We investigate the chiral phase transition at nonzero temperature T and baryon-chemical potential µ B within the framework of the linear sigma model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in both models a smooth crossover transition for nonzero T and µ B = 0 and a first order transition for T = 0 and nonzero µ B . We calculate explicitly the first order phase transition line and spinodal lines in the (T, µ B ) plane. As expected they all end in a critical point. We find that, in the linear sigma model, the sigma mass goes to zero at the critical point. This is in contrast to the NJL model, where the sigma mass, as defined in the random phase approximation, does not vanish. We also compute the adiabatic lines in the (T, µ B ) plane. Within the models studied here, the critical point does not serve as a "focusing" point in the adiabatic expansion.

We discuss homogeneous nucleation in a first-order chiral phase transition within an effective field theory approach to low-energy QCD. Exact decay rates and bubble profiles are obtained numerically and compared to analytic results obtained with the thin-wall approximation. The thin-wall approximation overestimates the nucleation rate for any degree of supercooling. The time scale for critical thermal fluctuations is calculated and compared to typical expansion times for high-energy hadronic or heavy-ion collisions. We find that significant supercooling is possible, and the relevant mechanism for phase conversion might be that of spinodal decomposition. Some potential experimental signatures of supercooling, such as an increase in the correlation length of the scalar condensate, are also discussed.

We perform a field-theoretical computation of hadron production in large systems at the QCD confinement phase transition associated with restoration of the Z(3) global symmetry. This occurs from the decay of a condensate for the Polyakov loop. From the effective potential for the Polyakov loop, its mass just below the confinement temperature Tc is in between the vacuum masses of the pion and that of the kaon. Therefore, due to phase-space restrictions the number of produced kaons is roughly an order of magnitude smaller than that of produced pions, in agreement with recent results from collisions of gold ions at the BNL-RHIC. From its mass, we estimate that the Polyakov loop condensate is characterized by a (spatial) correlation scale of 1/m ℓ ≃ 1/2 fm. For systems of deconfined matter of about that size, the free energy may not be dominated by a condensate for the Polyakov loop, and so the process of hadronization may be qualitatively different as compared to large systems. In that vein, experimental data on hadron abundance ratios, for example K/π, in high-multiplicity pp events at high energies should be very interesting.

We study the expansion dynamics of a quark-antiquark plasma droplet from an initial state with restored chiral symmetry. The calculations are made within the linear σ model scaled with an additional scalar field representing the gluon condensate. We solve numerically the classical equations of motion for the meson fields coupled to the fluid-dynamical equations for the plasma. Strong space-time oscillations of the meson fields are observed in the course of the chiral transition. A new phenomenon, the formation and collapse of vacuum bubbles, is predicted. The particle production due to the bremsstrahlung of the meson fields is estimated.

We consider an effective Lagrangian containing contributions from glueball and gluon degrees of freedom with a scale-invariant coupling between the two. The thermodynamic potential is calculated taking into account thermal fluctuations of both fields. The glueball mean field dominates at low temperature, while the high temperature phase is governed by low-mass gluonlike excitations. The model shows some similarities to the lattice results in the pure glue sector of QCD. In particular, it exhibits a strong first order phase transition at a critical temperature of approximately 265 MeV when reasonable parameters are taken.

We propose a novel mechanism for disoriented chiral condensate (DCC) formation in a first-order chiral phase transition. In this case the effective potential for the chiral order parameter has a local minimum at F ϳ 0 in which the chiral field can be "trapped." If the expansion is fast, a bubble of disoriented chiral field can emerge and decouple from the rest of the fireball. The bubble may overshoot the mixed phase and supercool until the barrier disappears, when the potential resembles that at T 0. This situation corresponds to the initial condition realized in a "quench." Thus, the subsequent alignment in the vacuum direction leads to strong amplification of low-momentum modes of the pion field. We propose that these DCCs could accompany the previously suggested baryon rapidity fluctuations. 11.30.Qc, 11.30.Rd, 24.85. + p Relativistic heavy-ion collisions might offer the interesting opportunity to study chiral symmetry restoration at nonzero temperature and density, which could possibly lead to the formation of domains of disoriented chiral condensate (DCC) [1][2][3][4][5]. The strongest amplification of the pion field is obtained for the so-called "quenched" initial condition [3]. It is assumed that the heat bath is removed instantaneously after restoration of chiral symmetry.However, dynamical simulations [4,5] show that the "quench" does not emerge naturally in a heavy-ion collision, if the chiral phase transition is second order or a smooth crossover. In this Letter, we instead propose a new approach to obtain the quenched initial conditions naturally in the presence of a first-order phase transition.It has been argued [6] that the phase transition for two massless quarks at baryon-chemical potential m 0 is second order which then becomes a smooth crossover for small quark masses. On the other hand, a first-order phase transition is predicted for small temperatures and large m. If, indeed, there is a smooth crossover for m 0 and nonzero T , and a first-order transition for small T and nonzero m, then the first-order phase transition line in the ͑m, T ͒ plane must end in a second-order critical point. This point is predicted to be at T ϳ 100 MeV and m ϳ 600 MeV. However, some lattice QCD results indicate a first-order transition even at vanishing baryon-chemical potential [7]. Such temperatures and baryon-chemical potentials can be reached in the central region of heavy-ion collisions in the forthcoming Pb͑40A GeV͒ 1 Pb experiments at the CERN-SPS [8], and in the fragmentation regions of more energetic collisions at the CERN-SPS, BNL-RHIC, and CERN-LHC ( p s Ӎ 20A, 200A, 5000A GeV) [9]. Furthermore, fluctuations in individual events can also provide rapidity bins with significantly higher m and lower T than on average [10][11][12][13]. In any case, the dynamical scenario for DCC formation described in this Letter applies to the case of a first-order chiral phase transition, and is qualitatively independent of the value of m. Our calculation described below has been performed at m 0, and the parameters ...

No abstract

We investigate dynamics of the chiral transition in expanding quark-antiquark plasma produced in an ultra-relativistic heavy ion collision. The chiral symmetry break-down and dynamical generation of the constituent quark mass are studied within the linear sigma model and Nambu-Jona-Lasinio model. Time dependence of the quark and antiquark densities is obtained from the scaling solution of the relativistic Vlasov equation. Fast initial growth and strong oscillations of the constituent quark mass are found in the linear sigma model as well as in the NJL model, when derivative terms are taken into account.PACS numbers: 25.75.+r, 11.30.Rd, 12.38Mh, 24.85.+p Keywords: non-equilibrium chiral transition, constituent quarks, pion field oscillations, relativistic heavy ion collisions, scaling expansion.Introduction.-It is commonly believed that colour deconfinement and chiral symmetry restoration take place at early stages of ultra-relativistic heavy-ion collisions. At intermediate stages of the reaction the quark-gluon plasma may be formed and evolve through the states close to thermodynamical equilibrium. However, at later stages of the expansion the transition to the hadronic phase with broken chiral symmetry should take place. The breakdown of chiral symmetry will possibly lead to such interesting phenomena as formation of disoriented chiral condensates (DCCs) and classical pion fields as well as clustering of quarks and antiquarks. These phenomena were studied recently in many publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14], using QCD motivated effective models, such as the linear and non-linear sigma models and the Nambu-Jona-Lasinio (NJL) model. Of course, these models have some significant shortcomings, e.g. they do not possess colour confinement and the NJL-model is non-renormalizable. The key point is, however, that these models obey the same chiral symmetry as the QCD Lagrangian.In most applications of the sigma model the quark degrees of freedom are disregarded (see e.g. [2-9,14]). The inclusion of quarks [10, 11] makes it possible to study the hadronization