IMPROVED PREDICTIONS FOR QCD EFFECTS IN E(-) ANNIHILATION()E()

The three-loop QCD correction to the Re+e- ratio is discussed. It is p ointed out that the three-loop coefficient is dominated by the term pr oportional to pi(2), which appears as a result of analytic continuatio n from spacelike, to timelike momenta. The possibility of all-order re summation of some of the large contributions of this type is considere d. It is demonstrated that the resummed predictions are much less sens itive to the change of the renormalization scheme than the predictions obtained with the conventional expansion. Also the difference between two-loop and three-loop results is significantly reduced. Similar rem arks are shown to apply in the case of QCD correction to Gamma(Z)(had) .