Little miracles of supersymmetric evolution of gauge couplings

International Journal of Modern Physics A

Volumn 11, Issue 32, 1996, Pages 5761-5784

  Shifman, M ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000188540     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X96002650     Document Type: Article

References (63)

1. The paper of Gol'fand and Likhtman was published in April 1971 (JETP Lett. 13, 323). The work of Wess and Zumino, who came to supersymmetry from a totally different direction and were unaware of Gol'fand and Likhtman, appeared at the end of 1973 [Nucl. Phys. B70, 39 (1974)].
2. The paper of Gol'fand and Likhtman was published in April 1971 (JETP Lett. 13, 323). The work of Wess and Zumino, who came to supersymmetry from a totally different direction and were unaware of Gol'fand and Likhtman, appeared at the end of 1973 [Nucl. Phys. B70, 39 (1974)].
3. M. Shifman, Mod. Phys. Lett. A10, 605 (1995).
4. M. Shifman, Int. J. Mod. Phys. A11, 3195 (1996).
5. 2 structure functions of the deep inelastic neutrino nucleon scattering," preprint INR-0919/96 [hep-ph/9605367].
6. Z) in the most naive version of grand unification, see e.g. L. Roszkowski and M. Shifman, Phys. Rev. D53, 404 (1996).
7. H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).
8. See e.g. the recent review papers P. Langacker, Tests of the Standard Model and Searches for New Physics, in Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World Scientific, Singapore, 1994); G. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena, "Unification of couplings in the MSSM," Proc. Int. Europhysics Conf. on High Energy Physics, Brussels, 1995, eds. J. Lemonne, C. Vander Velde and F. Verbeure (World Scientific, Singapore, 1996), p. 481 [hep-ph/9603370] and and references therein.
9. See e.g. the recent review papers P. Langacker, Tests of the Standard Model and Searches for New Physics, in Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World Scientific, Singapore, 1994); G. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena, "Unification of couplings in the MSSM," Proc. Int. Europhysics Conf. on High Energy Physics, Brussels, 1995, eds. J. Lemonne, C. Vander Velde and F. Verbeure (World Scientific, Singapore, 1996), p. 481 [hep-ph/9603370] and and references therein.
10. See e.g. the recent review papers P. Langacker, Tests of the Standard Model and Searches for New Physics, in Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World Scientific, Singapore, 1994); G. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena, "Unification of couplings in the MSSM," Proc. Int. Europhysics Conf. on High Energy Physics, Brussels, 1995, eds. J. Lemonne, C. Vander Velde and F. Verbeure (World Scientific, Singapore, 1996), p. 481 [hep-ph/9603370] and and references therein.
11. H. Georgi, H. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974).
12. M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982).
13. M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982).
14. J. Ellis, S. Kelley and D. Nanopoulos, Phys. Lett. B260, 131 (1991); P. Langacker and M. X. Luo, Phys. Rev. D44, 817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260, 447 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991).
15. J. Ellis, S. Kelley and D. Nanopoulos, Phys. Lett. B260, 131 (1991); P. Langacker and M. X. Luo, Phys. Rev. D44, 817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260, 447 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991).
16. J. Ellis, S. Kelley and D. Nanopoulos, Phys. Lett. B260, 131 (1991); P. Langacker and M. X. Luo, Phys. Rev. D44, 817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260, 447 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991).
17. J. Ellis, S. Kelley and D. Nanopoulos, Phys. Lett. B260, 131 (1991); P. Langacker and M. X. Luo, Phys. Rev. D44, 817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260, 447 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991).
18. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229, 381 (1983); Phys. Lett. B166, 329 (1986).
19. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229, 381 (1983); Phys. Lett. B166, 329 (1986).
20. A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43, 1596 (1986) [Sov. J. Nucl. Phys. 43, 1028 (1986)], Sec. 3; see also Pis'ma ZhETF 42, 182 (1985) [JETP Lett. 42, 224 (1985)].
21. A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43, 1596 (1986) [Sov. J. Nucl. Phys. 43, 1028 (1986)], Sec. 3; see also Pis'ma ZhETF 42, 182 (1985) [JETP Lett. 42, 224 (1985)].
22. A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43, 1596 (1986) [Sov. J. Nucl. Phys. 43, 1028 (1986)], Sec. 3; see also Pis'ma ZhETF 42, 182 (1985) [JETP Lett. 42, 224 (1985)].
23. A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43, 1596 (1986) [Sov. J. Nucl. Phys. 43, 1028 (1986)], Sec. 3; see also Pis'ma ZhETF 42, 182 (1985) [JETP Lett. 42, 224 (1985)].
24. M. Shifman and A. Vainshtein, Nucl. Phys. B359, 571 (1991).
25. E. Cremmer, S. Ferrara, L. Girardello and A. van Proeyen, Nucl. Phys. B212, 413 (1983).
26. M. Shifman and A. Vainshtein, Nucl. Phys. B277, 456 (1986).
27. N. Seiberg, Phys. Lett. B318, 469 (1993).
28. M. Shifman and A. Vainshtein, Nucl. Phys. B296, 445 (1988).
29. L. Dixon, V. Kaplunovsky and J. Louis, Nucl. Phys. B355, 649 (1991).
30. M. Grisaru, M. Roček and W. Siegel, Nucl. Phys. B159, 429 (1979.
31. If all matter fields we have in the model belong to the fundamental representation of the gauge group then it is possible to prove that the NSVZ β function is exact also including nonperturbative effects. The proof can be abstracted from Ref. 16. In this work the gaugino condensate 〈λλ〉 was exactly calculated. Since 〈λλ〉 is in the same superfield as the anomaly of the trace of the stress tensor 〈λλ〉 has zero anomalous dimension; if it is known exactly the full β function that follows immediately.
32. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
33. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
34. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
35. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
36. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
37. The literature on this subject is so vast I cannot even scratch the top of the iceberg. Some recent publications are V. Barger, M. S. Berger and P. Ohnmann, Phys. Rev. D47, 1093 (1993); D. Castano, E. J. Piard and P. Ramond, Phys. Rev. D49, 4882 (1994); G. L. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D49, 6173 (1994); M. Carena et al., Phys. Lett. B317, 346 (1993); L. Clavelli and P. W. Coulter, Phys. Rev. D51, 3913 (1995); H. Dreiner and H. Pois, "Two loop supersymmetric renormalization group equations including R parity violation and aspects of unification," preprint ETH-TH-95-30 [hep-ph/9511444].
38. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
39. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
40. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
41. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
42. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
43. 0 Resonance, CERN Yellow Report 95-03, eds. D. Bardin, W. Hollik and G. Passarino, p. 313 [hep-ph/9502383], see also references therein. In the supersymmetric context various smoothing procedures are considered in the following papers: A. Faraggi and B. Grinstein, Nucl. Phys. B422, 3 (1994); M. Bastero-Gil and J. Perez-Mercader, Nucl. Phys. B450, 21 (1995); L. Clavelli and P. W. Coulter. "SUSY unification with smooth threshold behavior," preprint UAHEP-954 [hep-ph/9507261].
44. S. Dimopoulos 61nd H. Georgi, Nucl. Phys. B193, 150 (1981); N. Sakai, Z. Phys. C11, 153 (1981); For a review, see e.g. R. N. Mohapatra, Unification and Supersymmetry, 2nd Edition (Springer-Verlag, Berlin, 1992), Chap. 13.
45. S. Dimopoulos 61nd H. Georgi, Nucl. Phys. B193, 150 (1981); N. Sakai, Z. Phys. C11, 153 (1981); For a review, see e.g. R. N. Mohapatra, Unification and Supersymmetry, 2nd Edition (Springer-Verlag, Berlin, 1992), Chap. 13.
46. S. Dimopoulos 61nd H. Georgi, Nucl. Phys. B193, 150 (1981); N. Sakai, Z. Phys. C11, 153 (1981); For a review, see e.g. R. N. Mohapatra, Unification and Supersymmetry, 2nd Edition (Springer-Verlag, Berlin, 1992), Chap. 13.
47. Perhaps some elements can be maintained in a certain limited sense. The hope is not yet lost completely.
48. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
49. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
50. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
51. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
52. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
53. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
54. D. R. T. Jones and L. Mezincescu, Phys. Lett. B136, 242 (1984); A. Parkes and P. West, Phys. Lett. B138, 99 (1984); P. West, Phys. Lett. B137, 371 (1984); D. R. T. Jones and L. Mezincescu, Phys. Lett. B138, 293 (1984); J. E. Björkman and D. R. T. Jones, Nucl. Phys. B259, 533 (1985); I. Jack, D. R. T. Jones and C. G. North, "N = 1 supersymmetry and the three loop anomalous dimensions for the chiral superfield," preprint LTH 368 [hep-ph/9603386]; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
55. D. Kazakov, private communication; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
56. D. Kazakov, private communication; P. M. Fereira, I. Jack and D. R. T. Jones, "The three loop SSM β functions," preprint LTH 372 [hep-ph/9605440].
57. N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982); S. Weinberg, Phys. Rev. D26, 287 (1982); M. Vysotsky, Phys. Lett. B114, 125 (1982); T. M. Aliev and M. Vysotsky, Phys. Lett. B120, 119 (1983).
58. N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982); S. Weinberg, Phys. Rev. D26, 287 (1982); M. Vysotsky, Phys. Lett. B114, 125 (1982); T. M. Aliev and M. Vysotsky, Phys. Lett. B120, 119 (1983).
59. N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982); S. Weinberg, Phys. Rev. D26, 287 (1982); M. Vysotsky, Phys. Lett. B114, 125 (1982); T. M. Aliev and M. Vysotsky, Phys. Lett. B120, 119 (1983).
60. N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982); S. Weinberg, Phys. Rev. D26, 287 (1982); M. Vysotsky, Phys. Lett. B114, 125 (1982); T. M. Aliev and M. Vysotsky, Phys. Lett. B120, 119 (1983).
61. J. Hisano, H. Murayama and T. Yanagida, Nucl. Phys. B402, 46 (1993).
62. B. Blok, Cai-Dian Lu and Da-Xin Zhang, "Proton lifetime, Yukawa couplings and dynamical SUSY breaking in SU(5) GUT," preprint TECHNION-PH-96-5, [hep-ph/9602310].
63. Z) vs. proton lifetime," reprint OHSTPY-HEP-T-95-028 [hep-ph/9601303].