An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

Abstract

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, ${\mu }_{\text{b}}=0,170,340,425\text{MeV}$ over temperatures ranging from $130\text{MeV}$ to $200\text{MeV}$ 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 $\left({\mu }_b,r\right)=\left(170,0.05\right),\left(340,0.1\right),\text{and}\left(340,0.15\right)$ , where ${\mu }_{\text{b}}$ is in MeV and $r$ is in fm. For the vanishing chemical potential, the uncorrelated model $\left(r=0\right)$ , 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 ${\mu }_{\text{b}}\in \left[170,340\text{MeV}\right]$ .