Chiral phase transition in the presence of spinodal decomposition

The thermodynamics of a first order chiral phase transition is considered in the presence of spinodal phase separation within the Nambu-Jona-Lasinio (NJL) model. The properties of the basic thermodynamic observables in the coexistence phase are discussed for zero and non-zero quark masses. We focus on observables that probe the chiral phase transition. In particular, the behavior of the specific heat and entropy as well as charge fluctuations are calculated and analyzed. We show that the specific heat and charge susceptibilities diverge at the isothermal spinodal lines. We determine the scaling behavior and compute the critical exponent $\gamma$ of the net quark number susceptibility at the isothermal spinodal lines within the NJL model and the Ginsburg-Landau theory. We show that in the chiral limit the critical exponent $\gamma=1/2$ at the tricritical point as well as along the isothermal spinodal lines. On the other hand, for finite quark masses the critical exponent at the spinodal lines, $\gamma=1/2$, differs from that at the critical end point, $\gamma=2/3$, indicating a change in the universality class. These results are independent of the particular choice of the chiral Lagrangian and should be common for all mean field approaches.Comment: 12 pages, 11 figure

Nonlinear evolution of the momentum dependent condensates in strong interaction: the ``pseudoscalar laser''

We discuss the relaxation of the scalar and pseudoscalar condensates after a rapid quench from an initial state with fluctuations. If we include not only the zero-mode but also higher modes of the condensates in the classical evolution, we observe parametric amplification of those ``hard'' modes. Thus, they couple nonlinearly to the ``soft'' modes. As a consequence, domains of coherent pi-field emerge long after the initial spinodal decomposition. The momentum-space distribution of pions emerging from the decay of that momentum-dependent condensate is discussed.Comment: 6 Pages, REVTEX, 8 Figures; one reference and one figure adde

Field dynamics and kink-antikink production in rapidly expanding systems

Field dynamics in a rapidly expanding system is investigated by transforming from space-time to the rapidity - proper-time frame. The proper-time dependence of different contributions to the total energy is established. For systems characterized by a finite momentum cut-off, a freeze-out time can be defined after which the field propagation in rapidity space ends and the system decays into decoupled solitons, antisolitons and local vacuum fluctuations. Numerical simulations of field evolutions on a lattice for the (1+1)-dimensional $\Phi^4$ model illustrate the general results and show that the freeze-out time and average multiplicities of kinks (plus antikinks) produced in this 'phase transition' can be obtained from simple averages over the initial ensemble of field configurations. An extension to explicitly include additional dissipation is discussed. The validity of an adiabatic approximation for the case of an overdamped system is investigated. The (3+1)-dimensional generalization may serve as model for baryon-antibaryon production after heavy-ion collisions.Comment: 18 pages, 7 figures. Two references added. New subsection III.E added. Final version accepted for publication in PR

From QFT to DCC

A quantum field theoretical model for the dynamics of the disoriented chiral condensate is presented. A unified approach to relate the quantum field theory directly to the formation, decay and signals of the DCC and its evolution is taken. We use a background field analysis of the O(4) sigma model keeping one-loop quantum corrections (quadratic order in the fluctuations). An evolution of the quantum fluctuations in an external, expanding metric which simulates the expansion of the plasma, is carried out. We examine, in detail, the amplification of the low momentum pion modes with two competing effects, the expansion rate of the plasma and the transition rate of the vacuum configuration from a metastable state into a stable state.We show the effect of DCC formation on the multiplicity distributions and the Bose-Einstein correlations.Comment: 34 pages, 10 figure

The K/pi ratio from condensed Polyakov loops

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 T_c 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_\ell ~ 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/pi, in high-multiplicity pp events at high energies should be very interesting.Comment: 7 pages, 4 figures; discussion of the two-point function of Polyakov Loops in small versus large systems adde

Space-time evolution and HBT analysis of relativistic heavy ion collisions in a chiral SU(3) x SU(3) model

The space-time dynamics and pion-HBT radii in central heavy ion-collisions at CERN-SPS and BNL-RHIC are investigated within a hydrodynamic simulation. The dependence of the dynamics and the HBT-parameters on the EoS is studied with different parametrisations of a chiral SU(3) sigma-omega model. The selfconsistent collective expansion includes the effects of effective hadron masses, generated by the nonstrange and strange scalar condensates. Different chiral EoS show different types of phase transitions and even a crossover. The influence of the order of the phase transition and of the difference in the latent heat on the space-time dynamics and pion-HBT radii is studied. A small latent heat, i.e. a weak first-order chiral phase transition, or even a smooth crossover leads to distinctly different HBT predictions than a strong first order phase transition. A quantitative description of the data, both at SPS energies as well as at RHIC energies, appears difficult to achieve within the ideal hydrodynamical approach using the SU(3) chiral EoS. A strong first-order quasi-adiabatic chiral phase transition seems to be disfavored by the pion-HBT data from CERN-SPS and BNL-RHIC

Scalar density fluctuation at critical end point in NJL model

Soft mode near the critical end point in the phase diagram of two-flavor Nambu--Jona-Lasinio (NJL) model is investigated within the leading 1/N_c approximation with N_c being the number of the colors. It is explicitly shown by studying the spectral function of the scalar channel that the relevant soft mode is the scalar density fluctuation, which is coupled with the quark number density, while the sigma meson mode stays massive.Comment: 9 pages, 4 figure

Chiral Fluid Dynamics and Collapse of Vacuum Bubbles

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 $\sigma$ 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 also predicted. The particle production due to the bremsstrahlung of the meson fields is estimated.Comment: 12 pages Revtex,5 figures, Figures modified, minor changes in text. To be published in Phys. Rev. Let

Spectral functions in the sigma-channel near the critical end point

Spectral functions in the $\sigma$-channel are investigated near the chiral critical end point (CEP), that is, the point where the chiral phase transition ceases to be first-ordered in the $(\mu,T)$-plane of the QCD phase diagram. At that point the $\sigma$ meson becomes massless in spite of explicit breaking of the chiral symmetry. It is expected that experimental signatures peculiar to CEP can be observed through spectral changes in the presence of abnormally light $\sigma$ mesons. As a candidate, the invariant-mass spectrum for diphoton emission is estimated with the chiral quark model incorporated. The results show the characteristic shape with a peak in the low energy region, which may serve as a signal for CEP. However, we find that the diphoton multiplicity is highly suppressed by infrared behaviors of the $\sigma$ meson. Experimentally, in such a low energy region below the threshold of two pions, photons from $\pi^0\to2\gamma$ are major sources of the background for the signal.Comment: 12 pages, 8 figures, 1 figure replaced, minor modification

Hydrodynamical instabilities in an expanding quark gluon plasma

We study the mechanism responsible for the onset of instabilities in a chiral phase transition at nonzero temperature and baryon chemical potential. As a low-energy effective model, we consider an expanding relativistic plasma of quarks coupled to a chiral field, and obtain a phenomenological chiral hydrodynamics from a variational principle. Studying the dispersion relation for small fluctuations around equilibrium, we identify the role played by chiral waves and pressure waves in the generation of instabilities. We show that pressure modes become unstable earlier than chiral modes.Comment: 7 pages, 4 figure