Beth-Uhlenbeck approach for repulsive interactions between baryons in a hadron gas

Abstract

The quantum mechanical Beth-Uhlenbeck (BU) approach for repulsive hard-core interactions between baryons is applied to the thermodynamics of a hadron gas. The second virial coefficient ${a}_{2}$---the ``excluded volume'' parameter---calculated within the BU approach is found to be temperature dependent, and it differs dramatically from the classical excluded volume (EV) model result. At temperatures $T=100--200$ MeV, the widely used classical EV model underestimates the EV parameter for nucleons at a given value of the nucleon hard-core radius by large factors of 3--4. Previous studies, which employed the hard-core radii of hadrons as an input into the classical EV model, have to be re-evaluated using the appropriately rescaled EV parameters. The BU approach is used to model the repulsive baryonic interactions in the hadron resonance gas (HRG) model. Lattice data for the second- and fourth-order net baryon susceptibilities are described fairly well when the temperature dependent BU baryonic excluded volume parameter corresponds to nucleon hard-core radii of ${r}_{c}=0.25--0.3$ fm. Role of the attractive baryonic interactions is also considered. It is argued that HRG model with a constant baryon-baryon EV parameter ${v}_{NN}\ensuremath{\simeq}1\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{3}$ provides a simple yet efficient description of baryon-baryon interaction in the crossover temperature region.