This article is cited in 43 papers

Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory

D. S. Kurashev^a, B. A. Magradze<sup>b

a</sup> M. V. Lomonosov Moscow State University
^b A. Razmadze Mathematical Institute, Georgian Academy of Sciences

Abstract: We study the possibility of expressing the invariant QCD coupling function (i.e., the effective coupling constant) in an explicit analytic form in two- and three-loop approximations as well as in the case of the Padé-transformed $\beta$-function. Both the timelike and spacelike domains are investigated. Technical aspects of the Shirkov–Solovtsov analytic perturbation theory are considered. Explicit expressions for the two- and three-loop effective coupling functions in the timelike domain are obtained. In the last case, we apply a new method of expanding functions represented in an arbitrary loop order of perturbation theory in powers of the two-loop function. The comparison with numerical data in the infrared region shows that the obtained explicit expressions for the three-loop functions agree fully with the exact numerical results.

Keywords: quantum chromodynamics, perturbation theory, renormalization group equation, running coupling constant, renormalization schemes.

Received: 25.01.2002
Revised: 03.07.2002

DOI: 10.4213/tmf175

 English version: Theoretical and Mathematical Physics, 2003, 135:1, 531–540

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