Probability distributions in statistical ensembles with conserved charges

The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles are equivalent. This equivalence is proven on the most general, probability distribution level.Comment: 5 pages. A little bit shorter version due to some editorial and language changes. To be published in Phys. Rev.

Particle Production in Heavy Ion Collisions

The status of thermal model descriptions of particle production in heavy ion collisions is presented. We discuss the formulation of statistical models with different implementation of the conservation laws and indicate their applicability in heavy ion and elementary particle collisions. We analyze experimental data on hadronic abundances obtained in ultrarelativistic heavy ion collisions, in a very broad energy range starting from RHIC/BNL ($\sqrt s=200$ A GeV), SPS/CERN ($\sqrt s\simeq 20$ A GeV) up to AGS/BNL ($\sqrt s\simeq 5$ A GeV) and SIS/GSI ($\sqrt s\simeq 2$ A GeV) to test equilibration of the fireball created in the collision. We argue that the statistical approach provides a very satisfactory description of experimental data covering this wide energy range. Any deviations of the model predictions from the data are indicated. We discuss the unified description of particle chemical freeze--out and the excitation functions of different particle species. At SPS and RHIC energy the relation of freeze--out parameters with the QCD phase boundary is analyzed. Furthermore, the application of the extended statistical model to quantitative understanding of open and hidden charm hadron yields is considered.Comment: Invited review for Quark Gluon Plasma 3, eds. R. C. Hwa and Xin-Nian Wang, World Scientific Publishin

Statistical Model and the mesonic-baryonic transition region

The statistical model assuming chemical equilibriumand local strangeness conservation describes most of the observed features of strange particle production from SIS up to RHIC. Deviations are found as the maximum in the measured K+/pi+ ratio is much sharper than in the model calculations. At the incident energy of the maximum, the statistical model shows that freeze out changes regime from one being dominated by baryons at the lower energies toward one being dominated by mesons. It will be shown how deviations from the usual freeze-out curve influence the various particle ratios. Furthermore, other observables exhibit also changes just in this energy regime.Comment: 9 pages, 7 figures, CPOD conference proceeding

Conservation Laws and Particle Production in Heavy Ion Collisions

We discuss the role of the conservation laws related with U(1) internal symmetry group in the statistical model description of particle productions in ultrarelativistic heavy ion collisions. We derive and show the differences in particle multiplicities in the canonical and the grand canonical formulation of quantum number conservation. The time evolution and the approach to chemical equilibrium in the above ensembles is discussed in terms of kinetic master equation. The application of the statistical model to the description of (multi)strange particle yields at GSI/SIS and the SPS energies is also presented.Comment: Invited talk at International Symposium on Hadron and Nuclei, Seoul, Korea, 20-22 Feb 200

The statistical model in Pb-Pb collisions at the LHC

We briefly review the predictions of the thermal model for hadron production in comparison to latest data from RHIC and extrapolate the calculations to LHC energy. Our main emphasis is to confront the model predictions with the recently released data from ALICE at the LHC. This comparison reveals an apparent anomaly for protons and anti-protons which we discuss briefly. We also demonstrate that our statistical hadronization predictions for J/$\psi$ production agree very well with the most recent LHC data, lending support to the picture in which there is complete charmonium melting in the quark-gluon plasma (QGP) followed by statistical generation of J/$\psi$ mesons at the phase boundary.Comment: 4 pages, 3 figures, proceedings of QM201