QCD Running Coupling: Freezing Versus Enhancement in the Infrared Region
  We discuss whether or not "freezing" of the QCD running coupling constant in the infrared region is consistent with the Schwinger -- Dyson (SD) equations. Since the consistency of the "freezing" was not found, the conclusion is made that the "analytization" method does not catch an essential part of nonperturbative contributions. Proceeding from the results on consistency of the infrared enhanced behaviour of the gluon propagator with SD equations, the running coupling constant is modified taking into account the minimality principle for the nonperturbative contributions in the ultraviolet region and convergence condition for the gluon condensate. It is shown that the requirements of asymptotic freedom, analyticity, confinement and the value of the gluon condensate are compatible in the framework of our approach. Possibilities to find an agreement of the enhanced behaviour of the running coupling constant with integral estimations in the infrared region are also discussed. 
Aleksey I. Alekseev