  One of the main open questions in physics is the understanding of the
internal structure of the strongly interacting particles, or hadrons. It is
still a challenge to describe consistently the dynamics of scattering processes
and hadronic structure at moderate energy scales. The study of Parton
Distribution Functions (PDFs) sets a connection between the perturbative and
non-perturbative worlds, through the following scheme: one builds models
consistent with QCD in a moderate energy range, PDFs are evaluated in these
models, and, finally, the scale dependence of these distributions is studied.
In these proceedings, we revisit the standard procedure to match
non-perturbative models to perturbative QCD, using experimental data. The
strong coupling constant plays a central role in the QCD evolution of parton
densities. We will extend this procedure with a non-perturbative generalization
of the QCD running coupling and use this new development to understand why
perturbative treatments are working reasonably well in the context of hadronic
models. Vice versa, this new procedure broadens the ways of analyzing the
freezing of the running coupling constant.
