Influence of a dynamical gluon mass in the $pp$ and $\bar{p}p$ forward scattering

We compute the tree level cross section for gluon-gluon elastic scattering taking into account a dynamical gluon mass, and show that this mass scale is a natural regulator for this subprocess cross section. Using an eikonal approach in order to examine the relationship between this gluon-gluon scattering and the elastic $pp$ and $\bar{p}p$ channels, we found that the dynamical gluon mass is of the same order of magnitude as the {\it ad hoc} infrared mass scale $m_0$ underlying eikonalized QCD-inspired models. We argue that this correspondence is not an accidental result, and that this dynamical scale indeed represents the onset of non-perturbative contributions to the elastic hadron-hadron scattering. We apply the eikonal model with a dynamical infrared mass scale to obtain predictions for ${\sigma }_{tot}^{pp,\bar{p}p}$, ${\rho }^{pp,\bar{p}p}$, slope $B^{pp,\bar{p}p}$, and differential elastic scattering cross section $d{\sigma }^{\bar{p}p}\mathrm{/}dt$ at Tevatron and CERN-LHC energies.