Impact of radiative corrections on sterile neutrino scenarios

Journal of High Energy Physics

Volumn 4, Issue 2, 2000, Pages 1-13

  Ibarra, A ^a   Navarro, I ^a  

^a INSTITUTO DE ESTRUCTURA DE LA MATERIA   (Spain)

Author keywords

Beyond Standard Model; Neutrino Physics; Solar and Atmospheric Neutrinos

Indexed keywords

EID: 7044263309     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/02/031     Document Type: Article

References (51)

1. SUPER-KAMIOKANDE collaboration, Measurement of a small atmospheric nu/mu/nu/e ratio, Phys. Lett. B 433 (1998) 9 [hep-ex/9803006]; Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003]; KAMIOKANDE collaboration, Measurement of the flux and zenith angle distribution of upward through-going muons in kamiokande II + III, Phys. Rev. Lett. 81 (1998) 2016 [hep-ex/9806038].
2. SUPER-KAMIOKANDE collaboration, Measurement of a small atmospheric nu/mu/nu/e ratio, Phys. Lett. B 433 (1998) 9 [hep-ex/9803006]; Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003]; KAMIOKANDE collaboration, Measurement of the flux and zenith angle distribution of upward through-going muons in kamiokande II + III, Phys. Rev. Lett. 81 (1998) 2016 [hep-ex/9806038].
3. SUPER-KAMIOKANDE collaboration, Measurement of a small atmospheric nu/mu/nu/e ratio, Phys. Lett. B 433 (1998) 9 [hep-ex/9803006]; Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003]; KAMIOKANDE collaboration, Measurement of the flux and zenith angle distribution of upward through-going muons in kamiokande II + III, Phys. Rev. Lett. 81 (1998) 2016 [hep-ex/9806038].
4. SOUDAN2 collaboration, Measurement of the atmospheric neutrino flavor composituin in SOUDAN-2, Phys. Lett. B 391 (1997) 491 [hep-ex/9611007]; SOUDAN2 Collaboration, The atmospheric neutrino flavor ratio from a 3.9 fiducial kiloton year exposure of SOUDAN-2, Phys. Lett. B 449 (1999) 137 [hep-ex/9901024]; MACRO Collaboration, Measurement of the atmospheric neutrino induced upgoing muon flux using macro, Phys. Lett. B 434 (1998) 451 [hep-ex/9807005]; THE MACRO collaboration, M. Spurio, Low energy atmospheric nu/mu in macro, hep-ex/9808001.
5. SOUDAN2 collaboration, Measurement of the atmospheric neutrino flavor composituin in SOUDAN-2, Phys. Lett. B 391 (1997) 491 [hep-ex/9611007]; SOUDAN2 Collaboration, The atmospheric neutrino flavor ratio from a 3.9 fiducial kiloton year exposure of SOUDAN-2, Phys. Lett. B 449 (1999) 137 [hep-ex/9901024]; MACRO Collaboration, Measurement of the atmospheric neutrino induced upgoing muon flux using macro, Phys. Lett. B 434 (1998) 451 [hep-ex/9807005]; THE MACRO collaboration, M. Spurio, Low energy atmospheric nu/mu in macro, hep-ex/9808001.
6. SOUDAN2 collaboration, Measurement of the atmospheric neutrino flavor composituin in SOUDAN-2, Phys. Lett. B 391 (1997) 491 [hep-ex/9611007]; SOUDAN2 Collaboration, The atmospheric neutrino flavor ratio from a 3.9 fiducial kiloton year exposure of SOUDAN-2, Phys. Lett. B 449 (1999) 137 [hep-ex/9901024]; MACRO Collaboration, Measurement of the atmospheric neutrino induced upgoing muon flux using macro, Phys. Lett. B 434 (1998) 451 [hep-ex/9807005]; THE MACRO collaboration, M. Spurio, Low energy atmospheric nu/mu in macro, hep-ex/9808001.
7. SOUDAN2 collaboration, Measurement of the atmospheric neutrino flavor composituin in SOUDAN-2, Phys. Lett. B 391 (1997) 491 [hep-ex/9611007]; SOUDAN2 Collaboration, The atmospheric neutrino flavor ratio from a 3.9 fiducial kiloton year exposure of SOUDAN-2, Phys. Lett. B 449 (1999) 137 [hep-ex/9901024]; MACRO Collaboration, Measurement of the atmospheric neutrino induced upgoing muon flux using macro, Phys. Lett. B 434 (1998) 451 [hep-ex/9807005]; THE MACRO collaboration, M. Spurio, Low energy atmospheric nu/mu in macro, hep-ex/9808001.
8. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
9. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
10. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
11. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
12. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
13. HOMESTAKE collaboration, Measurement of the solar electron neutrino flux with the homestake chlorine detector, Astrophys. J. 496 (1998) 505; KAMIOKANDE collaboration, Y. Fukuda et al., Solar neutrino data covering solar cycle 22, Phys. Rev. Lett. 77 (1996) 1683; GALLEX collaboration, Gallex solar neutrino observations: results for gallex III., Phys. Lett. B 388 (1996) 384; D.N. Abdurashitov et al., The russian-american gallium experiment (sage) cr neutrino source measurement, Phys. Rev. Lett. 77 (1996) 4708; SUPER-KAMIOKANDE collaboration, Constraints on neutrino oscillation parameters from the measurement of day-night solar neutrino fluxes at SUPER-KAMIOKANDE, Phys. Rev. Lett. 82 (1999) 1810 [hep-ex/9812009]; SUPER-KAMIOKANDE collaboration, Measurement of the solar neutrino energy spectrum using neutrino electron scattering, Phys. Rev. Lett. 82 (1999) 2430 [hep-ex/9812011].
14. e neutrino oscillations from LSND, Phys. Rev. Lett. 81 (1998) 1774 [nucl-ex/9709006].
15. e neutrino oscillations from LSND, Phys. Rev. Lett. 81 (1998) 1774 [nucl-ex/9709006].
16. e neutrino oscillations from LSND, Phys. Rev. Lett. 81 (1998) 1774 [nucl-ex/9709006].
17. Particle Data Group, Review of particle physics, Eur. Phys. J. C 3 (1998) 1.
18. J.T. Peltoniemi and J.W. F. Valle, Reconciling dark matter, solar and atmospheric neutrinos, Nucl. Phys. B 406 (1993) 409 [hep-ph/9302316]; D.O. Caldwell and R.N. Mohapatra, Neutrino mass explanations of solar and atmospheric neutrino deficits and hot dark matter, Phys. Rev. D 48 (1993) 3259.
19. J.T. Peltoniemi and J.W. F. Valle, Reconciling dark matter, solar and atmospheric neutrinos, Nucl. Phys. B 406 (1993) 409 [hep-ph/9302316]; D.O. Caldwell and R.N. Mohapatra, Neutrino mass explanations of solar and atmospheric neutrino deficits and hot dark matter, Phys. Rev. D 48 (1993) 3259.
20. S.M. Bilenky, C. Giunti and W. Grimus, Neutrino mass spectrum from the results of neutrino oscillation experiments, Eur. Phys. J. C 1 (1998) 247 [hep-ph/9607372]; Long baseline neutrino oscillation experiments and CP violation in the lepton sector, Phys. Rev. D 58 (1998) 033001 [hep-ph/9712537]; S.M. Bilenkii and C. Giunti, Sterile neutrinos?, hep-ph/9905246; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mass spectra and the SUPER-KAMIOKANDE atmospheric up-down asymmetry, Phys. Rev. D 60 (1999) 073007 [hep-ph/9903454].
21. S.M. Bilenky, C. Giunti and W. Grimus, Neutrino mass spectrum from the results of neutrino oscillation experiments, Eur. Phys. J. C 1 (1998) 247 [hep-ph/9607372]; Long baseline neutrino oscillation experiments and CP violation in the lepton sector, Phys. Rev. D 58 (1998) 033001 [hep-ph/9712537]; S.M. Bilenkii and C. Giunti, Sterile neutrinos?, hep-ph/9905246; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mass spectra and the SUPER-KAMIOKANDE atmospheric up-down asymmetry, Phys. Rev. D 60 (1999) 073007 [hep-ph/9903454].
22. S.M. Bilenky, C. Giunti and W. Grimus, Neutrino mass spectrum from the results of neutrino oscillation experiments, Eur. Phys. J. C 1 (1998) 247 [hep-ph/9607372]; Long baseline neutrino oscillation experiments and CP violation in the lepton sector, Phys. Rev. D 58 (1998) 033001 [hep-ph/9712537]; S.M. Bilenkii and C. Giunti, Sterile neutrinos?, hep-ph/9905246; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mass spectra and the SUPER-KAMIOKANDE atmospheric up-down asymmetry, Phys. Rev. D 60 (1999) 073007 [hep-ph/9903454].
23. S.M. Bilenky, C. Giunti and W. Grimus, Neutrino mass spectrum from the results of neutrino oscillation experiments, Eur. Phys. J. C 1 (1998) 247 [hep-ph/9607372]; Long baseline neutrino oscillation experiments and CP violation in the lepton sector, Phys. Rev. D 58 (1998) 033001 [hep-ph/9712537]; S.M. Bilenkii and C. Giunti, Sterile neutrinos?, hep-ph/9905246; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mass spectra and the SUPER-KAMIOKANDE atmospheric up-down asymmetry, Phys. Rev. D 60 (1999) 073007 [hep-ph/9903454].
24. J.N. Bahcall, P.I. Krastev and A.Y. Smirnov, Where do we stand with solar neutrino oscillations?, Phys. Rev. D 58 (1998) 096016 [hep-ph/9807216]; M.C. Gonzalez-Garcia, P.C. de Holanda, C. Pena-Garay and J.W. F. Valle, Status of the msw solutions of the solar neutrino problem, hep-ph/9906469.
25. J.N. Bahcall, P.I. Krastev and A.Y. Smirnov, Where do we stand with solar neutrino oscillations?, Phys. Rev. D 58 (1998) 096016 [hep-ph/9807216]; M.C. Gonzalez-Garcia, P.C. de Holanda, C. Pena-Garay and J.W. F. Valle, Status of the msw solutions of the solar neutrino problem, hep-ph/9906469.
26. Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870.
27. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566.
28. P. Langacker, A mechanism for ordinary sterile neutrino mixing, Phys. Rev. D 58 (1998) 093017 [hep-ph/9805281].
29. P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333]; K.S. Babu, C.N. Leung and J. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223]; B. Grzadkowski and M. Lindner, Nonlinear evolution of Yukawa couplings, Phys. Lett. B 193 (1987) 71; Y.F. Pirogov and O.V. Zenin, Two-loop renormalization group restrictions on the standard model and the fourth chiral family, Eur. Phys. J. C 10 (1999) 629 [hep-ph/9808396].
30. P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333]; K.S. Babu, C.N. Leung and J. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223]; B. Grzadkowski and M. Lindner, Nonlinear evolution of Yukawa couplings, Phys. Lett. B 193 (1987) 71; Y.F. Pirogov and O.V. Zenin, Two-loop renormalization group restrictions on the standard model and the fourth chiral family, Eur. Phys. J. C 10 (1999) 629 [hep-ph/9808396].
31. P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333]; K.S. Babu, C.N. Leung and J. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223]; B. Grzadkowski and M. Lindner, Nonlinear evolution of Yukawa couplings, Phys. Lett. B 193 (1987) 71; Y.F. Pirogov and O.V. Zenin, Two-loop renormalization group restrictions on the standard model and the fourth chiral family, Eur. Phys. J. C 10 (1999) 629 [hep-ph/9808396].
32. P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333]; K.S. Babu, C.N. Leung and J. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223]; B. Grzadkowski and M. Lindner, Nonlinear evolution of Yukawa couplings, Phys. Lett. B 193 (1987) 71; Y.F. Pirogov and O.V. Zenin, Two-loop renormalization group restrictions on the standard model and the fourth chiral family, Eur. Phys. J. C 10 (1999) 629 [hep-ph/9808396].
33. J.A. Casas, J.R. Espinosa, A. Ibarra and I. Navarro, Naturalness of nearly degenerate neutrinos, Nucl. Phys. B 556 (1999) 3 [hep-ph/9904395].
34. J. Ellis, G.K. Leontaris, S. Lola and D.V. Nanopoulos, Neutrino textures in the light of SUPERKAMIOKANDE data and a realistic string model, Eur. Phys. J. C 9 (1999) 389.
35. J. Ellis and S. Lola, Phys. Lett. B 458 (1999) 310.
36. J.A. Casas, J.R. Espinosa, A. Ibarra and I. Navarro, Nearly degenerate neutrinos, supersymmetry and radiative corrections, hep-ph/9905381.
37. J.A. Casas, J.R. Espinosa, A. Ibarra and I. Navarro, Theoretical constraints on the vacuum oscillation solution to the solar neutrino problem, J. High Energy Phys. 09 (1999) 015 [hep-ph/9906281].
38. R. Barbieri, G.G. Ross and A. Strumia, Vacuum oscillations of quasi degenerate solar neutrinos, J. High Energy Phys. 10 (1999) 020 [hep-ph/9906470].
39. N. Haba, Y. Matsui, N. Okamura and M. Sugiura, Energy-scale dependence of the lepton-flavor-mixing matrix, Eur. Phys. J. C 10 (1999) 677 [hep-ph/9904292]; N. Haba and N. Okamura, Stability of the lepton-flavor mixing matrix against quantum corrections, hep-ph/9906481.
40. N. Haba, Y. Matsui, N. Okamura and M. Sugiura, Energy-scale dependence of the lepton-flavor-mixing matrix, Eur. Phys. J. C 10 (1999) 677 [hep-ph/9904292]; N. Haba and N. Okamura, Stability of the lepton-flavor mixing matrix against quantum corrections, hep-ph/9906481.
41. E. Ma, Stability of neutrino mass degeneracy, J. Phys. G 25 (1999) L97 [hep-ph/9907400].
42. P.H. Chankowski, W. Krolikowski and S. Pokorski, Fixed points in the evolution of neutrino mixings, hep-ph/9910231.
43. J.A. Casas, J.R. Espinosa, A. Ibarra and I. Navarro, General RG equations for physical neutrino parameters and their phenomenological implications, hep-ph/9910420.
44. F. Vissani and A.Y. Smirnov, Neutrino masses and b - τ unification in the supersymmetric standard model, Phys. Lett. B 341 (1994) 173 [hep-ph/9405399]; A. Brignole, H. Murayama and R. Rattazzi, Upper bound on hot dark matter density from SO(10) Yukawa unification, Phys. Lett. B 335 (1994) 345 [hep-ph/9406397].
45. F. Vissani and A.Y. Smirnov, Neutrino masses and b - τ unification in the supersymmetric standard model, Phys. Lett. B 341 (1994) 173 [hep-ph/9405399]; A. Brignole, H. Murayama and R. Rattazzi, Upper bound on hot dark matter density from SO(10) Yukawa unification, Phys. Lett. B 335 (1994) 345 [hep-ph/9406397].
46. N. Okada and O. Yasuda, A sterile neutrino scenario constrained by experiments and cosmology, Int. J. Mod. Phys. A 12 (1997) 3669 [hep-ph/9606411]; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mixing and big-bang nucleosynthesis, Astropart. Phys. 11 (1999) 413 [hep-ph/9804421]; Four-neutrino mixing, oscillations and BBN, hep-ph/9807569; C. Giunti, S.M. Bilenkii, W. Grimus and T. Schwetz, Four-neutrino mixing, oscillations and big-bang nucleosynthesis, hep-ph/9809466.
47. N. Okada and O. Yasuda, A sterile neutrino scenario constrained by experiments and cosmology, Int. J. Mod. Phys. A 12 (1997) 3669 [hep-ph/9606411]; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mixing and big-bang nucleosynthesis, Astropart. Phys. 11 (1999) 413 [hep-ph/9804421]; Four-neutrino mixing, oscillations and BBN, hep-ph/9807569; C. Giunti, S.M. Bilenkii, W. Grimus and T. Schwetz, Four-neutrino mixing, oscillations and big-bang nucleosynthesis, hep-ph/9809466.
48. N. Okada and O. Yasuda, A sterile neutrino scenario constrained by experiments and cosmology, Int. J. Mod. Phys. A 12 (1997) 3669 [hep-ph/9606411]; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mixing and big-bang nucleosynthesis, Astropart. Phys. 11 (1999) 413 [hep-ph/9804421]; Four-neutrino mixing, oscillations and BBN, hep-ph/9807569; C. Giunti, S.M. Bilenkii, W. Grimus and T. Schwetz, Four-neutrino mixing, oscillations and big-bang nucleosynthesis, hep-ph/9809466.
49. N. Okada and O. Yasuda, A sterile neutrino scenario constrained by experiments and cosmology, Int. J. Mod. Phys. A 12 (1997) 3669 [hep-ph/9606411]; S.M. Bilenkii, C. Giunti, W. Grimus and T. Schwetz, Four-neutrino mixing and big-bang nucleosynthesis, Astropart. Phys. 11 (1999) 413 [hep-ph/9804421]; Four-neutrino mixing, oscillations and BBN, hep-ph/9807569; C. Giunti, S.M. Bilenkii, W. Grimus and T. Schwetz, Four-neutrino mixing, oscillations and big-bang nucleosynthesis, hep-ph/9809466.
50. 2 mixing, Phys. Lett. B 467 (1999) 83 [hep-ph/9906456].
51. S.M. Bilenkii, C. Giunti, W. Grimus, B. Kayser and S.T. Petcov, Constraints from neutrino oscillation experiments on the effective majorana mass in neutrinoless double beta decay, Phys. Lett. B 465 (1999) 193 [hep-ph/9907234].