Extraction of baryon number susceptibilities at finite density from heavy-ion collisions

Abstract

We present, to our knowledge, the first Bayesian extraction of baryon number susceptibilities of QCD matter at finite baryon density from heavy-ion collision data on proton number cumulants. The framework embeds arbitrary equation-of-state susceptibilities ${\chi }_n^B$ into realistic hydrodynamic particlization hypersurfaces through maximum-entropy freeze-out, maps the resulting (anti)baryon fluctuations onto protons, applies the experimental kinematic acceptance, and accounts for exact baryon number conservation. Applying the framework to measurements of (net-)proton number fluctuations in 0--5\% central Au-Au collisions from the RHIC Beam Energy Scan in the collider mode, we extract, at each collision energy, the second-order susceptibility normalized by the hadron resonance gas value, ${\chi }_2^B/{\bar{\chi }}_2^B$, and the higher-order susceptibility ratios ${\chi }_3^B/{\chi }_1^B$ and ${\chi }_4^B/{\chi }_2^B$. We obtain tight constraints on ${\chi }_2^B$, with extracted values in quantitative agreement with lattice QCD based estimates along the chemical freeze-out line for ${\mu }_B\lesssim 300$~MeV. At larger ${\mu }_B$, the extracted values indicate an enhancement of baryon number fluctuations relative to the noncritical lattice-based extrapolation and HRG baseline considered here. The third- and fourth-order susceptibilities are only weakly constrained. In particular, we find that the observed nonmonotonic collision-energy dependence of the proton factorial cumulant ratio ${\hat{C}}_3/{\hat{C}}_1$ can be described without irreducible three- or four-baryon correlations. This behavior emerges from the interplay between the energy dependence of ${\chi }_2^B$ and exact baryon number conservation.