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

TL;DR

The paper addresses charm-sector fluctuations in QCD matter and the limitations of non-interacting HRG models at higher temperatures and finite baryon density. It adopts the van der Waals Hadron Resonance Gas (VDWHRG) framework, which includes both attractive and repulsive interactions, to compute partial charm pressures and generalized susceptibilities by projecting the total pressure onto charmed meson and baryon sectors via derivatives of $P/T^4$. The study finds that VDWHRG substantially improves agreement with lattice QCD data for charm observables up to $T\approx180$ MeV and provides detailed predictions for charm susceptibilities across collision energies and baryon densities, while signaling potential deconfinement effects above this temperature range. It also extends the analysis to baryon-rich environments, offering insights for beam energy scan programs and highlighting the role of a possible finite charm chemical potential in interpreting charm yields and fluctuations. Overall, the work strengthens the case that hadronic interactions must be included in charm-sector studies and outlines experimental and lattice avenues to further constrain charm-hadron interactions and the transition to deconfined charm degrees of freedom.

Abstract

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 (HRG), which assumes no interactions between hadrons, and the excluded volume hadron resonance gas (EVHRG), which includes only repulsive interactions, fail to explain the 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 lattice quantum chromodynamics (lQCD) due to the fermion sign problem. Our study further solidifies the notion that the hadrons shouldn't be treated as non-interacting particles, especially when studying higher order fluctuations, but rather one should consider both attractive and repulsive interactions between the hadrons.

Figures (7)

• Figure 1: Partial pressure of charmed baryons (left panel) and charmed mesons (right panel) as functions of temperature at vanishing baryo-chemical potential. The markers are for lattice QCD results Kaczmarek:2025dqt, the solid red line is for VDWHRG, the dashed blue line is for ideal HRG, and the dotted green line is for EVHRG.
• Figure 2: Partial pressure of charmed baryon (left panel) and charmed meson (right panel) as a function of chemical potential and temperature.
• Figure 3: Partial pressure of charmed meson with strangeness = 1 (left), charmed baryon with strangeness = 1 (middle), and strangeness = 2 (right) as a function of temperature at $\mu_{\rm{B}}=0$. The markers are for lattice QCD results Kaczmarek:2025dqt.
• Figure 4: Partial pressure ratio at $\mu_{\rm{B}}=0$: Numerator: Charmed meson with strangeness = 1 (left), charmed baryons with strangeness = 1 (middle), and charmed baryons with strangeness = 2 (right). Denominator: Total charm pressure (meson + baryon), as a function of temperature. Compared with lattice QCD results from Ref. Sharma:2024edf.
• Figure 5: Partial pressure ratio at $\mu_{\rm{B}}=0$: Numerator: Charmed hadron with electric charge = 2. Denominator: Total charm pressure (meson + baryon), as a function of temperature compared with lattice QCD calculations Sharma:2024edf.