RENORMALIZATION-SCHEME DEPENDENCE OF PADE SUMMATION IN QCD

We study the renormalization-scheme (RS) dependence of Pade approximan ts (PA's), and compare them with the principle of minimal sensitivity (PMS) and the effective charge (ECH) approaches. Although the formulas provided by the PA, PMS, and ECH predictions for higher-order terms i n a QCD perturbation expansion differ in general, their predictions ca n be very close numerically for a wide range of renormalization scheme s. Using the Bjorkem sum rule as a test case, we find that Pade summat ion (PS) reduces drastically the RS dependence of the Bjorken effectiv e charge. We use these results to estimate the theoretical error due t o the choice of RS in the extraction of alpha(s) from the Bjorken sum rule, and use the available data at Q2 = 3 GeV2 to estimate alpha(s) ( M(Z)) = 0.117(-0.007)(+0.004)+/-0.002, where the first error is experi mental and the second is theoretical.