Scale- and scheme-independent extension of Padé approximants: Bjorken polarized sum rule as an example

A renormalization-scale-invariant generalization of the diagonal Pade approximants (DPA), developed previously, is extended so that it becomes renormalization-scheme invariant as well. We do this explicitly when two terms beyond the leading order (NNLO, similar to alpha (3)(s)) are known in the truncated perturbation series (TPS). At first, the scheme dependence shows up as a dependence on the first two scheme parameters c(2) and c(3). Invariance under the change of the leading parameter ct is achieved via a variant of the principle of minimal sensitivity. The subleading parameter c(3) is fixed so that a scale- and scheme-invariant Borel transform of the resummation approximant gives the correct location of the leading infrared renormalon pole. The leading higher-twist contribution, or a part of it, is thus believed to be contained implicitly in the resummation. We applied the approximant to the Bjorken polarized sum rule (BPSR) at Q(ph)(2) = 5 and 3 GeV2, for the most recent data and the data available until 1997, respectively, and obtained alpha (s)(MS) over bar (M-Z(2)) = 0.119(-0.006)(+0.003) and 0.113(-0.019)(+0.004), respectively. Very similar results are obtained with Grunberg's effective charge method and Stevenson's TPS principle of minimal sensitivity, if we fix the c(3) parameter in them by the aforementioned procedure. The central values for alpha (s)(MS) over bar (M-Z(2)) increase to 0.120 (0.114) when applying DPA's, and 0.125 (0.118) when applying NNLO TPS.