Skip to main content
Springer Nature Link
Log in

The neutrino mass matrix and (selected) variants of A 4

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Recent neutrino oscillation experiments have measured leptonic mixing angles with considerable precision. Many theoretical attempts to understand the peculiar mixing structure, observed in these measurements, are based on non-Abelian flavour symmetries. This talk concentrates exclusively on models based on the non-Abelian symmetry A 4. A 4 is particularly well suited to describe three family mixing, and allows to explain the near tri-bimaximal mixing observed. Special emphasis is put here on the discussion of the neutrinoless double beta decay observable 〈:m ν 〉. Different models based on A 4 with very similar predictions for neutrino angles can yield vastly different expectations for 〈m ν 〉. Neutrinoless double beta decay can thus serve, in principle, as a discriminator between different neutrino mass models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Super-Kamiokande Collaboration: Y Fukuda et al, Phys. Rev. Lett. 81, 1562 (1998)

    Article  Google Scholar 

  2. SNO: Q R Ahmad et al, Phys. Rev. Lett. 89, 011301 (2002), nucl-ex/0204008

    Google Scholar 

  3. KamLAND: K Eguchi et al, Phys. Rev. Lett. 90, 021802 (2003), hep-ex/0212021

    Google Scholar 

  4. MINOS Collaboration: arXiv:0708.1495 [hep-ex]

  5. KamLAND Collaboration: arXiv:0801.4589 [hep-ex]

  6. S Weinberg, Phys. Rev. Lett. 43, 1566 (1979)

    Article  ADS  Google Scholar 

  7. S Weinberg, Phys. Rev. D22, 1694 (1980)

    ADS  Google Scholar 

  8. E Ma, Phys. Rev. Lett. 81, 1171 (1998), arXiv:hep-ph/9805219

    Article  Google Scholar 

  9. P Minkowski, Phys. Lett. B67, 421 (1977)

    Google Scholar 

  10. T Yanagida, in KEK Lectures edited by O Sawada and A Sugamoto, KEK, 1979

  11. M Gell-Mann, P Ramond and R Slansky, in Supergravity edited by P van Niewenhuizen and D Freedman (North Holland, 1979)

  12. R N Mohapatra and G Senjanovic, Phys. Rev. Lett. 44, 912 (1980)

    Article  ADS  Google Scholar 

  13. J Schechter and J W F Valle, Phys. Rev. D22, 2227 (1980)

    ADS  Google Scholar 

  14. T P Cheng and L F Li, Phys. Rev. D22, 2860 (1980)

    ADS  Google Scholar 

  15. R Foot, H Lew, X G He and G C Joshi, Z. Phys. C44, 441 (1989)

    Google Scholar 

  16. A Zee, Phys. Lett. B93, 389 (1980); Erratum, ibid. B95, 461 (1980)

    ADS  Google Scholar 

  17. A Zee, Nucl. Phys. B264, 99 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  18. K S Babu, Phys. Lett. B203, 132 (1988)

    ADS  Google Scholar 

  19. M Maltoni, T Schwetz, M A Tortola and J W F Valle, New J. Phys. 6, 122 (2004); Online version 6 in arXiv:hep-ph/0405172 contains updated fits with data included up to Sep. 2007

    Article  ADS  Google Scholar 

  20. P F Harrison, D H Perkins and W G Scott, Phys. Lett. B530, 167 (2002), hepph/0202074

    ADS  Google Scholar 

  21. J Kubo, A Mondragon, M Mondragon and E Rodriguez-Jauregui, Prog. Theor. Phys. 109, 795 (2003); Erratum, ibid. 114, 287 (2005), arXiv:hep-ph/0302196

    Article  MATH  ADS  Google Scholar 

  22. J Kubo, H Okada and F Sakamaki, Phys. Rev. D70, 036007 (2004), arXiv:hepph/0402089

  23. W Grimus and L Lavoura, J. High Energy Phys. 0508, 013 (2005), arXiv:hepph/0504153

    Article  ADS  MathSciNet  Google Scholar 

  24. W Grimus and L Lavoura, J. Phys. G34, 1757 (2007), arXiv:hep-ph/0611149

    ADS  Google Scholar 

  25. E Ma, arXiv:0705.0327 [hep-ph]

  26. For a related discussion, see also the contribution by M C Chen, these proceedings

  27. For a brief introduction to A 4 see for example, E Ma, arXiv:0710.3851 [hep-ph]

  28. For a short review on neutrinoless double beta decay, see for example, M Hirsch, arXiv:hep-ph/0609146

  29. As I have been reminded, one can also generate a see-saw mechanism for Dirac neutrinos (see for example [25]). In this case the ‘prediction’ for 〈m ν〉 is 〈m ν〉 ≡ 0, of course

    ADS  Google Scholar 

  30. P Roy and O U Shanker, Phys. Rev. D30, 1949 (1984); Erratum, ibid. 3D1, 2385 (1985)

    ADS  Google Scholar 

  31. E Ma and G Rajasekaran, Phys. Rev. D64, 113012 (2001), hep-ph/0106291

  32. K S Babu, E Ma and J W F Valle, Phys. Lett. B552, 207 (2003), hep-ph/0206292

    ADS  Google Scholar 

  33. M Hirsch, J C Romao, S Skadhauge, J W F Valle and A Villanova del Moral, Phys. Rev. D69, 093006 (2004)

    Google Scholar 

  34. M Hirsch, A Villanova del Moral, J W F Valle and E Ma, Phys. Rev. D72, 091301 (2005), hep-ph/0507148

  35. M Hirsch, A S Joshipura, S Kaneko and J W F Valle, Phys. Rev. Lett. 99, 151802 (2007), arXiv:hep-ph/0703046

    Google Scholar 

  36. S Dev, S Kumar, S Verma and S Gupta, Phys. Rev. D76, 013002 (2007), arXiv:hepph/0612102

  37. S-L Chen, M Frigerio and E Ma, Nucl. Phys. B724, 423 (2005), hep-ph/0504181

    Article  ADS  Google Scholar 

  38. P H Frampton, S L Glashow and D Marfatia, Phys. Lett. B536, 79 (2002), hepph/0201008

    ADS  Google Scholar 

  39. M Hirsch, S Morisi and J W F Valle, arXiv:0804.1521 [hep-ph]

  40. E Ma, Phys. Rev. D70, 031901 (2004), hep-ph/0404199

  41. G Altarelli and F Feruglio, Nucl. Phys. B720, 64 (2005), hep-ph/0504165

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AHEP Group, Instituto de Física Corpuscular — C.S.I.C./Universitat de València, Edificio de Institutos de Paterna, Apartado 22085, E-46071, València, Spain

    Martin Hirsch

Authors
  1. Martin Hirsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Hirsch.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirsch, M. The neutrino mass matrix and (selected) variants of A 4 . Pramana - J Phys 72, 183–193 (2009). https://doi.org/10.1007/s12043-009-0015-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-009-0015-x

Keywords

PACS Nos

Search

Navigation