Effects of the centrality determination method for the equation of state and nucleonic observables from Au+Au collisions at $\sqrt{s_{NN}}$ = 2.4 GeV

TL;DR

This work investigates how centrality determination methods bias nucleonic observables in Au+Au collisions at $\sqrt{s_{NN}}=2.4$ GeV using UrQMD with soft and hard EoS. By comparing $M_\mathrm{ch}$, $b_f$, and Glauber MC-based $b_r$ centralities, it demonstrates that the $b$-distributions differ significantly, especially between $M_\mathrm{ch}$ and $b_r$, and that these differences propagate into yields, $p_T$ spectra, and higher-flow observables, while mid-rapidity flows $v_{11}$ and $v_{20}$ are mainly governed by the EoS. The study finds that the geometrical centrality $b_f$ generally yields smaller centrality-induced biases than the Glauber MC method, which can introduce large systematic effects at this energy, underscoring the need for a consistent mapping between multiplicity and geometry when constraining the high-density EoS. Glauber MC-based centrality is shown to be unreliable at SIS energies, guiding future analyses toward geometry-based or machine-learning–driven mappings and validating Bayesian techniques to quantify residual model–data deviations and uncertainties.

Abstract

Centrality determination remains one of the major sources of systematic uncertainty in intermediate-energy heavy-ion collision analyses, especially for probing the nuclear equation of state (EoS) at supra-saturation densities. To quantitatively assess the uncertainties associated with different centrality determination methods and to investigate their effects on final-state EoS-sensitive observables. Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, Au+Au collisions at $\sqrt{s_{NN}}$=2.4 GeV are performed within a soft and a hard EoS. Event centrality is determined using the multiplicity of all charged particles ($M_\mathrm{ch}$) and two impact parameter-based centrality filters, one based on a geometrical interpretation and the other based on the Glauber Monte Carlo (MC) model, denoted as $b_{f}$ and $b_{r}$, respectively. It is shown that there exist significant differences between the real impact parameter distributions of event samples selected by $M_\mathrm{ch}$, $b_{f}$, and $b_{r}$, particularly between $M_\mathrm{ch}$ and $b_{r}$. When the $b_{f}$ is employed, uncertainties associated with centrality selection have a weaker influence on observables than the effects induced by the EoS. In contrast, when the $b_{r}$ is used, the influence of centrality-related uncertainties becomes more pronounced than that of the EoS. These results demonstrate that a rigorous and consistent mapping between $M_\mathrm{ch}$ and impact parameter is essential to impose quantitative constraints on the high-density nuclear EoS. Furthermore, our study indicates that the geometrical interpretation of centrality remains valid and consistent with dynamical multiplicity selection, whereas the Glauber MC-based centrality determination becomes unreliable at the investigated energy.

Figures (8)

• Figure 1: (Color online) The distribution of the multiplicity of all charged particles $M_\mathrm{ch}$ from Au+Au collisions at $\sqrt{s_{NN}}=2.4$ GeV with $b$=0-$b_{\text{max}}$.
• Figure 2: (Color online) The impact parameter distributions of the event samples selected by $b_{f}$, $b_{r}$, and $M_\mathrm{ch}$ given in Tab. \ref{['Table.2']} from Au+Au collisions at $\sqrt{s_{NN}}$ = 2.4 GeV with $b$=0-$b_{\text{max}}$.
• Figure 3: (Color online) Rapidity distribution of free protons within $0.4<p_\mathrm{T}<1.6$ GeV/$c$ in central (0-10%) Au+Au collisions at $\sqrt{s_{NN}}$ = 2.4 GeV for different EoS and centrality determination methods. The experimental data (red stars) are taken from the HADES Collaboration HADES:dndy. For the theoretical results, the error bars fall within the symbols.
• Figure 4: (Color online) Top panels: Centrality dependence of the free proton yields within $0.4<p_{\mathrm{T}}<1.6$ GeV/c and $|y|<0.25$ for four scenarios; symbol conventions follow Fig. \ref{['fig:3']}. Bottom panels: Centrality dependence of the yield ratios between different EoS (cyan lines with downward triangles) and centrality determinations (magenta lines with upward triangles). Where not visible, error bars are smaller than the symbols.
• Figure 5: (Color online) Rapidity distribution of the directed flow $v_{1}$ [top panels (a1) and (b1)] and the elliptic flow $v_{2}$ [bottom panels (a2) and (b2)] of free protons at 20-30% centrality with different impact parameter filters and EoS, respectively. The solid stars represent the experimental data taken from Ref. HADES:2020lob.