Ten years of the analytic perturbation theory in QCD

Theoretical and Mathematical Physics

Volumn 150, Issue 1, 2007, Pages 132-152

  Shirkov, D V ^a   Solovtsov, I L ^a,b  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^b GOMEL STATE TECHNICAL UNIVERSITY   (Belarus)

Author keywords

Causality; K llen Lehmann representation; Nonanalyticity in

Indexed keywords

EID: 33846389642     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-007-0010-7     Document Type: Article

References (76)

1. N. N. Bogoliubov, A. A. Logunov, and D. V. Shirkov, Zh. Eksp. Teor. Fiz., 37, No. 3(9), 805 (1959).
2. N. N. Bogoliubov and D. V. Shirkov, Dokl. Akad. Nauk SSSR, 103, 391 (1955).
3. N. N. Bogoliubov and D. V. Shirkov, Nuovo Cimento, 3, 845 (1956).
4. N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantum Fields [in Russian], Nauka, Moscow (1957, 1973, 1976, 1986); English transl., Wiley, New York (1959, 1980).
5. N. N. Bogoliubov, A. A. Logunov, and I. T. Todorov, Foundations of the Axiomatic Approach in Quantum Field Theory [in Russian], Nauka, Moscow (1969);
6. English transl.: Introduction to Axiomatic Quantum Field Theory, Benjamin, Reading, Mass. (1975);
7. N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, and I. T. Todorov, General Principles of Quantum Field Theory [in Russian], Nauka, Moscow (1987); English transl., Kluwer, Dordrecht (1990).
8. P. A. M. Dirac, "Theorie du positron," in: Structure et propertiétes des noyaux atomiques (Septiéme Conseil du Physique Solvay, Bruxelles, 22-29 October 1933, J. Cockcroft et al., eds.), Gauthier-Villars, Paris (1934), p. 203.
9. D. V. Shirkov and I. L. Solovtsov, JINR Rapid Commun., 76, 5 (1996); hep-ph/9604363 (1996).
10. D. V. Shirkov and I. L. Solovtsov, Phys. Rev. Lett., 79, 1209 (1997); hep-ph/9704333 (1997).
11. K. A. Milton and I. L. Solovtsov, Phys. Rev. D, 55, 5295 (1997); hep-ph/9611438 (1996).
12. K. A. Milton and I. L. Solovtsov, Phys. Rev. D, 59, 107701 (1999); hep-th/9812171 (1998).
13. N. N. Bogoliubov and D. V. Shirkov, Dokl. Akad. Nauk SSSR, 105, 685 (1955).
14. J. Schwinger, Proc. Natl. Acad. Sci. USA, 71, 3024, 5047 (1974).
15. K. A. Milton and O. P. Solovtsova, Phys. Rev. D, 57, 5402 (1998); hep-ph/9710316 (1997).
16. B. A. Magradze, Internat. J. Mod. Phys. A, 15, 2715 (2000); hep-ph/0010070 (2000);
17. S. Kurashev and B. A. Magradze, Theor. Math. Phys., 135, 531 (2003); hep-ph/0104142 (2001).
18. F. J. Dyson, Phys. Rev., 85, 631 (1952).
19. D. V. Shirkov, Lett. Math. Phys., 1, 179 (1976);
20. Lett. Nuovo Cimento, 18, 452 (1977).
21. D. V. Shirkov, Theor. Math. Phys., 40, 785 (1979);
22. I. Kazakov and D. V. Shirkov, Fortsch. Phys., 28, 465 (1980).
23. D. V. Shirkov, Theor. Math. Phys., 119, 438 (1999); hep-th/9810246 (1998);
24. Lett. Math. Phys., 48, 135 (1999).
25. D. V. Shirkov, Theor. Math. Phys., 136, 893 (2003); hep-th/0210013 (2002).
26. A. V. Radyushkin, JINR Rapid Commun., 78, 96 (1996); hep-ph/9907228 (1999);
27. N. V. Krasnikov and A. A. Pivovarov, Phys. Lett. B, 116, 168 (1982);
28. J. D. Bjorken, "Two topics in quantum chromodynamics," in: Particle Physics: Cargèse, 1989 (NATO Sci. Ser. B, Vol. 223, M. Levy, J. L. Basdevant, M. Jacob, and D. Speiser, eds.), Plenum, New York (1990), p. 217.
29. I. Caprini and J. Fischer, Phys. Rev. D, 62, 054007 (2000); hep-ph/0002016 (2000);
30. Eur. Phys. J. C, 24, 127 (2002); hep-ph/0110344 (2001).
31. D. V. Shirkov, Nucl Phys. B, 371, 467 (1992);
32. Theor. Math. Phys., 93, 1403 (1992).
33. D. V. Shirkov and S. V. Mikhailov, Z. Phys. C, 63, 463 (1994); hep-ph/9401270 (1994).
34. W. J. Marciano, Phys. Rev. D, 29, 580 (1984).
35. D. V. Shirkov, Theor. Math. Phys., 127, 409 (2001); hep-ph/0012283 (2000).
36. D. V. Shirkov, Eur. Phys. J. C, 22, 331 (2001); hep-ph/0107282 (2001).
37. A. I. Alekseev and B. A. Arbuzov, Modern Phys. Lett. A, 13, 1747 (1998); hep-ph/9704228 (1997);
38. 20, 103 (2005); hep-ph/0411339 (2004);
39. A. I. Alekseev, Theor. Math. Phys., 145, 1559 (2005).
40. A. V. Nesterenko and J. Papavassiliou, J. Phys. G, 32, 1025 (2006); hep-ph/0511215 (2005).
41. G. Cvetič, C. Valenzuela, and I. Schmidt, "A modification of minimal analytic QCD at low energies," hep-ph/0508101 (2005);
42. G. Cvetič and C. Valenzuela, J. Phys. G, 32, L27 (2006); hep-ph/0601050 (2006).
43. I. L. Solovtsov and D. V. Shirkov, Theor. Math. Phys., 120, 1220 (1999); hep-ph/9909305 (1999).
44. D. V. Shirkov and A. V. Zayakin, "Analytic perturbation theory for practitioners and Upsilon decay," Phys. Atomic Nuciei (to appear); hep-ph/0512325 (2005).
45. O. P. Solovtsova, JETP Lett., 64, 714 (1996);
46. K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova, Phys. Lett. B, 415, 104 (1997); hep-ph/9706409 (1997);
47. O. P. Solovtsova, Theor. Math. Phys., 134, 365 (2003);
48. K. A. Milton and O. P. Solovtsova, Internat. J. Mod. Phys. A, 17, 3789 (2002).
49. K. A. Milton, I. L. Solovtsov, O. P. Solovtsova, and V. I. Yasnov, Eur. Phys. J. C, 14, 495 (2000); hepph/0003030 (2000).
50. -) Collisions from φ to J/ψ (Novosibirsk, Russia, March 1-5, 1999, G. V. Fedotovich and S. I. Redin, eds.), Budker Inst. Nucl. Phys., Novosibirsk, Russia (2000), p. 122; hep-ph/9906495 (1999);
51. K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova, Phys. Rev. D, 64, 016005 (2001); hep-ph/0102254 (2001).
52. E. C. Poggio, H. R. Quinn, and S. Weinberg, Phys. Rev. D, 13, 1958 (1976).
53. A. C. Mattingly and P. M. Stevenson, Phys. Rev. D, 49, 437 (1994); hep-ph/9307266 (1993).
54. S. Eidelman, F. Jegerlehner, A. L. Kataev, and O. Veretin, Phys. Lett. B, 454, 369 (1999); hep-ph/9812521 (1998).
55. I. L. Solovtsov and D. V. Shirkov, Phys. Lett. B, 442, 344 (1998); hep-ph/9711251 (1997).
56. K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova, Phys. Lett. B, 439, 421 (1998); hep-ph/9809510 (1998);
57. Phys. Rev. D, 60, 016001 (1999); hep-ph/9809513 (1998).
58. K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova, Modern Phys. Lett. A, 21, 1355 (2006); hep-ph/0512209 (2005).
59. M. Davier, S. Eidelman, A. Höcker, and Z. Zhang, Eur. Phys. J. C, 31, 503 (2003); hep-ph/0308213 (2003);
60. A. Höcker, "The hadronic contribution to the muon g -2," in: Proc. 32nd Intl. Conf., on High-Energy Physics (ICHEP'04) (Beijing, China, 16-22 August 2004, H. Chen et al., eds.), Vol. 2, World Scientific, Singapore (2005), p. 710; hep-ph/0410081 (2004);
61. G. W. Bennett et al. (Muon 5-2 Collab.), Phys. Rev. Lett., 92, 161802 (2004); hep-ex/0401008 (2004);
62. A. Czarnecki, Nucl. Phys. B (Proc. Suppl.), 144, 201 (2005).
63. K. Hagiwara, A. D. Martin, D. Nomura, and T. Teubner, Phys. Rev. D, 69, 093003 (2004); hep-ph/0312250 (2003).
64. M. Baldicchi and G. M. Prosperi, Phys. Rev. D, 66, 074008 (2002); hep-ph/0202172 (2002);
65. AIP Conf. Proc., 756, 152 (2005); hep-ph/0412359 (2004).
66. N. G. Stefanis, W. Schroers, and H.-Ch. Kim, Eur. Phys. J. C, 18, 137 (2000); hep-ph/0005218 (2000).
67. A. P. Bakulev et al., Phys. Rev. D, 70, 033014, Erratum, 079906 (2004); hep-ph/0405062 (2004).
68. A. P. Bakulev, A. I. Karanikas, and N. G. Stefanis, Phys. Rev. D, 72, 074015 (2005); hep-ph/0504275 (2005).
69. N. G. Stefanis et al., "Fractional analytic perturbation theory in QCD and exclusive reaction," hep-ph/0601270 (2006).
70. R. Jost and H. Lehmann, Nuovo Cimento, 5, 1598 (1957).
71. N. N. Bogoliubov, V. S. Vladimirov, and A. N. Tavkhelidze, Theor. Math. Phys., 12, 839 (1972).
72. N. N. Bogoliubov and D. V. Shirkov, Dokl. Akad. Nauk SSSR, 113, 529 (1957).
73. B. Geyer, D. Robaschik, and E. Wieczorek, Fortschr. Phys., 27, 75 (1979);
74. Sov. J. Part. Mid., 11, 52 (1980).
75. H. Georgi and H. D. Politzer, Phys. Rev. D, 14, 1829 (1976).
76. I. L. Solovtsov, Part. Nucl. Lett., 4[101], 10 (2000).