PADE APPROXIMANTS, OPTIMAL RENORMALIZATION SCALES, AND MOMENTUM FLOW IN FEYNMAN DIAGRAMS

We show that the Pade approximant (PA) approach for resummation of per turbative series in QCD provides a systematic method for approximating the flow of momentum in Feynman diagrams. In the large-beta(0) limit, diagonal PA's generalize the Brodsky-Lepage-Mackenzie (BLM) scale-set ting method to higher orders in a renormalization scale- and scheme-in variant manner, using multiple scales that represent Neubert's concept of the distribution of momentum flow through a virtual gluon. If the distribution is non-negative, the PA's have only real roots, and appro ximate the distribution function by a sum of delta functions, whose lo cations and weights are identical to the optimal choice provided by th e Gaussian quadrature method for numerical integration. We show how th e first few coefficients in a perturbative series can set rigorous bou nds on the all-order momentum distribution function, if it is positive . We illustrate the method with the vacuum polarization function and t he Bjorken sum rule computed in the large-beta(0) limit. [S0556-2821(9 7)03323-7].