Importance of repulsive interactions for the equation of state and other properties of strongly interacting matter

We illustrate the role of repulsive interactions in a hadron-resonance gas at freeze-out and in a gas of quark-gluon bags. Taking into account non-zero size of particles in hadron gas leads to a significant decrease and shift of the net-baryon density maximum. The transition point from baryon to meson dominated matter depends on the difference between baryon and meson radii. We also show that depending on the properties of the quark-gluon bags one may obtain any type of the phase transition from hadron gas to quark-gluon plasma: the first or second order, as well as four types of the crossover.Comment: Talk at the 32th Max-Born-Symposium and HECOLS workshop on "Three Days of Phase Transitions in Compact Stars, Heavy-Ion Collisions and Supernovae", Institute for Theoretical Physics, University of Wroc\l{}aw, Wroc\l{}aw, Poland, February 17--19, 201

High temperature Bose-Einstein condensation

The indications of a possible pion condensation at the LHC are summarized. The condensation is predicted by the non-equilibrium hadronization model for 2.76 TeV Pb+Pb collisions at the LHC. The model solves the proton/pion puzzle and reproduces the low $p_T$ enhancement of the pion spectra, as well as the spectra of protons and antiprotons, charged kaons, $K^0_S$, $K^*(892)^0$ and $\phi(1020)$. The obtained parameters allow to estimate the amount of pion condensate on the level of 5\% from the total number of pions at the LHC. The condensate is located at $p_T<250$ MeV

Correlations and fluctuations of pions at the LHC

The intriguing possibility of Bose-Einstein condensation of pions at the LHC is examined with the use of higher order moments of the multiplicity distribution. The scaled variance, skewness and kurtosis are calculated for the pion system. The obtained results show that the normalized kurtosis has a significant increase for the case of the pion condensation.Comment: Talk presented at XI Workshop on Particle Correlations and Femtoscopy, 3-7 November 2015, Warsaw, Polan

Hadron multiplicities and chemical freeze-out conditions in proton-proton and nucleus-nucleus collisions

New results of the NA61/SHINE Collaboration at the CERN SPS on mean hadron multiplicities in proton-proton (p+p) interactions are analyzed within the transport models and the hadron resonance gas (HRG) statistical model. The chemical freeze-out parameters in p+p interactions and central Pb+Pb (or Au+Au) collisions are found and compared with each other in the range of the center of mass energy of the nucleon pair $\sqrt{s_{NN}}=3.2-17.3$ GeV. The canonical ensemble formulation of the HRG model is used to describe mean hadron multiplicities in p+p interactions and the grand canonical ensemble in central Pb+Pb and Au+Au collisions. The chemical freeze-out temperatures in p+p interactions are found to be larger than the corresponding temperatures in central nucleus-nucleus collisions.Comment: Some misprints are corrected in the text, as well as in Fig.1(f

Hadron-Resonance Gas at Freeze-out: Reminder on Importance of Repulsive Interactions

An influence of the repulsive interactions on matter properties is considered within the excluded volume van der Waals hadron-resonance gas model. Quantitative results are presented for matter at the chemical freeze-out in central nucleus-nucleus collisions at relativistic energies. In particular, it is shown that repulsive interactions connected to non-zero size of created particles lead to a significant decrease of collision energy at which the net-baryon density has a maximum. A position of the transition point from baryon to meson dominated matter depends on the difference between baryon and meson hard-core radiuses

Particle Number Fluctuations in Statistical Models

The influence of global conservation laws, quantum statistics, resonance decays, and finite detector acceptance on particle number fluctuation is studied. The prediction for the scaled variances of negatively and positively charged hadrons is shown for the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS to LHC

Fluctuations in the Canonical Ensemble

The particle number and energy fluctuations in the system of charged particles are studied in the canonical ensemble for non-zero net values of the conserved charge. In the thermodynamic limit the fluctuations in the canonical ensemble are different from the fluctuations in the grand canonical one. The system with several species of particles is considered. We calculate the quantum statistics effects which can be taken into account for the canonical ensemble fluctuations in the infinite volume limit. The fluctuations of the particle numbers in the pion-nucleon gas are considered in the canonical ensemble as an example of the system with two conserved charges - baryonic number and electric charge.Comment: 15 pages, 6 figure

Modified Bag Models for the Quark Gluon Plasma Equation of State

The modified versions of the bag model equation of state (EoS) are considered. They are constructed to satisfy the main qualitative features observed for the quark-gluon plasma EoS in the lattice QCD calculations. A quantitative comparison with the lattice results at high temperatures T are done in the SU(3) gluodynamics and in the full QCD with dynamical quarks. Our analysis advocates a negative value of the bag constant B.Comment: We have added the fit for entropy density, pressure over energy density and speed of sound. The recent lattice results from Wuppertal-Budapest collaboration for QCD with quarks are fitte

Quantum Gases in the Microcanonical Ensemble near the Thermodynamic Limit

A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number fluctuations in the microcanonical ensemble. It gives also the finite-volume corrections due to exact energy conservation for the total average number of particles and for higher moments of the particle number distribution in a system approaching the thermodynamic limit. A present consideration confirms our previous findings that the scaled variance for particle number fluctuations in the microcanonical ensemble is different from that in the grand canonical ensemble even in the thermodynamic limit.Comment: ReVTeX4, 12 pages, 2 figure

Strongly Intensive Measures for Particle Number Fluctuations: Effects of Hadronic Resonances

Strongly intensive measures $\Delta$ and $\Sigma$ are used to study event-by-event fluctuations of hadron multiplicities in nucleus-nucleus collisions. The effects of resonance decays are investigated within statistical model and relativistic transport model. Two specific examples are considered: resonance decays to two positively charged particles (e.g., $\Delta^{++}\rightarrow p+ \pi^+$) and to $\pi^+\pi^-$-pairs. (e.g., $\rho^0\rightarrow \pi^-+\pi^+$). It is shown that resonance abundances at the chemical freeze-out can be estimated by measuring the fluctuations of the number of stable hadrons. These model results are compared to the full hadron-resonance gas analysis within both the grand canonical and canonical ensemble. The ultra-relativistic quantum molecular dynamics (UrQMD) model of nucleus-nucleus collisions is used to illustrate the role of global charge conservation, centrality selection, and limited experimental acceptance.Comment: expanded discussions; added references; version published in J. Phys.