Fractals, non-extensive statistics and QCD

TL;DR

This paper explores fractal-like scaling in QCD using non-extensive statistics, deriving the Tsallis index from field theory, and successfully explaining experimental high-energy collision phenomena.

Contribution

It introduces a non-perturbative, fractal-based approach to QCD that links scale invariance with non-extensive statistics, providing new insights into particle collision data.

Findings

Derivation of the Tsallis index from QCD parameters.

Agreement of theoretical q with experimental data.

Explanation of multiplicity and distribution patterns in high-energy collisions.

Abstract

In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for recurrent non-perturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the non-perturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the non extensive statistics is obtained, and the Tsallis index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where $q$ can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions and the fractal dimension observed in intermittency analysis.