Hadron Structure and the Running Coupling Constant (Seminario Extraordinario)

    We present recent developments on the role of the running coupling constant in the intersection of perturbative and nonperturbative QCD. 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, at which a collective hadronic representation takes over the partonic description.  

    Our work is twofold and starts from the observation that the outcome of a number of experiments shows a smooth transition from small to large scales given by the four-momentum transfer in the reactions. This is at variance with what predicted in perturbative QCD where the running coupling constant becomes infinite when the scale equals \Lambda_{QCD} (Landau pole). Approaches using an effective coupling constant could help interpret the opposite trend of the data as compared to standard perturbative QCD predictions. Scenarios were in fact developed where the QCD running coupling freezes in the deep infrared. This property can be understood, for instance, by a dynamical gluon mass generation, or other non-perturbative mechanisms leading to a taming of the Landau pole. Recent work also includes studies in AdS/CFT. On the other hand, the Parton Distribution Functions provide a framework to study the transition from nonperturbative model inpterpretations to perturbative QCD.  The strong coupling constant plays a central role in the QCD evolution of parton densities. We extend the standard procedure to match nonperturbative models to perturbative QCD, using experimental data,  with the nonperturbative 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.
    Although these two approaches have been considered so far complementary to each other, a unified description might derive through the definition of the effective coupling, as they both broaden the ways of analyzing the freezing of the running coupling constant.