Exploring the properties of the Hadronic Phase in Heavy-Ion Collisions at RHIC Energies via Partial Chemical Equilibrium

TL;DR

This work addresses how the hadronic phase shapes final-state hadron abundances in heavy-ion collisions by employing the HRG-PCE framework within Thermal-FIST to extract chemical freeze-out $T_{ch}$, kinetic freeze-out $T_{kin}$, baryon chemical potential $\mu_B$, fireball radius $R$, and strangeness saturation $\gamma_S$ from stable hadrons and resonances across $\sqrt{s_{\rm NN}} = 7.7$–$200$ GeV. It extends HRG-PCE to include baryon–antibaryon annihilation via $B\overline{B} \leftrightarrow n\pi$, enabling a data-driven estimate of the annihilation freeze-out temperature $T_{ann}^{frz}$ by matching $\overline{p}/p$ centrality trends. The results show $T_{ann}^{frz}$ lies between $T_{kin}$ and $T_{ch}$, indicating annihilation persists in the hadronic phase but ceases before kinetic decoupling, while resonance yields (notably $K^{*0}$) are better described when resonance chemistry is allowed to evolve in PCE. This yields a coherent, flow-free narrative of hadronic evolution and provides a robust baseline for incorporating hadronic-phase dynamics into dynamical models of heavy-ion collisions at RHIC and beyond.

Abstract

The hadronic phase in heavy-ion collisions plays a crucial role in shaping the final-state hadron abundances. In this work, we study Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7-200 GeV using the Hadron Resonance Gas model in Partial Chemical Equilibrium (HRG-PCE). By fitting the yields of stable hadrons and short-lived resonances such as K$^*(892)^0$, we extract both chemical and kinetic freeze-out temperatures as functions of center-of-mass energy and centrality. The analysis, performed using the Thermal-FIST package, avoids assumptions about radial flow profile or freeze-out hypersurfaces. Furthermore, we estimate the baryon annihilation freeze-out temperature from the experimentally measured $\bar{\rm p}/$p ratio, using the HRG-PCE framework extended to include $B\bar{B} \leftrightarrow nπ$ reactions. The inferred annihilation freeze-out temperature lies between the chemical and kinetic freeze-out temperatures, suggesting that baryon annihilation remains active in the early hadronic phase but ceases prior to kinetic freeze-out. These results provide a consistent picture of the sequential decoupling of hadronic processes and demonstrate that inelastic hadronic interactions significantly influence the chemical composition of the system between chemical and kinetic freeze-outs at RHIC energies.

Figures (10)

• Figure 1: (Left) Centrality dependence of $\rm \overline{p}$/p ratio normalized to the 60–80% peripheral value in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7--200 GeV. (Right) Corresponding HRG-PCE predictions of $\rm (\overline{p}/p)_{T_{ann}}/(\overline{p}/p)_{T_{had}}$ as a function of temperature. Experimental values from the left panel are mapped onto the theoretical curve to extract $\rm T_{ann}^{frz}$.
• Figure 2: Ratio of experimentally measured hadron yields to thermal model fits for $\pi$, K, $\rm K_S^0$, p, $\phi$, $\Lambda$, $\Xi$, and $\mathrm{K}^{*0}$ in the 0–10%, 10–20%, 20–40%, and 40–80% centrality classes of Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 27 GeV. Results from the standard HRG model are shown as blue square markers, while those from the HRG-PCE model are shown as red circle markers.
• Figure 3: Chemical (solid square markers), kinetic (solid circle markers), and baryon-antibaryon annihilation (solid diamond markers) freeze-out temperatures extracted using the HRG-PCE framework as a function of charged-particle multiplicity ($\rm \langle dN_{\text{ch}}/d\eta \rangle^{1/3}$) in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7--200 GeV. For comparison, chemical (open square markers) and kinetic (open circle markers) freeze-out temperatures reported by STAR using THERMUS and blast-wave fits, respectively, are also shown STAR:2017salSTAR:2008med.
• Figure 4: Baryon chemical potential, radius, and strangeness suppression factor at chemical freeze-out, extracted using the HRG-PCE framework (solid circles), as a function of charged-particle multiplicity ($\rm \langle dN_{\text{ch}}/d\eta \rangle^{1/3}$) in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7, 11.5, 19.6, 27, 39, and 200 GeV. For comparison, STAR values using THERMUS are shown as open circles STAR:2017salSTAR:2008med.
• Figure 5: Ratio of experimentally measured hadron yields to thermal model fits for $\pi$, K, $\rm K_S^0$, p, $\phi$, $\Lambda$, $\Xi$, $\mathrm{K}^{*0}$, and $\Lambda^*$ in 0–10% centrality of Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. Results from the HRG and HRG-PCE models are shown as blue square and red circle markers, respectively.