With neutrino masses revealed, proton decay is the missing link

International Journal of Modern Physics A

Volumn 14, Issue 19, 1999, Pages 2949-2976

  Pati, Jogesh C ^a  

^a Bldg 142   (United States)

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[No Author keywords available]

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EID: 0142117128     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X99001433     Document Type: Article

References (125)

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2. J. C. Pati, in Salam Festschrift, eds. A. Ali, J. Ellis and S. Randjbar-Daemi (World Scientific, 1993) pp. 368-391.
3. J. C. Pati, "Recollections of Abdus Salam: Scientist and Humanitarian" - Physics Today (abridged version), August (1997); News Letter of the American Chapter of the Indian Physics Association (1997).
4. J. C. Pati, "Recollections of Abdus Salam: Scientist and Humanitarian" - Physics Today (abridged version), August (1997); News Letter of the American Chapter of the Indian Physics Association (1997).
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8. For attempts to derive the current algebra framework using the singlet U(1) vector gluon see e.g. H. Fritzsch and M. Gell-Mann, Proc. 15th High Energy Conf., Batavia (1972), pages 135-165, and references therein. The difficulty of SU(9) or SU(12) global symmetry associated with the U(1) vector gluon coupling was one reason for abandoning this possibility: See J. C. Pati and A. Salam, ICTP preprint IC/73/81 (unpublished), and L. B. Okun and V. I. Zacharov, Phys. Lett. B47, 258 (1973).
9. For attempts to derive the current algebra framework using the singlet U(1) vector gluon see e.g. H. Fritzsch and M. Gell-Mann, Proc. 15th High Energy Conf., Batavia (1972), pages 135-165, and references therein. The difficulty of SU(9) or SU(12) global symmetry associated with the U(1) vector gluon coupling was one reason for abandoning this possibility: See J. C. Pati and A. Salam, ICTP preprint IC/73/81 (unpublished), and L. B. Okun and V. I. Zacharov, Phys. Lett. B47, 258 (1973).
10. For attempts to derive the current algebra framework using the singlet U(1) vector gluon see e.g. H. Fritzsch and M. Gell-Mann, Proc. 15th High Energy Conf., Batavia (1972), pages 135-165, and references therein. The difficulty of SU(9) or SU(12) global symmetry associated with the U(1) vector gluon coupling was one reason for abandoning this possibility: See J. C. Pati and A. Salam, ICTP preprint IC/73/81 (unpublished), and L. B. Okun and V. I. Zacharov, Phys. Lett. B47, 258 (1973).
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14. J. C. Pati and A. Salam, Proc. 15th High Energy Conference, published by National Accelerator Laboratory, Batavia, reported by J. D. Bjorken, Vol. 2, p. 301 (1972); Phys. Rev. 8, 1240 (1973).
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16. J. C. Pati and A. Salam, Phys. Rev. Lett. 31, 661 (1973); Phys. Rev. D10, 275 (1974).
17. 8 assuming that all three forces have a gauge-origin.
18. c which would lead to gauge integer charge quarks (icq), with possibly semiconfined but ultimately liberated quarks. The two alternatives arise within the same theory depending upon the nature of SSB. Salam and I, (Phys. Rev. Lett. 36, 11 (1976)), as well as others, notably G. Rajasekaran and P. Roy (Pramana 6, 303 (1975)), therefore proposed key experiments which could distinguish between the two alternatives. Eventually, by the 1980's, on the basis of these tests, especially the two-photon experiments (see e.g. R. Godbole, J. Pati, S. Rindani, T. Jayaraman and G. Rajasekaran, Phys. Lett. 142, 91 (1984)), fcq was clearly favored over gauge icq. The basic ideas of higher unification, as also the success of the (combined) standard model symmetry, are of course independent of the nature of quark-charges.
19. c which would lead to gauge integer charge quarks (icq), with possibly semiconfined but ultimately liberated quarks. The two alternatives arise within the same theory depending upon the nature of SSB. Salam and I, (Phys. Rev. Lett. 36, 11 (1976)), as well as others, notably G. Rajasekaran and P. Roy (Pramana 6, 303 (1975)), therefore proposed key experiments which could distinguish between the two alternatives. Eventually, by the 1980's, on the basis of these tests, especially the two-photon experiments (see e.g. R. Godbole, J. Pati, S. Rindani, T. Jayaraman and G. Rajasekaran, Phys. Lett. 142, 91 (1984)), fcq was clearly favored over gauge icq. The basic ideas of higher unification, as also the success of the (combined) standard model symmetry, are of course independent of the nature of quark-charges.
20. c which would lead to gauge integer charge quarks (icq), with possibly semiconfined but ultimately liberated quarks. The two alternatives arise within the same theory depending upon the nature of SSB. Salam and I, (Phys. Rev. Lett. 36, 11 (1976)), as well as others, notably G. Rajasekaran and P. Roy (Pramana 6, 303 (1975)), therefore proposed key experiments which could distinguish between the two alternatives. Eventually, by the 1980's, on the basis of these tests, especially the two-photon experiments (see e.g. R. Godbole, J. Pati, S. Rindani, T. Jayaraman and G. Rajasekaran, Phys. Lett. 142, 91 (1984)), fcq was clearly favored over gauge icq. The basic ideas of higher unification, as also the success of the (combined) standard model symmetry, are of course independent of the nature of quark-charges.
21. D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); D. Politzer, ibid. 30, 1346 (1973).
22. D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); D. Politzer, ibid. 30, 1346 (1973).
23. R. N. Mohapatra and J. C. Pati, Phys. Rev. D11, 566 (1974); Phys. Rev. D11, 2558 (1975); G. Senjanovic and R. N. Mohapatra, Phys. Rev. D12, 1502 (1975).
24. R. N. Mohapatra and J. C. Pati, Phys. Rev. D11, 566 (1974); Phys. Rev. D11, 2558 (1975); G. Senjanovic and R. N. Mohapatra, Phys. Rev. D12, 1502 (1975).
25. R. N. Mohapatra and J. C. Pati, Phys. Rev. D11, 566 (1974); Phys. Rev. D11, 2558 (1975); G. Senjanovic and R. N. Mohapatra, Phys. Rev. D12, 1502 (1975).
26. V. Kuzmin, Va. Rubakov and M. Shaposhnikov, Phys. Lett BM155, 36 (1985); M. Fukugita and T. Yanagida, Phys. Lett. B174, 45 (1986); M. A. Luty, Phys. Rev. D45, 455 (1992); W. Buchmuller and M. Plumacher, hep-ph/9608308.
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29. V. Kuzmin, Va. Rubakov and M. Shaposhnikov, Phys. Lett BM155, 36 (1985); M. Fukugita and T. Yanagida, Phys. Lett. B174, 45 (1986); M. A. Luty, Phys. Rev. D45, 455 (1992); W. Buchmuller and M. Plumacher, hep-ph/9608308.
30. J. C. Pati, Proc. Seoul Symposium on Elementary Particle Physics in Memory of B. W. Lee (1978), p. 481.
31. J. C. Pati, A. Salam and J. Strathdee, Il. Nuovo Com. A26, 77 (1975).
32. H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).
33. H. Georgi, in Particles and Fields, ed. C. Carlson (AIP, New York, 1975), p. 575; H. Fritzsch and P. Minkowski, Ann. Phys. 93, 193 (1975).
34. H. Georgi, in Particles and Fields, ed. C. Carlson (AIP, New York, 1975), p. 575; H. Fritzsch and P. Minkowski, Ann. Phys. 93, 193 (1975).
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36. F. Gürsey, P. Ramond and P. Sikivie, Phys. Lett. B60, 177 (1976).
37. The SuperKamiokande Collaboration: "Evidence for oscillation of atmospheric neutrinos," ICRR-Report-422-98-18 (July, 1998).
38. J. C. Pati, "Implications of the SuperKamiokande result on the nature of the new physics," UMD-PP-99-01, hep-ph/9807315; to appear in Proc. Neutrino-98 Conf. held at Takayama, Japan, June, 1998.
39. J. C. Pati, "Implications of the SuperKamiokande result on the nature of the new physics," UMD-PP-99-01, hep-ph/9807315; to appear in Proc. Neutrino-98 Conf. held at Takayama, Japan, June, 1998.
40. See e.g. K. R. Dienes and J. March-Russell, hep-th/9604112; K. R. Dienes, hep-ph/9606467.
41. M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, eds. F. van Nieuwenhuizen and D. Freedman (Amsterdam, North-Holland, 1979) p. 315; T. Yanagida, in Workshop on the Unified Theory and Baryon Number in the Universe, eds. O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979), p. 95; R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
42. M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, eds. F. van Nieuwenhuizen and D. Freedman (Amsterdam, North-Holland, 1979) p. 315; T. Yanagida, in Workshop on the Unified Theory and Baryon Number in the Universe, eds. O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979), p. 95; R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
43. M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, eds. F. van Nieuwenhuizen and D. Freedman (Amsterdam, North-Holland, 1979) p. 315; T. Yanagida, in Workshop on the Unified Theory and Baryon Number in the Universe, eds. O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979), p. 95; R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
44. For reviews, see e.g. P. Langacker, talk at Gatlinburg Conference, June 94, hep-ph 9411247, and P. Langacker and N. Polonsky, Phys. Rev. D52, 3081 (1995), and references therein.
45. For reviews, see e.g. P. Langacker, talk at Gatlinburg Conference, June 94, hep-ph 9411247, and P. Langacker and N. Polonsky, Phys. Rev. D52, 3081 (1995), and references therein.
46. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
47. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
48. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
49. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
50. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
51. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
52. For recent work, see P. Langacker and M. Luo, Phys. Rev. D44,817 (1991); U. Amaldi, W. de Boer and H. Furstenau, Phys. Lett. B260 (1991); J. Ellis, S. Kelley and D. V. Nanopoulos, Phys. Lett. B260, 131 (1991); F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A104, 1817 (1991). The essential features pertaining to coupling unification in SUSY GUTS were noted earlier by S. Dimopoulos, S. Raby and F. Wilczek, Phys. Rev. D24, 1681 (1981); W. Marciano and G. Senjanovic, Phys. Rev. D25, 3092 (1982); M. Einhorn and D. R. T. Jones, Nucl. Phys. B196, 475 (1982).
53. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
54. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
55. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
56. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
57. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
58. M. Green and J. H. Schwarz, Phys. Lett. B149, 117 (1984); D. J. Gross, J. A. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 54, 502 (1985); P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985). For introductions and reviews, see: M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vois. 1 and 2 (Cambridge University Press); M. Dine, String Theory in Four Dimensions (North-Holland, 1988); J. Polchinski, What is String Theory?, 1994 Les Houches Lectures, hep-th/9411028.
59. The literature on string-dualities and M theory is large. A few pioneering papers relevant to gauge-coupling unification are: E. Witten, Nucl. Phys. B443, 85 (1995), P. Horava and E. Witten, Nucl. Phys. B460, 506 (1996). For reviews, see e.g. J. Polchinski, hep-th/9511157; A. Sen, hep-th/9802051, and references therein. For a layman's guide, see M. Duff (talk at this meeting), hep-ph/9805177 V3.
60. The literature on string-dualities and M theory is large. A few pioneering papers relevant to gauge-coupling unification are: E. Witten, Nucl. Phys. B443, 85 (1995), P. Horava and E. Witten, Nucl. Phys. B460, 506 (1996). For reviews, see e.g. J. Polchinski, hep-th/9511157; A. Sen, hep-th/9802051, and references therein. For a layman's guide, see M. Duff (talk at this meeting), hep-ph/9805177 V3.
61. The literature on string-dualities and M theory is large. A few pioneering papers relevant to gauge-coupling unification are: E. Witten, Nucl. Phys. B443, 85 (1995), P. Horava and E. Witten, Nucl. Phys. B460, 506 (1996). For reviews, see e.g. J. Polchinski, hep-th/9511157; A. Sen, hep-th/9802051, and references therein. For a layman's guide, see M. Duff (talk at this meeting), hep-ph/9805177 V3.
62. P. Ginsparg, Phys. Lett. B197, 139 (1987); V. S. Kaplunovsky, Nucl. Phys. B307, 145 (1988); erratum, ibid. B382, 436 (1992).
63. P. Ginsparg, Phys. Lett. B197, 139 (1987); V. S. Kaplunovsky, Nucl. Phys. B307, 145 (1988); erratum, ibid. B382, 436 (1992).
64. For an early review on this issue, see e.g. S. Weinberg, summary talk, Proc. 26th Int. Conf. on High Energy Physics (Dallas, Texas, 1992).
65. For a recent discussion, see K. Dienes, Phys. Rep. 287, 447 (1997), (hep-th/9602045), and references therein.
66. E. Witten, hep-th/9602070.
67. See e.g. D. Lewellen, Nucl. Phys. B337, 61 (1990); A. Font, L. Ibanez and F. Quevedo, Nucl. Phys. B345, 389 (1990); S. Chaudhari, G. Hockney and J. Lykken, Nucl. Phys. B456, 89 (1995) and hep-th/9510241; G. Aldazabal, A. Font, L. Ibanez and A. Uranga, Nucl. Phys. B452, 3 (1995); ibid. B465, 34 (1996); D. Finnell, Phys. Rev. D53, 5781 (1996); A. A. Maslikov, I. Naumov and G. G. Volkov, Int. J. Mod. Phys. A11, 1117 (1996); J. Erler, hep-th/9602032 and G. Cleaver, hep-th/9604183; and Z. Kakushadze and S. H. Tye, hep-th/9605221, and hep-th/9609027; Z. Kakushadze et al., hep-ph/9705202.
68. See e.g. D. Lewellen, Nucl. Phys. B337, 61 (1990); A. Font, L. Ibanez and F. Quevedo, Nucl. Phys. B345, 389 (1990); S. Chaudhari, G. Hockney and J. Lykken, Nucl. Phys. B456, 89 (1995) and hep-th/9510241; G. Aldazabal, A. Font, L. Ibanez and A. Uranga, Nucl. Phys. B452, 3 (1995); ibid. B465, 34 (1996); D. Finnell, Phys. Rev. D53, 5781 (1996); A. A. Maslikov, I. Naumov and G. G. Volkov, Int. J. Mod. Phys. A11, 1117 (1996); J. Erler, hep-th/9602032 and G. Cleaver, hep-th/9604183; and Z. Kakushadze and S. H. Tye, hep-th/9605221, and hep-th/9609027; Z. Kakushadze et al., hep-ph/9705202.
69. See e.g. D. Lewellen, Nucl. Phys. B337, 61 (1990); A. Font, L. Ibanez and F. Quevedo, Nucl. Phys. B345, 389 (1990); S. Chaudhari, G. Hockney and J. Lykken, Nucl. Phys. B456, 89 (1995) and hep-th/9510241; G. Aldazabal, A. Font, L. Ibanez and A. Uranga, Nucl. Phys. B452, 3 (1995); ibid. B465, 34 (1996); D. Finnell, Phys. Rev. D53, 5781 (1996); A. A. Maslikov, I. Naumov and G. G. Volkov, Int. J. Mod. Phys. A11, 1117 (1996); J. Erler, hep-th/9602032 and G. Cleaver, hep-th/9604183; and Z. Kakushadze and S. H. Tye, hep-th/9605221, and hep-th/9609027; Z. Kakushadze et al., hep-ph/9705202.
70. See e.g. D. Lewellen, Nucl. Phys. B337, 61 (1990); A. Font, L. Ibanez and F. Quevedo, Nucl. Phys. B345, 389 (1990); S. Chaudhari, G. Hockney and J. Lykken, Nucl. Phys. B456, 89 (1995) and hep-th/9510241; G. Aldazabal, A. Font, L. Ibanez and A. Uranga, Nucl. Phys. B452, 3 (1995); ibid. B465, 34 (1996); D. Finnell, Phys. Rev. D53, 5781 (1996); A. A. Maslikov, I. Naumov and G. G. Volkov, Int. J. Mod. Phys. A11, 1117 (1996); J. Erler, hep-th/9602032 and G. Cleaver, hep-th/9604183; and Z. Kakushadze and S. H. Tye, hep-th/9605221, and hep-th/9609027; Z. Kakushadze et al., hep-ph/9705202.
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