition in a finite volume

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudotransition temperature T_c of the crossover, showing a significant decrease in T_c as L decreases below 3 fm.     

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.     

Chiral symmetry in nuclei and nuclear matter

We discuss a model for hadrons based on chiral symmetry, Hadronic masses are generated via spontaneous symmetry breaking. Within this model we investigate nuclear matter and finite nuclei. Since the model is SU_F(3)-symmetric we are also able to investigate hypernuclei. Numerical results in comparison with experimental data are presented.     

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.     

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.