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This article is cited in 43 scientific papers (total in 43 papers)
Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory
D. S. Kurasheva, B. A. Magradzeb a 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
Citation:
D. S. Kurashev, B. A. Magradze, “Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory”, TMF, 135:1 (2003), 95–106; Theoret. and Math. Phys., 135:1 (2003), 531–540
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https://www.mathnet.ru/eng/tmf175https://doi.org/10.4213/tmf175 https://www.mathnet.ru/eng/tmf/v135/i1/p95
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