Description of Hot and Dense Hadron Gas Properties in a New Excluded-Volume model

TL;DR

This paper introduces a new thermodynamically consistent excluded-volume model for hot and dense hadron gas that accurately describes thermodynamic properties, freeze-out criteria, and experimental particle ratios without violating causality.

Contribution

The model uniquely assigns hard-core volume only to baryons, incorporates quantum statistics explicitly, and remains valid at extreme temperatures and densities, improving upon existing approaches.

Findings

Model matches well with microscopic hadron gas results.

Explains experimental particle multiplicity ratios.

Provides transport coefficients like shear viscosity and speed of sound.

Abstract

A new equation of state for a hot and dense hadron gas (HG) is obtained where the finite hard-core size of baryons has been incorporated in a thermodynamically consistent formulation of excluded volume correction. Our model differs from other existing approaches on the following points. We assign a hard-core volume only to each baryon and mesons though possess a small volume but they can fuse and interpenetrate into one another. Use of the full quantum statistics is made in obtaining the grand canonical partition function where excluded-volume correction has been incorporated by explicitly integrating over volume. We thus find that the new model works even for the cases of extreme temperatures and/or densities where most of other approaches fail. The model does not violate causality even at extreme densities. The temperature and density dependence of various thermodynamical quantities, e.g. pressure, baryon density, entropy and energy density compare well with the results of other microscopic HG models. After suitable parametrization of the centre-of-mass energy in terms of temperature and baryon chemical potential, we explore some new freeze-out criteria which exhibit full independence of the collision energy and of the structures of the colliding nuclei. We further demonstrate the suitability of our model in explaining various experimental results of the multiplicity-ratios of various particles and their antiparticles. Finally, we use our excluded-volume model to obtain the transport behaviour of the hot and/or dense HG such as shear viscosity to entropy ratio, speed of sound etc. and compare the results with earlier calculations.