Multiplicity fluctuations in relativistic nuclear collisions

Multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. In the canonical ensemble conservation of three charges (baryon number, electric charge, and strangeness) is enforced. In addition, in the micro-canonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. Multiplicity distributions and scaled variances for negatively charged hadrons are presented along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than a Poisson reference distribution, and clearly favor expectations for the micro-canonical ensemble.Comment: 6 pages, 3 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

Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions at the CERN SPS

Multiplicity fluctuations of positively, negatively and all charged hadrons in the forward hemisphere were studied in central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV. The multiplicity distributions and their scaled variances are presented in dependence of collision energy as well as of rapidity and transverse momentum. The distributions have bell-like shape and their scaled variances are in the range from 0.8 to 1.2 without any significant structure in their energy dependence. No indication of the critical point in fluctuations are observed. The string-hadronic model UrQMD significantly overpredicts the mean, but approximately reproduces the scaled variance of the multiplicity distributions. The predictions of the statistical hadron-resonance gas model obtained within the grand-canonical and canonical ensembles disagree with the measured scaled variances. The narrower than Poissonian multiplicity fluctuations measured in numerous cases may be explained by the impact of conservation laws on fluctuations in relativistic systems.Comment: 26 pages, 34 figures, updated version including referee comment

System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40A GeV and158A GeV beam energy

Measurements of charged pion and kaon production are presented in centrality selected Pb+Pb collisions at 40A GeV and 158A GeV beam energy as well as in semi-central C+C and Si+Si interactions at 40A GeV. Transverse mass spectra, rapidity spectra and total yields are determined as a function of centrality. The system-size and centrality dependence of relative strangeness production in nucleus-nucleus collisions at 40A GeV and 158A GeV beam energy are derived from the data presented here and published data for C+C and Si+Si collisions at 158A GeV beam energy. At both energies a steep increase with centrality is observed for small systems followed by a weak rise or even saturation for higher centralities. This behavior is compared to calculations using transport models (UrQMD and HSD), a percolation model and the core-corona approach.Comment: 32 pages, 14 figures, 4 tables, typo table II correcte

Search for the QCD critical point in nuclear collisions at the CERN SPS

Pion production in nuclear collisions at the SPS is investigated with the aim to search, in a restricted domain of the phase diagram, for power-laws in the behavior of correlations which are compatible with critical QCD. We have analyzed interactions of nuclei of different size (p+p, C+C, Si+Si, Pb+Pb) at 158$A$ GeV adopting, as appropriate observables, scaled factorial moments in a search for intermittent fluctuations in transverse dimensions. The analysis is performed for $\pi^+\pi^-$ pairs with invariant mass very close to the two-pion threshold. In this sector one may capture critical fluctuations of the sigma component in a hadronic medium, even if the $\sigma$-meson has no well defined vacuum state. It turns out that for the Pb+Pb system the proposed analysis technique cannot be applied without entering the invariant mass region with strong Coulomb correlations. As a result the treatment becomes inconclusive in this case. Our results for the other systems indicate the presence of power-law fluctuations in the freeze-out state of Si+Si approaching in size the prediction of critical QCD.Comment: 31 pages, 11 figure

Bose-Einstein correlations of pion pairs in central Pb+Pb collisions at CERN SPS energies

Measurements of Bose-Einstein correlations of pion pairs in central Pb+Pb collisions were performed with the NA49 detector at the CERN SPS for beam energies of 20A, 30A, 40A, 80A, and 158A GeV. Correlation functions were measured in the longitudinally co-moving ``out-side-long'' reference frame as a function of rapidity and transverse momentum in the forward hemisphere of the reaction. Radius and correlation strength parameters were obtained from fits of a Gaussian parametrization. The results show a decrease of the radius parameters with increasing transverse momentum characteristic of strong radial flow in the pion source. No striking dependence on pion-pair rapidity or beam energy is observed. Static and dynamic properties of the pion source are obtained from simultaneous fits with a blast-wave model to radius parameters and midrapidity transverse momentum spectra. Predictions of hydrodynamic and microscopic models of Pb+Pb collisions are discussed.Comment: 22 pages, 23 figure

High p_T Spectra of Identified Particles Produced in Pb+Pb Collisions at 158A GeV Beam Energy

Results of the NA49 collaboration on the production of hadrons with large transverse momentum in Pb+Pb collisions at 158A GeV beam energy are presented. A range up to p_T = 4 GeV/c is covered. The nuclear modification factor R_CP is extracted for pions, kaons and protons, and the baryon to meson ratios p/pi+, pbar/pi- and Lambda/K^0_s are studied. All results are compared to other measurements at SPS and RHIC and to theoretical calculations.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 5 pages, 3 figure

Strangeness production at SPS energies

We present a summary of measurements of strange particles performed by the experiment NA49 in central and minimum bias Pb+Pb collisions in the beam energy range 20A - 158A GeV. New results on Xi production in central Pb+Pb collisions and on Lambda, Xi production in minimum bias collisions are shown. Transverse mass spectra and rapidity distributions of strange particles at different energies are compared. The energy dependence of the particle yields and ratios is discussed. NA49 measurements of the Lambda and Xi enhancement factors are shown for the first time.Comment: Submitted to J. Phys. G (Proceedings of the 9th International Conference on Strangeness in Quark Matter, Los Angeles, USA, March 26-31, 2006). 9 pages, 9 figure

Energy dependence of multiplicity fluctuations in heavy ion collisions

The energy dependence of multiplicity fluctuations was studied for the most central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV by the NA49 experiment at the CERN SPS. The multiplicity distribution for negatively and positively charged hadrons is significantly narrower than Poisson one for all energies. No significant structure in energy dependence of the scaled variance of multiplicity fluctuations is observed. The measured scaled variance is lower than the one predicted by the grand-canonical formulation of the hadron-resonance gas model. The results for scaled variance are in approximate agreement with the string-hadronic model UrQMD