PADE APPROXIMANTS, BOREL TRANSFORMS AND RENORMALONS - THE BJORKEN SUM-RULE AS A CASE-STUDY

We prove that Pade approximants yield increasingly accurate prediction s of higher-order coefficients in QCD perturbation series whose high-o rder behaviour is governed by a renormalon. We also prove that this co nvergence is accelerated if the perturbative series is Borel transform ed. We apply Pade approximants and Borel transforms to the known pertu rbative coefficients for the Bjorken sum rule. The Pade approximants r educe considerably the renormalization-scale dependence of the perturb ative correction to the Bjorken sum rule. We argue that the known pert urbative series is already dominated by an infra-red renormalon, whose residue we extract and compare with QCD sum-rule estimates of higher- twist effects. We use the experimental data on the Bjorken sum rule to extract alpha(r)(M(Z)(2)) = 0.116(-0.006)(+0.004) including theoretic al errors due to the finite order of available perturbative QCD calcul ations, renormalization-scale dependence and higher-twist effects.