Skip to main content
SpringerLink
Log in

Higher-order QCD perturbation theory in different schemes: from FOPT to CIPT to FAPT

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Results on the resummation of non-power-series expansions of the Adler function of a scalar, D S , and a vector, D V , correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width \( {\Gamma_{H \to b\overline b }} \) of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the e + e − annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of R S and D V using oneand two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.V. Shirkov and I.L. Solovtsov, Analytic model for the QCD running coupling with universal \( {\overline \alpha_s}(0) \) value, Phys. Rev. Lett. 79 (1997) 1209 [hep-ph/9704333] [SPIRES].

    Article  ADS  Google Scholar 

  2. A.V. Radyushkin, Optimized Λ - parametrization for the QCD running coupling constant in space - like and time - like regions, JINR Rapid Commun. 78 (1996) 96 [hep-ph/9907228] [SPIRES].

    Google Scholar 

  3. N.V. Krasnikov and A.A. Pivovarov, The influence of the analytical continuation effects on the value of the QCD scale parameter Λ extracted from the data on charmonium and upsilon hadron decays, Phys. Lett. B 116 (1982) 168 [SPIRES].

    ADS  Google Scholar 

  4. K.A. Milton and I.L. Solovtsov, Analytic perturbation theory in QCD and Schwinger’s connection between the β-function and the spectral density, Phys. Rev. D 55 (1997) 5295 [hep-ph/9611438] [SPIRES].

    ADS  Google Scholar 

  5. K.A. Milton and O.P. Solovtsova, Analytic perturbation theory: A new approach to the analytic continuation of the strong coupling constant α s into the timelike region, Phys. Rev. D 57 (1998) 5402 [hep-ph/9710316] [SPIRES].

    ADS  Google Scholar 

  6. I.L. Solovtsov and D.V. Shirkov, Analytic approach to perturbative QCD and renormalization scheme dependence, Phys. Lett. B 442 (1998) 344 [hep-ph/9711251] [SPIRES].

    ADS  Google Scholar 

  7. B.A. Magradze, Analytic approach to perturbative QCD, Int. J. Mod. Phys. A 15 (2000) 2715 [hep-ph/9911456] [SPIRES].

    ADS  Google Scholar 

  8. B.A. Magradze, QCD coupling up to third order in standard and analytic perturbation theories, hep-ph/0010070 [SPIRES].

  9. D.S. Kourashev and B.A. Magradze, Explicit expressions for Euclidean and Minkowskian QCD observables in analytic perturbation theory, hep-ph/0104142 [SPIRES].

  10. B.A. Magradze, Practical techniques of analytic perturbation theory of QCD, hep-ph/0305020 [SPIRES].

  11. D.S. Kurashev and B.A. Magradze, Explicit expressions for timelike and spacelike observables of quantum chromodynamics in analytic perturbation theory, Theor. Math. Phys. 135 (2003) 531 [Teor. Mat. Fiz. 135 (2003) 95] [SPIRES].

    Article  MATH  Google Scholar 

  12. B.A. Magradze, A Novel series solution to the renormalization group equation in QCD, Few Body Syst. 40 (2006) 71 [hep-ph/0512374] [SPIRES].

    Article  ADS  Google Scholar 

  13. D.V. Shirkov and I.L. Solovtsov, Ten years of the Analytic Perturbation Theory in QCD, Theor. Math. Phys. 150 (2007) 132 [hep-ph/0611229] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  14. A.I. Karanikas and N.G. Stefanis, Analyticity and power corrections in hard-scattering hadronic functions, Phys. Lett. B 504 (2001) 225 [Erratum ibid. B 636 (2006) 330] [hep-ph/0101031] [SPIRES].

    ADS  Google Scholar 

  15. N.G. Stefanis, Perturbative logarithms and power corrections in QCD hadronic functions: A unifying approach, Lect. Notes Phys. 616 (2003) 153 [hep-ph/0203103] [SPIRES].

    Article  ADS  Google Scholar 

  16. N.G. Stefanis, W. Schroers and H.-C. Kim, Pion form factors with improved infrared factorization, Phys. Lett. B 449 (1999) 299 [hep-ph/9807298] [SPIRES].

    ADS  Google Scholar 

  17. N.G. Stefanis, W. Schroers and H.-C. Kim, Analytic coupling and Sudakov effects in exclusive processes: Pion and γ*γ → π0 form factors, Eur. Phys. J. C 18 (2000) 137 [hep-ph/0005218] [SPIRES].

    Article  ADS  Google Scholar 

  18. A.P. Bakulev, K. Passek-Kumericki, W. Schroers and N.G. Stefanis, Pion form factor in QCD: From nonlocal condensates to NLO analytic perturbation theory, Phys. Rev. D 70 (2004) 033014 [hep-ph/0405062] [SPIRES].

    ADS  Google Scholar 

  19. N.G. Stefanis, Pion form factor analysis using NLO analytic perturbation theory, invited talk given at 11th International Conference in Quantum ChromoDynamics (QCD 04), Montpellier, France, 5-9 July (2004) Nucl. Phys. Proc. Suppl. 152 (2006) 245 [hep-ph/0410245] [SPIRES].

    Article  ADS  Google Scholar 

  20. A.P. Bakulev, S.V. Mikhailov and N.G. Stefanis, QCD analytic perturbation theory: From integer powers to any power of the running coupling, Phys. Rev. D 72 (2005) 074014 [Erratum ibid. D 72 (2005) 119908] [hep-ph/0506311] [SPIRES].

    ADS  Google Scholar 

  21. A.P. Bakulev, A.I. Karanikas and N.G. Stefanis, Analyticity properties of three-point functions in QCD beyond leading order, Phys. Rev. D 72 (2005) 074015 [hep-ph/0504275] [SPIRES].

    ADS  Google Scholar 

  22. A.P. Bakulev, S.V. Mikhailov and N.G. Stefanis, Fractional analytic perturbation theory in Minkowski space and application to Higgs boson decay into a \( b\overline b \) pair, Phys. Rev. D 75 (2007) 056005 [Erratum ibid. D 77 (2008) 079901] [hep-ph/0607040] [SPIRES].

    ADS  Google Scholar 

  23. N.G. Stefanis and A.I. Karanikas, Analyticity of QCD observables beyond leading-order perturbation theory, in Proceedings of International Seminar on Contemporary Problems of Elementary Particle Physics, dedicated to the Memory of I. L. Solovtsov, Dubna, January 17-18 (2008), A.P. Bakulev et al. eds., JINR, Dubna (2008), pg. 104 arXiv:0802.3176 [SPIRES].

  24. N.G. Stefanis, Taming Landau singularities in QCD perturbation theory: The analytic approach, invited topical article prepared for the Modern Encyclopedia of Mathematical Physics (MEMPhys), Springer Verlag arXiv:0902.4805 [SPIRES].

  25. D.V. Shirkov, Analytic perturbation theory for QCD observables, Theor. Math. Phys. 127 (2001) 409 [hep-ph/0012283] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  26. D.V. Shirkov, Analytic perturbation theory in analyzing some QCD observables, Eur. Phys. J. C 22 (2001) 331 [hep-ph/0107282] [SPIRES].

    Article  ADS  Google Scholar 

  27. A.P. Bakulev, Global fractional analytic perturbation theory in QCD with selected applications, Phys. Part. Nucl. 40 (2009) 715 [arXiv:0805.0829] [SPIRES].

    Article  Google Scholar 

  28. S.V. Mikhailov, Generalization of BLM procedure and its scales in any order of pQCD: A practical approach, JHEP 06 (2007) 009 [hep-ph/0411397] [SPIRES].

    Article  ADS  Google Scholar 

  29. A.P. Bakulev and S.V. Mikhailov, Resummation in (F)APT, in Proceedings of International Seminar on Contemporary Problems of Elementary Particle Physics, dedicated to the Memory of I. L. Solovtsov, Dubna, January 17-18 (2008) A.P. Bakulev et al. eds., JINR, Dubna (2008) pg. 119 arXiv:0803.3013 [SPIRES].

  30. G. Cvetič and C. Valenzuela, Various versions of analytic QCD and skeleton-motivated evaluation of observables, Phys. Rev. D 74 (2006) 114030 [hep-ph/0608256] [SPIRES].

    ADS  Google Scholar 

  31. L.N. Lipatov, Divergence of the perturbation theory series and the quasiclassical theory, Sov. Phys. JETP 45 (1977) 216 [Zh. Eksp. Teor. Fiz. 72 (1977) 411] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  32. P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Scalar correlator at O(α4 s ), Higgs decay into bquarks and bounds on the light quark masses, Phys. Rev. Lett. 96 (2006) 012003 [hep-ph/0511063] [SPIRES].

    Article  ADS  Google Scholar 

  33. P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Order α4 s QCD corrections to Z and τ decays, Phys. Rev. Lett. 101 (2008) 012002 [arXiv:0801.1821] [SPIRES].

    Article  ADS  Google Scholar 

  34. P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Adler Function, Bjorken Sum rule and the crewther relation to order α4 s in a general gauge theory, Phys. Rev. Lett. 104 (2010) 132004 [1001.3606] [SPIRES].

    Article  ADS  Google Scholar 

  35. M. Davier, S. Descotes-Genon, A. Hocker, B. Malaescu and Z. Zhang, The determination of α s from τ decays revisited, Eur. Phys. J. C 56 (2008) 305 [arXiv:0803.0979] [SPIRES].

    Article  Google Scholar 

  36. A.L. Kataev and V.V. Starshenko, Estimates of the higher order QCD corrections to R s , R τ and deep inelastic scattering sum rules, Mod. Phys. Lett. A 10 (1995) 235 [hep-ph/9502348] [SPIRES].

    ADS  Google Scholar 

  37. A.A. Pivovarov, Renormalization group analysis of the tau-lepton decay within QCD, Z. Phys. C 53 (1992) 461 [Sov. J. Nucl. Phys. 54 (1991) 676] [Yad. Fiz. 54 (1991) 1114] [hep-ph/0302003] [SPIRES].

    ADS  Google Scholar 

  38. F. Le Diberder and A. Pich, Testing QCD with τ decays, Phys. Lett. B 289 (1992) 165 [SPIRES].

    ADS  Google Scholar 

  39. S. Groote, J.G. Korner and A.A. Pivovarov, Spectral moments of two-point correlators in perturbation theory and beyond, Phys. Rev. D 65 (2002) 036001 [hep-ph/0105227] [SPIRES].

    ADS  Google Scholar 

  40. A.L. Kataev and V.T. Kim, Uncertainties of QCD predictions for Higgs boson decay into bottom quarks at NNLO and beyond, PoS(ACAT08)004 [arXiv:0902.1442] [SPIRES].

  41. D.V. Shirkov, Renormalization group, causality and nonpower perturbation expansion in QFT, Theor. Math. Phys. 119 (1999) 438 [Teor. Mat. Fiz. 119 (1999) 55] [hep-th/9810246] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  42. M. Neubert, Scale setting in QCD and the momentum flow in Feynman diagrams, Phys. Rev. D 51 (1995) 5924 [hep-ph/9412265] [SPIRES].

    ADS  Google Scholar 

  43. P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Towards order α4 s accuracy in tau decays, Phys. Rev. D 67 (2003) 074026 [hep-ph/0212299] [SPIRES].

    ADS  Google Scholar 

  44. M. Beneke and M. Jamin, α s and the τ hadronic width: fixed-order, contour-improved and higher-order perturbation theory, JHEP 09 (2008) 044 [arXiv:0806.3156] [SPIRES].

    Article  ADS  Google Scholar 

  45. D.I. Kazakov and D.V. Shirkov, Asymptotic series of quantum field theory and their summation, Fortsch. Phys. 28 (1980) 465 [SPIRES].

    Article  MathSciNet  Google Scholar 

  46. J. Fischer, The use of power expansions in quantum field theory, Int. J. Mod. Phys. A 12 (1997) 3625 [hep-ph/9704351] [SPIRES].

    ADS  Google Scholar 

  47. D.J. Broadhurst and A.G. Grozin, Matching QCD and HQET heavy - light currents at two loops and beyond, Phys. Rev. D 52 (1995) 4082 [hep-ph/9410240] [SPIRES].

    ADS  Google Scholar 

  48. D.J. Broadhurst and A.L. Kataev, Connections between deep inelastic and annihilation processes at next to next-to-leading order and beyond, Phys. Lett. B 315 (1993) 179 [hep-ph/9308274] [SPIRES].

    ADS  Google Scholar 

  49. K.G. Chetyrkin, Correlator of the quark scalar currents and Γ tot (H → hadrons) at O(α3 s ) in pQCD, Phys. Lett. B 390 (1997) 309 [hep-ph/9608318] [SPIRES].

    ADS  Google Scholar 

  50. D.J. Broadhurst, A.L. Kataev and C.J. Maxwell, Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules, Nucl. Phys. B 592 (2001) 247 [hep-ph/0007152] [SPIRES].

    Article  ADS  Google Scholar 

  51. K.G. Chetyrkin, B.A. Kniehl and A. Sirlin, Estimations of order α3 s and α4 s corrections to mass-dependent observables, Phys. Lett. B 402 (1997) 359 [hep-ph/9703226] [SPIRES].

    ADS  Google Scholar 

  52. D.J. Broadhurst and A.L. Kataev, Bjorken unpolarized and polarized sum rules: Comparative analysis of large-N(F) expansions, Phys. Lett. B 544 (2002) 154 [hep-ph/0207261] [SPIRES].

    ADS  Google Scholar 

  53. J.H. Kuhn and M. Steinhauser, Determination of α s and heavy quark masses from recent measurements of R(s), Nucl. Phys. B 619 (2001) 588 [Erratum ibid. B 640 (2002) 415] [hep-ph/0109084] [SPIRES].

    Article  ADS  Google Scholar 

  54. A.A. Penin and M. Steinhauser, Heavy quarkonium spectrum at \( \mathcal{O}\left( {\alpha_s^5{m_q}} \right) \) and bottom/top quark mass determination, Phys. Lett. B 538 (2002) 335 [hep-ph/0204290] [SPIRES].

    ADS  Google Scholar 

  55. CDF and D0 collaborations, K. Herner, Standard Model higgs searches at the Tevatron, talk given at DIS2010, Firenze, Italy, April 20 (2010).

  56. ATLAS collaboration, E. Coniavitis, Search for the higgs boson at the ATLAS experiment, talk given at DIS2010, Firenze, Italy, April 20 (2010).

  57. D.V. Shirkov and S.V. Mikhailov, Mass dependent alpha-s evolution and the light gluino existence, Z. Phys. C 63 (1994) 463 [hep-ph/9401270] [SPIRES].

    ADS  Google Scholar 

  58. D.V. Shirkov and I.L. Solovtsov, Analytic QCD running coupling with finite IR behavior and universal α s (0) value., JINR Rapid Commun. 2[76] (1996) 5 [hep-ph/9604363] [SPIRES].

    Google Scholar 

  59. T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The four-loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [SPIRES].

    ADS  Google Scholar 

  60. K.G. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order α3 s , Phys. Rev. Lett. 83 (1999) 4001 [hep-ph/9907509] [SPIRES].

    Article  ADS  Google Scholar 

  61. K.G. Chetyrkin and M. Steinhauser, The relation between the MS-bar and the on-shell quark mass at order α3 s , Nucl. Phys. B 573 (2000) 617 [hep-ph/9911434] [SPIRES].

    Article  ADS  Google Scholar 

  62. N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three loop relation of quark (modified) MS and pole masses, Z. Phys. C 48 (1990) 673 [SPIRES].

    ADS  Google Scholar 

  63. A.L. Kataev and V.T. Kim, Higgs boson decay into bottom quarks and uncertainties of perturbative QCD predictions, arXiv:0804.3992 [SPIRES].

  64. K.G. Chetyrkin et al., Charm and bottom quark masses: an update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [SPIRES].

    ADS  Google Scholar 

  65. J.H. Kuhn, Multi-loop results, Charm- and bottom-quark masses and the strong coupling constant, arXiv:0809.1780 [SPIRES].

Download references

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie 6, 141980, Dubna, Russia

    A. P. Bakulev, S. V. Mikhailov & N. G. Stefanis

  2. Institut für Theoretische Physik II, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, Universitässtrasse 150, 44801, Bochum, Germany

    N. G. Stefanis

Authors
  1. A. P. Bakulev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. V. Mikhailov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. G. Stefanis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. G. Stefanis.

Additional information

ArXiv ePrint: 1004.4125

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bakulev, A.P., Mikhailov, S.V. & Stefanis, N.G. Higher-order QCD perturbation theory in different schemes: from FOPT to CIPT to FAPT. J. High Energ. Phys. 2010, 85 (2010). https://doi.org/10.1007/JHEP06(2010)085

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2010)085

Keywords

Search

Navigation