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

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.