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 (2023) [1], where no indication of criticality was observed.

中文翻译：

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对称性打破阶段的超收缩性和阶乘矩缩放


寻找 QCD 手性临界点的残余物是当前和未来高能离子碰撞实验的中心目标。以前的研究表明，将强子多重性波动的高阶阶因矩与第二阶乘矩联系起来的缩放定律可以作为检测 QCD 临界点的工具。然而，我们证明了这种缩放定律并不是临界现象所独有的。相反，它通过将超收缩性的概念（最初应用于普通时刻）扩展到阶乘时刻，作为分布的一般属性出现。我们提供了分布类的示例，这些分布类表现出与对称性破坏阶段中的多重性波动相同的高阶因子矩缩放。这一见解使我们能够解释最近在 RHIC （2023） [1] 进行的 STAR 实验的间歇性分析结果，其中没有观察到临界迹象。