Global approximants with renormalization scale invariance in pQCD

Abstract

Truncated perturbative series (TPS's) of any observable have the unphysical dependence on the choice of the renormalization scale (RScl). The diagonal Padé approximants (dPA's) to any TPS of an observable possess the favorable property of being invariant in the large-${\beta }_0$ limit. This means that they are invariant under the change of the RScl ${\mu }^2$ when the ``running'' coupling parameter ${\alpha }_s({\mu }^2)$ evolves according to the one-loop renormalization group equation. We present a method which generalizes this result -- the resulting new approximants are fully RScl-invariant in the perturbative QCD (pQCD). Further, we present some numerical examples. Both the dPA's and the new approximants are global, i.e., their structure goes beyond the usual (polynomial) TPS form and thus they could reveal some non-perturbative effects.

LaTeX, 4 pages; based on an invited talk at QCD'98, Montpellier, France, July 1998; appears in Nucl.Phys.Proc.Suppl

References in corpus (6)

• The four-loop beta-function in Quantum Chromodynamics
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• Estimations of Order alpha_s^3 and alpha_s^4 Corrections to Mass-Dependent Observables
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Renormalization-scale-invariant continuation of truncated QCD (QED) series -- an analysis beyond large-beta_0 approximation
• Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants

Cited by in corpus (9)

• Renormalon-motivated evaluation of QCD observables
• Resummation of the hadronic tau decay width with the modified Borel transform method
• Applying generalized Padé approximants in analytic QCD models
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Resummations of free energy at high temperature
• Achieving renormalization-scale- and scheme-independence in Pade-related resummation in QCD
• Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms
• Method for comparing finite temperature field theory results with lattice data
• Spiral Multi-component Structure in Pade - Approximant QCD