1995/09/17 by John Ellis, Einan Gardi, Marek Karliner +1 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Mathematical functions and polynomials #Padé approximant #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Perturbative QCD #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Series (stratigraphy) #Sum rule in quantum mechanics #hep-ph
paper · pdf · doi:10.1016/0370-2693(95)01326-1
published as Phys.Lett.B366:268-275,1996 · 13 pages (latex) + 4 ps figures uuencoded in a self-unpacking file
arxiv created 1995/09/17 · openalex publication_date 1996/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove that Pade approximants yield increasingly accurate predictions of higher-order coefficients in QCD perturbation series whose high-order behaviour is governed by a renormalon. We also prove that this convergence is accelerated if the perturbative series is Borel transformed. We apply Pade approximants and Borel transforms to the known perturbative coefficients for the Bjorken sum rule. The Pade approximants reduce considerably the renormalization-scale dependence of the perturbative correction to the Bjorken sum rule. We argue that the known perturbative series is already dominated by an infra-red renormalon, whose residue we extract and compare with QCD sum-rule estimates of higher-twist effects. We use the experimental data on the Bjorken sum rule to extract αs(MZ2) = 0.116-0.006+0.004, including theoretical errors due to the finite order of available perturbative QCD calculations, renormalization-scale dependence and higher-twist effects.