Analytic Perturbation Theory Model for QCD and Upsilon Decay

An elegant and more precise formula for the 3-loop perturbative QCD coupling is discussed. It improves the common expression (e.g., canonized by PDG) in few GeV region. On its base, we propose simple analytic Model for ghost-free QCD running couplings and their effective powers within the Analytic Perturbation Theory, in both the space-like (Euclidean) and time-like (Minkowskian) regions, very accurate in the range above 1 GeV. Effectiveness of the new Model is illustrated by the example of Upsilon(1S) decay where the standard analysis gives $\alpha_s(M_{\Ups})=0.170\pm 0.004$ value that is inconsistent with the bulk of data. Instead, we obtain $\alpha_s(M_{\Ups})=0.185\pm 0.005$ that corresponds to $\alpha_s(M_Z)=0.120\pm 0.002$ that is close to the world average.