Exact Baryon, Strangeness and Charge Conservation in Hadronic Gas Models

Relativistic heavy ion collisions are studied assuming that particles can be described by a hadron gas in thermal and chemical equilibrium. The exact conservation of baryon number, strangeness and charge are explicitly taken into account. For heavy ions the effect arising from the neutron surplus becomes important and leads to a substantial increase in e.g. the $\pi^-/\pi^+$ ratio. A method is developed which is very well suited for the study of small systems.Comment: 5 pages, 5 Postscript figure

Fluctuations, strangeness and quasi-quarks in heavy-ion collisions from lattice QCD

We report measurements of diagonal susceptibilities for the baryon number, chi_B, electrical charge, chi_Q, third component of isospin, chi_I, strangeness, chi_S, and hypercharge, chi_Y, as well as the off-diagonal chi_BQ, chi_BY, chi_BS, etc. We show that the ratios of susceptibilities in the high temperature phase are robust variables, independent of lattice spacing, and therefore give predictions for experiments. We also investigate strangeness production and flavour symmetry breaking matrix elements at finite temperature. Finally, we present evidence that in the high temperature phase of QCD the different flavour quantum numbers are excited in linkages which are exactly the same as one expects from quarks. We present some investigations of these quark-like quasi particles

Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions

One of the most remarkable results to emerge from heavy-ion collisions over the past two decades is the striking regularity shown by particle yields at all energies. This has led to several very successful proposals describing particle yields over a very wide range of beam energies, reaching from 1 A GeV up to 200 A GeV, using only one or two parameters. A systematic comparison of these proposals is presented here. The conditions of fixed energy per particle, baryon+anti-baryon density, normalized entropy density as well as percolation model are investigated. The results are compared with the most recent chemical freeze-out parameters obtained in the thermal-statistical analysis of particle yields. The sensitivity and dependence of the results on parameters is analyzed and discussed. It is shown that in the energy range above the top AGS energy, within present accuracies, all chemical freeze-out criteria give a fairly good description of the particle yields. However, the low energy heavy-ion data favor the constant energy per particle as a unified condition of chemical particle freeze-out. This condition also shows the weakest sensitivity on model assumptions and parameters.Comment: 15 pages 7 figures uses revte

Neutral Pions and Eta Mesons as Probes of the Hadronic Fireball in Nucleus-Nucleus Collisions around 1A GeV

Chemical and thermal freeze-out of the hadronic fireball formed in symmetric collisions of light, intermediate-mass, and heavy nuclei at beam energies between 0.8A GeV and 2.0A GeV are discussed in terms of an equilibrated, isospin-symmetric ideal hadron gas with grand-canonical baryon-number conservation. For each collision system the baryochemical potential mu_B and the chemical freeze-out temperature T_c are deduced from the inclusive neutral pion and eta yields which are augmented by interpolated data on deuteron production. With increasing beam energy mu_B drops from 800 MeV to 650 MeV, while T_c rises from 55 MeV to 90 MeV. For given beam energy mu_B grows with system size, whereas T_c remains constant. The centrality dependence of the freeze-out parameters is weak as exemplified by the system Au+Au at 0.8A GeV. For the highest beam energies the fraction of nucleons excited to resonance states reaches freeze-out values of nearly 15 %, suggesting resonance densities close to normal nuclear density at maximum compression. In contrast to the particle yields, which convey the status at chemical freeze-out, the shapes of the related transverse-mass spectra do reflect thermal freeze-out. The observed thermal freeze-out temperatures T_th are equal to or slightly lower than T_c, indicative of nearly simultaneous chemical and thermal freeze-out.Comment: 42 pages, 12 figure

Equation of state of resonance-rich matter in the central cell in heavy-ion collisions at s\sqrt{s}=200 AGeV

The equilibration of hot and dense nuclear matter produced in the central cell of central Au+Au collisions at RHIC ($\sqrt{s}=200$ AGeV) energies is studied within a microscopic transport model. The pressure in the cell becomes isotropic at $t\approx 5$ fm/$c$ after beginning of the collision. Within the next 15 fm/$c$ the expansion of matter in the cell proceeds almost isentropically with the entropy per baryon ratio $S/A \approx 150$, and the equation of state in the $(P,\epsilon)$ plane has a very simple form, $P=0.15\epsilon$. Comparison with the statistical model of an ideal hadron gas indicates that the time $t \approx 20$ fm/c may be too short to reach the fully equilibrated state. Particularly, the creation of long-lived resonance-rich matter in the cell decelerates the relaxation to chemical equilibrium. This resonance-abundant state can be detected experimentally after the thermal freeze-out of particles.Comment: LATEX, 21 pages incl. 7 figure

Multiplicity Distributions in Canonical and Microcanonical Statistical Ensembles

The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace's asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.Comment: 53 pages, 7 figure

Influence of Impact Parameter on Thermal Description of Relativistic Heavy Ion Collisions at GSI/SIS

Attention is drawn to the role played by the size of the system in the thermodynamic analysis of particle yields in relativistic heavy ion collisions at SIS energies. This manifests itself in the non-linear dependence of K+ and K- yields in $AA$ collisions at 1 -- 2 A.GeV on the number of participants. It is shown that this dependence can be quantitatively well described in terms of a thermal model with a canonical strangeness conservation. The measured particle multiplicity ratios (pi+/p, pi-/pi+, d/p, K+/pi+ and K+/K- but not eta/pi0) in central Au-Au and Ni-Ni collisions at 0.8 -- 2.0 A.GeV are also explained in the context of a thermal model with a common freeze-out temperature and chemical potential. Including the concept of collective flow a consistent picture of particle energy distributions is derived with the flow velocity being strongly impact-parameter dependent.Comment: revtex, 20 figure

Comparison of Strangeness Production between A+A and p+p Reactions from 2 to 160 AGeV

The measured K$^+/\pi^+$ ratios from heavy-ion reactions are compared with the K$^+/\pi^+$ ratios from p+p reactions over the energy range 2-160 AGeV. The K/$\pi$ enhancement in heavy-ion reactions is largest at the lower energies, consistent with strangeness production in secondary scattering becoming relatively more important than initial collisions near the kaon production threshold. The enhancement decreases steadily from 4 to 160 AGeV, suggesting that the same enhancement mechanism of hadronic rescattering and decay of strings may be applicable over this full energy range. Based on existing data, the mid-rapidity K$^+/\pi^+$ ratio is predicted to be $0.27\pm0.05$ for the forthcoming Pb+Pb reactions at 40 AGeV/c.Comment: 14 pages, 4 figures, submitted to Phys. Rev.

Examine the species and beam-energy dependence of particle spectra using Tsallis Statistics

Tsallis Statistics was used to investigate the non-Boltzmann distribution of particle spectra and their dependence on particle species and beam energy in the relativistic heavy-ion collisions at SPS and RHIC. Produced particles are assumed to acquire radial flow and be of non-extensive statistics at freeze-out. J/psi and the particles containing strangeness were examined separately to study their radial flow and freeze-out. We found that the strange hadrons approach equilibrium quickly from peripheral to central A+A collisions and they tend to decouple earlier from the system than the light hadrons but with the same final radial flow. These results provide an alternative picture of freeze-outs: a thermalized system is produced at partonic phase; the hadronic scattering at later stage is not enough to maintain the system in equilibrium and does not increase the radial flow of the copiously produced light hadrons. The J/psi in Pb+Pb collisions at SPS is consistent with early decoupling and obtains little radial flow. The J/psi spectra at RHIC are also inconsistent with the bulk flow profile.Comment: 12 pages, 4 figures, added several references and some clarifications et

Are we close to the QGP? - Hadrochemical vs. microscopic analysis of particle production in ultrarelativistic heavy ion collisions

Ratios of hadronic abundances are analyzed for pp and nucleus-nucleus collisions at sqrt(s)=20 GeV using the microscopic transport model UrQMD. Secondary interactions significantly change the primordial hadronic cocktail of the system. A comparison to data shows a strong dependence on rapidity. Without assuming thermal and chemical equilibrium, predicted hadron yields and ratios agree with many of the data, the few observed discrepancies are discussed.Comment: 12 pages, 4 figure