The small $x$ behavior of the gluon structure function from total cross sections

Abstract

Within a QCD-based eikonal model with a dynamical infrared gluon mass scale we discuss how the small $x$ behavior of the gluon distribution function at moderate $Q^{2}$ is directly related to the rise of total hadronic cross sections. In this model the rise of total cross sections is driven by gluon-gluon semihard scattering processes, where the behavior of the small $x$ gluon distribution function exhibits the power law $xg(x,Q^2)= h(Q^2)x^{-\epsilon}$. Assuming that the $Q^{2}$ scale is proportional to the dynamical gluon mass one, we show that the values of $h(Q^2)$ obtained in this model are compatible with an earlier result based on a specific nonperturbative Pomeron model. We discuss the implications of this picture for the behavior of input valence-like gluon distributions at low resolution scales.