RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (318 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Shi01} \by D.~V.~Shirkov \paper Analytic Perturbation Theory for QCD Observables \jour TMF \yr 2001 \vol 127 \issue 1 \pages 3--20 \mathnet{http://mi.mathnet.ru/tmf445} \crossref{https://doi.org/10.4213/tmf445} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1863116} \zmath{https://zbmath.org/?q=an:0993.81054} \transl \jour Theoret. and Math. Phys. \yr 2001 \vol 127 \issue 1 \pages 409--423 \crossref{https://doi.org/10.1023/A:1010302206227} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000170446000001} 

• http://mi.mathnet.ru/eng/tmf445
• https://doi.org/10.4213/tmf445
• http://mi.mathnet.ru/eng/tmf/v127/i1/p3

 SHARE:

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

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
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
3. D. V. Shirkov, “Behavior of the Effective QCD Coupling in the Infrared Region”, Theoret. and Math. Phys., 132:3 (2002), 1309–1319
4. Milton, KA, “Perturbative expansions in the inclusive decay of the tau-lepton”, International Journal of Modern Physics A, 17:26 (2002), 3789
5. Caprini, I, “Analytic continuation and perturbative expansions in QCD”, European Physical Journal C, 24:1 (2002), 127
6. Schrempp, F, “Tracking QCD-instantons”, Journal of Physics G-Nuclear and Particle Physics, 28:5 (2002), 915
7. Milton, KA, “Remark on the perturbative component of inclusive tau decay”, Physical Review D, 65:7 (2002), 076009
8. Phys. Usp., 45:5 (2002), 507–525
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
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
11. D. V. Shirkov, “Fourier Transformation of the Renormalization-Invariant Coupling”, Theoret. and Math. Phys., 136:1 (2003), 893–907
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
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
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
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
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
17. Bakulev, AP, “The pion form factor in QCD in NLO analytic perturbation theory”, Physics of Particles and Nuclei, 36 (2005), S164
18. Nesterenko, AV, “Massive analytic invariant charge in QCD”, Physical Review D, 71:1 (2005), 016009
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
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
21. Cvetic G, Valenzuela C, “Various versions of analytic QCD and skeleton-motivated evaluation of observables”, Physical Review D, 74:11 (2006), 114030
22. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387
23. Magradze, BA, “A novel series solution to the renormalization-group equation in QCD”, Few-Body Systems, 40:1–2 (2006), 71
24. Shirkov, D, “Nonpower expansions for QCD observables at low energies”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 51
25. Stefanis, NG, “Pion form factor analysis using NLO analytic perturbation theory”, Nuclear Physics B-Proceedings Supplements, 152 (2006), 245
26. Shirkov D.V., “Analytic perturbation theory model for QCD and upsilon decay”, Nuclear Phys B Proc Suppl, 162 (2006), 33–38
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
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
29. Shirkov, DV, “Analytic perturbation theory for QCD practitioners and upsilon decay”, Physics of Atomic Nuclei, 70:4 (2007), 775
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
31. Cvetic G, Valenzuela C, “Exponentially modified QCD coupling”, Physical Review D, 77:7 (2008), 074021
32. Cvetic, G, “Analytic QCD - a Short Review”, Brazilian Journal of Physics, 38:3B (2008), 371
33. Pasechnik, RS, “Bjorken sum rule and perturbative QCD frontier on the move”, Physical Review D, 78:7 (2008), 071902
34. Baikov, PA, “Order alpha(4)(s) QCD corrections to Z and tau decays”, Physical Review Letters, 101:1 (2008), 012002
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
36. Cvetic, G, “Rational approximations in analytic QCD”, Journal of Physics G-Nuclear and Particle Physics, 36:12 (2009), 125006
37. Bakulev, AP, “Global Fractional Analytic Perturbation Theory in QCD with Selected Applications”, Physics of Particles and Nuclei, 40:5 (2009), 715
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
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
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
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
42. Cvetic G., Koegerler R., “Applying generalized Pade approximants in analytic QCD models”, Phys Rev D, 84:5 (2011), 056005
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
44. Cvetic G. Kotikov A.V., “Analogs of Noninteger Powers in General Analytic QCD”, J. Phys. G-Nucl. Part. Phys., 39:6 (2012), 065005
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
46. Wu X.-G. Brodsky S.J. Mojaza M., “The Renormalization Scale-Setting Problem in QCD”, Prog. Part. Nucl. Phys., 72 (2013), 44–98
47. Ayala C. Cvetic G., “Calculation of Binding Energies and Masses of Quarkonia in Analytic QCD Models”, Phys. Rev. D, 87:5 (2013), 054008
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
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
50. Ayala C. Cvetic G., “anQCD: A Mathematica package for calculations in general analytic QCD models”, Comput. Phys. Commun., 190 (2015), 182–199
51. Ayala C. Cvetic G. Koegerler R., “Lattice-Motivated Holomorphic Nearly Perturbative QCD”, J. Phys. G-Nucl. Part. Phys., 44:7 (2017), 075001
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
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
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
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
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
•  Number of views: This page: 358 Full text: 122 References: 59 First page: 2