RESUMMATION OF (BETA-0-ALPHA(S))(N) CORRECTIONS IN QCD - TECHNIQUES AND APPLICATIONS TO THE TAU-HADRONIC WIDTH AND THE HEAVY-QUARK POLE MASS

We propose to resum exactly any number of one-loop vacuum polarization insertions into the scale of the coupling of lowest order radiative corrections. This makes maximal use of the information contained in one-loop perturbative corrections combined with the one-loop running of the effective coupling and provides a natural extension of the familiar BLM scale-fixing prescription to all orders in the perturbation theory. It is suggested that the remaining radiative corrections should be reduced after resummation. In this paper we implement this resummation by a dispersion technique and indicate a possible generalization to incorporate two-loop evolution. We investigate in some detail higher-order perturbative corrections to the tau-decay width and the pole mass of a heavy quark, We find that these corrections tend to reduce alpha(s)(m(tau)) determined from tau-decays by approximately 10% and increase the difference between the bottom pole and MS-renormalized mass by 30%.