Renormalization-scale-invariant continuation of truncated QCD (QED) series -- an analysis beyond large-beta_0 approximation

Abstract

An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker-Gammel approximants, and is independent of the renormalization scale (RScl) $\mu$ -- the coupling parameter $\alpha (\mu )$ in the series and in the resulting approximants can evolve according to the perturbative renormalization group equation (RGE) to any chosen loop order. The proposed algorithm is a natural generalization of the recently proposed method of diagonal Padé approximants, the latter making the result RScl-invariant in large-${\beta }_0$ approximation for $\alpha (\mu )$. The algorithm described below can extract large amount of information from a calculated available truncated perturbative series for an observable, by implicitly resumming large classes of diagrams.

LaTeX (REVTeX), 15 pages, minor stylistic changes, version to appear in Nucl. Phys. B

References in corpus (7)

• The four-loop beta-function in Quantum Chromodynamics
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• On the role of power expansions in quantum field theory
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Asymptotic Padé Approximants and the SQCD $\beta$-function
• A Convergent Reformulation of QCD Perturbation Theory
• Direct Estimation of Sizes of Higher-Order Graphs

Cited by in corpus (20)

• Higher twists and ${\alpha }_s(M_Z)$ extractions from the NNLO QCD analysis of the CCFR data for $x{F}_3$ structure function
• Bilocal expansion of the Borel amplitude and the hadronic tau decay width
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• Operator Product Expansion with analytic QCD in tau decay physics
• Renormalon-motivated evaluation of QCD observables
• Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
• Resummation of the hadronic tau decay width with the modified Borel transform method
• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants
• Applying generalized Padé approximants in analytic QCD models
• Lattice-motivated holomorphic nearly perturbative QCD
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Resummations of free energy at high temperature
• Global approximants with renormalization scale invariance in pQCD
• Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms
• Evaluations of low-energy physical quantities in QCD with IR freezing of the coupling
• Method for comparing finite temperature field theory results with lattice data
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Self-similar interpolation in high-energy physics