PERTURBATIVE RELATIONS BETWEEN E(-) ANNIHILATION AND TAU-DECAY OBSERVABLES INCLUDING RESUMMATION EFFECTS()E()

By exploiting the analyticity properties of the two-point current-curr ent correlator we obtain numerical predictions for the e(+)e(-) moment s in terms of the tau decay rate. We perform a partial resummation of the pertinent perturbative series expansion by solving the renormaliza tion group equation for Adler's function, Our predictions are renormal ization scheme independent but depend on the order of the perturbative beta-function expansion. The analysis involves the unknown five-loop coefficient k(3) for which we give some new estimates. (C) 1997 Elsevi er Science B.V.