Reconciling supersymmetric grand unification with αs(mZ)≈0.11

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 53, Issue 1, 1996, Pages 404-412

  Roszkowski, L ^a   Shifman, M ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001532099     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.53.404     Document Type: Article

References (197)

1. P. Langacker, Precision Tests of the Standard Electroweak Model, edited by P. Langacker (World Scientific, Singapore, 1994); presented at the International Symposium on Radiative Corrections, Gaitlinburg, Tennessee, 1994 (unpublished); Report No. hep ph/9411247 (unpublished).
2. P. Langacker and N. Polonsky, Phys. Rev. D 47, 4028 (1993).[For an update see N. Polonsky, Ph.D. thesis, University of Pennsylvania, 1994.]
3. Earlier calculations were phrased in different terms, but the conclusions were the same;
4. see, e.g., U. Amaldi, W. de Boer and H. Fürstenau, Phys. Lett. B 260, 443 (1991);
5. J. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. B 260, 131 (1991);
6. P. Langacker and M. X. Luo, Phys. Rev. D 44, 817 (1991);
7. F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A 104, 1817 (1991);
8. F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A 105, 581 (1992).
9. For reviews, see, e.g., H. P. Nilles, Phys. Rep. 110, 1 (1984);
10. H.E. Haber and G.L. Kane, Phys. Rep. 117, 75 (1985);
11. L.E. Ibánez and G.G. Ross, in Perspectives in Higgs, edited by G.L. Kane (World Scientific, Singapore, 1993)
12. R. Mohapatra, Unification and Supersymmetry, 2nd ed. (Springer Verlag, Berlin, 1992).
13. A. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49, 970 (1982);
14. L.E. Ibánez, Phys. Lett. 118B, 73 (1982);
15. J. Ellis, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. 121B, 123 (1983);
16. H.P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. 120B, 346 (1982);
17. R. Barbieri, S. Ferrara and C. Savoy, Phys. Lett. 119B, 343 (1982).
18. R.G. Roberts and G.G. Ross, Nucl. Phys. B377, 571 (1992).
19. R.G. Roberts and L. Roszkowski, Phys. Lett. B 309, 329 (1993).
20. G. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D 49, 6173 (1994).
21. R. Arnowitt and P. Nath, Phys. Lett. B 287, 89 (1992);
22. S. Kelley, J.L. Lopez, D.V. Nanopoulos, H. Pois and K. Yuan, Phys. Lett. B 273, 423 (1991);
23. D.J. Castano, E.J. Piard and P. Ramond, Phys. Rev. D 49, 4882 (1994);
24. B. de Carlos and A. Casas, Phys. Lett. B 309, 320 (1993);
25. V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 49, 4908 (1994).
26. L.E. Ibánez and G.G. Ross, Phys. Lett. 110B, 215 (1982);
27. K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Progr. Theor. Phys. 68, 927 (1982);
28. L. Alvarez Gaumé, J. Polchinski and M. Wise, Nucl. Phys. B221, 495 (1983);
29. J. Ellis, D.V. Nanopoulos, and K. Tamvakis citeminisugra.
30. P. Langacker and N. Polonsky, Phys. Rev. D 52, 3081 (1995).
31. Reference citeLangacker quotes even a higher value, αs(mZ)=0.127 pm0.005. The errors are believed to be dominated by theoretical uncertainties. The most exhaustive theoretical analysis is done for the total hadronic width Γ (Z→hadrons). The error quoted above, Δαs(mZ) = pm 0.005, is essentially determined by analyzing Γ (Z→hadrons).
32. M. Shifman, Mod. Phys. Lett. A 10, 605 (1995).
33. G. Altarelli, in QCD 20 Years Later, Proceedings of the Workshop, Aachen, Germany, 1992, edited by P. Zerwas and H. Kastrup (World Scientific, Singapore, 1993), Vol. 1, p. 172
34. S. Bethke, in QCD '94, Proceedings of the International Conference, Montpellier, France, 1994, edited by S. Narison [Nucl. Phys. B (Proc. Suppl.) 39B (1995).
35. An example of the DIS data analysis can be found, e.g., in M. Virchaux and A. Milsztajn, Phys. Lett. B 274, 221 (1992);
36. A. Martin, W. Stirling and R. Roberts, Phys. Lett. B 354, 155 (1995).
37. A nice compilation is given in cite Altarelli.
38. A.X. El Khadra, G. Hockney, A. Kronfeld and P. Mackenzie, Phys. Rev. Lett. 69, 729 (1992).
39. C. Davies, K. Hornbostel, G.P. Lepage, A. Lidsey, J. Shigemitsu and J. Sloan, Phys. Lett. B 345, 42 (1995).
40. G. Altarelli, R. Barbieri, and F. Caravaglios, in Results and Perspectives in Particle Physics, Proceedings of the 1993 Rencontres de Physique de la Vallée d’Aoste, edited by M. Greco (Editions Frontières, Gif sur Yvette, 1993), p. 351.
41. A. Blondel and C. Verzegnassi, Phys. Lett. B 311, 346 (1993).
42. S. Eidelman, L. Kurdadze and A. Vainshtein, Phys. Lett. 82B, 278 (1979).
43. M. Voloshin, Int. J. Mod. Phys. A 10, 2865 (1995).
44. The following terminology is used throughout the paper: if () is 0.12 or larger it will be referred to as “large "; if () is close to 0.11 it will be referred to as “small.
45. M. Consoli and F. Ferroni, Phys. Lett. B 349, 375 (1995).
46. D. Ring, S. Urano and R. Arnowitt, Phys. Rev. D 52, 6623 (1995).
47. T. Dasgupta, P. Mamales and P. Nath, Phys. Rev. D 52, 5366 (1995).
48. L. Clavelli and P.W. Coulter, Phys. Rev. D 51, 3913 (1995).
49. D. G. Lee and R.N. Mohapatra, Phys. Rev. D 52, 4125 (1995).
50. M. Dine, A.E. Nelson, Y. Nir, and Y. Shirman, Phys. Rev. D (to be published).
51. J. Ellis, S. Kelley and D.V. Nanopoulos, Nucl. Phys. B373, 55 (1992);
52. J. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. B 287, 95 (1992)
53. J. Hisano, H. Murayama and T. Yanagida, Phys. Rev. Lett. 69, 1014 (1992).
54. V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 47, 1093 (1993).
55. Particle Data Group (PDG), L. Montanet, et al., Phys. Rev. D 50, 1173 (1994).
56. A. Martin and D. Zeppenfeld, Phys. Lett. B 345, 558 (1995);
57. M.L. Swartz, “Reevaluation of the Hadronic Contribution to α (,” Report No. SLAC PUB 6710, hep ph/9411353 (unpublished)
58. S. Eidelman and F. Jegerlehner, Z. Phys. C 67, 585 (1995).
59. Let us parenthetically note that some authors investigate a wider range of variations of sin2 thetaW(mZ). For instance, in the first paper of citeurano the highest value considered was sin2 thetaW(mZ)=0.2327. As was explained above inching sin2 thetaW(mZ) up one lowers the minimal value of αs(mZ). Thus, these authors find that in the CMSSM with the Planck mass correction switched off is αs(mZ) min approx 0.114. The question whether the value sin2 thetaW(mZ)=0.2327 is admissible left open; we stick to Eq. (refs2winput: eq).
60. J. Erler and P. Langacker, Phys. Rev. D 52, 441 (1995).
61. CDF Collaboration, F. Abe, et al., Phys. Rev. Lett. 74, 2626 (1995).
62. D0 Collaboration, S. Abachi, et al., Phys. Rev. Lett. 74, 2632 (1995).
63. J. Chyla and A. Kataev, in Reports, Proceedings of the Workshop Group on Precision calculations for the Z. Resonance, Geneva, Switzerland, 1994, edited by D. Badin et al. (CERN Report No. 95 03, Geneva, 1995), Report No. hep ph/9502383 (unpublished).
64. L.E. Ibánez and C. López, Nucl. Phys. B233, 511 (1984);
65. L.E. Ibánez, C. López and C. Munoz, Nucl. Phys. B256, 218 (1985).
66. See, e.g., L. Galtieri, in Beyond the Standard Model IV, Proceeding of the Conference, Lake Tahoe, 1994, edited by J. Gunion, T. Han, and J. Ohnemus (World Scientific, Singapore, 1995)
67. D0 Collaboration, A. Jonckheere, Beyond the Standard Model IV, Proceeding of the Conference, Lake Tahoe, 1994, edited by J. Gunion, T. Han, and J. Ohnemus (World Scientific, Singapore, 1995);
68. D0 Collaboration, S. Eno, in Electroweak Interactions and Unified Theories, Proceedings of the XXX Rencontre de Moriond, Les Arcs, France, 1995, edited by J. Tran Thanh Van (Editions Frontieres, Gif sur Yvette, in press);
69. D0 Collaboration, M. Paterno, in Proceedings of Les Rencontres de Physique de la Vallee d’Aoste, La Thuile, Italy, 1995, edited by G. Belletini (unpublished)
70. CDF CollaborationF. Abe, Phys. Rev. Lett. 69, 3439 (1992);
71. D0 Collaboration, S. Abachi, et al., Phys. Rev. Lett. 75, 618 (1995).
72. In a recent work of J. Bagger, et al., Phys. Lett. B 348, 443 (1995), the nonleading mass threshold effects were found to be substantial in the CMSSM for 150 rmGeV a corrected evolution curve significantly deviates from the leading log (LL) result. The reason is quite obvious: a jump in the slope of the LL evolution curve is due to the fact that at approx 120 rmGeV the W ino becomes lighter than Z and freezes out. Nothing of the kind happens in our analysis and we generally do not expect the nonleading mass threshold effects to be large.
73. L.R. thanks Dennis Silverman for this remark.
74. K. Griest and L. Roszkowski, Phys. Rev. D 46, 3309 (1992).
75. A. Bartl, H. Fraas, W. Majerotto and N. Oshima, Phys. Rev. D 40, 1594 (1989);
76. M. Drees and X. Tata, Phys. Rev. D 43, 1971 (1991).
77. J. Ellis, K. Enqvist, D. Nanopoulos and K. Tamvakis, Phys. Lett. 155B, 381 (1985).
78. M. Drees, Phys. Lett. 158B, 409 (1985).
79. R. Arnowitt (private communication); K. Kounnas (private communication).
80. K. Hagiwara and H. Murayama, Phys. Lett. B 246, 533 (1990).
81. G. Bhattacharyya and A. Raychaudhuri, Phys. Rev. D 47, 2014 (1993);
82. A. Djouadi, M. Drees and H. Konig, Phys. Rev. D 48, 308 (1993);
83. N. Krasnikov, Phys. Lett. B 318, 174 (1993).
84. J. Wells, G. Kane and C. Kolda, Phys. Lett. B 338, 219 (1994).
85. I. Bigi, B. Blok, M. Shifman and A. Vainshtein, Phys. Lett. B 323, 408 (1994).
86. E. Bagan, P. Ball and V. Braun, Nucl. Phys. B432, 3 (1994);
87. E. Bagan, P. Ball, V. Braun and P. Gosdzinsky, Phys. Lett. B 342, 362 (1995).
88. E. Bagan, P. Ball, B. Fiol and P. Gosdzinsky, Phys. Lett. B 351, 546 (1995).
89. R. Patterson, in Proceedings of the International Conference on High Energy Physics, Glasgow, Scotland, 1994, edited by P. J. Bussey and I. G. Knowles (IOP, London, 1995)
90. P. Roudeau, in Proceedings of the International Conference on High Energy Physics, Glasgow, Scotland, 1994, edited by P. J. Bussey and I. G. Knowles (IOP, London, 1995)
91. A. Kagan (private communication); and (unpublished).
92. A. Kagan, Phys. Rev. D 51, 6196 (1995).
93. CLEO Collaboration, M.S. Alam, et al., Phys. Rev. Lett. 74, 2885 (1995).
94. V. Barger, M.S. Berger, P. Ohmann and R.J.N. Phillips, Phys. Lett. B 314, 351 (1993);
95. M. Carena, S. Pokorski and C. Wagner, Nucl. Phys. B406, 59 (1993).
96. P. Langacker and N. Polonsky, Phys. Rev. D 49, 1454 (1994).
97. V. Barger, M.S. Berger, and P. Ohmann, in Supersymmetry and Unification of Fundamental Interaction (SUSY 93), Proceedings of the International Workshop, Boston, Massachusetts, 1993, edited by P. Nath (World Scientific, Singapore, 1993), Report No. hep/ph 9305236 (unpublished).
98. H. Georgi and S.L. Glashow, Phys. Rev. Lett. 32, 438 (1974);
99. H. Georgi, H.R. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974).
100. P. Langacker, Precision Tests of the Standard Electroweak Model, edited by P. Langacker (World Scientific, Singapore, 1994); presented at the International Symposium on Radiative Corrections, Gaitlinburg, Tennessee, 1994 (unpublished); Report No. hep ph/9411247 (unpublished).
101. P. Langacker and N. Polonsky, Phys. Rev. D 47, 4028 (1993). [For an update see N. Polonsky, Ph.D. Thesis, University of Pennsylvania, 1994.]
102. Earlier calculations were phrased in different terms, but the conclusions were the same
103. see, e.g., U. Amaldi, W. de Boer and H. Fürstenau, Phys. Lett. B 260, 443 (1991);
104. J. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. B 260, 131 (1991);
105. P. Langacker and M. X. Luo, Phys. Rev. D 44, 817 (1991);
106. F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A 104, 1817 (1991);
107. F. Anselmo, L. Cifarelli, A. Peterman and A. Zichichi, Nuovo Cimento A 105, 581 (1992).
108. For reviews, see, e.g., H. P. Nilles, Phys. Rep. 110, 1 (1984);
109. H.E. Haber and G.L. Kane, Phys. Rep. 117, 75 (1985);
110. L.E. Ibánez and G.G. Ross, in Perspectives in Higgs, edited by G.L. Kane (World Scientific, Singapore, 1993).
111. R. Mohapatra, Unification and Supersymmetry, 2nd edition (Springer Verlag, Berlin, 1992).
112. A. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49, 970 (1982);
113. L.E. Ibánez, Phys. Lett. B 118, 73 (1982);
114. J. Ellis, D.V. Nanopoulos and K. Tamvakis, Phys. Lett. B 121, 123 (1983);
115. H.P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B 120B, 346 (1982);
116. R. Barbieri, S. Ferrara and C. Savoy, Phys. Lett. B 119B, 343 (1982).
117. R.G. Roberts and G.G. Ross, Nucl. Phys. B377, 571 (1992).
118. R.G. Roberts and L. Roszkowski, Phys. Lett. B 309, 329 (1993).
119. G. Kane, C. Kolda, L. Roszkowski and J. Wells, Phys. Rev. D 49, 6173 (1994).
120. R. Arnowitt and P. Nath, Phys. Lett. B 287, 89 (1992);
121. S. Kelley, J.L. Lopez, D.V. Nanopoulos, H. Pois and K. Yuan, Phys. Lett. B 273, 423 (1991);
122. D. J. Castano, E. J. Piard and P. Ramond, Phys. Rev. D 49, 4882 (1994);
123. B. De Carlos and A. Casas, Phys. Lett. B 309, 320 (1993).
124. V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 49, 4908 (1994).
125. L.E. Ibánez and G.G. Ross, Phys. Lett. 110B, 215 (1982);
126. K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Progr. Theor. Phys. 68, 927 (1982);
127. L. Alvarez Gaumé, J. Polchinski and M. Wise, Nucl. Phys. B221, 495 (1983);
128. Ellis, Nanopoulos, and Tamvakis citeminisugra.
129. P. Langacker and N. Polonsky, Phys. Rev. D 52, 3081 (1995).
130. Reference citeLangacker quotes even a higher value, αs(mZ)=0.127 pm0.005. The errors are believed to be dominated by theoretical uncertainties. The most exhaustive theoretical analysis is done for the total hadronic width Γ (Z→hadrons). The error quoted above, Δαs(mZ) = pm 0.005, is essentially determined by analyzing Γ (Z→hadrons).
131. M. Shifman, Mod. Phys. Lett. A 10, 605 (1995).
132. G. Altarelli, QCD 20 Years Later, Proceedings of the Workshop, Aachen, Germany, 1992, edited by P. Zerwas and H. Kastrup (World Scientific, Singapore, 1993), Vol. 1, p. 172; S. Bethke, QCD '94, Proceedings of the International Conference, Montpellier, France, 1994, [edited by S. Narison [Nucl. Phys. B (Proc. Suppl.) 39B, (1991)].
133. An example of the DIS data analysis can be found, e.g., in M. Virchaux and A. Milsztajn, Phys. Lett. B 274, 221 (1992)
134. A. Martin, W. Stirling and R. Roberts, Phys. Lett. B 354, 155 (1995).
135. A nice compilation is given in citeAltarelli.
136. A.X. El Khadra, G. Hockney, A. Kronfeld and P. Mackenzie, Phys. Rev. Lett. 69, 729 (1992).
137. C. Davies, K. Hornbostel, G.P. Lepage, A. Lidsey, J. Shigemitsu and J. Sloan, Phys. Lett. B 345, 42 (1995).
138. G. Altarelli, R. Barbieri, and F. Caravaglios, in Results and Perspectives in Particle Physics, Proceedings of the 1993 Rencontres de Physique de la Vallée d’Aoste, edited by M. Greco (Editions Frontières, Gif sur Yvette, 1993), p. 351.
139. A. Blondel and C. Verzegnassi, Phys. Lett. B B11, 346 (1993).
140. S. Eidelman, L. Kurdadze and A. Vainshtein, Phys. Lett. 82B, 278 (1979).
141. M. Voloshin, Int. J. Mod. Phys. A 10, 2865 (1995).
142. The following terminology is used throughout the paper: if () is 0.12 or larger it will be referred to as “large "; if () is close to 0.11 it will be referred to as “small.”
143. M. Consoli and F. Ferroni, Phys. Lett. B 389, 375 (1995).
144. D. Ring, S. Urano and R. Arnowitt, Phys. Rev. D 52, 6623 (1995).
145. T. Dasgupta, P. Mamales and P. Nath, Phys. Rev. D 52, 5366 (1995).
146. L. Clavelli and P.W. Coulter, Phys. Rev. D 51, 3913 (1995).
147. D. G. Lee and R.N. Mohapatra, Phys. Rev. D 52, 4125 (1995).
148. M. Dine, A.E. Nelson, Y. Nir, and Y. Shirman, Phys Rev. D (to be published).
149. J. Ellis, S. Kelley and D.V. Nanopoulos, Nucl. Phys. B373, 55 (1992);
150. J. Ellis, S. Kelley and D.V. Nanopoulos, Phys. Lett. B 287, 95 (1992)
151. J. Hisano, H. Murayama and T. Yanagida, Phys. Rev. Lett. 69, 1014 (1992).
152. V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D 47, 1093 (1993).
153. Particle Data Group (PDG) L. Montanet, et al., Phys. Rev. D 50, 1173 (1994).
154. A. Martin and D. Zeppenfeld, Phys. Lett. B 345, 558 (1995);
155. M.L. Swartz, “Reevaluation of the Hadronic Contribution to α (M(Z)2", Report No. SLAC PUB 6710, hep ph/9411353;
156. S. Eidelman and F. Jegerlehner, Z Phys. C 67, 585 (1995).
157. Let us parenthetically note that some authors investigate a wider range of variations of sin2 thetaW(mZ). For instance, in the first paper of citeurano the highest value considered was sin2 thetaW(mZ)=0.2327. As was explained above inching sin2 thetaW(mZ) up one lowers the minimal value of αs(mZ). Thus, these authors find that in the CMSSM with the Planck mass correction switched off is αs(mZ)min approx 0.114. The question whether the value sin2 thetaW(mZ)=0.2327 is admissible left open; we stick to Eq. (refs2winput: eq).
158. J. Erler and P. Langacker, Phys. Rev. D 52, 441 (1995).
159. CDF Collaboration, F. Abe, Phys. Rev. Lett. 74, 2626 (1995).
160. D0 Collaboration, S. Abachi, et al., Phys. Rev. Lett. 74, 2632 (1995).
161. J. Chyla and A. Kataev, Theoretical Ambiguities of QCD Predictions at the Z0 Peak, Report No. PRA HEP/95 03 [hep ph/9502383].
162. L.E. Ibánez and C. López, Nucl. Phys. B233, 511 (1984);
163. L.E. Ibánez, C. López and C. Munoz, Nucl. Phys. 256, 218 (1985).
164. See, e.g., L. Galtieri, to appear in the Proceeding of the Conference on Beyond the Standard Model IV, Lake Tahoe, December 13 18, 1994, edited by J. Gunion, T. Han, and J. Ohnemus
165. A. Jonckheere (D0), Proceeding of the Conference on Beyond the Standard Model IV, Lake Tahoe, December 13 18, 1994, edited by J. Gunion, T. Han, and J. Ohnemus
166. S. Eno (D0), to appear in the Proceeding of the Rencontres De Moriond XXX, Electroweak Interactions and Unified Theories, edited by J. Tran Thanh Van, March 1995;
167. M. Paterno (D0), to appear in the Proceeding of the Les Rencontres de Physique de la Vallee d’Aoste, LaThuile, edited by G. Belletini, March 1995
168. F. Abe, et al. (CDF), Phys. Rev. Lett. 69 (1992) 3439
169. D0 Collaboration, S. Abachi, Phys. Rev. Lett. 75, 618 (1995).
170. In a recent work of J. Bagger, Phys. Lett. B 348, 443 (1995), the nonleading mass threshold effects were found to be substantial in the CMSSM for m1/2150 rmGeV a corrected evolution curve significantly deviates from the leading log (LL) result. The reason is quite obvious: a jump in the slope of the LL evolution curve is due to the fact that at m1/2 approx 120 rmGeV the W ino becomes lighter than Z and freezes out. Nothing of the kind happens in our analysis and we generally do not expect the nonleading mass threshold effects to be large.
171. L.R. thanks Dennis Silverman for this remark.
172. K. Griest and L. Roszkowski, Phys. Rev. D 46, 3309 (1992).
173. A. Bartl, H. Fraas, W. Majerotto and N. Oshima, Phys. Rev. D 40, 1594 (1989);
174. M. Drees and X. Tata, Phys. Rev. D 43, 1971 (1991).
175. J. Ellis, K. Enqvist, D. Nanopoulos and K. Tamvakis, Phys. Lett. 155B, 381 (1985).
176. M. Drees, Phys. Lett. 158B, 409 (1985).
177. R. Arnowitt (private communication); K. Kounnas, (private communication).
178. K. Hagiwara and H. Murayama, Phys. Lett. B 246, 533 (1990).
179. G. Bhattacharyya and A. Raychaudhuri, Phys. Rev. D 47, 2014 (1993);
180. A. Djouadi, M. Drees and H. Konig, Phys. Rev. D 48, 308 (1993);
181. N. Krasnikov, Phys. Lett. B 318, 174 (1993).
182. J. Wells, G. Kane and C. Kolda, Phys. Lett. B 338, 219 (1994).
183. I. Bigi, B. Blok, M. Shifman and A. Vainshtein, Phys. Lett. B 323, 408 (1994).
184. E. Bagan, P. Ball and V. Braun, Nucl. Phys. B432, 3 (1994);
185. E. Bagan, P. Ball, V. Braun and P. Gosdzinsky, Phys. Lett. B 342, 362 (1995).
186. E. Bagan, P. Ball, B. Fiol and P. Gosdzinsky, Phys. Lett. B 351, 546 (1995).
187. R. Patterson, in Proceedings of the International Conference on High Energy Physics, Glasgow, Scotland, 1994; edited by P. J. Bussey and I. G. Knowles (IOP, London, 1995)
188. P. Roudeau, in Proceedings of the International Conference on High Energy Physics, Glasgow, Scotland, 1994; edited by P. J. Bussey and I. G. Knowles (IOP, London, 1995)
189. A. Kagan (private communication) and (unpublished).
190. A. Kagan, Phys. Rev. D 51, 6196 (1995).
191. M.S. Alam, et al. (CLEO), Phys. Rev. Lett. 74, 2885 (1995).
192. V. Barger, M.S. Berger, P. Ohmann and R.J.N. Phillips, Phys. Lett. B 314, 315 (1993);
193. M. Carena, S. Pokorski and C. Wagner, Nucl. Phys. B406, 59 (1993).
194. P. Langacker and N. Polonsky, Phys. Rev. D 49, 1454 (1994).
195. V. Barger, M.S. Berger, and P. Ohmann, General Issues in the Evolution of Fermion Masses and Mixings, talk given by M.S. Berger at the SUSY93 Workshop, March 29 April 1, 1993, in the Proceedings, edited by P. Nath [hep/ph 9305236].
196. H. Georgi and S.L. Glashow, Phys. Rev. Lett. 32, 438 (1974);
197. H. Georgi, H.R. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974).