An approach of statistical corrections to interactions in hadron resonance gas

TL;DR

This paper introduces a new statistical model for hadrons incorporating quantum mechanical interactions with a correlation length, and compares its thermodynamics predictions with lattice data across various chemical potentials and temperatures.

Contribution

The paper presents a novel hadron interaction model based on quantum correlations and tests its accuracy against lattice QCD data, highlighting the importance of correlations at non-zero chemical potentials.

Findings

Model fits lattice data well near the chiral transition temperature.

Quantum correlations are more significant at higher chemical potentials.

Uncorrelated model fits best at zero chemical potential.

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$]$.