Analytic Perturbation Theory for Practitioners and Upsilon Decay

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1–100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of $\mathrm{{\rm Y}}(1\mathrm{S})$ decay where the standard analysis gives ${\alpha }_s(M_{\mathrm{{\rm Y}}})=0.170\pm 0.004$ value that is inconsistent with the bulk of data for ${\alpha }_s$. Instead, we obtain ${\alpha }_s^{Mod}(M_{\mathrm{{\rm Y}}})=0.185\pm 0.005$ that corresponds to ${\alpha }_s^{Mod}(M_Z)=0.120\pm 0.002$ that is close to the world average.\par The issue of scale uncertainty for $\mathrm{{\rm Y}}$ decay is also discussed.