Hypercontractivity and factorial moment scaling in the symmetry broken phase

TL;DR

This paper demonstrates that factorial moment scaling, previously thought to indicate critical phenomena in QCD, is a general property of distributions and not exclusive to criticality, explaining recent experimental null results.

Contribution

It extends hypercontractivity to factorial moments, showing that factorial moment scaling is a general distribution property, not a unique signature of critical phenomena.

Findings

Factorial moment scaling is not unique to critical phenomena.

The scaling law is a general property of distributions.

Explains null results in recent STAR experiment analysis.

Abstract

The search for remnants of the QCD chiral critical point is a central objective of current and future high-energy ion collision experiments. Previous studies suggest that a scaling law relating higher-order factorial moments of hadron multiplicity fluctuations to the second factorial moment could serve as a tool for detecting the QCD critical point. However, we demonstrate that this scaling law is not unique to critical phenomena. Instead, it emerges as a general property of distributions by extending the concept of hypercontractivity, originally applied to ordinary moments, to factorial moments. We present examples of distribution classes that exhibit the same higher-order factorial moment scaling as multiplicity fluctuations in the symmetry-broken phase. This insight allows us to explain the recent intermittency analysis results from the STAR experiment at RHIC (arXiv:2301.11062), where no indication of criticality was observed.