We construct an equation of state for Quantum Chromodynamics (QCD) at finite temperature and chemical potentials for baryon number B, electric charge Q and strangeness S. We use the Taylor expansion method, up to the fourth power for the chemical potentials. This requires the knowledge of all diagonal and non-diagonal BQS correlators up to fourth order: these results recently became available from lattice QCD simulations, albeit only at a finite lattice spacing Nt = 12. We smoothly merge these results to the Hadron Resonance Gas (HRG) model, to be able to reach temperatures as low as 30 MeV; in the high temperature regime, we impose a smooth approach to the Stefan-Boltzmann limit. We provide a parameterization for each one of these BQS correlators as functions of the temperature. We then calculate pressure, energy density, entropy density, baryonic, strangeness, electric charge densities and compare the two cases of strangeness neutrality and µS = µQ = 0. Finally, we calculate the isentropic trajectories and the speed of sound, and compare them in the two cases. Our equation of state can be readily used as an input of hydrodynamical simulations of matter created at the Relativistic Heavy Ion Collider (RHIC).
The authors propose a class of procedures for local likelihood estimation from data that are either intervalansod or that have been aggregated into bins. One such procedure relies on an algorithm that generalizes existing self-consistency algorithms by introducing kernel smoothing at each step of the itemtion. The entire class of procedures yields estimates that are obtained as solutions of fixed point equations. By discretizing and applying numerical integration, the authom use Exed point theory to study convergence of algorithm for the class. Rapid convergence is effected by the implementation of a local EM algorithm as a global Newton itemtion. The latter quires an explicit solution of the local likelihood equations which can be found by using the symbolic Newton-Raphson algorithm, if necessary.Estimation de la densite par vraisemblance locale a partir de donnbs censurws par intervalle R b u d : Les auteun proposent une classe de proddures pour l'estimation de la densit6 par vraisemblance locale lorsque les donnks sont censudes par intervde ou qu'elles ont 6t6 repup6es en classes. L'une de ces proc6dures s'appuie sur un algorithme qui, en faisant appel h un noyau lissant h chaque ithtion, g6-n6ralise les algorithmes autoconvergents d6jh existants. Les estimations auxquelles la classe conduit sont des points Exes de cettaines equations. En s'appuyant sur des techniques de discn?tisation et d'intbgration numerique, les auteurs se servent de la thkrie des points fixes pour ttudier la convergence des algorithmes de la classe. La convergence est ac&l6& par l'emploi d'un algorithme EM local dam l'it6mtion globale de la m6thode de Newton. Cette demihe fait intervenir une solution d'huations de vraisemblance locale qui, au besoin, peut €tre tmuv6e au moyen d'un algorithme de Newton-Raphson symbolique.
We compare the mean-over-variance ratio of the net-kaon distribution calculated within the hadron resonance gas model to the latest experimental data from the Beam Energy Scan at the Relativistic Heavy Ion Collider by the STAR Collaboration. Our analysis indicates that it is not possible to reproduce the experimental results using the freeze-out parameters from the existing combined fit of net-proton and net-electric charge mean over variance. The strange mesons need about 15 MeV higher temperatures than the light hadrons at the highest collision energies. In view of the future fluctuation measurements, we predict the variance over mean and skewness times variance at the light and strange chemical freeze-out parameters. We observe that the fluctuations are sensitive to the difference in the freeze-out temperatures established in this analysis. Our results have implications for other phenomenological models in the field of relativistic heavy ion collisions.
Like fluctuations, non-diagonal correlators of conserved charges provide a tool for the study of chemical freeze-out in heavy ion collisions. They can be calculated in thermal equilibrium using lattice simulations, and be connected to moments of event-by-event net-particle multiplicity distributions. We calculate them from continuum extrapolated lattice simulations at µB = 0, and present a finite-µB extrapolation, comparing two different methods. In order to relate the grand canonical observables to the experimentally available net-particle fluctuations and correlations, we perform a Hadron Resonance Gas (HRG) model analysis, which allows us to completely break down the contributions from different hadrons. We then construct suitable hadronic proxies for fluctuations ratios, and study their behavior at finite chemical potentials. We also study the effect of introducing acceptance cuts, and argue that the small dependence of certain ratios on the latter allows for a direct comparison with lattice QCD results, provided that the same cuts are applied to all hadronic species. Finally, we perform a comparison for the constructed quantities for experimentally available measurements from the STAR Collaboration. Thus, we estimate the chemical freeze-out temperature to 165 MeV using a strangeness-related proxy. This is a rather high temperature for the use of the Hadron Resonance Gas, thus, further lattice studies are necessary to provide first principle results at intermediate µB.Hadron Collider (LHC) have been able to create the Quark Gluon Plasma (QGP) in the laboratory, and explore the low-to-moderate baryon density region of the QCD phase diagram.At low baryon density, the transition from a hadron gas to a deconfined QGP was shown by lattice QCD calculations to be a broad crossover [1] at T 155 MeV [1][2][3][4]. At large baryon densities, the nature of the phase transition is expected to change into first order, thus implying the presence of a critical end point. A strong experimental effort is currently in place through the second Beam
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