Based on a study of the analytic running coupling obtained from the standard perturbation theory results up to four-loop order, the QCD "synthetic" running coupling αsyn is built. In so doing the perturbative time-like discontinuity is preserved and nonperturbative contributions not only remove the nonphysical singularities of the perturbation theory in the infrared region but also decrease rapidly in the ultraviolet region. In the framework of the approach, on the one hand, the running coupling is enhanced at zero and, on the other hand, the dynamical gluon mass mg arises. Fixing the parameter which characterize the infrared enhancement corresponding to the string tension σ and normalization, say, at Mτ completely define the synthetic running coupling. In this case the dynamical gluon mass appears to be fixed and the higher loop stabilization property of mg is observed. For σ = (0.42 GeV) 2 and αsyn(M 2 τ ) = 0.33 ±0.01 it is obtained that mg = 530 ±80 MeV.

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It is shown, that the possibility of a freezing of QCD running coupling constant at zero in the approach with "forced analyticity" can not be in accord with Schwinger-Dyson equation for gluon propagator. We propose to add to the analytic expression the well-known infrared singular term 1/q 2 as well as pole term corresponding to "excited gluon". With this example we formulate the principle of minimality of nonperturbative contributions in perturbative (ultraviolet) region, which allows us to fix ambiguities in introduction of nonperturbative terms and maintain the finiteness of the gluon condensate. As a result we obtain estimates of the gluon condensate, which quite agree with existing data. The nonzero effective mass of the "excited gluon" leads also to some interesting qualitative consequences.

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The QCD analytic running coupling α an which has no nonphysical singularities for all Q 2 > 0 is considered for the initial perturbation theory approximations up to four loop order. The finiteness of the analytic coupling at zero is shown to be a consequence of the asymptotic freedom property of the initial theory. The nonperturbative contributions to the analytic coupling are extracted explicitly. For all Q > Λ they are represented in the form of an expansion in inverse powers of Euclidean momentum squared. The effective method for a precise calculation of the analytic running coupling is developed on the basis of the stated expansion. The energy scale evolution of the analytic running coupling for the one-to fourloop cases is studied and the higher loop stability and low dependence on the quark threshold matching conditions in comparison with the perturbative running coupling were found. Normalizing the analytic running coupling at the scale of the rest mass of the Z boson with the world average value of the strong coupling constant, α an (M 2 Z ) = 0.1181 ± 0.002, one obtains as a result of the energy scale evolution of the analytic running coupling α an (M 2 τ ) = 0.2943−0.0106 that is notably lower than the estimations of the coupling strength available at the scale of the mass of the τ lepton.