Bayesian Calibration of the Crossterms Eigenvolume HRG Model: Integrating Lattice QCD and Experimental Data

We perform a Bayesian calibration of the Cross–term Excluded-Volume Hadron Resonance Gas (Cross EV–HRG) model, which incorporates flavor-dependent repulsive interactions within a thermodynamically consistent framework. For the first time, the thermal model is simultaneously constrained using lattice QCD (LQCD) thermodynamic observables and centrality-resolved hadron yield data from Pb–Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=2.76\mathrm{T}\mathrm{e}\mathrm{V}$ measured by the ALICE Collaboration. We also find that the calibration outcome is strongly data-dependent in terms of constraining power and uncertainty structure. In particular, LQCD observables alone provide only weak constraints on the eigenvolume parameters, while the inclusion of hadron yield data substantially enhances the constraining power and induces a nontrivial reshaping of the posterior distributions. We further investigate the impact of correlated experimental systematic uncertainties by constructing a phenomenological covariance matrix and systematically varying its strength, demonstrating that a careful and consistent treatment of systematic correlations is essential for reliable parameter estimation. Across all calibration scenarios, the parameters associated with multi-strange hadrons remain only moderately constrained, which may reflect limitations of the currently established hadron resonance spectrum. No clear monotonic hierarchy of strange-hadron eigenvolume radii emerges within the present uncertainties, indicating that further dedicated studies are required.