Particle Number Fluctuations in Statistical Model with Exact Charge Conservation Laws

Even though the first momenta i.e. the ensemble average quantities in canonical ensemble (CE) give the grand canonical (GC) results in large multiplicity limit, the fluctuations involving second moments do not respect this asymptotic behaviour. Instead, the asymptotics are strikingly different, giving a new handle in study of statistical particle number fluctuations in relativistic nuclear reactions. Here we study the analytical large volume asymptotics to general case of multispecies hadron gas carrying fixed baryon number, strangeness and electric charge. By means of Monte Carlo simulations we have also studied the general multiplicity probability distributions taking into account the decay chains of resonance states.Comment: 4 pages, 2 figures. The report of the talk given in Strangeness in Quark Matter 2004, Cape Town. Submitted to J. Phys. G: Nucl. Part. Phy

Particle Number Fluctuations in the Microcanonical Ensemble

Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles and charged particles with zero net charge. The particle number fluctuations are calculated and we find that in the microcanonical ensemble they are suppressed in comparison to the fluctuations in the canonical and grand canonical ensembles. This remains valid in the thermodynamic limit too, so that the well-known equivalence of all statistical ensembles refers to average quantities, but does not apply to fluctuations. In the thermodynamic limit we are able to calculate the particle number fluctuations in the system of massive bosons and fermions when the exact conservation laws of both the energy and charge are taken into account.Comment: REVTeX, 17 pages, 9 figures, v3: misprints a correcte

Particle Number Fluctuations in Relativistic Bose and Fermi Gases

Particle number fluctuations are studied in relativistic Bose and Fermi gases. The calculations are done within both the grand canonical and canonical ensemble. The fluctuations in the canonical ensemble are found to be different from those in the grand canonical one. Effects of quantum statistics increase in the grand canonical ensemble for large chemical potential. This is, however, not the case in the canonical ensemble. In the limit of large charge density a strongest difference between the grand canonical and canonical ensemble results is observed.Comment: 13 pages, 6 figure

Methods to study event-by-event fluctuations in the NA61/SHINE experiment at the CERN SPS

Theoretical calculations locate the critical point of strongly interacting matter (CP) at energies accessible at the CERN SPS. Event-by-event transverse momentum and multiplicity fluctuations are considered as one of the most important tools to search for the CP. Pilot studies of the energy dependence and the system size dependence of both $p_T$ and multiplicity fluctuations were performed by the NA49 experiment. The NA61/SHINE ion program is a continuation of these efforts. After briefly recalling the essential NA49 results on fluctuations we will discuss the technical methods (removing Non-Target interactions) which we plan to apply for future transverse momentum and multiplicity fluctuation analyses.Comment: Proceedings of CPOD 2010, 23-29 August, JINR, Dubn

Multiplicity Fluctuations in Hadron-Resonance Gas

The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge and strangeness. The analytical formulae are presented that allow to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.Comment: 19 pages, 4 figure

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 Fluctuations in the Pion-Fireball Gas

The pion number fluctuations are considered in the system of pions and large mass fireballs decaying finally into pions. A formulation which gives an extension of the model of independent sources is suggested. The grand canonical and micro-canonical ensemble formulations of the pion-fireball gas are considered as particular examples.Comment: 13 pages, 4 figure