Digit anomalies in the hadronic mass spectrum, Shannon information entropy, and the dynamical QCD scale

TL;DR

This paper investigates how the dynamical QCD scale influences the clustering of hadronic masses by analyzing Shannon information entropy, revealing deviations from expected distributions and quantifying scale invariance breaking.

Contribution

It introduces a novel entropy-based analysis of the hadronic mass spectrum to understand the emergence of the QCD scale and its effects on mass clustering.

Findings

Hadronic masses cluster within specific ranges due to the QCD scale.

Shannon entropy analysis reveals deviations from anomalous number laws.

The study quantifies the information-entropy cost of scale invariance breaking.

Abstract

Quantum Chromodynamics (QCD) has an emergent dynamical energy scale $\Lambda_{\rm QCD}$ which sets the threshold between perturbative and nonperturbative regimes. This characteristic scale causes hadronic masses to cluster within certain mass ranges, instead of following a uniform distribution. Analyzing the Shannon information entropy underlying the hadronic mass spectrum provides novel insight into this phenomenon, revealing a pronounced deviation from the law of anomalous numbers. This deviation quantifies the emergence of the dynamical scale in strongly interacting systems, also encoding the information-entropy cost associated with the breaking of scale invariance in QCD.