Abstract
We elaborate on the relation between perturbative and power-like correctionsto short-distance sensitive QCD observables. We confront theoreticalexpectations with explicit perturbative calculations existing in literature. Asis expected, the quadratic correction is dual to a long perturbative series andone should use one of them but not both. However, this might be true only forvery long perturbative series, with number of terms needed in most casesexceeding by far the number of terms available. What has not been foreseen isthat the quartic corrections might also be dual to the perturbative series. Wereview possible reasons for this emerging duality. We also observe anapproximate geometric growth of the perturbative series for differentobservables evaluated in the euclidean region, signaling a simple structure ofthe series in large orders. Some phenomenological applications are discussed.The emerging values of the running light quark masses at 2 GeV, frompseudoscalar, e+e- to hadrons and tau-decay sum rules and including thequadratic corrections are: (m_u+m_d)(2)=8.7(1.3) MeV and m_s(2) = 106.2(15.4)MeV, while the one of the QCD coupling from tau-decay is: alpha_s(M_Z)=0.1192(10). These results are comparable with existing estimates.