Geodesic
Analytic Perturbation Theory for QCD Observables
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 3-20
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 $\alpha_{\text{an}}(Q^2)$ and nonpower expansion for observables in the spacelike domain. The function $\alpha_{\text{an}}(Q^2)$ and the expansion are free of unphysical singularities. The formulated self-consistent scheme, analytic perturbation theory (APT), relates renorm-invariant, effective coupling functions $\alpha_{\text{an}}(Q^2)$ 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. 
@article{TMF_2001_127_1_a0,
     author = {D. V. Shirkov},
     title = {Analytic {Perturbation} {Theory} for {QCD} {Observables}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--20},
     year = {2001},
     volume = {127},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a0/}
}
TY  - JOUR
AU  - D. V. Shirkov
TI  - Analytic Perturbation Theory for QCD Observables
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 3
EP  - 20
VL  - 127
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a0/
LA  - ru
ID  - TMF_2001_127_1_a0
ER  - 
%0 Journal Article
%A D. V. Shirkov
%T Analytic Perturbation Theory for QCD Observables
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 3-20
%V 127
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a0/
%G ru
%F TMF_2001_127_1_a0
D. V. Shirkov. Analytic Perturbation Theory for QCD Observables. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a0/

[1] N. N. Bogolyubov, D. V. Shirkov, DAN SSSR, 103 (1955), 203 ; ЖЭТФ, 30 (1956), 77 ; N. N. Bogolubov, D. V. Shirkov, Nuovo Cimento, 3 (1956), 845 | MR | Zbl | MR | DOI | MR | Zbl

[2] P. A. M. Dirac, Theorie du Positron, 7-eme Conseil du Physique Solvay: Structure et propriete de noyaux atomiques (Oct. 1933), Gauthier-Villars, Paris, 1934, 203

[3] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, GTI, M., 1957 ; 1973; 1976; Наука, М., 1984 | MR | Zbl

[4] D. E. Groom et al., Eur. Phys. J. C, 15 (2000), 1

[5] S. Bethke, J. Phys. G, 26 (2000), R27 ; E-print hep-ex/0004021 | DOI

[6] D. Yu. Bardin, G. Passarino, The Standard model in the Making, Clarendon Press, Oxford, 1999

[7] A. V. Radyushkin, Optimizated $\Lambda$-parametrization for the QCD running coupling constant in space like and time like regions, JINR preprint E2-82-159; А. В. Радюшкин, Кратк. сообщ. ОИЯИ, 1996, No 4[78]-96, 9; E-print hep-ph/9907228

[8] N. V. Krasnikov, A. A. Pivovarov, Phys. Lett. B, 116 (1982), 168 | DOI

[9] B. Schrempp, F. Schrempp, Z. Phys. C, 6 (1980), 7 | DOI

[10] J. D. Bjorken, Two topics in QCD, Preprint SLAC-PUB-5103, Dec. 1989; Proc. Cargese Summer Institute, Nato Adv. Inst. Ser. B, 223, eds. M. Levy et al., Plenum Press, N.Y., 1990

[11] A. L. Kataev, V. V. Starshenko, Mod. Phys. Lett. A, 19 (1995), 235 | DOI

[12] H. F. Jones, I. L. Solovtsov, Phys. Lett. B, 349 (1995), 519 | DOI

[13] Yu. L. Dokshitzer et al., Nucl. Phys. B, 469 (1996), 93 | DOI

[14] K. A. Milton, I. L. Solovtsov, Phys. Rev. D, 55 (1997), 5295 | DOI | MR

[15] A. P. Bakulev, A. V. Radyushkin, N. G. Stefanis, Form Factors and QCD in spacelike and timelike regions, E-print hep-ph/0005085

[16] D. V. Shirkov, Toward the correlated analysis of perturbative QCD observables, JINR preprint E2-2000-46

[17] B. V. Magradze, QCD coupling up to 3rd order in standard and analytic perturbation theories, JINR preprint E2-2000-222

[18] D. V. Shirkov, Lett. Math. Phys., 48 (1999), 135 ; Д. В. Ширков, ТМФ, 119 (1999), 55 ; E-print hep-th/9810246 | DOI | MR | Zbl | DOI | MR | Zbl

[19] N. N. Bogolyubov, A. A. Logunov, D. V. Shirkov, ZhETF, 37 (1959), 805 | Zbl

[20] D. V. Shirkov, I. L. Solovtsov, Kratk. soobsch. OIYaI, 1996, no. 2[76]-96, 5; E-print hep-ph/9604363

[21] D. V. Shirkov, I. L. Solovtsov, Phys. Rev. Lett., 79 (1997), 1209 ; E-print hep-ph/9704333 | DOI

[22] D. V. Shirkov, I. L. Solovtsov, Phys. Lett. B, 442 (1998), 344 ; E-print hep-ph/9711251 | DOI

[23] D. V. Shirkov, Nucl. Phys. B (Proceed. Suppl.), 64 (1998), 106 | DOI

[24] I. L. Solovtsov, D. V. Shirkov, TMF, 120 (1999), 482 ; E-print hep-ph/9909305 | DOI | MR | Zbl

[25] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, Phys. Lett. B, 415 (1997), 104 | DOI

[26] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, Phys. Lett. B, 439 (1998), 421 ; E-print hep-ph/9809510 | DOI

[27] K. A. Milton, O. P. Solovtsova, Phys. Rev. D, 57 (1998), 5402 | DOI | MR

[28] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, Phys. Rev. D, 60 (1999), 016001 ; E-print hep-ph/9809513 | DOI

[29] N. G. Stefanis, W. Schroers, H.-Ch. Kim, Phys. Lett. B, 449 (1999), 299 ; E-print hep-ph/9812280 | DOI

[30] E. Gardi, G. Grunberg, M. Karliner, JHEP, 07 (1998), 007 ; E-print hep-ph/9806462 | DOI

[31] B. A. Magradze, “The gluon propagator in analytic perturbation theory”, Proc. X Intern. Seminar “QUARKS-98”, V. 1 (Suzdal, Russia, May, 1998), eds. F. L. Besrukov et al., INR Publ., M., 2000, 158; E-print hep-ph/9808247

[32] B. A. Magradze, An analytic approach to perturbative QCD, ; Int. J. Mod. Phys. A, 15 (2000), 2713 E-print hep-ph/9911456 | DOI | MR

[33] D. S. Kurashev, Exact analytic two-loop expressions for QCD observables in the time-like region, E-print hep-th/0010072

[34] A. A. Pivovarov, Z. Phys. C, 53 (1992), 461 | DOI

[35] B. V. Geshkenbein, B. L. Ioffe, Pisma v ZhETF, 70 (1999), 167

[36] J. Schwinger, Proc. Nat. Acad. Sci. USA, 71 (1974), 3024 ; 5047 | DOI | MR

[37] R. M. Corless et al., Adv. Comput. Math., 5 (1996), 329 | DOI | MR | Zbl

[38] W. Bernreuther, W. Wetzel, Nucl. Phys. B, 197 (1982), 228 ; W. Marciano, Phys. Rev. D, 29 (1984), 580 | DOI | DOI

[39] D. V. Shirkov, TMF, 49 (1981), 291 ; D. V. Shirkov, Nucl. Phys. B, 371 (1992), 467 | DOI | MR

[40] D. V. Shirkov, S. V. Mikhailov, Z. Phys. C, 63 (1994), 463 | DOI

[41] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, V. I. Yasnov, Eur. J. Phys. C, 14 (2000), 495 ; E-print hep-ph/0003030 | DOI

[42] A. J. Weinstein, Nucl. Phys. B (Proc. Suppl.), 76 (1999), 497 | DOI

[43] A. Adams et al. \rom(SMC Collaboration\rom), Phys. Rev. D, 56 (1997), 5330 | DOI

[44] D. V. Shirkov, Lett. Math. Phys., 1 (1976), 179 ; Lett. Nuovo Cimento, 18 (1977), 452 | DOI | MR | DOI