Phenomenological exploration of the strong coupling constant in the perturbative and nonperturbative regions

Abstract

The QCD running coupling costant is studied in the perturbative region, considering the existing experimental data, and also in the nonperurbative region, at low momentum transfer. A continous phenomenological function is determined by means of three different models also calculating the corresponding finite value of the vector quark self-energy. These two quantities are used for the vector interaction of a Dirac relativistic model for the charmonium spectrum. The process required to fit the spectrum is discussed and the relationship with previous models is analyzed.