Impact of Limited Statistics on the Measured Hyper-Order Cumulants of Net-Proton Distributions in Heavy-Ion Collisions

• DOI: 10.48550/arxiv.2401.09745
• Publication Date: 2024-01-01
• Authors: Lizhu Chen; Ye-Yin Zhao; Yunshan Cheng; Gang Wang; Zhiming Li; Yuanfang Wu
• Keywords: Cumulant; Beam energy; Baryon number

Hyper-order cumulants $C_5/C_1$ and $C_6/C_2$ of net-baryon distributions are anticipated to offer crucial insights into the phase transition from quark-gluon plasma hadronic matter in heavy-ion collisions. However, accuracy $C_5$ $C_6$ is highly contingent on fine shape distribution's tail, detectable range which could be essentially truncated by low statistics. In this paper, we use fast Skellam-based simulations, as well Ultrarelativistic Quantum Molecular Dynamics model, assess impact limited statistics measurements net-proton at lower RHIC energies. Both ratios decrease unity baseline reduce statistics, even turn negative without a pertinent physics mechanism. By incorporating akin experimental data, can replicate values comparable corresponding for Au+Au collisions $\sqrt{s_{NN}} =$ 7.7, 11.5 14.5 GeV. Our findings underscore caveat interpretation observed beam energy dependence hyper-order cumulants.