Effects of neutrino mixing on high-energy cosmic neutrino flux

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 62, Issue 10, 2000, Pages 1-8

  Athar, H ^a   Jezabek, M ^b   Yasuda, O ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

^b INSTITUTE OF NUCLEAR PHYSICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037656751     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.62.103007     Document Type: Article

References (127)

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3. SuperK Collaboration, Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998); Phys. Lett. B 433, 9 (1998); 436, 33 (1998); Phys. Rev. Lett. 82, 2430 (1999); Phys. Lett. B 467, 185 (1999).
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5. SuperK Collaboration, Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998); Phys. Lett. B 433, 9 (1998); 436, 33 (1998); Phys. Rev. Lett. 82, 2430 (1999); Phys. Lett. B 467, 185 (1999).
6. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
7. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
8. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
9. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
10. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
11. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
12. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
13. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
14. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
15. V. S. Berezinsky and V. L. Ginzburg, Mon. Not. R. Astron. Soc. 194, 3 (1981); M. C. Begelman, B. Rudak, and M. Sikora, Astrophys. J. 362, 38 (1990); F. W. Stecker et al., Phys. Rev. Lett. 66, 2697 (1991); 69, 2738(E) (1992); L. Nellen, K. Mannheim, and P. L. Biermann, Phys. Rev. D 47, 5270 (1993); A. P. Szabo and R. J. Protheroe, Astropart. Phys. 2, 375 (1994); S. J. R. Battersby, B. Drolias, and J. J. Quenby, ibid. 4, 151 (1995); E. Waxman and J. Bahcall, Phys. Rev. Lett. 78, 2292 (1997); Phys. Rev. D 59, 023002 (1999). For a review article, see R. J. Protheroe, Nucl. Phys. B (Proc. Suppl.) 77, 465 (1999) and references cited therein.
16. See, for a review, Thomas K. Gaisser, Francis Halzen, and Todor Stanev, Phys. Rep. 258, 173 (1995); 271, 355(E) (1996); E. Zas, talk given in "Very High Energy Phenomena in the Universe," XXXIInd Rencontres de Moriond, 1997 (astro-ph/9704016) and references cited therein.
17. See, for a review, Thomas K. Gaisser, Francis Halzen, and Todor Stanev, Phys. Rep. 258, 173 (1995); 271, 355(E) (1996); E. Zas, talk given in "Very High Energy Phenomena in the Universe," XXXIInd Rencontres de Moriond, 1997 (astro-ph/9704016) and references cited therein.
18. See, for a review, Thomas K. Gaisser, Francis Halzen, and Todor Stanev, Phys. Rep. 258, 173 (1995); 271, 355(E) (1996); E. Zas, talk given in "Very High Energy Phenomena in the Universe," XXXIInd Rencontres de Moriond, 1997 (astro-ph/9704016) and references cited therein.
19. See, for example, E. Waxman, talk presented at the Nobel Symposium, Sweden, Phys. Scr. T85, 117 (2000) and references cited therein.
20. J. G. Learned and S. Pakvasa in Ref. [8].
21. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
22. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
23. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
24. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
25. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
26. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
27. Preliminary results of this work were presented in the following conferences: Sixth International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 1999, Paris, France (to appear in its proceedings edited by M. Froissart, J. Dumarchez, and D. Vignaud, hep-ph/9912417), scanned transparencies of the talk are available at URL http:// taup99.in2p3.fr/TAUP99/Thursday/thursday.html; 9th Lomonosov Conference on Elemetary Particle Physics, 1999, Moscow, Russia (to appear in its proceedings edited by A. Studenikin, hep-ph/0001128; YITP Workshop on Theoretical Problems related to Neutrino Oscillations, 2000, Kyoto, Japan (to appear in its proceedings report, hep-ph/0004083); Workshop on Neutrino oscillations and their origin, 2000, Fujiyoshida, Japan (to appear in its proceedings, hep-ph/0005135); 8th Asia Pacific Physics Conference (APPC 2000), 2000, Taipei, Taiwan (to appear in its proceedings, hep-ph/0008121; see also L. Bento, P. Keränen, and J. Maalampi, Phys. Lett. B 476, 205 (2000).
28. For recent updates on large high-energy neutrino detectors, see respective transparencies of presentations in 19th International Conference on Neutrino Physics and Astrophysics (Neutrino 2000), 2000, Sudbury, Canada at URL http:// ALUMNI.LAURENTIAN.CA/www/physics/nu2000/.
29. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
30. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
31. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
32. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
33. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
34. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
35. T. J. Weiler et al., hep-ph/9411432; J. G. Learned and S. Pakvasa, Astropart. Phys. 3, 267 (1995); F. Halzen and G. Jaczko, Phys. Rev. D 54, 2779 (1996); R. Gandhi, C. Quigg, M. H. Reno, and I. Sarcevic, Astropart. Phys. 5, 81 (1996); Phys. Rev. D 58, 093009 (1998); R Halzen and D. Saltzberg, Phys. Rev. Lett. 81, 4305 (1998); J. Capelle et al., Astropart. Phys. 8, 321 (1998); J. Kwiecinski, A. D. Martin, and A. M. Stasto, Phys. Rev. D 59, 093002 (1999); S. Iyer, M. H. Reno, and I. Sarcevic, ibid. 61, 053003 (2000); D. Fargion, astro-ph/0002453 and references cited therein; F. Becattini and S. Bottai, astro-ph/0003179; D. B. Cline and F. W. Stecker, astro-ph/0003459; S. I. Dutta, M. H. Reno, and I. Sarcevic, hep-ph/0005310; J. Alvarez-Muñiz, F. Halzen, and D. W. Hooper, Phys. Rev. D 62, 093015 (2000); H. Athar, G. Parente, and E. Zas, ibid. 62, 093010 (2000).
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58. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
59. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
60. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
61. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
62. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
63. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
64. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
65. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
66. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
67. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
68. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
69. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and
70. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
71. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
72. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
73. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
74. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
75. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
76. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
77. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
78. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
79. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
80. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
81. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
82. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
83. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
84. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980); V. Barger et al., Phys. Rev. Lett. 45, 692 (1980); V. Barger et al., Phys. Rev. D 43, 1759 (1991); D. O. Caldwell and R. N. Mohapatra, ibid. 48, 3259 (1993); J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B406, 409 (1993); J. T. Peltoniemi, D. Tommasini, and J. W. F. Valle, Phys. Lett. B 298, 383 (1993); S. M. Bilenky and C. Giunti, ibid. 320, 323 (1994); Z. Phys. C 68, 495 (1995); Z. G. Berezhiani and R. N. Mohapatra, Phys. Rev. D 52, 6607 (1995); E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Lett. B 357, 608 (1995); R. Foot and R. R. Volkas, Phys. Rev. D 52, 6595 (1995); Ernest Ma and Probir Roy, ibid. 52, R4780 (1995); J. T. Peltoniemi, hep-ph/9511323; E. J. Chun, A. S. Joshipura, and A. Yu. Smirnov, Phys. Rev. D 54, 4654 (1996); P. Krastev, S. T. Petcov, and Q. Y. Liu, ibid. 54, 7057 (1996); J. J. Gomez-Cadenas and M. C. Gonzalez-Garcia, Z. Phys. C 71, 443 (1996); K. Benakli and A. Yu. Smirnov, Phys. Rev. Lett. 79, 4314 (1997); R. N. Mohapatra, hep-ph/9711444; H. Nunokawa et al., Phys. Rev. D 56, 1704 (1997); V. Barger, K. Whisnant, and T. J. Weiler, Phys. Lett. B 427, 97 (1998); V. Barger et al., Phys. Rev. D 58, 093016 (1998); J. R. Espinosa, Nucl. Phys. B (Proc. Suppl.) 62, 187 (1998); G. Cleaver et al., Phys. Rev. D 57, 2701 (1998); M. Maris and S. T. Petcov, ibid. 58, 113008 (1998); Q. Y. Liu and A. Yu. Smirnov, Nucl. Phys. B524, 5051 (1998); D. O. Caldwell, Int. J. Mod. Phys. A 13, 4409 (1998); N. Gaur et al., Phys. Rev. D 58, 071301 (1998); B. Bramachari and R. N. Mohapatra, Phys. Lett. B 437, 100 (1998); A. S. Joshipura and A. Yu. Smirnov, ibid. 439, 103 (1998); S. M. Bilenky, C. Giunti, and W. Grimus, hep-ph/9809368; S. M. Bilenky, C. Giunti, and W. Grimus, Phys. Rev. D 58, 033001 (1998); Prog. Part. Nucl. Phys. 43, 1 (1999); S. C. Gibbons et al., Phys. Lett. B 430, 296 (1998); E. Ma, D. P. Roy, and U. Sarkar, ibid. 444, 391 (1998); N. Fornengo, M. C. Gonzlez-Garcia, and J. W. F. Valle, Nucl. Phys. B580, 58 (2000).
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104. C. J. Copi, D. N. Schramm, and M. S. Turner, Phys. Rev. Lett. 75, 3981 (1995); K. A. Olive and G. Steigman, Phys. Lett. B 354, 357 (1995); P. J. Kernan and S. Sarkar, Phys. Rev. D 54, R3681 (1996); S. Sarkar, Rep. Prog. Phys. 59, 1 (1996); K. A. Olive, talk at 5th International Workshop on Topics in Astroparticle and Underground Physics (TAUP 97), Gran Sasso, Italy, 1997 [Nucl. Phys. B (Proc. Suppl.) 70, 521 (1999)]; K. A. Olive, in Proceedings of 5th International Conference on Physics Beyond the Standard Model, Balholm, Norway, 1997.
105. C. J. Copi, D. N. Schramm, and M. S. Turner, Phys. Rev. Lett. 75, 3981 (1995); K. A. Olive and G. Steigman, Phys. Lett. B 354, 357 (1995); P. J. Kernan and S. Sarkar, Phys. Rev. D 54, R3681 (1996); S. Sarkar, Rep. Prog. Phys. 59, 1 (1996); K. A. Olive, talk at 5th International Workshop on Topics in Astroparticle and Underground Physics (TAUP 97), Gran Sasso, Italy, 1997 [Nucl. Phys. B (Proc. Suppl.) 70, 521 (1999)]; K. A. Olive, in Proceedings of 5th International Conference on Physics Beyond the Standard Model, Balholm, Norway, 1997.
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111. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
112. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
113. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
114. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
115. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
116. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
117. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
118. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
119. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
120. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
121. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
122. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
123. X. Shi, D. N. Schramm, and J. N. Bahcall, Phys. Rev. Lett. 69, 717 (1992); V. Barger, R. J. N. Phillips, and K. Whisnant, ibid. 69, 3135 (1992); S. A. Bludman et al., Phys. Rev. D 47, 2220 (1993); L. M. Krauss, E. Gates, and M. White, Phys. Lett. B 299, 95 (1993); P. I. Krastev and S. T. Petcov, ibid. 299, 99 (1993); G. L. Fogli and E. Lisi, Astropart. Phys. 2, 91 (1994); P. I. Krastev and A. Yu. Smirnov, Phys. Lett. B 338, 282 (1994); G. Fiorentini et al., Phys. Rev. D 49, 6298 (1994); N. Hata and P. Langacker, ibid. 50, 632 (1994); E. Calabresu et al., Astropart. Phys. 4, 159 (1995); P. I. Krastev and S. T. Petcov, Nucl. Phys. B449, 605 (1995); P. I. Krastev, S. T. Petcov, and L. Qiuyu, Phys. Rev. D 54, 7057 (1996); P. I. Krastev and S. T. Petcov, ibid. 53, 1665 (1996); J. N. Bahcall, P. I. Krastev, and A. Yu. Smirnov, ibid. 58, 096016 (1998); M. C. Gonzalez-Garcia et al., Nucl. Phys. B573, 3 (2000).
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