Geodesic
Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 95-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Explicit {Expressions} for {Timelike} and {Spacelike} {Observables} of {Quantum} {Chromodynamics} in {Analytic} {Perturbation} {Theory}},
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D. S. Kurashev; B. A. Magradze. Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 135 (2003) no. 1, pp. 95-106. http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a4/

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