Snapshots of Hadrons - Or the Story of How the Vacuum Medium Determines the Properties of the Classical Mesons which are Produced, Live and Die in the QCD Vacuum

Progress of Theoretical Physics Supplement

Volumn , Issue 131, 1998, Pages 1-70

  Shifman, Mikhail ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032259603     PISSN: 03759687     EISSN: None     Source Type: Journal    
DOI: 10.1143/ptps.131.1     Document Type: Article

References (191)

1. M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B147 (1979), 385, 448.
2. Vacuum Structure and QCD Sum Rules, ed. M. Shifman (North-Holland, Amsterdam, 1992).
3. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B191 (1981), 301.
4. D. Gross and F. Wilczek, Phys. Rev. Lett. 30 (1973), 1343. H. D. Politzer, Phys. Rev. Lett. 30 (1973), 1346.
5. D. Gross and F. Wilczek, Phys. Rev. Lett. 30 (1973), 1343. H. D. Politzer, Phys. Rev. Lett. 30 (1973), 1346.
6. V. Novikov et al., Phys. Rep. 41 (1978), 1.
7. See e.g., the review paper, I. Hinchliffe, Phys. Rev. D54 (1996), 77 and references therein.
8. G. 't Hooft, The Confinement Phenomenon in Quantum Field Theory, 1981 Cargese Summer School Lecture Notes on Fundamental Interactions, ed. M. Levy and J.-L. Basdevant, NATO Adv. Study Inst. Series B: Phys. vol. 85. p. 639 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), p. 514]. S. Mandelstam, Phys. Rep. 23 (1976), 245.
9. G. 't Hooft, The Confinement Phenomenon in Quantum Field Theory, 1981 Cargese Summer School Lecture Notes on Fundamental Interactions, ed. M. Levy and J.-L. Basdevant, NATO Adv. Study Inst. Series B: Phys. vol. 85. p. 639 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), p. 514]. S. Mandelstam, Phys. Rep. 23 (1976), 245.
10. G. 't Hooft, The Confinement Phenomenon in Quantum Field Theory, 1981 Cargese Summer School Lecture Notes on Fundamental Interactions, ed. M. Levy and J.-L. Basdevant, NATO Adv. Study Inst. Series B: Phys. vol. 85. p. 639 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), p. 514]. S. Mandelstam, Phys. Rep. 23 (1976), 245.
11. For a review see e.g., A. Di Giacomo, Nucl. Phys. (Proc. Suppl.) 47 (1996), 136; hep-lat/9509036; Monopole Condensation in Gauge Theory Vacuum, in Confinement 95, Proc. International Workshop on Color Confinement and Hadrons Japan, March 1995, ed. H. Toki, Y. Mizuno, H. Suganuma, T. Suzuki and O. Miyamura (World Scientific, Singapore, 1995); hep- lat/9505006; Mechanisms for Color Confinement, in Selected Topics in Nonperturbative QCD, Proc. Int. School of Physics "Enrico Fermi", ed. A. Di Giacomo and D. Diakonov (IOS Press, 1996), p. 147.
12. For a review see e.g., A. Di Giacomo, Nucl. Phys. (Proc. Suppl.) 47 (1996), 136; hep-lat/9509036; Monopole Condensation in Gauge Theory Vacuum, in Confinement 95, Proc. International Workshop on Color Confinement and Hadrons Japan, March 1995, ed. H. Toki, Y. Mizuno, H. Suganuma, T. Suzuki and O. Miyamura (World Scientific, Singapore, 1995); hep-lat/9505006; Mechanisms for Color Confinement, in Selected Topics in Nonperturbative QCD, Proc. Int. School of Physics "Enrico Fermi", ed. A. Di Giacomo and D. Diakonov (IOS Press, 1996), p. 147.
13. For a review see e.g., A. Di Giacomo, Nucl. Phys. (Proc. Suppl.) 47 (1996), 136; hep-lat/9509036; Monopole Condensation in Gauge Theory Vacuum, in Confinement 95, Proc. International Workshop on Color Confinement and Hadrons Japan, March 1995, ed. H. Toki, Y. Mizuno, H. Suganuma, T. Suzuki and O. Miyamura (World Scientific, Singapore, 1995); hep- lat/9505006; Mechanisms for Color Confinement, in Selected Topics in Nonperturbative QCD, Proc. Int. School of Physics "Enrico Fermi", ed. A. Di Giacomo and D. Diakonov (IOS Press, 1996), p. 147.
14. N. Seiberg and E. Witten, Nucl. Phys. B426 (1994), 19; (E) B430 (1994), 485; B431 (1994), 484.
15. N. Seiberg and E. Witten, Nucl. Phys. B426 (1994), 19; (E) B430 (1994), 485; B431 (1994), 484.
16. N. Seiberg and E. Witten, Nucl. Phys. B426 (1994), 19; (E) B430 (1994), 485; B431 (1994), 484.
17. G. 't Hooft, Nucl. Phys. B72 (1974), 461. E. Witten, Nucl. Phys. B160 (1979), 57. For a brief review see Chapter 8 in Ref. 2).
18. G. 't Hooft, Nucl. Phys. B72 (1974), 461. E. Witten, Nucl. Phys. B160 (1979), 57. For a brief review see Chapter 8 in Ref. 2).
19. A. B. Kaidalov, Usp. Fiz. Nauk 105 (1971), 97 [Sov. Phys. Uspekhi 14 (1972), 600]. P. D. B. Collins, An Introduction to Regge Theory and High Energy Physics (Cambridge Univ. Press, 1977).
20. A. B. Kaidalov, Usp. Fiz. Nauk 105 (1971), 97 [Sov. Phys. Uspekhi 14 (1972), 600]. P. D. B. Collins, An Introduction to Regge Theory and High Energy Physics (Cambridge Univ. Press, 1977).
21. A. B. Kaidalov, Usp. Fiz. Nauk 105 (1971), 97 [Sov. Phys. Uspekhi 14 (1972), 600]. P. D. B. Collins, An Introduction to Regge Theory and High Energy Physics (Cambridge Univ. Press, 1977).
22. A. Yu. Dubin, A. B. Kaidalov and Yu. A. Simonov, Phys. Lett. B323 (1994), 41.
23. A. Casher, N. Neurberger and S. Nussinov, Phys. Rev. D20 (1979), 179.
24. B. Blok, M. Shifman and Da-Xin Zhang, hep-ph/9709333 (Phys. Rev. D, to appear).
25. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
26. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
27. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
28. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
29. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
30. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
31. G. 't Hooft, Nucl. Phys. B75 (1974), 461 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore 1994), p. 443]. See also: F. Lenz, M. Thies, S. Levit and K. Yazaki, Ann. of Phys. 208 (1991), 1. C. Callan, N. Coote and D. Gross, Phys. Rev. D13 (1976), 1649. M. Einhorn, Phys. Rev. D14 (1976), 3451. M. Einhorn, S. Nussinov and E. Rabinovici, Phys. Rev. D15 (1977), 2282. I. Bars and M. Green, Phys. Rev. D17 (1978), 537.
32. M. Shifman, Theory of Preasymptotic Effects in Weak Inclusive Decays, in Proc. Workshop on Continuous Advances in QCD, ed. A. Smilga (World Scientific, Singapore, 1994), p. 249; hep-ph/9405216; Recent Progress in the Heavy Quark Theory, in Particles, Strings and Cosmology, Proc. of the XIX Johns Hopkins Workshop on Current Problems in Particle Theory and the V PASCOS Interdisiplinary Symposium, Baltimore, March 1995, ed. J. Bagger (World Scientific, Singapore, 1996), p. 69; hep-ph/9505289.
33. M. Shifman, Theory of Preasymptotic Effects in Weak Inclusive Decays, in Proc. Workshop on Continuous Advances in QCD, ed. A. Smilga (World Scientific, Singapore, 1994), p. 249; hep-ph/9405216; Recent Progress in the Heavy Quark Theory, in Particles, Strings and Cosmology, Proc. of the XIX Johns Hopkins Workshop on Current Problems in Particle Theory and the V PASCOS Interdisiplinary Symposium, Baltimore, March 1995, ed. J. Bagger (World Scientific, Singapore, 1996), p. 69; hep-ph/9505289.
34. F. David, Nucl. Phys. B209 (1982), 433; B234 (1984), 237.
35. F. David, Nucl. Phys. B209 (1982), 433; B234 (1984), 237.
36. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B249 (1985), 445.
37. I. Bigi, M. Shifman, N. Uraltsev and A. Vainshtein, Phys. Rev. D52 (1995), 196.
38. R. Crewther, Phys. Rev. Lett. 28 (1972), 1421. M. Chanowitz and J. Ellis, Phys. Lett. B40 (1972), 397; Phys. Rev. D7 (1973), 2490. J. Collins, L. Duncan and S. Joglekar, Phys. Rev. D16 (1977), 438.
39. R. Crewther, Phys. Rev. Lett. 28 (1972), 1421. M. Chanowitz and J. Ellis, Phys. Lett. B40 (1972), 397; Phys. Rev. D7 (1973), 2490. J. Collins, L. Duncan and S. Joglekar, Phys. Rev. D16 (1977), 438.
40. R. Crewther, Phys. Rev. Lett. 28 (1972), 1421. M. Chanowitz and J. Ellis, Phys. Lett. B40 (1972), 397; Phys. Rev. D7 (1973), 2490. J. Collins, L. Duncan and S. Joglekar, Phys. Rev. D16 (1977), 438.
41. R. Crewther, Phys. Rev. Lett. 28 (1972), 1421. M. Chanowitz and J. Ellis, Phys. Lett. B40 (1972), 397; Phys. Rev. D7 (1973), 2490. J. Collins, L. Duncan and S. Joglekar, Phys. Rev. D16 (1977), 438.
42. M. Neubert, Phys. Rev. D51 (1995), 5924.
43. P. Ball, M. Beneke and V. Braun, Nucl. Phys. B452 (1995), 563.
44. G. 't Hooft, Can We Make Sense out of "Quantum Chromodynamics"? in The Whys Of Subnuclear Physics, Erice, 1977, ed. A. Zichichi (Plenum, New York, 1977), p. 943 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), p. 547].
45. G. 't Hooft, Can We Make Sense out of "Quantum Chromodynamics"? in The Whys Of Subnuclear Physics, Erice, 1977, ed. A. Zichichi (Plenum, New York, 1977), p. 943 [reprinted in G. 't Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), p. 547].
46. B. Lautrup, Phys. Lett. 69B (1977), 109. G. Parisi, Phys. Lett. 76B (1978), 65; Nucl. Phys. B150 (1979), 163. A. Mueller, Nucl. Phys. B250 (1985), 327.
47. B. Lautrup, Phys. Lett. 69B (1977), 109. G. Parisi, Phys. Lett. 76B (1978), 65; Nucl. Phys. B150 (1979), 163. A. Mueller, Nucl. Phys. B250 (1985), 327.
48. B. Lautrup, Phys. Lett. 69B (1977), 109. G. Parisi, Phys. Lett. 76B (1978), 65; Nucl. Phys. B150 (1979), 163. A. Mueller, Nucl. Phys. B250 (1985), 327.
49. B. Lautrup, Phys. Lett. 69B (1977), 109. G. Parisi, Phys. Lett. 76B (1978), 65; Nucl. Phys. B150 (1979), 163. A. Mueller, Nucl. Phys. B250 (1985), 327.
50. A. H. Mueller, in Proc. Int. Conf. QCD - 20 Years Later, Aachen 1992, ed. P. Zerwas and H. Kastrup (World Scientific, Singapore, 1993), vol. 1, p. 162.
51. R. Akhoury and V. I. Zakharov, hep-ph/9710257.
52. R. Akhoury and V. Zakharov, Nucl. Phys. (Proc. Suppl.) 54A (1997), 217. M. Beneke, hep-ph/9706457. V. Braun, hep-ph/9708386. B. R. Webber, hep-ph/9712236.
53. R. Akhoury and V. Zakharov, Nucl. Phys. (Proc. Suppl.) 54A (1997), 217. M. Beneke, hep-ph/9706457. V. Braun, hep-ph/9708386. B. R. Webber, hep-ph/9712236.
54. R. Akhoury and V. Zakharov, Nucl. Phys. (Proc. Suppl.) 54A (1997), 217. M. Beneke, hep-ph/9706457. V. Braun, hep-ph/9708386. B. R. Webber, hep-ph/9712236.
55. R. Akhoury and V. Zakharov, Nucl. Phys. (Proc. Suppl.) 54A (1997), 217. M. Beneke, hep-ph/9706457. V. Braun, hep-ph/9708386. B. R. Webber, hep-ph/9712236.
56. A. Di Giacomo, Lattice Gauge Theories and SVZ Expansion, in Nonperturbative Methods, Proc. 1985 Montpellier Int. Workshop, ed. S. Narison (World Scientific, Singapore, 1986), p. 135.
57. X. Ji, hep-ph/9506216 (unpublished).
58. M. Shifman, A. Vainshtein, M. Voloshin and V. Zakharov, Phys. Lett. B77 (1978), 80.
59. J. Gasser and H. Leutwyler, Nucl. Phys. B94 (1975), 269.
60. S. Weinberg, in A Festschrift for I.I. Rabi, ed. L. Motz, Trans. New York Acad. Sci. Ser. II 38 (1977), 185.
61. H. Leutwyler, hep-ph/9609467 and a forthcoming book.
62. T. Bhattacharya and R. Gupta, Talk at Lattice 97, XV Int. Symp. on Lattice Field Theory, Edinburgh, Scotland, July 1997; hep-lat/9710095.
63. For a review see; B. L. Ioffe, Acta Phys. Polon. B16 (1985), 543.
64. V. Novikov et al., in Neutrinos 78, Proc. VIII Int. Conference on Physics and Neutrino Astrophysics, West Lafayette, April 1978, ed. E. C. Fowler (Purdue University, 1978), p. C278.
65. M. Voloshin, Nucl. Phys. B154 (1979), 365. L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rep. 127 (1985), 1. S. N. Nikolaev and A. V. Radyushkin, Nucl. Phys. B213 (1983), 285; Phys. Lett. B124 (1983), 243.
66. M. Voloshin, Nucl. Phys. B154 (1979), 365. L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rep. 127 (1985), 1. S. N. Nikolaev and A. V. Radyushkin, Nucl. Phys. B213 (1983), 285; Phys. Lett. B124 (1983), 243.
67. M. Voloshin, Nucl. Phys. B154 (1979), 365. L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rep. 127 (1985), 1. S. N. Nikolaev and A. V. Radyushkin, Nucl. Phys. B213 (1983), 285; Phys. Lett. B124 (1983), 243.
68. M. Voloshin, Nucl. Phys. B154 (1979), 365. L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rep. 127 (1985), 1. S. N. Nikolaev and A. V. Radyushkin, Nucl. Phys. B213 (1983), 285; Phys. Lett. B124 (1983), 243.
69. M. Dubovikov and A. Smilga, Nucl. Phys. B185 (1981), 109.
70. M. Crisafulli et al., Phys. Lett. B369 (1996), 325.
71. K. G. Chetyrkin et al., Phys. Lett. B174 (1986), 104. L. Reinders and S. Yazaki, Nucl. Phys. B288 (1987), 789. K. Chetyrkin and A. Pivovarov, Nuovo Cim. A100 (1988), 899. Literally speaking, these authors test factorization for the four-quark operators averaged over the Goldstone mesons, π, K, etc. rather than over the vacuum state. Within the soft pion technique the former matrix elements are reducible to the latter.
72. K. G. Chetyrkin et al., Phys. Lett. B174 (1986), 104. L. Reinders and S. Yazaki, Nucl. Phys. B288 (1987), 789. K. Chetyrkin and A. Pivovarov, Nuovo Cim. A100 (1988), 899. Literally speaking, these authors test factorization for the four-quark operators averaged over the Goldstone mesons, π, K, etc. rather than over the vacuum state. Within the soft pion technique the former matrix elements are reducible to the latter.
73. K. G. Chetyrkin et al., Phys. Lett. B174 (1986), 104. L. Reinders and S. Yazaki, Nucl. Phys. B288 (1987), 789. K. Chetyrkin and A. Pivovarov, Nuovo Cim. A100 (1988), 899. Literally speaking, these authors test factorization for the four-quark operators averaged over the Goldstone mesons, π, K, etc. rather than over the vacuum state. Within the soft pion technique the former matrix elements are reducible to the latter.
74. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
75. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
76. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
77. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
78. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
79. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
80. The two-loop correction was found by K. Chetyrkin, A. Kataev and F. Tkachev, Phys. Lett. B85 (1979), 277. M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979), 668. W. Celmaster and R. Gonsalves, Phys. Rev. Lett. 44 (1980), 560. Three-loop calculations are due to S. Gorishny, A. Kataev and S. Larin, Phys. Lett. B259 (1991), 144. L. Surguladze and M. Samuel, Phys. Rev. Lett. 66 (1991), 560; (E) 66 (1991), 2416. K. Chetyrkin, Phys. Lett. B391 (1997).
81. S. Eidelman, L. Kurdadze, M. Shifman and A. Vainshtein, unpublished.
82. S. Gorishny, A. Kataev and S. Larin, Pisma ZhETF 53 (1991), 121 [JETP Lett. 53 (1991), 127].
83. S. Gorishny, A. Kataev and S. Larin, Pisma ZhETF 53 (1991), 121 [JETP Lett. 53 (1991), 127].
84. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Fortsch. Phys. 32 (1984), 585.
85. L. Surguladze and F. Tkachev. Nucl. Phys. B331 (1990), 35.
86. D. Broadhurst and A. G. Grozin, in Proc. Int. Workshop on Software Engineering and Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics New Computing Techniques in Physics Research IV, Pisa, Italy, April 1995, ed. B. Denby and D. Perret-Gallix (World Scientific, Singapore, 1995), p. 217; hep-ph/9504400. L. Surguladze and M. Samuel, Rev. Mod. Phys. 68 (1996), 259.
87. D. Broadhurst and A. G. Grozin, in Proc. Int. Workshop on Software Engineering and Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics New Computing Techniques in Physics Research IV, Pisa, Italy, April 1995, ed. B. Denby and D. Perret-Gallix (World Scientific, Singapore, 1995), p. 217; hep-ph/9504400. L. Surguladze and M. Samuel, Rev. Mod. Phys. 68 (1996), 259.
88. R. Barate et al. (ALEPH Collab.), Z. Phys. C76 (1997), 15.
89. B. Chibisov, R. D. Dikeman, M. Shifman and N. Uraltsev, Int. J. Mod. Phys. A12 (1997), 2075.
90. M. Shifman, Yad. Fiz. 36 (1982), 1290 [Sov. J. Nucl. Phys. 36 (1982), 749].
91. M. Shifman, Yad. Fiz. 36 (1982), 1290 [Sov. J. Nucl. Phys. 36 (1982), 749].
92. K. Wilson, Phys. Rev. 179 (1969), 1499. K. Wilson and J. Kogut, Phys. Rep. 12 (1974), 75.
93. K. Wilson, Phys. Rev. 179 (1969), 1499. K. Wilson and J. Kogut, Phys. Rep. 12 (1974), 75.
94. Large-Order Behaviour of Perturbation Theory, ed. J. C. Le Guillou and J. Zinn-Justin (North-Holland, Amsterdam, 1990).
95. M. S. Dubovikov and A. V. Smilga, Yad. Fiz. 37 (1983), 984 [Sov. J. Nucl. Phys. 37 (1983), 585].
96. M. S. Dubovikov and A. V. Smilga, Yad. Fiz. 37 (1983), 984 [Sov. J. Nucl. Phys. 37 (1983), 585].
97. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Phys. Rep. 116 (1984), 103.
98. X. Ji, hep-ph/9506216; hep-ph/9507322 (unpublished).
99. E. Shuryak, Nucl. Phys. B198 (1982), 83. D. Diakonov and V. Petrov, Nucl. Phys. B245 (1984), 259.
100. E. Shuryak, Nucl. Phys. B198 (1982), 83. D. Diakonov and V. Petrov, Nucl. Phys. B245 (1984), 259.
101. E. Shuryak, The QCD Vacuum, Hadrons and the Superderise Matter (World Scientific, Singapore, 1988) [Lecture Notes in Phys. 8]. T. Schäfer and E. Shuryak, hep-ph/9610451 (Rev. Mod. Phys., to appear) and references therein.
102. E. Shuryak, The QCD Vacuum, Hadrons and the Superderise Matter (World Scientific, Singapore, 1988) [Lecture Notes in Phys. 8]. T. Schäfer and E. Shuryak, hep-ph/9610451 (Rev. Mod. Phys., to appear) and references therein.
103. E. Shuryak, The QCD Vacuum, Hadrons and the Superderise Matter (World Scientific, Singapore, 1988) [Lecture Notes in Phys. 8]. T. Schäfer and E. Shuryak, hep-ph/9610451 (Rev. Mod. Phys., to appear) and references therein.
104. R. Crewther, Phys. Lett. B70 (1977), 349. For a review see: G. A. Christos, Phys. Rep. 116 (1984), 251.
105. R. Crewther, Phys. Lett. B70 (1977), 349. For a review see: G. A. Christos, Phys. Rep. 116 (1984), 251.
106. E. Witten, Nucl. Phys. B156 (1979), 269.
107. G. Veneziano, Nucl. Phys. B159 (1979), 213.
108. M. Voloshin, Yad. Fiz. 44 (1986), 738 [Sov. J. Nucl. Phys. 44 (1986), 478]; Yad. Fiz. 45 (1987), 190 [Sov. J. Nucl. Phys. 45 (1987), 122].
109. M. Voloshin, Yad. Fiz. 44 (1986), 738 [Sov. J. Nucl. Phys. 44 (1986), 478]; Yad. Fiz. 45 (1987), 190 [Sov. J. Nucl. Phys. 45 (1987), 122].
110. M. Voloshin, Yad. Fiz. 44 (1986), 738 [Sov. J. Nucl. Phys. 44 (1986), 478]; Yad. Fiz. 45 (1987), 190 [Sov. J. Nucl. Phys. 45 (1987), 122].
111. M. Voloshin, Yad. Fiz. 44 (1986), 738 [Sov. J. Nucl. Phys. 44 (1986), 478]; Yad. Fiz. 45 (1987), 190 [Sov. J. Nucl. Phys. 45 (1987), 122].
112. H. Leutwyler and M. Shifman, Phys. Lett. B221 (1989), 384.
113. I. Balitsky, D. Diakonov and A. Yung, Phys. Lett. B112 (1982), 71; Z. Phys. C33 (1986), 265. For a review see: D. Diakonov, in Proc. XXI Winter School of Physics (LINP. Leningrad, 1986), p. 3.
114. I. Balitsky, D. Diakonov and A. Yung, Phys. Lett. B112 (1982), 71; Z. Phys. C33 (1986), 265. For a review see: D. Diakonov, in Proc. XXI Winter School of Physics (LINP. Leningrad, 1986), p. 3.
115. I. Balitsky, D. Diakonov and A. Yung, Phys. Lett. B112 (1982), 71; Z. Phys. C33 (1986), 265. For a review see: D. Diakonov, in Proc. XXI Winter School of Physics (LINP. Leningrad, 1986), p. 3.
116. M. Shifman, Phys. Rep. 209 (1991), 341.
117. M. Shifman, Z. Phys. C9 (1981), 347.
118. T. Schäfer and E. Shuryak, Phys. Rev. Lett. 75 (1995), 1707.
119. C. Michael, in Proc. X Les Rencontres de Physique de la Vallee d'Aoste: Results and Perspectives in Particle Physics, La Thuile, Italy, March 1996 Results and Perspectives in Particle Physics, ed. M. Greco (Istituto Naz. Fis. Nucl., 1996) [hep-ph/9605243], T. DeGrand, hep-th/9610132.
120. C. Michael, in Proc. X Les Rencontres de Physique de la Vallee d'Aoste: Results and Perspectives in Particle Physics, La Thuile, Italy, March 1996 Results and Perspectives in Particle Physics, ed. M. Greco (Istituto Naz. Fis. Nucl., 1996) [hep-ph/9605243], T. DeGrand, hep-th/9610132.
121. P. van Baal and A. Kronfeld, Nucl. Phys. B (Proc. Suppl.) 9 (1989), 227.
122. K. Ishikawa, G. Schierholz, H. Schneider and M. Teper, Nucl. Phys. B227 (1983), 221. T. DeGrand, Phys. Rev. D36 (1987), 176. R. Gupta et al., Phys. Rev. D43 (1991), 2301.
123. K. Ishikawa, G. Schierholz, H. Schneider and M. Teper, Nucl. Phys. B227 (1983), 221. T. DeGrand, Phys. Rev. D36 (1987), 176. R. Gupta et al., Phys. Rev. D43 (1991), 2301.
124. K. Ishikawa, G. Schierholz, H. Schneider and M. Teper, Nucl. Phys. B227 (1983), 221. T. DeGrand, Phys. Rev. D36 (1987), 176. R. Gupta et al., Phys. Rev. D43 (1991), 2301.
125. P. de Forcrand and K.-F. Liu, Phys. Rev. Lett. 69 (1992), 245.
126. C. E. Carlson, T. H. Hansson and C. Peterson, Phys. Rev. D27 (1983), 1556; (E) D28 (1983), 2895. M. Chanowitz and S. Sharpe, Nucl. Phys. B222 (1983), 211.
127. C. E. Carlson, T. H. Hansson and C. Peterson, Phys. Rev. D27 (1983), 1556; (E) D28 (1983), 2895. M. Chanowitz and S. Sharpe, Nucl. Phys. B222 (1983), 211.
128. C. E. Carlson, T. H. Hansson and C. Peterson, Phys. Rev. D27 (1983), 1556; (E) D28 (1983), 2895. M. Chanowitz and S. Sharpe, Nucl. Phys. B222 (1983), 211.
129. B. L Ioffe and A. V. Smilga, JETP Lett. 37 (1983), 298; Nucl. Phys. B232 (1984), 109. I. Balitsky and A. Yung, Phys. Lett. B129 (1983), 328; see also chap. 7 in Ref. 2).
130. B. L Ioffe and A. V. Smilga, JETP Lett. 37 (1983), 298; Nucl. Phys. B232 (1984), 109. I. Balitsky and A. Yung, Phys. Lett. B129 (1983), 328; see also chap. 7 in Ref. 2).
131. B. L Ioffe and A. V. Smilga, JETP Lett. 37 (1983), 298; Nucl. Phys. B232 (1984), 109. I. Balitsky and A. Yung, Phys. Lett. B129 (1983), 328; see also chap. 7 in Ref. 2).
132. V. Nesterenko and A. Radyushkin, Phys. Lett. B115 (1982), 410. B. L Ioffe and A. V. Smilga, Nucl. Phys. B216 (1983), 373; see also chap. 6 in Ref. 2).
133. V. Nesterenko and A. Radyushkin, Phys. Lett. B115 (1982), 410. B. L Ioffe and A. V. Smilga, Nucl. Phys. B216 (1983), 373; see also chap. 6 in Ref. 2).
134. B. Blok and M. Shifman, Sov. J. Nucl. Phys. 45 (1987), 135, 301, 522; 46 (1987), 1310. For a review and a representative list of references see A. Khodjamirian and R. Rückl, hep-ph/9801443.
135. B. Blok and M. Shifman, Sov. J. Nucl. Phys. 45 (1987), 135, 301, 522; 46 (1987), 1310. For a review and a representative list of references see A. Khodjamirian and R. Rückl, hep-ph/9801443.
136. V. Belyaev and B. L. Ioffe. Int. J. Mod. Phys. A6 (1991), 1533. B. L. Ioffe and A. Khodjamirian, Phys. Rev. D51 (1995), 3373.
137. V. Belyaev and B. L. Ioffe. Int. J. Mod. Phys. A6 (1991), 1533. B. L. Ioffe and A. Khodjamirian, Phys. Rev. D51 (1995), 3373.
138. E. Shuryak, Nucl. Phys. B198 (1982), 83.
139. T. Aliev and V. Eletsky, Sov. J. Nucl. Phys. 38 (1983), 936.
140. E. Bagan, P. Ball, V. Braun and H. G. Dosch, Phys. Lett. B278 (1992), 457.
141. V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25 (1977), 510. A. V. Efremov and A. V. Radyushkin, Phys. Lett. B94 (1980), 245. G. P. Lepage and S. J. Brodsky, Phys. Lett. B87 (1979), 359; Phys. Rev. D22 (1980), 2157. For a review see: V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112 (1984), 173.
142. V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25 (1977), 510. A. V. Efremov and A. V. Radyushkin, Phys. Lett. B94 (1980), 245. G. P. Lepage and S. J. Brodsky, Phys. Lett. B87 (1979), 359; Phys. Rev. D22 (1980), 2157. For a review see: V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112 (1984), 173.
143. V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25 (1977), 510. A. V. Efremov and A. V. Radyushkin, Phys. Lett. B94 (1980), 245. G. P. Lepage and S. J. Brodsky, Phys. Lett. B87 (1979), 359; Phys. Rev. D22 (1980), 2157. For a review see: V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112 (1984), 173.
144. V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25 (1977), 510. A. V. Efremov and A. V. Radyushkin, Phys. Lett. B94 (1980), 245. G. P. Lepage and S. J. Brodsky, Phys. Lett. B87 (1979), 359; Phys. Rev. D22 (1980), 2157. For a review see: V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112 (1984), 173.
145. V. L. Chernyak and A. R. Zhitnitsky, JETP Lett. 25 (1977), 510. A. V. Efremov and A. V. Radyushkin, Phys. Lett. B94 (1980), 245. G. P. Lepage and S. J. Brodsky, Phys. Lett. B87 (1979), 359; Phys. Rev. D22 (1980), 2157. For a review see: V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112 (1984), 173.
146. V. M. Belyaev, V. M. Braun, A. Khodjamiryan and R. Rückl Phys. Rev. D51 (1995), 6177.
147. A. V. Radyushkin, Nucl. Phys. A532 (1991), 141; hep-ph/9707335.
148. A. Khodjamirian, hep-ph/9712451.
149. P. Ball, V. M. Braun and H. G. Dosch, Phys. Rev. D44 (1991), 3567.
150. N. S. Craigie and J. Stern, Nucl. Phys. B216 (1983), 209. I. Balitsky, V. Braun and A. Kolesnichenko, Nucl. Phys. B312 (1989), 509 and earlier works of the same authors cited therein.
151. N. S. Craigie and J. Stern, Nucl. Phys. B216 (1983), 209. I. Balitsky, V. Braun and A. Kolesnichenko, Nucl. Phys. B312 (1989), 509 and earlier works of the same authors cited therein.
152. V. Braun, hep-ph/9801222.
153. S. V. Mikhailov and A. V. Radyushkin, Phys. Rev. D45 (1992), 1754. A. V. Radyushkin, Phys. Lett. B271 (1991), 218. A. P. Bakulev and A. V. Radyushkin, Phys. Lett. B271 (1991), 223.
154. S. V. Mikhailov and A. V. Radyushkin, Phys. Rev. D45 (1992), 1754. A. V. Radyushkin, Phys. Lett. B271 (1991), 218. A. P. Bakulev and A. V. Radyushkin, Phys. Lett. B271 (1991), 223.
155. S. V. Mikhailov and A. V. Radyushkin, Phys. Rev. D45 (1992), 1754. A. V. Radyushkin, Phys. Lett. B271 (1991), 218. A. P. Bakulev and A. V. Radyushkin, Phys. Lett. B271 (1991), 223.
156. I. Bigi et al., Phys. Lett. B339 (1994), 160.
157. N. Isgur and M. Wise, Phys. Rev. D43 (1991), 819.
158. M. C. Chu et al., Nucl. Phys. B (Proc. Suppl.) 30 (1993), 495. J. W. Negele, M. Burkardt and J. M. Grandy, Ann. of Phys. 238 (1995), 441.
159. M. C. Chu et al., Nucl. Phys. B (Proc. Suppl.) 30 (1993), 495. J. W. Negele, M. Burkardt and J. M. Grandy, Ann. of Phys. 238 (1995), 441.
160. H. G. Dosch, O. Nachtmann and M. Reuter, hep-ph/9503386 (unpublished).
161. C. Michael, Nucl. Phys. B280 (1987), 13.
162. H. Rothe, Phys. Lett. B364 (1995), 227.
163. N. Evans, S. Hsu and M. Schwetz, hep-th/9707260.
164. M. Vysotsky, I. Kogan and M. Shifman, Yad. Fiz. 42 (1985), 504 [Sov. J. Nucl. Phys. 42 (1985), 318].
165. M. Vysotsky, I. Kogan and M. Shifman, Yad. Fiz. 42 (1985), 504 [Sov. J. Nucl. Phys. 42 (1985), 318].
166. G. 't Hooft, in Recent Developments in Gauge Theories, ed. G. 't Hooft et al. (Plenum Press, New York, 1980).
167. S. Dimopoulos, Nucl. Phys. B168 (1980), 69. M. Peskin, Nucl. Phys. B175 (1980), 197.
168. S. Dimopoulos, Nucl. Phys. B168 (1980), 69. M. Peskin, Nucl. Phys. B175 (1980), 197.
169. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229 (1983), 381; Phys. Lett. B166 (1986), 329. M. Shifman and A. Vainshtein, Nucl. Phys. B296 (1988), 445.
170. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229 (1983), 381; Phys. Lett. B166 (1986), 329. M. Shifman and A. Vainshtein, Nucl. Phys. B296 (1988), 445.
171. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229 (1983), 381; Phys. Lett. B166 (1986), 329. M. Shifman and A. Vainshtein, Nucl. Phys. B296 (1988), 445.
172. A. Kovner and M. Shifman, Phys. Rev. D56 (1997), 2396.
173. A. Belavin and A. Migdal, Pis'ma ZhETF 19 (1974), 317 [JETP Lett. 19 (1974), 181]; Scale Invariance and Bootstrap in the Non-Abelian Gauge Theories, Landau Institute Preprint-74-0894, 1974 (unpublished).
174. A. Belavin and A. Migdal, Pis'ma ZhETF 19 (1974), 317 [JETP Lett. 19 (1974), 181]; Scale Invariance and Bootstrap in the Non-Abelian Gauge Theories, Landau Institute Preprint-74-0894, 1974 (unpublished).
175. A. Belavin and A. Migdal, Pis'ma ZhETF 19 (1974), 317 [JETP Lett. 19 (1974), 181]; Scale Invariance and Bootstrap in the Non-Abelian Gauge Theories, Landau Institute Preprint-74-0894, 1974 (unpublished).
176. T. Banks and Zaks, Nucl. Phys. B196 (1982), 189.
177. T. Schäfer and E. Shuryak, Phys. Rev. D53 (1996), 6522.
178. Y. Iwasaki et al., Z. Phys. C71 (1996), 343.
179. A. Casher, Phys. Lett, B83 (1979), 395.
180. W. A. Bardeen et al., Phys. Rev. D18 (1978), 3998.
181. W. Marciano, Phys. Rev. D29 (1984), 580. R. M. Barnett, H. E. Haber and D. E. Soper, Nucl. Phys. B306 (1988), 697. G. Rodrigo and A. Santamaria, Phys. Lett, B313 (1993), 441.
182. W. Marciano, Phys. Rev. D29 (1984), 580. R. M. Barnett, H. E. Haber and D. E. Soper, Nucl. Phys. B306 (1988), 697. G. Rodrigo and A. Santamaria, Phys. Lett, B313 (1993), 441.
183. W. Marciano, Phys. Rev. D29 (1984), 580. R. M. Barnett, H. E. Haber and D. E. Soper, Nucl. Phys. B306 (1988), 697. G. Rodrigo and A. Santamaria, Phys. Lett, B313 (1993), 441.
184. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
185. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
186. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
187. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
188. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
189. W. Wetzel, Nucl. Phys. B196 (1982), 259. W. Bernreuther and W. Wetzel, Nucl. Phys. B197 (1982), 228. W. Bernreuther, Ann. of Phys. 151 (1983), 127; Z. Phys. C20 (1983), 331. S. Larin, T. van Ritbergen and J. A. M. Vermaseren, Nucl. Phys. B438 (1995), 278. K. Chetyrkin, B. A. Kniehl and M. Steinhauser, Phys. Rev. Lett. 79 (1997), 2184.
190. S. Brodsky, M. Gill and J. Rathman, hep-ph/9801330 and references therein.
191. M. Shifman, Int. J. Mod. Phys. A11 (1996), 5761.