Hadronic Equation of State and Speed of Sound in Thermal and Dense Medium

The equation of state $p(\epsilon)$ and speed of sound squared $c_s^2$ are studied in grand canonical ensemble of all hadron resonances having masses $\leq 2\,$GeV. This large ensemble is divided into strange and non-strange hadron resonances and furthermore to pionic, bosonic and femionic sectors. It is found that the pions represent the main contributors to $c_s^2$ and other thermodynamic quantities including the equation of state $p(\epsilon)$ at low temperatures. At high temperatures, the main contributions are added in by the massive hadron resonances. The speed of sound squared can be calculated from the derivative of pressure with respect to the energy density, $\partial p/\partial \epsilon$, or from the entropy-specific heat ratio, $s/c_v$. It is concluded that the physics of these two expressions is not necessarily identical. They are distinguishable below and above the critical temperature $T_c$. This behavior is observed at vanishing and finite chemical potential. At high temperatures, both expressions get very close to each other and both of them approach the asymptotic value, $1/3$. In the HRG results, which are only valid below $T_c$, the difference decreases with increasing the temperature and almost vanishes near $T_c$. It is concluded that the HRG model can very well reproduce the results of the lattice quantum chromodynamics (QCD) of $\partial p/\partial \epsilon$ and $s/c_v$, especially at finite chemical potential. In light of this, energy fluctuations and other collective phenomena associated with the specific heat might be present in the HRG model. At fixed temperatures, it is found that $c_s^2$ is not sensitive to the chemical potential.Comment: 19 pages, 6 figures with 13 eps graph

Particle Yields and Ratios within Equilibrium and Non-Equilibrium Statistics

In characterizing the yields and ratios various of well identified particles in the ALICE experiment, we utilize extensive {\it additive} thermal approaches, to which various missing states of the hadron resonances are taken into consideration, as well. Despite some non-equilibrium conditions that are slightly driving this statistical approach away from equilibrium, the approaches are and remain additive and extensive. Besides van der Waals repulsive interactions (assuming that the gas constituents are no longer point-like, i.e. finite-volume corrections taken into consideration), finite pion chemical potentials as well as perturbations to the light and strange quark occupation factors are taken into account. When confronting our calculations to the ALICE measurements, we conclude that the proposed conditions for various aspects deriving the system out of equilibrium notably improve the reproduction of the experimental results, i.e. improving the statistical fits, especially the finite pion chemical potential. This points out to the great role that the non-equilibrium pion production would play, and the contributions that the hadron resonance missing states come up with, even when the principles of statistical extensivity and additivity aren't violated. These results seem to propose revising the conclusions propagated by most of the field, that the produced particles quickly reach a state of local equilibrium leading to a collective expansion often described by fluid dynamics. This situation seems not remaining restrictively valid, at very large collision energies.Comment: 15 pages, 4 figures, submitted to EP

Extensive/nonextensive statistics for pTp_T distributions of various charged particles produced in p+p and A+A collisions in a wide range of energies

We present a systematic study for the statistical fits of the transverse momentum distributions of charged pions, Kaons and protons produced at energies ranging between 7.7 and 2670 GeV to the extensive Boltzmann-Gibbs (BG) and the nonextensive statistics (Tsallis as a special type and the generic axiomatic nonextensive approach). We also present a comprehensive review on various experimental parametrizations proposed to fit the transverse momentum distributions of these produced particles. The inconsistency that the BG approach is to be utilized in characterizing the chemical freezeout, while the Tsallis approach in determining the kinetic freezeout is elaborated. The resulting energy dependence of the different fit parameters largely varies with the particle species and the degree of (non)extensivity. This manifests that the Tsallis nonextensive approach seems to work well for p+p rather than for A+A collisions. Drawing a complete picture of the utilization of Tsallis statistics in modeling the transverse momentum distributions of several charged particle produced at a wide range of energies and accordingly either disprove or though confirm the relevant works are main advantages of this review. We propose analytical expressions for the dependence of the fit parameters obtained on the size of the colliding system, the energy, as well as the types of the statistical approach applied. We conclude that the statistical dependence of the various fit parameters, especially between Boltzmann and Tsallis approaches could be understood that the statistical analysis ad hoc is biased to the corresponding degree of extensivity (Boltzmann) or nonextensivity (Tsallis). Alternatively, the empirical parameterizations, the other models, and the generic (non)extensive approach seem to relax this biasness.Comment: 42 pages, 17 figures, IX tables, submitted to JSTA

Matter-Antimatter Asymmetry in the Large Hadron Collider

The matter-antimatter asymmetry is one of the greatest challenges in the modern physics. The universe including this paper and even the reader him(her)self seems to be built up of ordinary matter only. Theoretically, the well-known Sakharov's conditions remain the solid framework explaining the circumstances that matter became dominant against the antimatter while the universe cools down and/or expands. On the other hand, the standard model for elementary particles apparently prevents at least two conditions out of them. In this work, we introduce a systematic study of the antiparticle-to-particle ratios measured in various $NN$ and $AA$ collisions over the last three decades. It is obvious that the available experimental facilities turn to be able to perform nuclear collisions, in which the matter-antimatter asymmetry raises from $\sim 0$ at AGS to $\sim 100$ at LHC. Assuming that the final state of hadronization in the nuclear collisions takes place along the freezeout line, which is defined by a constant entropy density, various antiparticle-to-particle ratios are studied in framework of the hadron resonance gas (HRG) model. Implementing modified phase space and distribution function in the grand-canonical ensemble and taking into account the experimental acceptance, the ratios of antiparticle-to-particle over the whole range of center-of-mass-energies are very well reproduced by the HRG model. Furthermore, the antiproton-to-proton ratios measured by ALICE in $pp$ collisions is also very well described by the HRG model. It is likely to conclude that the LHC heavy-ion program will produce the same particle ratios as the $pp$ program implying the dynamics and evolution of the system would not depend on the initial conditions. The ratios of bosons and baryons get very close to unity indicating that the matter-antimatter asymmetry nearly vanishes at LHC.Comment: 9 pages, 5 eps-figures, revtex4-styl

The QCD phase diagram: A comparison of lattice and hadron resonance gas model calculations

We compare the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model (HRGM) calculations. Lines of constant energy density $\epsilon$ have been determined at different baryo-chemical potentials $\mu_B$. For the strangeness chemical potentials $\mu_S$, we use two models. In one model, we explicitly set $\mu_S=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, $\mu_S$ is calculated in dependence on $T$ and $\mu_B$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of $T_c$ on $\mu_B/T$ by applying Taylor expansion of $\epsilon$. In both cases, we compare HRGM results on $T_c-\mu_B$ diagram with the lattice calculations. The agreement is excellent, especially when the trigonometric function of $\epsilon$ is truncated up to the same order as done in lattice simulations. For studying the efficiency of the truncated Taylor expansion, we calculate the radius of convergence. For zero- and second-order radii, the agreement with lattice is convincing. Furthermore, we make predictions for QCD phase diagram for non-truncated expressions and physical masses. These predictions are to be confirmed by heavy-ion experiments and future lattice calculations with very small lattice spacing and physical quark masses.Comment: 25 pages, 8 eps figure

SOLVING MULTI-CRITERIA ALLOCATION PROBLEMS: A DECISION SUPPORT SYSTEM APPROACH

MCADSS is a multi-criteria allocation decision support system for assisting in the task of partitioning a set of individuals into groups. Based upon multiple criteria, MCADSSâs goal is to maximize the diversity of members within groups, while minimizing the average differences between groups. (The project may be viewed from several perspectives: as a multi-criteria decision making problem, as a "reverse" clustering problem, or as a personnel assignment problem). The system is currently being used to allocate MBA students into sections and study teams at INSEAD, a leading European business school. This paper describes the rationale for MCADSS, design criteria, system methodology, and application results. It also suggests how the approach outlined here might be used for further applications.Information Systems Working Papers Serie

Transverse Energy per Charged Particle and Freeze-Out Criteria in Heavy-Ion Collisions

In relativistic nucleus-nucleus collisions the transverse energy per charged particle, E_T/N_ch, increases rapidly with beam energy and remains approximately constant at about 800 MeV for beam energies from SPS to RHIC. It is shown that the hadron resonance gas model describes the energy dependence, as well as the lack of centrality dependence, qualitatively. The values of E_T/N_ch are related to the chemical freeze-out criterium E/N about 1 GeV valid for primordial hadrons.Comment: 8 pages, 5 figure