An Invariant Charge Model for All q^2>0 in QCD and Gluon Condensate

Abstract

Under assumption of singular behavior of invariant charge alpha_s(q^2) at q^2 sim 0 and of large q^2 behavior, corresponding to the perturbation theory up to four loops, a procedure is considered of smooth matching the beta-function at a boundary of perturbative and nonperturbative regions. The procedure results in a model for alpha_s for all q^2>0 with dimensionless parameters being fixed and dimensional parameters being expressed in terms of only one quantity Lambda_QCD. The gluon condensate which is defined by the nonperturbative part of the invariant charge is calculated for two variants of ``true perturbative'' invariant charge, corresponding to freezing option and to analytic one in nonperturbative region. Dimensional parameters are fixed by varying normalization condition alpha_s(m^2_tau) = 0.29, 0.30, ..., 0.36. It is obtained that on the boundary of perturbative region alpha_0 = alpha_s(q_0^2) simeq 0.44, the procedure results in nonperturbative Coulomb component alpha_Coulomb simeq 0.25, the nonperturbative region scale q_0 simeq 1 GeV, the model parameter sigma simeq (0.42 GeV)^2 which suits as string tension parameter, the gluon condensate appears to be close for two variants considered, K simeq (0.33 -- 0.36 GeV)^4 (for alpha_s(m^2_tau) = 0.33).