Abstract
The calculation of perturbative corrections to the moments of the hadronic mass distribution in τ decays is reconsidered. The exact order-α s 3 results and the resummation procedure of Le Diberder and Pich are compared with a partial resummation of the perturbative series provided by the calculation of so-called renormalon chains. The perturbative analysis is complemented by a model-independent description of power corrections. For the contributions of dimension four and six in the OPE, it is demonstrated how the infrared renormalon ambiguities of perturbation theory can be absorbed by a redefinition of non-perturbative parameters. We find that previous determinations of QCD parameters from a measurement of spectral moments in τ decays have underestimated the theoretical uncertainties. Given the present control over the asymptotic behaviour of perturbation theory, the running coupling constant can be measured at best with a theoretical uncertainty δα s ( m 2) ≅ ±0.03, and the gluon condensate with an uncertainty of the order of its magnitude. Two weighted integrals of the hadronic spectrum are constructed, which can be used to test the absence of dimension-two operators and to measure the gluon condensate.
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