The Tsallis entropy and the BKT-like phase transition in the impact parameter space for $pp$ and $\bar{p}p$ collisions

TL;DR

This paper applies Tsallis entropy to impact parameter space in proton-proton and antiproton-proton collisions, revealing a BKT-like phase transition linked to the black disk limit and multifractal properties of the cross-section.

Contribution

It introduces a novel entropy-based approach using Tsallis entropy to analyze phase transitions in hadronic collisions, highlighting a BKT-like transition and multifractality.

Findings

Identification of a BKT-like phase transition in impact parameter space.

Demonstration of multifractal character in total cross-sections.

Insight into the energy density filling mechanism at high energies.

Abstract

In this paper, one uses the Tsallis entropy in the impact parameter space to study $pp$ and $\bar{p}p$ inelastic overlap function and the energy density filling up mechanism responsible by the so-called black disk limit as the energy increases. The Tsallis entropy is non-additive and non-extensive and these features are of fundamental importance since the internal constituents of $pp$ and $\bar{p}p$ are strongly correlated and also the existence of the multifractal character of the total cross-section. The entropy approach presented here takes into account a phase transition occurring inside the hadrons as the energy increases. This phase transition in the impact parameter space is quite similar to the Berezinskii-Kosterlitz-Thouless phase transition, possessing also a topological feature due to the multifractal dimension of the total cross-sections in $pp$ and $\bar{p}p$ scattering.