Physical properties of hot,dense matter: The general case

The thermodynamic properties of hot, dense matter are examined in the density range 10^?5 fm^?3 ? n ? 0.35 fm^?3 and the temperature range 0 ? T ? 21 MeV, for fixed lepton fractions Y_? = 0.4, 0.3 and 0.2 and for matter in β-equilibrium with no neutrinos. Three phases of the matter are considered: the nuclei phase is assumed to consist of Wigner-Seitz cells with central nuclei surrounded by a nucleon vapor containing also α-particles; in the bubbles phase the cell contains a central spherical bubble of nucleon vapor surrounded by dense nuclear matter; the third phase is that of uniform nuclear matter. All are immersed in a sea of leptons (electrons and neutrinos) and photons. The nuclei and bubbles are described by a compressible liquid drop model which is self-consistent in the sense that all of the constituent properties — bulk, surface, Coulomb energies and other minor contributions — are calculated from the same nuclear effective hamiltonian, in this case the Skyrme 1' interaction. The temperature dependence of all of these energies is included, for bulk and surface energies by direct calculation, for the Coulomb energy by combining in a plausible way the usual electrostatic energy and the numerical results pertaining to a hot Coulomb plasma. Lattice contributions to the Coulomb energy are an essential ingredient, and lattice modifications to the nuclear translational energy are included. A term is constructed to allow also for the reduced density of excited states of light nuclei. All of these modifications incorporate necessary physical effects which modify significantly the matter properties in some regions.     

Spectral lines in hot dense matter

An algorithm is presented for the computation of photoabsorption cross sections at arbitrary temperature and matter density. The “average atom” model is refined to give an approximaate account for the different ionization stages. The broadening of spectral lines is accounted for in a simple approximation. Calculations are presented for the beryllium and germanium plasmas in the frequency region of spectral lines.     

Hadrons in hot and dense matter

I discuss our current understanding of the properties of hot and dense hadronic matter in equilibrium and its excitation spectrum. The latter allows for an experimental study of matter under extreme conditions through ‘in-medium spectroscopy’.     

Hadrons in dense and hot matter

Theoretical issues and perspectives of hadronic matter at high baryon density are discussed with focus on the restoration of chiral symmetry and observable consequences.Received: 30 September 2002, Published online: 22 October 2003PACS: 25.75.-q Relativistic heavy-ion collisions - 21.65. + f Nuclear matter     

Adiabatic index of hot dense stellar matter

We calculate the adiabatic index of hot dense stellar matter taking into account the full nuclear interaction in all possible channels.     

Pseudoscalar neutral mesons in hot and dense matter

The behavior of neutral pseudoscalar mesons π⁰,η and η′ in hot and dense matter is investigated, in the framework of the three flavor Nambu–Jona-Lasinio model. Three different scenarios are considered: zero density and finite temperature, zero temperature and finite density in a flavor asymmetric medium with and without strange valence quarks, and finite temperature and density. The behavior of mesons is analyzed in connection with possible signatures of restoration of symmetries. In the high density region and at zero temperature it is found that the mass of the η′ increases, the deviation from the mass of the η being more pronounced in matter without strange valence quarks.     

Mean-field QCD model for hot/dense matter

Perturbative estimates of thermodynamical quantities relevant for ultra-relativistic collisions of heavy nuclei are found unreliable and some recent effective models for hot and dense QCD matter are found to have very little in common with QCD. A mean-field model, resembling QCD and yielding qualitatively correct results, is suggested and discussed.     

Electromagnetic radiation from hot and dense hadronic matter

The modifications of hadronic masses and decay widths at finite temperature and baryon density are investigated using a phenomenological model of hadronic interactions in the Relativistic Hartree Approximation. We consider an exhaustive set of hadronic reactions and vector meson decays to estimate the photon emission from hot and dense hadronic matter. The reduction in the vector meson masses and decay widths is seen to cause an enhancement in the photon production. It is observed that the effect of p-decay width on photon spectra is negligible. The effects on dilepton production from pion annihilation are also indicated.     

Composition and equation of state of hot dense matter

The composition and equation of state of an equilibrium mixture of non-interacting baryons, pions and leptons is computed in the density range 10¹⁴–10^15.5 g/cm³ for two values of the entropy per baryon, S=1 and 2. These parameters are chosen because of their possible importance in the supernova explosion problem. The threshold densities for the appearance of hyperons are found to be lowered compared to the zero temperature case.     

Chiral symmetry and light resonances in hot and dense matter

We present a study of the π π scattering amplitude in the σ and ρ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral-symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear-density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar–isoscalar channel to account for finite nuclear-density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear-matter and heavy-ion collision experiments, such as ρ mass scaling versus broadening from dilepton spectra and chiral restoration signals in the σ channel. We also elaborate on the molecular nature of π π resonances.     

Probing dense and hot matter with low-mass di-leptons and photons

Results on low-mass di-leptons, covering the very broad energy range from the BEVALAC up to the SPS, are reviewed. The emphasis is on the open questions raised by the intriguing results obtained so far and the prospects for addressing them in the near future with the second generation of experiments, in particular HADES, NA60 and PHENIX. Arrival of the final proofs: 26 June 2005 Work supported by the Israeli Science Foundation     

Latest results on the hot dense partonic matter at RHIC

At the Relativistic Heavy-Ion Collider (RHIC) collisions of heavy ions at nucleon-nucleon energies of 200GeV appear to have created a new form of matter thought to be a deconfined state of the partons that ordinarily are bound in nucleons. We discuss the evidence that a thermalized partonic medium, usually called a Quark Gluon Plasma (QGP), has been produced. Then, we discuss the effect of this high-density medium on the production of jets and their pair correlations. Next, we look at direct photons as a clean electro-magnetic probe to constrain the initial hard scatterings. Finally, we review the developing picture for the effect of this medium on the production of open heavy quarks and on the screening by the QGP of heavy-quark bound states.     

Response functions of hot and dense matter in the Nambu-Jona-Lasino model

We investigate current-current correlation functions, or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics, namely mean-field theory and a beyond-mean-field theory, taking into account mesonic contributions. Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation, showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the self-energy or density-of-state contribution, and the Maki-Thompson contribution.Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to carefully treat the linear terms in external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities. These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.     

Bulk viscosity of hot dense Quark matter in the PNJL model

Starting from the Kubo formula and the QCD low energy theorem, we study the the bulk viscosity of hot dense quark matter in the PNJL model from the equation of state. We show that the bulk viscosity has a sharp peak near the chiral phase transition, and that the ratio of bulk viscosity over entropy rises dramatically in the vicinity of the phase transition. These results agree with those from the lattice and other model calculations. In addition, we show that the increase of chemical potential raises the bulk viscosity.