A STUDY OF ULTRAVIOLET RENORMALON AMBIGUITIES IN THE DETERMINATION OFALPHA(S) FROM TAU-DECAY

The divergent large-order behaviour of the perturbative series relevan t for the determination of alpha(S) from tau decay is controlled by th e leading ultraviolet (UV) renormalon. Even in the absence of the firs t infrared (IR) renormalon, an ambiguity of order Lambda(2)/m(t)(2) is introduced. We make a quantitative study of the practical implication s of this ambiguity. We discuss the magnitude of UV renormalon correct ions obtained in the large-N-f limit, which, although unrealistic, is nevertheless interesting to some extent. We then study a number of imp roved approximants for the perturbative series, based on a change of v ariable in the Borel representation, such as to displace the leading U V renormalon singularity at a larger distance from the origin than the first IR renormalon. The spread of the resulting values of alpha(S)(m (tau)(2)) obtained by different approximants, at different renormaliza tion 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 compu ted coefficients, the size of alpha(S)(m(tau)(2)) and what is known of the asymptotic properties of the series. Our conclusion is that a rea listic estimate of the theoretical error cannot go below delta alpha(S )(m(tau)(2)) similar to +/- 0.060, or delta alpha(S)(m(Z)(2)) similar to +/- 0.006.