Energy-scale dependence of the lepton flavor-mixing matrix

European Physical Journal C

Volumn 10, Issue 4, 1999, Pages 677-680

  Haba, N ^a,b   Matsui, Y ^c   Okamura, N ^d   Sugiura, M ^c  

^a OHIO STATE UNIVERSITY   (United States)

^b MIE UNIVERSITY   (Japan)

^c NAGOYA UNIVERSITY   (Japan)

^d HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040205647     PISSN: 14346044     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100529900152     Document Type: Article

References (53)

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28. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
29. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
30. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
31. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
32. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
33. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
34. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
35. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
36. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
37. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
38. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
39. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
40. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
41. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
42. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
43. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
44. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
45. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
46. See, for example, M. Bando, Izawa Ken-Iti, and T. Takahashi, Prog. Theor. Phys. 92, 1137 (1994); M. Schmaltz, Phys. Rev. D52, 1643 (1995); Y. Achiman and T. Greiner, Nucl. Phys. B443, 3 (1995); G.K. Leontaris, S. Lola, and G.G. Ross, Nucl. Phys. B454, 25 (1995); M. Tanimoto, Phys. Lett. B360, 41 (1995); G.K. Leontaris and S. Lola, hep-ph/9510340; Mar Bastero-Gil and B. Brahmachari, Nucl. Phys. B482, 39 (1996); G. Lazarides, Q. Shafi, and N.D. Vlachos, Phys. Lett. B427, 53 (1998); M.K. Parida and N. Nimai Singh, Phys. Rev. D59, 032002 (1999); B. Brahmachari and R.N. Mohapatra, Phys. Rev. D58, 015003 (1998); N. Haba and T. Matsuoka, Prog. Theor. Phys. 99, 831 (1998); G. Lazarides, hep-ph/9801340; C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998); G. Lazarides, hep-ph/9802415; B.C. Allanach, Phys. Lett. B450, 182 (1999); M. Tanimoto, hep-ph/9807517; N. Haba, Phys. Rev. D59, 035011 (1999); J. Ellis, G.K. Leontaris, S. Lola, and D.V. Nanopoulos, Eur. Phys. J. C9, 389 (1999); S. Lola and G.G. Ross, Nucl. Phys. B553, 81 (1999); Y. Nir and Y. Shadmi, JHEP 9905, 023 (1999) S. Lola, hep-ph/9903203
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