Effective method for calculating the analytic QCD coupling constant

The analytic running coupling constant αan for strong interactions is considered for approximations of standard perturbation theory up to the three-loop level. Nonperturbative contributions are singled out explicitly in αan. They are represented in the form of an expansion in a series in inverse powers of the Euclidean momentum squared. It is shown that two-and three-loop corrections lead to a partial compensation of the nonperturbative one-loop contribution of order 1/q2, which is leading in the ultraviolet region. An efficient method for calculating the analytic running coupling constant for all q>Λ is developed on the basis of the above expansion. A comparative analysis of perturbative and nonperturbative contributions is performed in the infrared region, where the latter play the most important role. A simultaneous consideration of the momentum dependence of αan and its perturbative component for one-to three-loop cases leads to the conclusion that the analytic running coupling constant is stable with respect to higher corrections and that it depends only slightly on conditions imposed in matching solutions that involve different numbers nf of active-quark flavors.