Ultraviolet Renormalon Ambiguities in the Determination of α S from τ Decay

The divergent large-order behaviour of the perturbative series relevant for the determination of α S from τ decay is controlled by the leading ultraviolet (UV) renormalon. Even in the absence of the first infrared (IR) renormalon, an ambiguity of order Λ 2 /m 2 τ is introduced. We make a quantitative study of the practical implications of this ambiguity. We discuss the magnitude of UV renor-malon corrections obtained in the large-N f limit, which, although unrealistic, is nevertheless interesting to some extent. We then study a number of improved approximants for the perturbative series, based on a change of variable in the Borel representation, such as to displace the leading UV renormalon singularity at a larger distance from the origin than the first IR renormalon. The spread of the resulting values of α S (m 2 τ) obtained by different approximants, at different renormalization scales, is exhibited as a measure of the underlying ambiguities. Finally, on the basis of mathematical models, we discuss the prospects of an actual improvement, given the signs and magnitudes of the computed coefficients , the size of α S (m 2 τ) and what is known of the asymptotic properties of the series. Our conclusion is that a realistic estimate of the theoretical error cannot go below δα S (m 2 τ) ∼ ±0.060, or δα S (m 2 Z) ∼ ±0.006.