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TMF, 2001, Volume 127, Number 1, Pages 3–20 (Mi tmf445)  

This article is cited in 56 scientific papers (total in 56 papers)

Analytic Perturbation Theory for QCD Observables

D. V. Shirkov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: We investigate the connection between ghost-free formulations of the RG-invariant QCD perturbation theory in the spacelike and timelike regions. Our basic tool is the “double spectral representation”, similar to the representation for the Adler function, which stems from the first principles of local QFT and relates real functions in the Euclidean and Minkowskian (i.e., timelike) regions. On this base, we establish a simple relation between the approach (known from the early 1980s) of resumming the $\pi^2$ terms for the invariant coupling function $\tilde\alpha(s)$ and QCD observables in the timelike region and the invariant analytic approach (devised a few years ago) leading to the “analyticized” coupling function $\alpha_{an}(Q^2)$ and nonpower expansion for observables in the spacelike domain. The function $\alpha_{an}(Q^2)$ and the expansion are free of unphysical singularities. The formulated self-consistent scheme, analytic perturbation theory (APT), relates renorm-invariant, effective coupling functions $\alpha_{an}(Q^2)$ and $\tilde\alpha(s)$, as well as nonpower perturbation expansions for observables in the Euclidean and Minkowskian domains, free of extra singularities and with better convergence in the infrared region. We present a global generalization of the new APT scheme in the case of real QCD, including the domain with various numbers of active quarks. Preliminary estimates indicate that calculations in the framework of the global scheme can produce results quite different from the usual ones for $\bar\alpha_{s}$ , even in the five-quark region. Numerical examples are given.


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Theoretical and Mathematical Physics, 2001, 127:1, 409–423

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Received: 22.11.2000

Citation: D. V. Shirkov, “Analytic Perturbation Theory for QCD Observables”, TMF, 127:1 (2001), 3–20; Theoret. and Math. Phys., 127:1 (2001), 409–423

Citation in format AMSBIB
\by D.~V.~Shirkov
\paper Analytic Perturbation Theory for QCD Observables
\jour TMF
\yr 2001
\vol 127
\issue 1
\pages 3--20
\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 1
\pages 409--423

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    This publication is cited in the following articles:
    1. Shirkov, DV, “Analytic perturbation theory in analyzing some QCD observables”, European Physical Journal C, 22:2 (2001), 331  crossref  zmath  adsnasa  isi  scopus  scopus
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    3. D. V. Shirkov, “Behavior of the Effective QCD Coupling in the Infrared Region”, Theoret. and Math. Phys., 132:3 (2002), 1309–1319  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Milton, KA, “Perturbative expansions in the inclusive decay of the tau-lepton”, International Journal of Modern Physics A, 17:26 (2002), 3789  crossref  zmath  adsnasa  isi  scopus  scopus
    5. Caprini, I, “Analytic continuation and perturbative expansions in QCD”, European Physical Journal C, 24:1 (2002), 127  crossref  zmath  adsnasa  isi  scopus  scopus
    6. Schrempp, F, “Tracking QCD-instantons”, Journal of Physics G-Nuclear and Particle Physics, 28:5 (2002), 915  crossref  adsnasa  isi  scopus  scopus
    7. Milton, KA, “Remark on the perturbative component of inclusive tau decay”, Physical Review D, 65:7 (2002), 076009  crossref  adsnasa  isi  scopus  scopus
    8. Phys. Usp., 45:5 (2002), 507–525  mathnet  crossref  crossref  isi
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    10. D. S. Kurashev, B. A. Magradze, “Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory”, Theoret. and Math. Phys., 135:1 (2003), 531–540  mathnet  crossref  crossref  zmath  isi
    11. D. V. Shirkov, “Fourier Transformation of the Renormalization-Invariant Coupling”, Theoret. and Math. Phys., 136:1 (2003), 893–907  mathnet  crossref  crossref  mathscinet  zmath  isi
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    13. Shirkov D.V., “Ghost-free APT analysis of perturbative QCD observables”, Particle Physics in the New Millennium, Lecture Notes in Physics, 616, 2003, 138–152  crossref  adsnasa  isi
    14. 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
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    18. Nesterenko, AV, “Massive analytic invariant charge in QCD”, Physical Review D, 71:1 (2005), 016009  crossref  adsnasa  isi  scopus  scopus
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    20. 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
    21. 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
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    23. 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
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    25. Stefanis, NG, “Pion form factor analysis using NLO analytic perturbation theory”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 245  crossref  adsnasa  isi  elib  scopus  scopus
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    27. 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
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    30. Nesterenko A.V., Papavassiliou J., “Impact of the pion mass on nonpower expansion for QCD observables”, Nuclear Phys B Proc Suppl, 164 (2007), 304–307  crossref  adsnasa  isi  elib  scopus  scopus
    31. Cvetic G, Valenzuela C, “Exponentially modified QCD coupling”, Physical Review D, 77:7 (2008), 074021  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    32. Cvetic, G, “Analytic QCD - a Short Review”, Brazilian Journal of Physics, 38:3B (2008), 371  adsnasa  isi
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