Conserved charge susceptibilities in the relativistic mean-field hadron resonance gas model: constraints on hadronic repulsive interactions

Abstract: We investigate the effect of repulsive interaction between hadrons on the susceptibilities of conserved charges, namely baryon number (B), electric charge (Q) and strangeness (S). We estimate second fourth and sixth-order susceptibilities of conserved charges, their differences, ratios, and correlations within the ambit of the mean-field hadron resonance gas (MFHRG) model. We consider repulsive mean-field interaction among meson pairs, baryon pairs and anti-baryon pairs separately and constrain them by confronting the results of various susceptibilities with the recent lattice QCD (LQCD) data. We find that the repulsive interactions between baryon-baryon pairs and antibaryon-antibaryon pairs are sufficient to describe the baryon susceptibilities of hadronic matter at temperatures below the QCD transition temperature. However, small but finite mesonic repulsive interaction is needed to describe electric charge and strangeness susceptibilities. We finally conclude that the repulsive interaction between hadrons plays a very important role in describing the thermodynamic properties of hadronic matter, especially near the quark-hadron phase transition temperature ($T_c$). The mean-field parameter for baryons ($K_B$) should be constrained in the range $0.40\le K_B\le 0.450$ $\text{GeV.fm}^{3}$ to get a good agreement of baryon susceptibilities with the LQCD results, whereas meson mean-field parameter $K_M\sim 0.05$ $\text{GeV.fm}^{3}$ must be included with $K_B$ to get a reasonable agreement of the MFHRG model with the LQCD results for electric charge and strangeness susceptibilities.