Odderon and Pomeron as Fractal Dimension in $pp$ and $\bar{p}p$ Total Cross Sections

TL;DR

This paper proposes a fractal-based model for $pp$ and $ar{p}p$ total cross sections, revealing a transition from negative to positive fractal dimensions that correlates with odderon and pomeron exchanges at different energies.

Contribution

It introduces a novel fractal dimension approach to describe the energy-dependent structure of total cross sections in proton-proton and antiproton-proton collisions.

Findings

Identification of two distinct fractal dimensions at different energy regimes.

Correlation of negative fractal dimension with odderon exchange.

Correlation of positive fractal dimension with pomeron exchange.

Abstract

In this paper one presents a naive parametrization to $pp$ and $\bar{p}p$ 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.