Several problems on the measured hyperorder cumulants of net-proton distributions in heavy-ion collisions

TL;DR

This paper investigates the application of the Centrality Bin Width Correction method to measure hyperorder cumulants of net-proton distributions in heavy-ion collisions, providing a recommended approach and baseline for future experimental analysis.

Contribution

It systematically examines the effects of different CBWC techniques on hyperorder cumulant measurements and proposes a standardized method for accurate results in heavy-ion collision experiments.

Findings

Identifies significant differences caused by various CBWC techniques.

Proposes a recommended approach for calculating cumulants in 0-40% centrality.

Provides a baseline for net-proton cumulant analysis at RHIC BES-II energies.

Abstract

Hyperorder cumulants $C_5/C_1$ and $C_6/C_2$ are recommended as sensitive observables to explore the QCD phase transition in heavy-ion collisions. Precisely measuring their results remains a difficult task in experiments, when employing the Centrality Bin Width Correction (CBWC) to suppress the initial volume fluctuations. Various techniques within the CBWC formula can lead to notable differences in the results. We will systematically investigate the application of the CBWC method to the measured net-proton $C_5/C_1$ and $C_6/C_2$ using the UrQMD model and Skellam-based simulations at $\sqrt{s_{NN}}$ = 11.5 GeV in Au + Au collisions. A recommended approach is proposed to calculate $C_5/C_1$ and $C_6/C_2$ in 0-40\% centrality. With statistics comparable to the RHIC Beam Energy Scan phase II (BES-II), our studies provide a baseline for analyzing net-proton $C_5/C_1$ and $C_6/C_2$ in relativistic heavy-ion collisions.