Applying generalized Padé approximants in analytic QCD models

Abstract

A method of resummation of truncated perturbation series, related to diagonal Padé approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in perturbative QCD. We now apply this method in analytic QCD models, i.e., models where the running coupling has no unphysical singularities, and we show that the method has attractive features such as a rapid convergence. The method can be regarded as a generalization of the scale-setting methods of Stevenson, Grunberg, and Brodsky-Lepage-Mackenzie. The method involves the fixing of various scales and weight coefficients via an auxiliary construction of diagonal Padé approximant. In low-energy QCD observables, some of these scales become sometimes low at high order, which prevents the method from being effective in perturbative QCD where the coupling has unphysical singularities at low spacelike momenta. There are no such problems in analytic QCD.

14 pages; extended presentation of the analytic QCD models in Sec.IV; two references added ([37,38]); version to appear in Phys.Rev.D

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• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• Explicit solutions for effective four- and five-loop QCD running coupling
• Lattice-motivated holomorphic nearly perturbative QCD
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD
• Evaluations of low-energy physical quantities in QCD with IR freezing of the coupling
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form
• Self-similar interpolation in high-energy physics