LARGE-ORDER PERTURBATION-THEORY FOR A PHYSICAL QUANTITY

We discuss renormalization scheme and normalization scale dependence of the order asymptotics of perturbative expansions due to renormalons based on an exact calculation of the Borel transform of the imaginary part of the electromagnetic current correlation function within an expansion in the number of fermions in quantum electrodynamics. Arguments are given that the leading uncertainty of perturbative series in quantum chromodynamics due to ultraviolet renormalons can be suppressed by an appropriate choice of normalization scale. Combining momentum analyticity with the Borel transformed renormalization-group equation, we relate the large-order behaviour of total cross sections to that of their polarization operator.