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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2003_135_1_a4,
     author = {D. S. Kurashev and B. A. Magradze},
     title = {Explicit {Expressions} for {Timelike} and {Spacelike} {Observables} of {Quantum} {Chromodynamics} in {Analytic} {Perturbation} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {135},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a4/}
}
TY  - JOUR
AU  - D. S. Kurashev
AU  - B. A. Magradze
TI  - Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 95
EP  - 106
VL  - 135
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a4/
LA  - ru
ID  - TMF_2003_135_1_a4
ER  - 
%0 Journal Article
%A D. S. Kurashev
%A B. A. Magradze
%T Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 95-106
%V 135
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2003_135_1_a4/
%G ru
%F TMF_2003_135_1_a4
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/