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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.

DOI: https://doi.org/10.4213/tmf445

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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
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\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 1
\pages 409--423
\crossref{https://doi.org/10.1023/A:1010302206227}
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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. Shirkov, DV, “Analytic perturbation theory in analyzing some QCD observables”, European Physical Journal C, 22:2 (2001), 331  crossref  zmath  adsnasa  isi  scopus  scopus
    2. Cvetic G., Dib C., Lee T., Schmidt I., “Resummation of the hadronic tau decay width with the modified Borel transform method”, Physical Review D, 64:9 (2001), 093016  crossref  mathscinet  adsnasa  isi  scopus  scopus
    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
    9. O. P. Solovtsova, “Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay”, Theoret. and Math. Phys., 134:3 (2003), 365–376  mathnet  crossref  crossref  isi
    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
    12. Stefanis N.G., “Perturbative logarithms and power corrections in QCD hadronic functions. A unifying approach”, Particle Physics in the New Millennium, Lecture Notes in Physics, 616, 2003, 153–166  crossref  adsnasa  isi
    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
    15. 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
    16. 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
    17. Bakulev, AP, “The pion form factor in QCD in NLO analytic perturbation theory”, Physics of Particles and Nuclei, 36 (2005), S164  isi
    18. Nesterenko, AV, “Massive analytic invariant charge in QCD”, Physical Review D, 71:1 (2005), 016009  crossref  adsnasa  isi  scopus  scopus
    19. Bakulev A.P., “Pion distribution amplitude - from theory to data”, Quark Confinement and the Hadron Spectrum VI, AIP Conference Proceedings, 756, 2005, 342–344  crossref  adsnasa  isi  elib  scopus  scopus
    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
    22. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387  crossref  adsnasa  isi  scopus  scopus
    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
    24. Shirkov, D, “Nonpower expansions for QCD observables at low energies”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 51  crossref  adsnasa  isi  elib  scopus  scopus
    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
    26. 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
    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
    28. 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
    29. Shirkov, DV, “Analytic perturbation theory for QCD practitioners and upsilon decay”, Physics of Atomic Nuclei, 70:4 (2007), 775  crossref  adsnasa  isi  scopus  scopus
    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
    33. Pasechnik, RS, “Bjorken sum rule and perturbative QCD frontier on the move”, Physical Review D, 78:7 (2008), 071902  crossref  adsnasa  isi  elib  scopus  scopus
    34. Baikov, PA, “Order alpha(4)(s) QCD corrections to Z and tau decays”, Physical Review Letters, 101:1 (2008), 012002  crossref  adsnasa  isi  elib  scopus  scopus
    35. Shirkov D.V., “Large Regular QCD Coupling At Low Energy?”, Quantum Field Theory and Beyond - Essays in Honor of Wolfhart Zimmermann, 2008, 34–45  crossref  mathscinet  zmath  adsnasa  isi
    36. Cvetic, G, “Rational approximations in analytic QCD”, Journal of Physics G-Nuclear and Particle Physics, 36:12 (2009), 125006  crossref  mathscinet  adsnasa  isi  scopus  scopus
    37. 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
    38. 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
    39. 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
    40. 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
    41. Kim V.T., “Higgs boson decay into heavy quarks and heavy leptons: higher order corrections”, Nuclear Phys B Proc Suppl, 198 (2010), 223–227  crossref  adsnasa  isi  scopus  scopus
    42. Cvetic G., Koegerler R., “Applying generalized Pade approximants in analytic QCD models”, Phys Rev D, 84:5 (2011), 056005  crossref  adsnasa  isi  elib  scopus  scopus
    43. 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
    44. 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
    45. 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
    46. Wu X.-G. Brodsky S.J. Mojaza M., “The Renormalization Scale-Setting Problem in QCD”, Prog. Part. Nucl. Phys., 72 (2013), 44–98  crossref  adsnasa  isi  elib  scopus  scopus
    47. 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
    48. Mirjalili A. Khellat M.R., “Higher-Order Prediction Terms and Fixing the Renormalization Scale Using the Blm Approach”, Int. J. Mod. Phys. A, 29:31 (2014), 1450178  crossref  zmath  adsnasa  isi  scopus  scopus
    49. 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
    50. 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
    51. Ayala C. Cvetic G. Koegerler R., “Lattice-Motivated Holomorphic Nearly Perturbative QCD”, J. Phys. G-Nucl. Part. Phys., 44:7 (2017), 075001  crossref  isi  scopus  scopus
    52. Khellat M.R. Mirjalili A., “Deviation Pattern Approach For Optimizing Perturbative Terms of QCD Renormalization Group Invariant Observables”, Xxiii International Baldin Seminar on High Energy Physics Problems Relativistic Nuclear Physics and Quantum Chromodynamics (Baldin Ishepp Xxiii), Epj Web of Conferences, 138, ed. Bondarenko S. Burov V. Malakhov A., E D P Sciences, 2017, UNSP 02004  crossref  isi  scopus  scopus
    53. Ayala C. Cvetic G. Koegerler R. Kondrashuk I., “Nearly Perturbative Lattice-Motivated QCD Coupling With Zero Ir Limit”, J. Phys. G-Nucl. Part. Phys., 45:3 (2018), 035001  crossref  isi  scopus  scopus
    54. Ayala C., Cvetic G., Kotikov A.V., Shaikhatdenov B.G., “Bjorken Sum Rule in QCD With Analytic Coupling”, Xvii Workshop on High Energy Spin Physics (Dspin-2017), Journal of Physics Conference Series, 938, IOP Publishing Ltd, 2018, UNSP 012055  crossref  mathscinet  isi  scopus  scopus
    55. 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
    56. Ayala C. Cvetic G. Kotikov A.V. Shaikhatdenov B.G., “Bjorken Polarized Sum Rule and Infrared-Safe Qcd Couplings”, Eur. Phys. J. C, 78:12 (2018), 1002  crossref  isi  scopus
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