A Centrality-independent Framework for Revealing Genuine Higher-Order Cumulants in Heavy-Ion Collisions

TL;DR

This work tackles the challenge that initial volume fluctuations from centrality definitions distort higher-order cumulants in heavy-ion collisions, especially at low energy. It introduces a centrality-independent framework that reconstructs proton-number distributions using Edgeworth expansion and refines cumulant-relevant parameters via differential evolution and Bayesian inference, under physics-informed polynomial constraints. The method is validated with UrQMD Au+Au data at $\sqrt{s_{NN}}=3.5$ GeV, producing cumulant trends in good agreement with $N_{part}$-based centrality results and showing robustness to centrality-definition choices. By mitigating volume fluctuations, the approach enables access to intrinsic thermodynamic properties of the produced medium through event-by-event fluctuations and can be extended to net-proton and other observables with efficiency corrections.

Abstract

We propose a novel centrality definition-independent method for analyzing higher-order cumulants, specifically addressing the challenge of volume fluctuations that dominate in low-energy heavy-ion collisions. This method reconstructs particle number distributions using the Edgeworth expansion, with parameters optimized via a combination of differential evolution algorithm and Bayesian inference. Its effectiveness is validated using UrQMD model simulations and benchmarked against traditional approaches, including centrality definitions based on particle multiplicity. Our results show that the proposed framework yields cumulant patterns consistent with those obtained using number of participant nucleon ($N_{\text{part}}$) based centrality observables, while eliminating the conventional reliance on centrality determination. This consistency confirms the method's ability to extract genuine physical signals, thereby paving the way for probing the intrinsic thermodynamic properties of the produced medium through event-by-event fluctuations.

Figures (16)

• Figure 1: Edgeworth expansion for the Poisson distribution with $\lambda = 10$. red line is the Edgeworth expansion, blue line is the Poisson distribution.
• Figure 2: Edgeworth expansion for the proton number distributions in each $N_{\text{part}}$-defined centrality from UrQMD.
• Figure 3: Variations of $C_2$ and $C_3$ with respect to the $C_1$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.5 GeV from UrQMD. Here red solid lines represent the results of a second-order polynomial fit, indicating that cumulants follow a certain pattern.
• Figure 4: On the left plot is the number of proton vs RefMult3, on the right is the number of proton vs $N_{\text{p}art}$.
• Figure 5: Centrality determined by RefMult3. The red dashed lines represent the 2% centrality interval.