Partial pressure and susceptibilities of the charmed sector in the van der Waals hadron resonance gas model

We investigate the general susceptibilities in the charm sector by using the van der Waals hadron resonance gas model (VDWHRG).We argue that the ideal hadron resonance gas, which assumes no interactions between hadrons, and the excluded volume hadron resonance gas, which includes only repulsive interactions, fail to explain the lattice quantum chromodynamics (lQCD) data at very high temperatures. In contrast, the VDWHRG model, incorporating both attractive and repulsive interactions, extends the degree of agreement with lQCD up to nearly 180 MeV. We estimate the partial pressure in the charm sector and study charm susceptibility ratios in a baryon-rich environment, which is tricky for lQCD due to the fermion sign problem. Our study further solidifies the notion that the hadrons should not be treated as noninteracting particles, especially when studying higher order fluctuations, but rather one should consider both attractive and repulsive interactions between the hadrons.