Achieving renormalization-scale- and scheme-independence in Pade-related resummation in QCD

Abstract

Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme parameter $c_2$ is eliminated by a variant of the method of the principle of minimal sensitivity. The subleading parameter $c_3$ in the approximant is then fixed in such a way that the correct known location of the leading infrared renormalon pole is reproduced. Thus, $beta$-functions which go beyond the last perturbatively calculated order in the observable are used. The $\beta$-functions in the approximant are quasianalytically continued by Pade approximants. Two aspects of nonperturbative physics are accounted for in the presented resummation: a mechanism of quasianalytic continuation from the weak- into the strong-coupling regime, and the (approximant-specific) contribution of the leading infrared renormalon. The case of the Bjorken polarized sum rule is considered as a specific example of how the method works.

14 pages, 2 eps-figures, revtex; presentation clearer and tightened; an inadvertently included obsolete curve in Fig.2 replaced by the new one; all numerical results and conclusions unchanged; to appear in Phys.Lett.B

References in corpus (1)

• Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions

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