Estimation of attractive and repulsive interactions from the fluctuation observables at RHIC using van der Waals hadron resonance gas Model

Experimental data on the moments of net-proton distribution in central Au-Au collisions for various center of mass energies ($\sqrt{\mathrm {s_{NN}}}$) measured by the STAR collaboration at the Relativistic Heavy-Ion Collider (RHIC) are compared to the corresponding results from a van der Waals type interacting hadron resonance gas (VDWHRG) model. The parameters representing the attractive and repulsive interactions in the VDWHRG model have been extracted by fitting the $\sigma^{2}$/$M$, $\it{S}\sigma$ and $\kappa\sigma^{2}$, where $M$ is the mean, $\sigma$ is the standard deviation, $\it{S}$ is the skewness and $\kappa$ the kurtosis of the net-proton distribution. Considering all the three moment products we observe that the strength of the repulsive interactions increases with decrease in $\sqrt{\mathrm {s_{NN}}}$ = 200 to 19.6 GeV while the strength of the attractive interaction is of the similar magnitude. For $\sqrt{\mathrm {s_{NN}}}$ = 11.5 and 7.7 GeV there is drop in the strength of both attractive and repulsive interactions relative to $\sqrt{\mathrm {s_{NN}}}$ = 19.6 GeV. On the other hand, if we consider only the higher order moment products, $\it{S}\sigma$ and $\kappa\sigma^{2}$, which are more sensitive to critical point physics, a segregation with respect to the strength of the attractive parameter is observed. The data for $\sqrt{\mathrm {s_{NN}}}$ = 19.6 and 27 GeV supports a larger attractive strength compared to other energies. For this latter case, the repulsive interaction values are of similar order for most of the beam energies studied, except for 7.7 GeV where the parameter value is not well constrained due to large uncertainties.