Softening of the Equation of State of Matter at Large Densities and Temperatures: Chiral-Symmetry Restoration Versus Quark Deconfinement

Abstract

We discuss two models for describing the behavior of matter at large densities and intermediate temperatures. In both models a softening of the equation of state takes place due to the appearance of new degrees of freedom. The first is an hadronic model in which the softening is due to chiral symmetry restoration. In the second model the softening is associated with the formation of clusters of quarks in the mixed phase. We show that both models allow a significant softening but, in the first case the bulk modulus is mainly dependent on the density, while in the mixed phase model it also strongly depends on the temperature. We also show that the bulk modulus is not vanishing in the mixed phase due to the presence of two conserved charges, the baryon and the isospin one. Only in a small region of densities and temperatures the incompressibility becomes extremely small. Finally we compare our results with recent analysis of heavy ion collisions at intermediate energies. Introduction. -The behavior of matter at large densities and temperatures is still poorly known but, on general grounds, new degrees of freedom are expected to appear and they should generate a softening of the Equation of State (EOS). In this Letter we discuss two models for the softening: the first model is based on a purely hadronic chirally symmetric EOS [1-3] and the softening is due to partial restoration of the chiral symmetry. In that model the calculations are performed beyond mean field approximation and quantum fluctuations play a crucial role. In a second model the softening is due to the formation of clusters of quarks, which are the precursors of deconfinement. These clusters are at first metastable and they stabilize only at larger densities.The aim of our calculation is to compare how the softening takes place in the two models and finally to relate our results to recent analysis of the experimental data. This may be helpful also in prevision of future experiments planned e.g. at facility FAIR at GSI [4].The extraction of experimental information about the EOS of matter at large densities and temperatures from the data of intermediate and high energy Heavy Ion Collisions (HICs) is very complicated. Possible indirect indications of a softening of the EOS at the energies reached at AGS have been discussed several times in the literature [5][6][7][8][9][10]. In particular, a recent analysis [11] based on a 3-fluid dynamics simulation suggests a progressive softening of the EOS tested through HICs at energies ranging from 2A GeV up to 8A GeV.In this letter we will show that in the chiral model the incompressibility strongly depends on the density but it is almost temperature independent at least up to T ∼ 150 MeV. At the contrary a strong temperature dependence is found in the mixed phase model. Since in HICs at intermediate energies not too large densities are reached, the mixed-phase model seems to provide a better description of the results of the experiments analysis.

Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies

“…This feature is remarkable evident by increasing the non-extensive entropic parameter ; it implies an abrupt variation in the incompressibility and may be particularly important in identifying the presence of non-extensive effects in highenergy compressed baryonic matter experiments. Indirect indications of a sensible softening of the EOS at the energies reached at AGS have already been raised elsewhere [41,52,[56][57][58]. In Fig.…”

“…As proposed in Ref. [52], a phenomenological approach can therefore be based on an effective "bag constant" B eff depending on the baryon chemical potential. It can be written as…”

Inhomogeneous condensation in effective models for QCD using the finite-mode approach

“…When restricting this condensate to be constant, chiral symmetry restoration at high densities occurs via a first-order phase transition [71][72][73][74][75]. However, when allowing for an inhomogeneous condensate, the latter occurs at slightly smaller chemical potentials than the first-order phase transition.…”

Kaon and strangeness production in an effective relativistic mean field model

“…In this context, we study the influence of the kaon-nucleon interaction in the determination of the kaon to anti-kaon ratio and in the strangeness production. The results are then compared with a minimal coupling scheme, calculated for different values of the antikaon optical potential.We investigate the nuclear medium in the context of relativistic mean field approach, where the nuclear force is mediated by the exchange of isoscalar-scalar (σ), isoscalar-vector (ω) and isovectorvector (ρ) mesons fields [1,2]. The hadronic lagrangian can be expressed as:…”