Impact of limited statistics on the measured hyperorder cumulants of net-proton distributions in heavy-ion collisions

Hyperorder cumulants C₅/C₁ and C₆/C₂ of net-baryon distributions are anticipated to offer crucial insights into the phase transition from quark-gluon plasma to hadronic matter in heavy-ion collisions. However, the accuracy of C₅ and C₆ is highly contingent on the fine shape of the distribution's tail, the detectable range of which could be essentially truncated by low statistics. In this paper, we use the fast Skellam-based simulations, as well as the ultrarelativistic quantum molecular dynamics model, to assess the impact of limited statistics on the measurements of C₅/C₁ and C₆/C₂ of net-proton distributions at lower energies available at the BNL Relativistic Heavy Ion Collider. Both ratios decrease from the unity baseline as we reduce statistics and could even turn negative without a pertinent physics mechanism. By incorporating statistics akin to experimental data, we can replicate the net-proton C₅/C₁ and C₆/C₂ values comparable to the corresponding measurements for Au+Au collisions at s₍₍=7. 7, 11. 5, and 14. 5 GeV. Our findings underscore a caveat to the interpretation of the observed beam energy dependence of hyperorder cumulants.