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.
Categories: hep-ph hep-ex