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A truncated solution of a gauge invariant subset of the Schwinger-Dyson (SD) equations for QCD leads to a functional form of the strong running coupling showing a freezing in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. The generation of such a mass is associated with the existence of infrared finite solutions for the gluon propagator that has been confirmed by lattice QCD. From this coupling and propagator a non confining One Gluon Exchange (OGE) non perturbative interaction comes out [1].
By assuming that the SD coupling contains the physics at intermediate and large momenta but it lacks some vertex corrections at low momenta, we incorporate an infrarred singularity in the simplest possible ad hoc manner. Then the non perturbative OGE interaction gives rise, with all the parameters fixed to their SD values, to a Cornell like potential for heavy quarkonia [2].
[1]: P. Gonzalez, V. Mathieu and V. Vento, Phys. Rev. D 84, 114008 (2011).
[2] : C. Ayala, P. González and V. Vento, J.Phys. G 43, 125002 (2016).
