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 TMF, 2003, Volume 135, Number 1, Pages 95–106 (Mi tmf175)

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

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

DOI: https://doi.org/10.4213/tmf175

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

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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

Citation in format AMSBIB
\Bibitem{KurMag03} \by D.~S.~Kurashev, B.~A.~Magradze \paper Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory \jour TMF \yr 2003 \vol 135 \issue 1 \pages 95--106 \mathnet{http://mi.mathnet.ru/tmf175} \crossref{https://doi.org/10.4213/tmf175} \zmath{https://zbmath.org/?q=an:1178.78013} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 135 \issue 1 \pages 531--540 \crossref{https://doi.org/10.1023/A:1023287519892} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183054500005} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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1. Bakulev AP, Passek-Kumericki K, Schroers W, et al, “Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory”, Physical Review D, 70:3 (2004), 033014
2. Howe DM, Maxwell CJ, “All-orders infrared freezing of observables in perturbative QCD”, Physical Review D, 70:1 (2004), 014002
3. A. I. Alekseev, “Analytic Invariant Charge in QCD with Suppression of Nonperturbative Contributions at Large $Q^2$”, Theoret. and Math. Phys., 145:2 (2005), 1559–1575
4. Bakulev AP, Mikhailov SV, Stefanis NG, “QCD analytic perturbation theory: From integer powers to any power of the running coupling”, Physical Review D, 72:7 (2005), 074014
5. Bakulev AP, Karanikas AI, Stefanis NG, “Analyticity properties of three-point functions in QCD beyond leading order”, Physical Review D, 72:7 (2005), 074015
6. Cvetic G, Valenzuela C, “Various versions of analytic QCD and skeleton-motivated evaluation of observables”, Physical Review D, 74:11 (2006), 114030
7. Alekseev AI, “Synthetic running coupling of QCD”, Few-Body Systems, 40:1–2 (2006), 57–70
8. Cvetic G, Valenzuela C, “An approach for the evaluation of observables in analytic versions of QCD”, Journal of Physics G-Nuclear and Particle Physics, 32:6 (2006), L27–L35
9. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387
10. Shirkov, D, “Nonpower expansions for QCD observables at low energies”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 51
11. Magradze, BA, “A novel series solution to the renormalization-group equation in QCD”, Few-Body Systems, 40:1–2 (2006), 71
12. Shirkov D.V., “Analytic perturbation theory model for QCD and upsilon decay”, Nuclear Phys B Proc Suppl, 162 (2006), 33–38
13. D. V. Shirkov, I. L. Solovtsov, “Ten years of the analytic perturbation theory in QCD”, Theoret. and Math. Phys., 150:1 (2007), 132–152
14. Baldicchi, M, “Bound-state approach to the QCD coupling constant at low-energy scales”, Physical Review Letters, 99:24 (2007), 242001
15. Bakulev, AP, “Fractional analytic perturbation theory in Minkowski space and application to Higgs boson decay into a bb(-) pair”, Physical Review D, 75:5 (2007), 056005
16. Shirkov, DV, “Analytic perturbation theory for QCD practitioners and upsilon decay”, Physics of Atomic Nuclei, 70:4 (2007), 775
17. Cvetic G., Valenzuela C., Schmidt I., “A modification of minimal analytic QCD at low energies”, Nuclear Phys B Proc Suppl, 164 (2007), 308–311
18. Cvetic G, Valenzuela C, “Exponentially modified QCD coupling”, Physical Review D, 77:7 (2008), 074021
19. Baldicchi M, Nesterenko AV, Prosperi GM, et al, “QCD coupling below 1 GeV from the quarkonium spectrum”, Physical Review D, 77:3 (2008), 034013
20. Cvetic, G, “Analytic QCD - a Short Review”, Brazilian Journal of Physics, 38:3B (2008), 371
21. Pasechnik, RS, “Bjorken sum rule and perturbative QCD frontier on the move”, Physical Review D, 78:7 (2008), 071902
22. Bakulev, AP, “Global Fractional Analytic Perturbation Theory in QCD with Selected Applications”, Physics of Particles and Nuclei, 40:5 (2009), 715
23. Pasechnik, RS, “Nucleon spin structure and perturbative QCD frontier on the move”, Physical Review D, 81:1 (2010), 016010
24. Cvetic G., Koegerler R., Valenzuela C., “Reconciling the analytic QCD with the ITEP operator product expansion philosophy”, Phys Rev D, 82:11 (2010), 114004
25. Bakulev A.P., Mikhailov S.V., Stefanis N.G., “Higher-order QCD perturbation theory in different schemes: from FOPT to CIPT to FAPT”, Journal of High Energy Physics, 2010, no. 6, 085
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28. Cvetic G., Villavicencio C., “Operator Product Expansion with Analytic QCD in Tau Decay Physics”, Phys. Rev. D, 86:11 (2012), 116001
29. Ayala C., Contreras C., Cvetic G., “Extended Analytic QCD Model with Perturbative QCD Behavior at High Momenta”, Phys. Rev. D, 85:11 (2012), 114043
30. Cvetic G. Kotikov A.V., “Analogs of Noninteger Powers in General Analytic QCD”, J. Phys. G-Nucl. Part. Phys., 39:6 (2012), 065005
31. Bakulev A.P., Khandramai V.L., “Fapt: a Mathematica Package for Calculations in QCD Fractional Analytic Perturbation Theory”, Comput. Phys. Commun., 184:1 (2013), 183–193
32. Ayala C., Cvetic G., “Calculation of Binding Energies and Masses of Quarkonia in Analytic QCD Models”, Phys. Rev. D, 87:5 (2013), 054008
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34. Allendes P., Ayala C., Cvetic G., “Gluon Propagator in Fractional Analytic Perturbation Theory”, Phys. Rev. D, 89:5 (2014), 054016
35. Cvetic G., “Techniques of Evaluation of QCD Low-Energy Physical Quantities With Running Coupling With Infrared Fixed Point”, Phys. Rev. D, 89:3 (2014), 036003
36. Khandramai V., “On Applications of Mathematica Package “Fapt” in QCD”, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Journal of Physics Conference Series, 523, IOP Publishing Ltd, 2014, 012062
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38. Deur A. Brodsky S.J. de Teramond G.F., “The QCD running coupling”, Prog. Part. Nucl. Phys., 90 (2016), 1–74
39. Nesterenko A., “Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach”, Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach, Elsevier Science BV, 2017, 1–204
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