Scaling for Count-in-cell and Factorial Moment Analysis

The investigation of remnants associated with the QCD chiral critical point is a primary objective in high-energy ion collision experiments. Numerous studies indicate that a scaling relation between higher-order factorial moments of hadron multiplicity distributions and the second factorial moment may serve as a diagnostic tool for identifying the QCD critical point. However, we demonstrate that this scaling behavior is not exclusive to critical phenomena but rather arises as a general consequence of the phase-space partitioning procedure employed in the analysis. This finding is examined in the context of recent intermittency analyses conducted by the STAR experiment at RHIC.