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

In this paper, one uses the Tsallis entropy (TE) in the impact parameter space to study pp and $\overline{p}p$ inelastic overlap function and the energy density filling up mechanism responsible by the so-called black disk limit as the energy increases. The TE is non-additive and non-extensive and these features are of fundamental importance since the internal constituents of pp and $\overline{p}p$ 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 $\overline{p}p$ scattering. (paper)