Geodesic
Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 416-429 Cet article a éte moissonné depuis la source Math-Net.Ru

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We perform a comparative analysis of different forms of pertubative expansions in spacelike and timelike regions. In the context of the inclusive -lepton decay, we compare the results obtained using the standard perturbation theory and the Shirkov–Solovtsov analytic approach, which modifies the perturbative expansions such that the new approximations reflect basic principles of the theory, such as renormalization invariance, spectrality, and causality. We show the advantages and self-consistency of the analytic approach in describing the $\tau$-lepton decay.
Keywords: quantum chromodynamics, renormalization group, perturbation theory
Mots-clés : $\tau$-lepton. 
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O. P. Solovtsova. Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 416-429. http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a7/

[1] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR | Zbl

[2] E. C. G. Stukelberg, A. Peterman, Helv. Phys. Acta, 26 (1953), 499 | MR

[3] M. Gell-Mann, F. E. Low, Phys. Rev., 95 (1954), 1300 | DOI | MR | Zbl

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

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

[6] D. V. Shirkov, I. L. Solovtsov, JINR Rapid Comm., 2 (1996), 5; Phys. Rev. Lett., 79 (1997), 1209 | DOI

[7] I. L. Solovtsov, D. V. Shirkov, TMF, 120:3 (1999), 482 | DOI | MR | Zbl

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

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

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

[11] I. L. Solovtsov, D. V. Shirkov, Phys. Lett. B, 442 (1998), 344 | DOI

[12] D. V. Shirkov, TMF, 119:1 (1998), 55 ; E-print hep-th/9810246 | DOI | MR

[13] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, Phys. Rev. D, 60 (1999), 016001 | DOI

[14] I. L. Solovtsov, Part. Nucl. Lett., 4 (2000), 10

[15] D. V. Shirkov, TMF, 127:1 (2001), 3 | DOI | MR | Zbl

[16] E. V. Shuryak, A. I. Vainshtein, Nucl. Phys. B, 199 (1982), 451 | DOI

[17] V. M. Braun, A. V. Kolesnichenko, Nucl. Phys. B, 283 (1987), 723 | DOI

[18] The ALEPH Collaboration, R. Barate et al., Eur. Phys. J. C, 4 (1998), 409 | DOI

[19] The OPAL Collaboration, K. Ackerstaff et al., Eur. Phys. J. C, 7 (1999), 571 | DOI

[20] S. H. Robertson, “Charged current review”, TAU 2000, Nucl. Phys. B. (Proc. Suppl.), 98, eds. R. J. Sobie, J. M. Roney, 2001, 67 | DOI

[21] Y. S. Tsai, Phys. Rev. D, 4 (1971), 2821 | DOI

[22] E. Braaten, S. Narison, A. Pich, Nucl. Phys. B, 373 (1992), 581 | DOI

[23] S. L. Adler, Phys. Rev. D, 10 (1974), 3714 | DOI | MR

[24] E. Braaten, Phys. Rev. Lett., 60 (1988), 1606 ; Phys. Rev. D, 39 (1989), 1458 | DOI | DOI

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

[26] A. V. Radyushkin, JINR Rapid Commun., 78 (1996), 96; E-print hep-ph/9907228

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

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

[29] D. V. Shirkov, Eur. Phys. J. C, 22 (2001), 331 ; E-print hep-ph/0107282 | DOI | Zbl

[30] K. G. Chetyrkin, Phys. Lett. B, 390 (1997), 309 | DOI

[31] P. M. Stevenson, Phys. Lett. B, 100 (1981), 61 | DOI

[32] J. Chyla, A. L. Kataev, S. G. Larin, Phys. Lett. B, 267 (1991), 269 | DOI

[33] A. C. Mattingly, P. M. Stevenson, Phys. Rev. Lett., 69 (1992), 1320 ; Phys. Rev. D, 49 (1994), 437 | DOI | DOI

[34] G. Grunberg, Phys. Lett. B, 95 (1980), 70 ; Phys. Rev. D, 29 (1984), 2315 | DOI | DOI

[35] A. Dhar, V. Gupta, Phys. Rev. D, 29 (1984), 2822 | DOI

[36] S. G. Gorishny, A. L. Kataev, S. A. Larin, L. R. Surguladze, Phys. Rev. D, 43 (1991), 1633 | DOI

[37] K. A. Milton, I. L. Solovtsov, “Infrared fixed point of the analytic running coupling”, Relativistic Nuclear Physics and Quantum Chromodynamics, V. I. Proc. XIV Int. Seminar on High Energy Physics Problems, eds. A. M. Baldin, V. V. Burov, JINR, Dubna, 2000, 47

[38] J. A. M. Vermaseren, S. A. Larin, T. van Ritbergen, Phys. Lett. B, 405 (1997), 327 | DOI

[39] S. G. Gorishny, A. L. Kataev, S. A. Larin, Phys. Lett. B, 259 (1991), 144 | DOI

[40] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, V. I. Yasnov, Eur. Phys. J. C, 14 (2000), 495 | DOI

[41] K. A. Milton, I. L. Solovtsov, Phys. Rev. D, 59 (1999), 107701 | DOI

[42] K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, Phys. Rev. D, 64 (2001), 016005 | DOI | MR

[43] E. Gardi, G. Grunberg, M. Karliner, JHEP, 07 (1998), 007 | DOI

[44] B. A. Magradze, Int. J. Mod. Phys. A, 15 (2000), 2715 | DOI | Zbl

[45] D. S. Kourashev, B. A. Magradze, Explicit expressions for Euclidean and Minkowskian QCD observables in analytic perturbation theory, E-print hep-ph/0104142

[46] F. Le Diberder, A. Pich, Phys. Lett. B, 286 (1992), 147 | DOI

[47] D. E. Groom et al., Particle Data Group. Eur. Phys. J. C, 15 (2000), 1

[48] B. V. Geshkenbein, B. L. Ioffe, K. N. Zyablyuk, Phys. Rev. D, 64 (2001), 093009 ; E-print hep-ph/0104048 | DOI

[49] P. A. Ra̧czka, A. Szymacha, Z. Phys. C, 70 (1996), 125 | DOI

[50] S. Peris, M. Perrottet, E. de Rafael, JHEP, 05 (1998), 011 | DOI

[51] A. N. Sisakyan, I. L. Solovtsov, O. P. Solovtsova, Pisma v ZhETF, 73 (2001), 186

[52] P. A. Ra̧czka, Z. Phys. C, 65 (1995), 481 | DOI

[53] N. V. Krasnikov, A. A. Pivovarov, Mod. Phys. Lett. A, 11 (1996), 835 | DOI