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

This article is cited in 40 scientific papers (total in 40 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

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

Full text: PDF file (251 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 135:1, 531–540

Bibliographic databases:

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

Citation in format AMSBIB
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\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}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    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  crossref  adsnasa  isi
    2. Howe DM, Maxwell CJ, “All-orders infrared freezing of observables in perturbative QCD”, Physical Review D, 70:1 (2004), 014002  crossref  mathscinet  adsnasa  isi
    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  mathnet  crossref  crossref  adsnasa  isi  elib
    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  crossref  adsnasa  isi  scopus  scopus
    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  crossref  adsnasa  isi  scopus  scopus
    6. Cvetic G, Valenzuela C, “Various versions of analytic QCD and skeleton-motivated evaluation of observables”, Physical Review D, 74:11 (2006), 114030  crossref  adsnasa  isi  elib  scopus  scopus
    7. Alekseev AI, “Synthetic running coupling of QCD”, Few-Body Systems, 40:1–2 (2006), 57–70  crossref  adsnasa  isi  scopus  scopus
    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  crossref  adsnasa  isi
    9. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387  crossref  adsnasa  isi  scopus  scopus
    10. Shirkov, D, “Nonpower expansions for QCD observables at low energies”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 51  crossref  adsnasa  isi  elib  scopus  scopus
    11. Magradze, BA, “A novel series solution to the renormalization-group equation in QCD”, Few-Body Systems, 40:1–2 (2006), 71  crossref  adsnasa  isi  scopus  scopus
    12. Shirkov D.V., “Analytic perturbation theory model for QCD and upsilon decay”, Nuclear Phys B Proc Suppl, 162 (2006), 33–38  crossref  adsnasa  isi  elib  scopus  scopus
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Baldicchi, M, “Bound-state approach to the QCD coupling constant at low-energy scales”, Physical Review Letters, 99:24 (2007), 242001  crossref  adsnasa  isi  elib  scopus  scopus
    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  crossref  adsnasa  isi  elib  scopus  scopus
    16. Shirkov, DV, “Analytic perturbation theory for QCD practitioners and upsilon decay”, Physics of Atomic Nuclei, 70:4 (2007), 775  crossref  adsnasa  isi  scopus  scopus
    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  crossref  adsnasa  isi  elib  scopus  scopus
    18. Cvetic G, Valenzuela C, “Exponentially modified QCD coupling”, Physical Review D, 77:7 (2008), 074021  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    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  crossref  adsnasa  isi  elib  scopus  scopus
    20. Cvetic, G, “Analytic QCD - a Short Review”, Brazilian Journal of Physics, 38:3B (2008), 371  adsnasa  isi
    21. Pasechnik, RS, “Bjorken sum rule and perturbative QCD frontier on the move”, Physical Review D, 78:7 (2008), 071902  crossref  adsnasa  isi  elib  scopus
    22. Bakulev, AP, “Global Fractional Analytic Perturbation Theory in QCD with Selected Applications”, Physics of Particles and Nuclei, 40:5 (2009), 715  crossref  adsnasa  isi  scopus  scopus
    23. Pasechnik, RS, “Nucleon spin structure and perturbative QCD frontier on the move”, Physical Review D, 81:1 (2010), 016010  crossref  adsnasa  isi  elib  scopus  scopus
    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  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    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  crossref  zmath  isi  scopus  scopus
    26. Magradze B.A., “Testing the Concept of Quark-Hadron Duality with the ALEPH tau Decay Data”, Few Body Systems, 48:2–4 (2010), 143–169  crossref  adsnasa  isi  elib  scopus  scopus
    27. Contreras C., Cvetic G., Espinosa O., Martinez H.E., “Simple analytic QCD model with perturbative QCD behavior at high momenta”, Phys Rev D, 82:7 (2010), 074005  crossref  adsnasa  isi  elib  scopus  scopus
    28. Cvetic G., Villavicencio C., “Operator Product Expansion with Analytic QCD in Tau Decay Physics”, Phys. Rev. D, 86:11 (2012), 116001  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    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  crossref  adsnasa  isi  elib  scopus  scopus
    30. Cvetic G. Kotikov A.V., “Analogs of Noninteger Powers in General Analytic QCD”, J. Phys. G-Nucl. Part. Phys., 39:6 (2012), 065005  crossref  adsnasa  isi  elib  scopus  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    32. Ayala C., Cvetic G., “Calculation of Binding Energies and Masses of Quarkonia in Analytic QCD Models”, Phys. Rev. D, 87:5 (2013), 054008  crossref  adsnasa  isi  elib  scopus  scopus
    33. Cvetic G., “Evaluations of Low-Energy Physical Quantities in QCD With Ir Freezing of the Coupling”, Few-Body Syst., 55:5-7 (2014), 567–577  crossref  adsnasa  isi  scopus  scopus
    34. Allendes P., Ayala C., Cvetic G., “Gluon Propagator in Fractional Analytic Perturbation Theory”, Phys. Rev. D, 89:5 (2014), 054016  crossref  adsnasa  isi  scopus  scopus
    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  crossref  adsnasa  isi  scopus  scopus
    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  crossref  isi  scopus  scopus
    37. Ayala C., Cvetic G., “anQCD: A Mathematica package for calculations in general analytic QCD models”, Comput. Phys. Commun., 190 (2015), 182–199  crossref  isi  scopus  scopus
    38. Deur A. Brodsky S.J. de Teramond G.F., “The QCD running coupling”, Prog. Part. Nucl. Phys., 90 (2016), 1–74  crossref  mathscinet  isi  elib  scopus
    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  isi
    40. Ayala C., Cvetic G., Kotikov A.V., Shaikhatdenov B.G., “Bjorken Sum Rule in QCD Frameworks With Analytic (Holomorphic) Coupling”, Int. J. Mod. Phys. A, 33:18-19 (2018), 1850112  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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