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A flavor symmetry for quasi-degenerate neutrinos: \(L_\mu - L_\tau\)

  • theoretical physics
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Abstract.

We consider the flavor symmetry \(L_\mu - L_\tau\) for the neutrino mass matrix. The most general neutrino mass matrix conserving \(L_\mu - L_\tau\) predicts quasi-degenerate neutrino masses with one maximal and two zero mixing angles. The presence of \(L_\mu - L_\tau\) can also be motivated by the near-bimaximal form of the neutrino mixing matrix. Furthermore, it is a special case of \(\mu \tau\) symmetric mass matrices. Breaking the flavor symmetry by adding a small flavor-blind term to the neutrino mass matrix and/or by applying radiative corrections is shown to reproduce the observed neutrino oscillation phenomenology. Both the normal and inverted mass ordering can be accommodated within this scheme. Moderate cancellation for neutrinoless double beta decay is expected. The observables |U e3|2 and \(\vert 1/2 - \sin^2\theta_{23}\vert\) are proportional to the inverse of the fourth power of the common neutrino mass scale. We comment on whether the atmospheric neutrino mixing is expected to lie above or below \(\pi/4\). We finally present a model based on the see-saw mechanism which generates a light neutrino mass matrix with an (approximate) \(L_\mu - L_\tau\) flavor symmetry. This is a minimal model with just one standard Higgs doublet and three heavy right-handed neutrinos. It needs only small values for the soft \(L_\mu - L_\tau\) breaking terms to reproduce the phenomenological viable mass textures analyzed.

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References

  1. B. Pontecorvo, Zh. Eksp. Teor. Fiz. 33, 549 (1957); 34, 247 (1958); Z. Maki, M. Nakagawa, S. Sakata, Prog. Theor. Phys. 28, 870 (1962)

    Google Scholar 

  2. M. Apollonio et al. (CHOOZ Collaboration), Eur. Phys. J. C 27, 331 (2003); F. Boehm et al. , Phys. Rev. D 64, 112001 (2001)

    Google Scholar 

  3. E. Kearns, talk given at Neutrino 2004 June 14-19, 2004, Paris, France, http://neutrino2004.in2p3.fr

  4. T. Nakaya et al. , talk given at Neutrino 2004, June 14-19, 2004, Paris, France, http://neutrino2004.in2p3.fr; M.H. Ahn et al. , Phys. Rev. Lett. 90, 041801 (2003); hep-ex/0411038

    Article  Google Scholar 

  5. B.T. Cleveland et al. , Astrophys. J. 496, 505 (1998); C. Cattadori, Talk at Neutrino 2004, Paris, France, June 14-19, 2004 http://neutrino2004.in2p3.fr; S. Fukuda et al. [Super-Kamiokande Collaboration], Phys. Lett. B 539, 179 (2002); S.N. Ahmed et al. (SNO Collaboration), Phys. Rev. Lett. 92, 181301 (2004)

    Google Scholar 

  6. T. Araki et al. (KamLAND Collaboration), hep-ex/0406035

  7. G.L. Fogli et al. , hep-ph/0408045

  8. See, e.g., A. Bandyopadhyay et al. , hep-ph/0406328; J.N. Bahcall, M.C. Gonzalez-Garcia, C. Pena-Garay, JHEP 0408, 016 (2004)

    Google Scholar 

  9. M. Maltoni et al. , hep-ph/0405172

  10. F. Vissani, hep-ph/9708483; V.D. Barger, S. Pakvasa, T.J. Weiler, K. Whisnant, Phys. Lett. B 437, 107 (1998); A.J. Baltz, A.S. Goldhaber, M. Goldhaber, Phys. Rev. Lett. 81, 5730 (1998); H. Georgi, S.L. Glashow, Phys. Rev. D 61, 097301 (2000); I. Stancu, D.V. Ahluwalia, Phys. Lett. B 460, 431 (1999)

    Google Scholar 

  11. M. Jezabek, Y. Sumino, Phys. Lett. B 457, 139 (1999) Z.z.Xing, Phys. Rev. D 64, 093013 (2001); C. Giunti, M. Tanimoto, Phys. Rev. D 66, 053013 (2002); D 66, 113006 (2002); G. Altarelli, F. Feruglio, I. Masina, Nucl. Phys. B 689, 157 (2004); A. Romanino, Phys. Rev. D 70, 013003 (2004); W. Rodejohann, hep-ph/0403236 (to appear in Phys. Rev. D); C.A.de S. Pires, J. Phys. G 30, B 29 (2004)

    Google Scholar 

  12. P.H. Frampton, S.T. Petcov, W. Rodejohann, Nucl. Phys. B 687, 31 (2004)

    Google Scholar 

  13. S.T. Petcov, W. Rodejohann, hep-ph/0409135

  14. F. Vissani, JHEP 9811, 025 (1998)

    Google Scholar 

  15. S.T. Petcov, Phys. Lett. B 110, 245 (1982); for more recent studies see, e.g., R. Barbieri et al. , JHEP 9812, 017 (1998); A.S. Joshipura, S.D. Rindani, Eur. Phys. J. C 14, 85 (2000); R.N. Mohapatra, A. Perez-Lorenzana, C.A. de Sousa Pires, Phys. Lett. B 474, 355 (2000); Q. Shafi, Z. Tavartkiladze, Phys. Lett. B 482, 145 (2000); L. Lavoura, Phys. Rev. D 62, 093011 (2000); W. Grimus, L. Lavoura, Phys. Rev. D 62, 093012 (2000); T. Kitabayashi, M. Yasue, Phys. Rev. D 63, 095002 (2001); A. Aranda, C.D. Carone, P. Meade, Phys. Rev. D 65, 013011 (2002); K.S. Babu, R.N. Mohapatra, Phys. Lett. B 532, 77 (2002); H.J. He, D.A. Dicus, J.N. Ng, Phys. Lett. B 536, 83 (2002); H.S. Goh, R.N. Mohapatra, S.P. Ng, Phys. Lett. B 542, 116 (2002); G.K. Leontaris, J. Rizos, A. Psallidas, Phys. Lett. B 597, 182 (2004)

    Google Scholar 

  16. L. Lavoura, W. Grimus, JHEP 0009, 007 (2000); hep-ph/0410279

    Google Scholar 

  17. P. Binetruy et al. , Nucl. Phys. B 496, 3 (1997)

    Google Scholar 

  18. N.F. Bell, R.R. Volkas, Phys. Rev. D 63, 013006 (2001)

    Google Scholar 

  19. K.S. Babu, E. Ma, J.W.F. Valle, Phys. Lett. B 552, 207 (2003); M. Hirsch et al. , Phys. Rev. D 69, 093006 (2004)

    Article  Google Scholar 

  20. X.G. He et al. , Phys. Rev. D 43, 22 (1991); D 44, 2118 (1991); see also E. Ma, D.P. Roy, S. Roy, Phys. Lett. B 525, 101 (2002)

    Google Scholar 

  21. See e.g., C.S. Lam, Phys. Lett. B 507, 214 (2001); T. Kitabayashi, M. Yasue, Phys. Rev. D 67, 015006 (2003); W. Grimus, L. Lavoura, Phys. Lett. B 572, 189 (2003); E. Ma, Phys. Rev. D 66, 117301 (2002); Y. Koide, Phys. Rev. D 69, 093001 (2004); W. Grimus et al. , hep-ph/0408123; R.N. Mohapatra, JHEP 0410, 027 (2004)

    Google Scholar 

  22. S. Hannestad, JCAP 0305, 004 (2003); hep-ph/0409108

    Google Scholar 

  23. U. Seljak et al. , astro-ph/0407372

  24. See, e.g., S.R. Elliott, J. Engel, J. Phys. G 30, R183 (2004) and references therein

  25. W. Rodejohann, Nucl. Phys. B 597, 110 (2001); Z.z.Xing, Phys. Rev. D 68, 053002 (2003); more realistic recent analyses are V. Barger et al. , Phys. Lett. B 540, 247 (2002); S. Pascoli, S.T. Petcov, W. Rodejohann, Phys. Lett. B 549, 177 (2002); F. Deppisch, H. Pas, J. Suhonen; hep-ph/0409306; A. Joniec, M. Zralek, hep-ph/0411070

    Google Scholar 

  26. W. Rodejohann, Phys. Rev. D 69, 033005 (2004)

    Google Scholar 

  27. M. Raidal, Phys. Rev. Lett. 93, 161801 (2004); H. Minakata, A.Y. Smirnov, hep-ph/0405088; P.H. Frampton, R.N. Mohapatra, hep-ph/0407139; see also J. Ferrandis, S. Pakvasa, hep-ph/0409204

    Google Scholar 

  28. See, e.g., J.A. Casas et al. , Nucl. Phys. B 573, 652 (2000); P.H. Chankowski, S. Pokorski, Int. J. Mod. Phys. A 17, 575 (2002); S. Antusch et al. , Nucl. Phys. B 674, 401 (2003)

    Google Scholar 

  29. S. Antusch et al. , hep-ph/0404268; H. Minakata, M. Sonoyama, H. Sugiyama, hep-ph/0406073; M.C. Gonzalez-Garcia, M. Maltoni, A.Y. Smirnov, hep-ph/0408170; S. Choubey, P. Roy, Phys. Rev. Lett. 93, 021803 (2004)

    Google Scholar 

  30. J. Bernabeu, S. Palomares Ruiz, S.T. Petcov, Nucl. Phys. B 669, 255 (2003); O.L.G. Peres, A.Y. Smirnov, Nucl. Phys. B 680, 479 (2004); S. Palomares-Ruiz, S.T. Petcov, hep-ph/0406096

    Google Scholar 

  31. A. Osipowicz et al. (KATRIN Collaboration), hep-ex/0109033

  32. H.V. Klapdor-Kleingrothaus et al. , Mod. Phys. Lett. A 16, 2409 (2001); C.E. Aalseth et al. , Mod. Phys. Lett. A 17, 1475 (2002); H.L. Harney, hep-ph/0205293; H.V. Klapdor-Kleingrothaus, hep-ph/0205228; F. Feruglio, A. Strumia, F. Vissani, Nucl. Phys. B 637, 345 (2002) [Addendum B 659, 359 (2003)]

    Article  Google Scholar 

  33. H.V. Klapdor-Kleingrothaus et al. , Phys. Lett. B 586, 198 (2004)

    Google Scholar 

  34. E.K. Akhmedov, Z.G. Berezhiani, G. Senjanovic, Phys. Rev. Lett. 69, 3013 (1992); E.K. Akhmedov et al. , Phys. Rev. D 47, 3245 (1993); A.de Gouvea, J.W.F. Valle, Phys. Lett. B 501, 115 (2001); F. Vissani, M. Narayan, V. Berezinsky, Phys. Lett. B 571, 209 (2003); hep-ph/0401029

    Google Scholar 

  35. P. Minkowski, Phys. Lett. B 67, 421 (1977); T. Yanagida, in Proceedings of the Workshop on Unified Theory and the Baryon Number of the Universe, edited by O. Sawada, A. Sugamoto (KEK, Tsukuba 1979), p. 95; M. Gell-Mann, P. Ramond, R. Slansky, in Supergravity, edited by F. van Nieuwenhuizen, D. Freedman (North Holland, Amsterdam 1979), p. 315; S.L. Glashow, in Quarks and Leptons, edited by M. Lévy et al. (Plenum, New York 1980), p. 707; R.N. Mohapatra, G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980)

    Article  Google Scholar 

  36. J. Schechter, J.W.F. Valle, Phys. Rev. D 22, 2227 (1980); M. Magg, C. Wetterich, Phys. Lett. B 94, 61 (1980); R.N. Mohapatra, G. Senjanovic, Phys. Rev. D 23, 165 (1981); G. Lazarides, Q. Shafi, C. Wetterich, Nucl. Phys. B 181, 287 (1981)

    Google Scholar 

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Authors and Affiliations

  1. Theoretical Physics, University of Oxford, Keble Road, OX1 3NP, Oxford, UK

    S. Choubey

  2. Physik-Department, Technische Universität München, James-Franck-Strasse, 85748, Garching, Germany

    W. Rodejohann

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  1. S. Choubey
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Correspondence to S. Choubey.

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Received: 18 November 2004, Revised: 13 December 2004, Published online: 15 February 2005

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Choubey, S., Rodejohann, W. A flavor symmetry for quasi-degenerate neutrinos: \(L_\mu - L_\tau\) . Eur. Phys. J. C 40, 259–268 (2005). https://doi.org/10.1140/epjc/s2005-02133-1

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