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 Beth-Uhlenbeck quantum mechanical non-ideal gas model \cite{uhlenbeck1937quantum}. We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, $\mu_{\mathtt{b}}= 0, 170, 340, 425~$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 $\simeq 160~$MeV, a decent fitting between the model and the lattice data is observed for different values of $r$, especially at $(\mu_{\mathtt{b}}, r) = (170,0.05), (340,0.1)$, and $(340,0.15)$, where $\mu_{\mathtt{b}}$ is in MeV and $r$ is in fm. For vanishing chemical potential, the uncorrelated model ($r=0$), which corresponds to ideal hadron resonance gas model seems to offer the best fit. The quantum hadron correlations seem to be more probable at non-vanishing chemical potentials, especially within the range $\mu_{\mathtt{b}}\in [170, 340~$MeV$]$.