Odderon and pomeron as fractal dimension in pp and p̄p total cross-sections

Abstract

In this paper, one presents a naive parametrization to [Formula: see text] and [Formula: see text] total cross-sections. The main goal of this parametrization is to study the possible fractal structure present in the total cross-section. The result of the fitting procedure shows two different fractal dimensions: a negative (low-energies) and a positive (high-energies). The negative fractal dimension represents the emptiness of the total cross-section structure and the positive represents the filling up process with the energy increase. Hence, the total cross-section presents a multifractal behavior. At low-energies, the odderon exchange may be associated with the negative fractal dimension and at high-energies, the pomeron may be associated with the positive fractal dimension. Therefore, the exchange of odderons and pomerons may be viewed as a transition from a less well-defined to a more well-defined internal structure, depending on the energy.

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

“…When the energy s grows and go through the transition point s c , the TE turns positive and stands for the system growing disorder. As obtained in [16], the total cross section to pp andpp possesses positive fractal dimensions to s > s c and both tends to the same value as s → ∞. Both results have shown that at high energies the arrangement of the internal constituents to pp andpp tends to the same behavior.…”

“…The phase transition occurring in the total cross section at s c represents a break in the symmetry predicted in the seminal paper [44] and, before that, in the [45]. These assumptions can provide a way to calculate the entropy generated due a phase transition in the total cross section as s increases [16]. In order to do that, the integral in (10) is rewritten assuming the collision event inside a disk of radius b > 0 and an entropic index s/s c…”

“…2. the entropic index w can be replaced by a single real evaluated function w = w(s/s c ) ≥ 0, where s c is the critical point associated to the phase transition occurring in the total cross section [16].…”

Analysis of pp and p̄p elastic scatterings based on theoretical bounds in high-energy physics: An update

“…It is important to stress the novel interpretation introduced in [3,4] concerning the total cross section in terms of fractal dimension and phase transition. The fractal structure present in the total cross section can viewed as a manifestation of a Berezinskii-Kosterliz-Thouless (BKT)-like phase transition [28,29].…”

Proton internal pressure in pp and p̄p elastic scattering

“…However, when s > s 0 the total cross section starts to rise as predicted by Cheng and Wu seminal papers [15,16]. Moreover, as shown in Borcsik and Campos [2], the total cross section behavior can be explained by the use of the concept of fractal dimensions. When s < s 0 , the fractal dimension of the total cross section is negative, measuring the emptiness of the hadron.…”