Leptonic CP violation phases using an ansatz for the neutrino mass matrix and application to leptogenesis

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 70, Issue 5, 2004, Pages

  Nasri, Salah ^a   Schechter, Joseph ^b   Moussa, Sherif ^c  

^a Bldg 142   (United States)

^b SYRACUSE UNIVERSITY   (United States)

^c Ain Shams University   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BARYON; LEPTON; MATHEMATICAL MODEL; NEUTRINO; PHOTON; QUANTUM MECHANICS; QUARK; RADIOCHEMISTRY;

EID: 84927759514     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.70.053005     Document Type: Article

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55. P. Langacker, R. D. Peccei, and T. Yanagida, Mod. Phys. Lett. A 1, 541 (1986); R. N. Mohapatra and X. Zhang, Phys. Rev. D 46, 5331 (1992); K. Enqvist and I. Vilja, Phys. Lett. B 299, 281 (1993); H. Murayama, H. Suzuki, T. Yanagida, and J. Yokoyama Phys. Rev. Lett. 70, 1912 (1993); T. Gherghetta and G. Jungman, Phys. Rev. D 48, 1546 (1993); A. Acker, H. Kikuchi, E. Ma, and U. Sarkar, Phys. Rev. D 48, 5006 (1993); P. J. O' Donnell and U. Sarkar, Phys. Rev. D 49, 2118 (1994); M. P. Worah, Phys. Rev. D 53, 3902 (1996); R. Jeannerot, Phys. Rev. Lett. 77, 3292 (1996); L. Covi, E. Roulet, and F. Vissani, Phys. Lett. B 384, 169 (1996); W. Buchmuller and M. Plumacher, Phys. Lett. B 389, 73 (1996); G. Lazarides, Q. Shafi, and N. D. Vlachos, Phys. Lett. B 427, 53 (1998); J. Liu and G. Segre, Phys. Rev. D 48, 4609 (1993); M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys. Lett. B 389, 693 (1996).
56. P. Langacker, R. D. Peccei, and T. Yanagida, Mod. Phys. Lett. A 1, 541 (1986); R. N. Mohapatra and X. Zhang, Phys. Rev. D 46, 5331 (1992); K. Enqvist and I. Vilja, Phys. Lett. B 299, 281 (1993); H. Murayama, H. Suzuki, T. Yanagida, and J. Yokoyama Phys. Rev. Lett. 70, 1912 (1993); T. Gherghetta and G. Jungman, Phys. Rev. D 48, 1546 (1993); A. Acker, H. Kikuchi, E. Ma, and U. Sarkar, Phys. Rev. D 48, 5006 (1993); P. J. O' Donnell and U. Sarkar, Phys. Rev. D 49, 2118 (1994); M. P. Worah, Phys. Rev. D 53, 3902 (1996); R. Jeannerot, Phys. Rev. Lett. 77, 3292 (1996); L. Covi, E. Roulet, and F. Vissani, Phys. Lett. B 384, 169 (1996); W. Buchmuller and M. Plumacher, Phys. Lett. B 389, 73 (1996); G. Lazarides, Q. Shafi, and N. D. Vlachos, Phys. Lett. B 427, 53 (1998); J. Liu and G. Segre, Phys. Rev. D 48, 4609 (1993); M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys. Lett. B 389, 693 (1996).
57. P. Langacker, R. D. Peccei, and T. Yanagida, Mod. Phys. Lett. A 1, 541 (1986); R. N. Mohapatra and X. Zhang, Phys. Rev. D 46, 5331 (1992); K. Enqvist and I. Vilja, Phys. Lett. B 299, 281 (1993); H. Murayama, H. Suzuki, T. Yanagida, and J. Yokoyama Phys. Rev. Lett. 70, 1912 (1993); T. Gherghetta and G. Jungman, Phys. Rev. D 48, 1546 (1993); A. Acker, H. Kikuchi, E. Ma, and U. Sarkar, Phys. Rev. D 48, 5006 (1993); P. J. O' Donnell and U. Sarkar, Phys. Rev. D 49, 2118 (1994); M. P. Worah, Phys. Rev. D 53, 3902 (1996); R. Jeannerot, Phys. Rev. Lett. 77, 3292 (1996); L. Covi, E. Roulet, and F. Vissani, Phys. Lett. B 384, 169 (1996); W. Buchmuller and M. Plumacher, Phys. Lett. B 389, 73 (1996); G. Lazarides, Q. Shafi, and N. D. Vlachos, Phys. Lett. B 427, 53 (1998); J. Liu and G. Segre, Phys. Rev. D 48, 4609 (1993); M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys. Lett. B 389, 693 (1996).
58. P. Langacker, R. D. Peccei, and T. Yanagida, Mod. Phys. Lett. A 1, 541 (1986); R. N. Mohapatra and X. Zhang, Phys. Rev. D 46, 5331 (1992); K. Enqvist and I. Vilja, Phys. Lett. B 299, 281 (1993); H. Murayama, H. Suzuki, T. Yanagida, and J. Yokoyama Phys. Rev. Lett. 70, 1912 (1993); T. Gherghetta and G. Jungman, Phys. Rev. D 48, 1546 (1993); A. Acker, H. Kikuchi, E. Ma, and U. Sarkar, Phys. Rev. D 48, 5006 (1993); P. J. O' Donnell and U. Sarkar, Phys. Rev. D 49, 2118 (1994); M. P. Worah, Phys. Rev. D 53, 3902 (1996); R. Jeannerot, Phys. Rev. Lett. 77, 3292 (1996); L. Covi, E. Roulet, and F. Vissani, Phys. Lett. B 384, 169 (1996); W. Buchmuller and M. Plumacher, Phys. Lett. B 389, 73 (1996); G. Lazarides, Q. Shafi, and N. D. Vlachos, Phys. Lett. B 427, 53 (1998); J. Liu and G. Segre, Phys. Rev. D 48, 4609 (1993); M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys. Lett. B 389, 693 (1996).
59. P. Langacker, R. D. Peccei, and T. Yanagida, Mod. Phys. Lett. A 1, 541 (1986); R. N. Mohapatra and X. Zhang, Phys. Rev. D 46, 5331 (1992); K. Enqvist and I. Vilja, Phys. Lett. B 299, 281 (1993); H. Murayama, H. Suzuki, T. Yanagida, and J. Yokoyama Phys. Rev. Lett. 70, 1912 (1993); T. Gherghetta and G. Jungman, Phys. Rev. D 48, 1546 (1993); A. Acker, H. Kikuchi, E. Ma, and U. Sarkar, Phys. Rev. D 48, 5006 (1993); P. J. O' Donnell and U. Sarkar, Phys. Rev. D 49, 2118 (1994); M. P. Worah, Phys. Rev. D 53, 3902 (1996); R. Jeannerot, Phys. Rev. Lett. 77, 3292 (1996); L. Covi, E. Roulet, and F. Vissani, Phys. Lett. B 384, 169 (1996); W. Buchmuller and M. Plumacher, Phys. Lett. B 389, 73 (1996); G. Lazarides, Q. Shafi, and N. D. Vlachos, Phys. Lett. B 427, 53 (1998); J. Liu and G. Segre, Phys. Rev. D 48, 4609 (1993); M. Flanz, E. A. Paschos, U. Sarkar, and J. Weiss, Phys. Lett. B 389, 693 (1996).
60. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
61. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
62. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
63. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
64. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
65. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
66. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
67. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
68. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
69. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
70. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
71. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
72. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
73. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
74. Recent discussions include: M. S. Berger and B. Brahmachari, Phys. Rev. D 60, 073009 (2000); D. Falcone and F. Tramantano, Phys. Rev. D 63, 073007 (2001); F. Bucella, Phys. Lett. B 524, 241 (2002); H. B. Nielsen and Y. Takanishi, Phys. Lett. B 507, 241 (2001); M. Hirsch and S. F. King, Phys. Rev. D 64, 113005 (2001); Z. Z. Xing, Phys. Lett. B 545, 352 (2002); P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002); T. Endoh et al., Phys. Rev. Lett. 89, 231601 (2002); S. Davidson and A. Ibarra, Nucl. Phys. B648, 345 (2003); G. C. Branco et al., Phys. Rev. D 67, 073025, (2003); J. Pati, Phys. Rev. D 68, 072002 (2003); J. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller, P. Di Bari, and M. Plumacher, Nucl. Phys. B643, 367 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Rev. D 68, 093007 (2003); E. Kh. Akhmedov, M. Frigerio, and A. Yu. Smirnov, J. High Energy Phys. 0309 (2003), 021; V. Barger, D. A. Dicus, H-J. He, and T. Li, Phys. Lett. B 583, 173 (2004).
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84. We use Fig. (5a) in [33] to roughly estimate the Di when necessary. Note that the horizontal axis is interpreted as roughly 10 -3 Ki and the vertical axis as roughly 2 x 10-8 Di.
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90. R. Johnson, S. Ranfone, and J. Schechter, Phys. Rev. 35, 282 (1987). Here, Tr(Mν) = 0 was studied in an SO(10) model together with the assumption of a special form for all the mass matrices. The more recent discovery of a top quark mass greater than about 90 GeV has ruled out that special form which, combined with Tr(Mν) = 0, would make M H a singular matrix; H. S. Goh, R. N. Mohapatra, and S. P. Ng, Phys. Lett. B 570, 215 (2003).