Phenomenological Analyses on Hadronic Cross-Sections at High and Asymptotic Energies

Quantum Chromodynamics constitutes the quantum field theory of the strong interaction. Despite the success of this theory in the description of several hadronic processes, the elastic scattering is still a theoretical challenge. This process is characterized by a small transferred momentum and the perturbative techniques are not applicable. Although nonperturbative results have been obtained in recent years, we still do not have a full description within QCD of the quantities related to the elastic scattering, for example, $\sigma_{tot}$, the $\rho$ parameter and $\sigma_{el}$. In this thesis, the main interest is in the energy dependence of the ratio $X=\sigma_{el}/\sigma_{tot}$, $\sigma_{tot}$ and $\rho$. These topics are divided into three different studies. In the first topic, we develop an empirical analysis on the ratio $X$. By means of parameterizations with a small number of free parameters, we have obtained good descriptions of the data on $pp$ and $\bar{p}p$ scattering. We conclude that the asymptotic black-disk scenario is not a unique solution and the results favour a grey-disk scenario. In the second topic, we study the rise of $\sigma_{tot}$ with the energy through parameterizations based on the Regge-Gribov formalism and we consider two options for the leading term: a log-square and a log-raised-to-$\gamma$, with $\gamma$ a free fit parameter. We discuss two analytic methods to connect the real and imaginary parts of the amplitude: Derivative Dispersion Relations (DDR) and Asymptotic Uniqueness, which lead to different parameterizations for $\sigma_{tot}$ and $\rho$. The results favour the DDR method in both formal and practical contexts. In the third topic, two sub-leading terms for $\sigma_{tot}$, obtained in a nonperturbative QCD approach, are considered in fits to $pp$ and $\bar{p}p$ data and also in fits to data from meson-baryon and other baryon-baryon scattering.