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TMF, 2012, Volume 170, Number 2, Pages 174–187 (Mi tmf6757)  

This article is cited in 25 scientific papers (total in 25 papers)

New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

A. L. Kataeva, S. V. Mikhailovb

a Institute for Nuclear Research, RAS, Moscow, Russia
b Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the $\overline{MS}$ scheme. We establish the validity of this representation in the $\overline{MS}$ approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function $D^{ns}_{A}$ for the electron–positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule $S_{Bjp}$ for the polarized deep-inelastic lepton–nucleon scattering. We find new relations between the $\alpha_{s}^4$ coefficients of $D^{ns}_{A}$. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order $\alpha_{s}^4$ in the expressions for these two quantities.

Keywords: quantum field theory, conformal symmetry breaking, perturbation theory, renormalization group, relation between characteristics of inclusive processes

DOI: https://doi.org/10.4213/tmf6757

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English version:
Theoretical and Mathematical Physics, 2012, 170:2, 139–150

Bibliographic databases:

Received: 12.02.2012

Citation: A. L. Kataev, S. V. Mikhailov, “New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models”, TMF, 170:2 (2012), 174–187; Theoret. and Math. Phys., 170:2 (2012), 139–150

Citation in format AMSBIB
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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:
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    2. S. J. Brodsky, X.-G. Wu, “Scale setting using the extended renormalization group and the principle of maximum conformality: the QCD coupling constant at four loops”, Phys. Rev. D, 85:3 (2012), 034038, 8 pp.  crossref  adsnasa  isi  elib  scopus
    3. S. J. Brodsky, L. Di Giustino, “Setting the renormalization scale in QCD: the principle of maximum conformality”, Phys. Rev. D, 86:8 (2012), 085026, 11 pp.  crossref  adsnasa  isi  elib  scopus
    4. S. J. Brodsky, X.-G. Wu, “Self-consistency requirements of the renormalization group for setting the renormalization scale”, Phys. Rev. D, 86:5 (2012), 054018, 14 pp.  crossref  adsnasa  isi  elib  scopus
    5. S. J. Brodsky, X.-G. Wu, “Application of the principle of maximum conformality to top-pair production”, Phys. Rev. D, 86:1 (2012), 014021, 13 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    6. S. J. Brodsky, X.-G. Wu, “Application of the principle of maximum conformality to the top-quark forward-backward asymmetry at the Tevatron”, Phys. Rev. D, 85:11 (2012), 114040, 9 pp.  crossref  adsnasa  isi  elib  scopus
    7. X.-G. Wu, S. J. Brodsky, M. Mojaza, “The renormalization scale-setting problem in QCD”, Prog. Part. Nucl. Phys., 72 (2013), 44–98  crossref  adsnasa  isi  elib  scopus
    8. M. Mojaza, S. J. Brodsky, X.-G. Wu, “Systematic all-orders method to eliminate renormalization-scale and scheme ambiguities in perturbative QCD”, Phys. Rev. Lett., 110:19 (2013), 192001  crossref  adsnasa  isi  elib  scopus
    9. A. Mirjalili, M. R. Khellat, “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
    10. Sh.-Q. Wang, X.-G. Wu, J.-M. Shen, H.-Y. Han, Ya. Ma, “QCD improved electroweak parameter $\rho$”, Phys. Rev. D, 89:11 (2014), 116001  crossref  adsnasa  isi  scopus
    11. Sh.-Q. Wang, X.-G. Wu, X.-Ch. Zheng, J.-M. Shen, Q.-L. Zhang, “The Higgs boson inclusive decay channels $H \to b\bar{b}$ and $H \to gg$ up to four-loop level”, Eur. Phys. J. C, 74:4 (2014), 2825  crossref  adsnasa  isi  scopus
    12. A. L. Kataev, “Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules”, J. High Energy Phys., 2014, no. 2, 092  crossref  isi  elib  scopus
    13. S. J. Brodsky, M. Mojaza, X.-G. Wu, “Systematic scale-setting to all orders: the principle of maximum conformality and commensurate scale relations”, Phys. Rev. D, 89:1 (2014), 014027  crossref  adsnasa  isi  elib  scopus
    14. A. L. Kataev, S. V. Mikhailov, “Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta\}$-expansion and the principle of maximal conformality”, Phys. Rev. D, 91:1 (2015), 014007  crossref  adsnasa  isi  scopus
    15. X.-G. Wu, Ya. Ma, Sh.-Q. Wang, H.-B. Fu, H.-H. Ma, S. J. Brodsky M. Mojaza, “Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review”, Rep. Prog. Phys., 78:12 (2015), 126201  crossref  adsnasa  isi  scopus
    16. H.-H. Ma, X.-G. Wu, Ya. Ma, S. J. Brodsky, M. Mojaza, “Setting the renormalization scale in perturbative QCD: comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach”, Phys. Rev. D, 91:9 (2015), 094028  crossref  isi  elib  scopus
    17. V. T. Kim, “Search for BFKL-evolution manifestations at high energies”, 9th Joint International Hadron Structure 15 Conference, International Journal of Modern Physics-Conference Series, 39, eds. S. Dubnicka, A. Dubnickova, E. Bartos, World Scientific Publ Co Pte Ltd, 2015  crossref  isi
    18. A. G. Grozin, J. M. Henn, G. P. Korchemsky, P. Marquard, “The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions”, J. High Energy Phys., 2016, no. 1, 140  crossref  mathscinet  zmath  isi  scopus
    19. A. L. Kataev, S. V. Mikhailov, “The $\{\beta\}$-expansion formalism in perturbative QCD and its extension”, J. High Energy Phys., 2016, no. 11, 079  crossref  mathscinet  isi  elib  scopus
    20. A. Deur, S. J. Brodsky, G. F. de Teramond, “The QCD running coupling”, Prog. Part. Nucl. Phys., 90 (2016), 1–74  crossref  mathscinet  isi  elib  scopus
    21. J.-M. Shen, X.-G. Wu, Ya. Ma, S. J. Brodsky, “The generalized scheme-independent Crewther relation in QCD”, Phys. Lett. B, 770 (2017), 494–499  crossref  mathscinet  isi  scopus
    22. P. Banerjee, P. K. Dhani, M. Mahakhud, V. Ravindran, S. Seth, “Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM”, J. High Energy Phys., 2017, no. 5, 085  crossref  mathscinet  isi  scopus
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    25. Aleshin S.S. Kataev A.L. Stepanyantz K.V., “The Three-Loop Adler D-Function For N=1 Sqcd Regularized By Dimensional Reduction”, J. High Energy Phys., 2019, no. 3, 196  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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