RESUMMATION OF PERTURBATIVE QCD BY PADE APPROXIMANTS

In this lecture I present some of the new developments concerning: the use of Padi: Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale an d scheme dependence as compared tb truncated series. In particular it is proven that in the limit where the beta function is dominated by th e 1-loop contribution, there is an exact symmetry that guarantees inva riance of diagonal PA's under changing the renormalization scale. In a ddition it is shown that in the large beta(0) approximation diagonal P A's call be interpreted as a systematic method for approximating the f low of momentum in Feynman diagrams. This corresponds to a new multipl e scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function.