Explicit expressions for Euclidean and Minkowskian QCD observables in analytic perturbation theory

2001/04/30 by D. S. Kourashev, B. A. Magradze
Physics and Astronomy · #hep-ph

paper · pdf

published as Theoretical and Mathematical Physics, Vol. 135 (1) p.p. 531-540 (2003): Translated from Teor. Mat. Fiz. Vol. 135 No 1 p.p. 95-106.(2003). · 17 pages, Latex, 6 tables, Eq.(31) has been corrected

arxiv created 2001/11/10 · arxiv updated 2009/11/30

Abstract

Technical aspects of the Shirkov-Solovtsov's analytic perturbation theory (APT) are considered. We construct explicitly two sets of specific functions, \mathfrakA_n(s) and \cal A_n(Q²) that determine the nonpower as ymptotic expansions for Minkowskian and Euclidean QCD observables in APT. The results, up to third order, are written in terms of the Lambert W-functions. As an input we used the exact two loop and the three loop (corresponding to Padé transformed be ta-function) RG solutions for common invariant coupling α_s. In addition, the exact three-loop coupling is expanded in powers of the exact two-loop solution. The excellent accuracy is achieved with few terms of this series. We derive order by order elegant systems of equations for both sets of the functions. Then we construct the global versions of the APT functions with quark thresholds in the MS scheme and give numerical results.

Related

• QCD coupling up to third order in standard and analytic perturbation theories
• Analytic Perturbation Theory for QCD observables
• Analytic Perturbation Theory and New Analysis of some QCD observables
• Practical techniques of analytic perturbation theory of QCD
• Fractional APT in QCD in the Euclidean and Minkowski regions