Ideal Hadron Resonance Gas Model Research Articles

Particle ratios within EPOS, UrQMD and thermal models at AGS, SPS and RHIC energies

The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely underestimate [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth, 1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, μ b = 0 , 170 , 340 , 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values of r , especially at μ b , r = 170 , 0.05 , 340 , 0.1 , and 340 , 0.15 , where μ b is in MeV and r is in fm. For the vanishing chemical potential, the uncorrelated model r = 0 , which corresponds to the ideal hadron resonance gas model, seems to offer the best fit. The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μ b ∈ 170 , 340 MeV .

Viscosity calculations from hadron resonance gas model: Finite size effect

We have attempted to review on microscopic calculation of transport coefficients like shear and bulk viscosities in the framework of hadron resonance gas (HRG) model, where a special attention is explored on the effect of finite system size. The standard expressions of transport coefficients, obtained from relaxation time approximation of kinetic theory or diagrammatic Kubo-type formalism, carry mainly two temperature-dependent components — thermodynamical phase space and relaxation time of medium constituent. Owing to the quantum effect of finite system size, thermodynamical phase space can be reduced as its momentum distribution will be started from some finite lower momentum cut-off instead of zero momentum. On the other hand, relaxation time of hadrons can also face finite size effect by considering only those relaxation scales, which are lower than the system size. Owing to these phenomenological issues, we have proposed a system size-dependent upper bound of transport coefficients for ideal HRG model, whose qualitative technique may also be applicable in other models. This finite size-prescription may guide to shorten the broad numerical band, within which earlier estimated values of transport coefficients for hadronic matter are located. It is also suspected that the hadronic matter may not be far from the (nearly) perfect fluid nature like the quark gluon plasma.

Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state

Thermal-FIST11Thermal-FIST — Thermal, Fast and Interactive Statistical Toolkit. is a C++ package designed for convenient general-purpose physics analysis within the family of hadron resonance gas (HRG) models. This mainly includes the statistical analysis of particle production in heavy-ion collisions and the phenomenology of hadronic equation of state. Notable features include fluctuations and correlations of conserved charges, effects of probabilistic decay, chemical non-equilibrium, and inclusion of van der Waals hadronic interactions. Calculations are possible within the grand canonical ensemble, the canonical ensemble, as well as in mixed-canonical ensembles combining the canonical treatment of certain conserved charges with the grand-canonical treatment of other conserved charges. The package contains a fast thermal event generator, which generates particle yields in accordance with the HRG chemistry, and particle momenta based on the Blast Wave model. A distinct feature of this package is the presence of the graphical user interface frontend – QtThermalFIST – which is designed for fast and convenient general-purpose HRG model applications. Program summaryProgram Title:Thermal-FIST, version 1.2Program Files doi:http://dx.doi.org/10.17632/pprr8p4fkp.1Licensing provisions: GPLv3Programming language: C++External routines:Eigen template library for the linear algebra routines [1], MINUIT2 package from CERN ROOT [2], Mersenne Twister random number generator [3], Qt5 framework [4] (for the GUI only), QCustomPlot Qt widget [5] (for the GUI only)Nature of problem: The HRG model and its various modifications constitute a common framework used for modeling of the hadronic equation of state and particle production in heavy-ion collisions. Even the simplest versions of the HRG model require careful considerations of the many details, including the resonance decay feed-down, implementation of charge conservation constraints relevant for heavy-ion collisions, chemical non-equilibrium effects. A notable extra effort is required in order to treat the fluctuations and correlations of various charges , which presently are being extensively studied in the heavy-ion collision experiments and lattice QCD calculations. The inclusion of hadronic interactions, modeled by an excluded-volume (EV) or a van der Waals (vdW) type framework, additionally requires a numerical solution to a system of many transcendental equations.Solution method: The Thermal-FIST package contains a class-based library which calculates relevant HRG observables for a specified setup. The setup includes a particle list, usually to be supplied with an external file, an HRG model specification (statistical ensemble, van der Waals interaction parameters, etc.), a set of thermal parameters, and conservation laws constraints. Whenever necessary, the systems of transcendental equations are solved numerically with the Broyden’s method. The package includes a fitter for extracting thermal parameters from hadron yield data through the χ2 minimization. The HRG model based Monte Carlo event generator is a complementary feature to analytic calculations. A general-purpose thermal analysis is made maximally convenient with QtThermalFIST — a GUI frontend based on the Qt framework where all typical calculations, such as the properties of the equation of state or the thermal fits, can be straightforwardly performed.Additional comments: If the EV/vdW interactions are present, exact analytic calculations are presently only possible within the grand canonical ensemble. Approximate calculations are possible for the strangeness-canonical ensemble on the condition that strange particles form a small subsystem relative to the total system. Effects of probabilistic decays on fluctuation observables are generally included only up to the moments of the 2nd order. The only exception is the ideal HRG model in the grand canonical ensemble, where these effects are included up to the moments of the 4th order. On the other hand, the Monte Carlo event generator is not constrained by the above restrictions.

Exploring the hadron resonance gas phase on the QCD phase diagram

Lattice computations of strongly interacting matter at finite temperature T and baryon chemical potential μB suggest that the QCD thermodynamics deep in the hadronic phase can be adequately modeled by an ideal hadron resonance gas (I-HRG). However, it is not clear where on the (μB, T) plane this description breaks down, making it essential to account for hadronic interactions and change in the nature of the degrees of freedom. We have studied several thermodynamic functions within the I-HRG model and try to identify the region of the QCD phase diagram where it becomes essential to include non-ideal effects into the I-HRG model. We work with only those thermodynamic quantities that show a monotonic rise with T and μB in I-HRG. Their high temperature limiting values where QCD becomes simply a Stefan–Boltzmann (SB) gas of massless quarks and gluons is known. The rise of these quantities in I-HRG beyond the corresponding SB limit values indicate the need to include interactions into I-HRG to study QCD thermodynamics. This works as a guiding principle on the QCD phase diagram where interacting HRGs can take over from I-HRG. For μB/T ≤ 2, shoots the SB limit at the smallest T, while for higher values of μB/T, takes over. We further comment on the relative positions between the freeze-out curve obtained by thermal fits to the measured hadron yields and the obtained line where the I-HRG overshoots the SB limit.

Phenomenological bound on the viscosity of the hadron resonance gas

We have explored some phenomenological issues during calculations of transport coefficients for hadronic matter, produced in the experiments of heavy ion collisions. Here, we have used an ideal hadron resonance gas model to demonstrate the issues. On the basis of dissipation mechanism, the hadronic zoo is classified into resonance and non-resonance members, who participate in dissipation via strong decay and scattering channels respectively. Imposing our phenomenological restriction, we are able to provide a rough upper and lower bound estimations of transport coefficients. Interestingly, we find that our proposed lower limit estimation for shear viscosity to entropy density ratio is little larger than its quantum lower bound. By taking a simple example, we have demonstrated how our proposed restriction help to tune any estimation of transport coefficients within its numerical band, proposed by us.

Role of new resonance states on fluctuations and correlations of conserved charges in hadron resonance gas model

We investigate the role of suspected resonance states, that are yet to be confirmed experimentally, on different thermodynamic quantities as well as the higher-order fluctuations and the correlation between conserved charges using ideal hadron resonance gas (HRG) model. We have discussed the temperature dependence of the various thermodynamic quantities and compared them with the lattice QCD result. We observe that the values of the bulk thermodynamic variables such as pressure, energy density, entropy density and second-order susceptibilities are increased by the inclusion of the additional resonances. Further, we find that the hadronic phase of lattice QCD result of [Formula: see text] and [Formula: see text] can be described well in ideal HRG model with the additional resonances. We have also studied the [Formula: see text] dependence of the fluctuation observables of net-proton, net-kaon and net-charge. Proper experimental acceptance cuts have been used in the model to compare with the data from experimental measurements. It has been observed that the experimental data of lower-order fluctuation observable can be described well by the ideal HRG model. However, higher-order fluctuation observables cannot be described by ideal HRG model for all [Formula: see text] studied here, which indicates the possibility of presence of critical or nonequilibrium physics for those energies. The effect of additional resonances on fluctuation observables of net-charge at different [Formula: see text] has also been studied. Finally, the chemical freeze-out parameters have been extracted from the experimental data of [Formula: see text] of net-proton and net-charge using two different sets of hadronic spectra. We find that for both the sets, the extracted temperature is slightly lower than those obtained from the hadronic yields. Moreover, it is observed that the extracted temperature of the system gets further reduced with addition of more resonances.

Universal descriptions of chemical freeze-out based on pressure and specific heat

The lattice QCD data of pressure and the energy density have been used to extract the hadronic radius parameter of the excluded volume hadron resonance gas (EVHRG) model. The equation of state can be described well with the extracted radius parameter [Formula: see text] fm. Specific heat is also calculated in the EVHRG model. Further, two new universal descriptions of chemical freeze-out parameters have been introduced based on pressure and specific heat, respectively. It is shown that the chemical freeze-out parameters obtained at various [Formula: see text] in ideal hadron resonance gas (HRG) model approximately correspond to [Formula: see text] and [Formula: see text], respectively. These two quantities are important to describe the thermodynamic properties of the hadronic matter created in heavy-ion collision experiment. The sensitivity of universal chemical freeze-out lines on repulsive interaction is also studied. It has been observed that the behaviors of chemical freeze-out lines for [Formula: see text] and [Formula: see text] in EVHRG model remain similar to ideal HRG model for the best fit value of hadronic radii.

Van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD.

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters a and b are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region T∼140-190 MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.