The Model for QCD Running Coupling Constant with Dynamically Generated   Mass and Enhancement in the Infrared Region
  Nonperturbative studies of the strong running coupling constant in the infrared region are discussed. Starting from the analyses of the Dyson -- Schwinger equations in the gauge sector of QCD, the conclusion is made on an incomplete fixing of the perturbation theory summation ambiguity within "(forced) analytization procedure" (called also a dispersive approach). A minimal model for $\bar\alpha_s(q^2)$ is proposed so that the perturbative time-like discontinuity is preserved and nonperturbative terms not only remove the Landau singularity but also provide the ultraviolet convergence of the gluon condensate. Within this model, on the one hand, the gluon zero modes are enhanced (the dual superconductor property of the QCD vacuum) and, on the other hand, dynamical gluon mass generation is realized, with $m_g$ estimated as $0.6 GeV$. The uncertainty connected with the division into perturbative and nonperturbative contributions is discussed with the gluon condensate taken as an example. 
Aleksey I. Alekseev