Abstract
In quantum theory, physical amplitudes are usually presented in the form of a Feynman perturbation series in powers of coupling constant α. However, it is known that these amplitudes are not regular functions at α = 0.
For QCD, we propose new sets of expansion parameters w k (α s ) that reflect singularity at α s = 0 and should be used instead of powers α k s . Their explicit form is motivated by the so-called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level α eff s (α s
1) = w 1(α s
1) ∼ 0.5. They can be used for the quantitative analysis of divers low-energy amplitudes.
We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. V. Shirkov, “Novel Sets of Expansion Parameters for Feynman Perturbation Theory,” in Proc. of the Crimean Conf. on New Trends in HEP, Ed. by P. N. Bogolyubov et al. (Kiev, 2007), pp. 231–237.
F. J. Dyson, Phys. Rev. 85, 631 (1952).
R. B. Dingle, Asymptotic Expansions (Academic, New York, 1973).
D. V. Shirkov, Lett. Math. Phys. 1, 179 (1976).
D. V. Shirkov, Lett. Nuovo Cim. 18, 452 (1977); G.’ t Hooft, “The Whys of Subnuclear Physics,” in Proc. of the 15th Erice 1997 School, Ed. by A. Zichichi (New York, 1979), p. 943.
D. V. Shirkov, “Analytic Perturbation Theory in Analyzing Some QCD Observables,” Eur. Phys. J. C 22, 331(2001); hep-ph/0107282.
D. V. Shirkov and I. L. Solovtsov, “Ten Years of the Analytic Perurbation Theory in QCD,” Theor. Math. Phys. 150, 132–152 (2007); hep-ph/0611229.
I. Caprini and Jan Fischer, Phys. Rev. D: Part. Fields 62, 054007 (2000); Eur. Phys. J. C 24, 127 (2002); hepph/0110344.
D. V. Shirkov and I. L. Solovtsov, JINR Rapid Commun., No. 2[76], 5 (1996); hep-ph/9604363; Phys. Rev. Lett. 79, 1209 (1997); hep-ph/9704333; K. A. Milton and I. Solovtsov, Phys. Rev. D 55, 5295–5298 (1997); hepph/9611438.
I. L. Solovtsov and D. V. Shirkov, “Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence,” Phys. Lett. B 442, 344–348 (1998); hepph/9711251; D. V. Shirkov, Lett. Math. Phys. 48, 135–144 (1999).
D. V. Shirkov, AIP Conf. Proc. 806, 97–103 (2006); hepph/0510247.
D. V. Shirkov and I. L. Solovtsov, “Analytic Perturbation Theory in QCD: Ten Years of History,” in Bogoliubov Laboratory 50 Years, Ed. by D. V. Shirkov (Dubna, 2006), p. 52.
D. V. Shirkov and A. V. Zayakin, Phys. At. Nucl. 70, 775–783 (2007); hep-ph/0512325.
W. E. Thirring, Ann. Phys. (N.Y.) 3, 91 (1958).
M. E. Mayer and D. V. Shirkov, Sov. Phys. Dokl. 3, 931(1958).
I. Ya. Aref’eva and V. E. Korepin, “S-Matrix for 2-Dimensional Theory with Lagrangian L = 1/γ[1/2(∂μ u)2 + m 2(cosu − 1)],” Pis’ma Zh. Eksp. Teor. Fiz. 20, 680–684 (1974) [JETP Lett. 20, 312 (1974)].
S. R. Coleman, Phys. Rev. D 11, 2088 (1975); S. Mandelstam, Phys. Rev. D 11, 3026 (1975).
D. J. Gross and A. Neveu, Phys. Rev. D: Part. Fields 10,3235 (1974).
A. A. Osipov, B. Hiller, and A. H. Blin, Phys. Lett. B 653, 346–349 (2007); hep-ph/0707.1427.
A. A. Vladimirov, D. I. Kazakov, and O. V. Tarasov, Sov. Phys. JETP 50, 521 (1979).
V. F. Kovalev, V. V. Pustovalov, and D. V. Shirkov, J. Math. Phys. 39, 1170–1188 (1998); hep-th/9706056.
D. V. Shirkov and V. F. Kovalev, Phys. Rep. 352, 219–249 (2001); hep-th/0001210; V. F. Kovalev and D. V. Shirkov, J. Phys. A 39, 8061–8073 (2006).
D. I. Kazakov and D. V. Shirkov, “Asymptotic Series of Quantum Field Theory and Their Summation,” Fortsch. Phys. 28, 465–499 (1980).
D. V. Shirkov, Theor. Math. Phys. 136, 893–907 (2003); hep-ph/0210113.
D. V. Shirkov, Nucl. Phys. Proc. 152,Suppl., 51–56 (2006); hep-ph/0408272.
Author information
Authors and Affiliations
Additional information
The text was submitted by the author in English.
A preliminary version with the main results was published in [1].
Rights and permissions
About this article
Cite this article
Shirkov, D.V. Novel sets of coupling expansion parameters for low-energy pQCD. Phys. Part. Nuclei Lett. 5, 489–493 (2008). https://doi.org/10.1134/S1547477108060010
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1547477108060010