Improved predictions for QCD effects in e(+)e(-) annihilation

The three-loop QCD correction to the Re+e- ratio is discussed. It is pointed out that the three-loop coefficient is dominated by the term proportional to pi(2), which appears as a result of analytic continuation from spacelike, to timelike momenta. The possibility of all-order resummation of some of the large contributions of this type is considered. It is demonstrated that the resummed predictions are much less sensitive 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 remarks are shown to apply in the case of QCD correction to Gamma(Z)(had).