Abstract
We study the possibility of expressing the invariant QCD coupling function (i.e., the effective coupling constant) in an explicit analytic form in two- and three-loop approximations as well as in the case of the Padé-transformed β-function. Both the timelike and spacelike domains are investigated. Technical aspects of the Shirkov–Solovtsov analytic perturbation theory are considered. Explicit expressions for the two- and three-loop effective coupling functions in the timelike domain are obtained. In the last case, we apply a new method of expanding functions represented in an arbitrary loop order of perturbation theory in powers of the two-loop function. The comparison with numerical data in the infrared region shows that the obtained explicit expressions for the three-loop functions agree fully with the exact numerical results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
I. L. Solovtsov and D. V. Shirkov, JINR Rapid Commun., 76, No. 2, 5 (1996); D. V. Shirkov and I. L. Solovtsov, Phys. Rev. Lett., 79, 1209 (1997); hep-ph/9704333 (1997).
D. V. Shirkov, Theor. Math. Phys., 119, 438 (1999); hep-th/9810246 (1998); Lett. Math. Phys., 48, 135 (1999).
I. L. Solovtsov and D. V. Shirkov, Theor. Math. Phys., 120, 1220 (1999); hep-ph/9909305 (1999).
K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova, Phys. Lett. B, 415, 104 (1997).
I. L. Solovtsov and D. V. Shirkov, Phys. Lett. B, 442, 344 (1998); hep-ph/9711251 (1997).
D. V. Shirkov, “Toward the correlated analysis of perturbative QCD observables,” JINR preprint E2-2000-46, Joint Inst. Nucl. Res., Dubna (2000); hep-ph/0003242 (2000); Theor. Math. Phys., 127, 409 (2001); hepph/ 0012283 (2000).
A. V. Radyushkin, JINR Rapid Commun., 78, 96 (1996); hep-ph/9907228 (1999).
N. V. Krasnikov and A. A. Pivovarov, Phys. Lett. B, 116, 168 (1982).
A. P. Bakulev, A. V. Radyushkin, and N. G. Stefanis, Phys. Rev. D, 62, 113001 (2000).
B. V. Geshkenbein and B. L. Ioffe, JETP Letters, 70, 161 (1999).
K. A. Milton, I. L. Solovtsov, O. P Solovtsova, and V. I. Yasnov, Eur. Phys. J. C, 14, 495 (2000).
B. Magradze, “The gluon propagator in analytic perturbation theory,” in: “QUARKs-98” (Suzdal, Russia, May 17-24, 1998, Vol. 1, F. L. Bezrukov et al., eds.), INR Publ., Moscow (2000), p. 158; hep-ph/9808247 (1998).
E. Gardi, G. Grunberg, and M. Karliner, JHEP, 07, 007 (1998).
B. A. Magradze, Internat. J. Mod. Phys. A, 15, 2715 (2000).
D. S. Kourashev, “The QCD observables expansion over the scheme-independent two-loop coupling constant powers, the scheme dependence reduction,” hep-ph/9912410 (1999).
C. J. Maxwell and A. Marjalili, Nucl. Phys. B, 577, 209 (2000).
O. V. Tarasov, A. A. Vladimirov, and A. Y. Zharkov, Phys. Lett. B, 93, 429 (1980).
K. A. Milton and I. L. Solovtsov, Phys. Rev. D, 55, 5295 (1997).
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, Adv. Comput. Math., 5, 329 (1996).
A. A. Pivovarov, Nuovo Cimento A, 105, 813 (1992).
A. L. Kataev and V. V. Starshenko, Modern Phys. Lett. A, 10, 235 (1995).
D. V. Shirkov, “The ?2 terms in the s-channel QCD observables,” JINR preprint E2-2000-211, Joint Inst. Nucl. Res., Dubna (2000); hep-ph/0009106 (2000); Theor. Math. Phys., 127, 409 (2001); hep-ph/0012283 (2000); Eur. Phys. J. C, 22, 331 (2001); hep-ph/0107282 (2001).
G. Rodrigo and A. Santamaria, Phys. Lett. B, 313, 441 (1993); K. G. Chetyrkin, B. A. Kniehl, and M. Steinhauser, Phys. Rev. Lett, 79, 2184 (1997); hep-ph/9706430 (1997).
W. A. Bardeen et al., Phys. Rev. D, 18, 3998 (1978).
K. A. Milton and I. L. Solovtsov, Phys. Rev. D, 59, 107701 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kurashev, D., Magradze, B. Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory. Theoretical and Mathematical Physics 135, 531–540 (2003). https://doi.org/10.1023/A:1023287519892
Issue Date:
DOI: https://doi.org/10.1023/A:1023287519892