IMPROVED EVALUATION OF THE NEXT-NEXT-TO-LEADING ORDER QCD CORRECTIONSTO E(-) ANNIHILATION INTO HADRONS()E()

The next-next-to-leading order QCD corrections to e(+)e(-) annihilatio n into hadrons are considered. The stability of the predictions with r espect to change of the renormalization scheme is discussed in detail for the case of five, four, and three active quark flavors. The analys is is based on the recently proposed condition for selecting renormali zation schemes according to the degree of cancellation that they intro duce in the expression for the scheme-invariant combination of the exp ansion coefficients. It is demonstrated that the scheme dependence amb iguity in the predictions obtained with the conventional expansion is substantial, particularly at lower energies. It is shown, however, tha t the stability of the predictions is greatly improved when QCD correc tions are evaluated in a more precise way, by utilizing the contour in tegral representation and calculating numerically the contour integral .