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Neutrino mixing and the exponential form of the Pontecorvo–Maki–Nakagawa–Sakata matrix

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Abstract

The form of the neutrino mixing matrix is discussed. The exponential parameterisation of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix is proposed and the generation of the new unitary parameterisation of the neutrino mixing matrix by the exponential form is demonstrated. The CP violating phase and the Majorana phases in the PMNS matrix are accounted for by a special term, separated from the rotational one. The O(3) rotation matrix in the angle-axis form is discussed in the context of such a representation of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement.

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References

  1. S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967)

    Article  ADS  Google Scholar 

  2. A. Salam, In: Elementary Particle Theory, ed. by N. Svartholm (Almquist Forlag AB, Stockholm, 1968)

    Google Scholar 

  3. S.L. Glashow, Nucl. Phys. 22, 579 (1961)

    Article  Google Scholar 

  4. Super-Kamiokande Collaboration, M.B. Smy et al., Phys. Rev. D 69, 011104 (2004)

    Article  ADS  Google Scholar 

  5. KamLAND Collaboration, T. Ataki et al., Phys. Rev. Lett. 94, 081801 (2005)

    Article  ADS  Google Scholar 

  6. Super-Kamiokande Collaboration, Y. Ashie et al., Phys. Rev. D 71, 112005 (2005)

    Article  ADS  Google Scholar 

  7. CHOOZ Collaboration, M. Apollonio et al., Eur. Phys. J. C 27, 331 (2003)

    Article  ADS  Google Scholar 

  8. B. Pontecorvo, Zh. Eksp. Teor. Fiz. 33, 549 (1957)

    Google Scholar 

  9. B. Pontecorvo, Zh. Eksp. Teor. Fiz. 53, 1717 (1967)

    Google Scholar 

  10. B. Pontecorvo, Sov. Phys. JETP 26, 984 (1968)

    ADS  Google Scholar 

  11. Z. Maki, M. Nakagawa, S. Sakata, Prog. Theor. Phys. 28, 870 (1962)

    Article  MATH  ADS  Google Scholar 

  12. H. Murayama, T. Yanagida, Phys. Lett. B 520, 263 (2001)

    Article  ADS  Google Scholar 

  13. G. Barenboim et al., JHEP 0210, 001 (2002)

    Article  ADS  Google Scholar 

  14. M.C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, Phys. Rev. D 68, 053007 (2003)

    Article  ADS  Google Scholar 

  15. L. Wolfenstein, Phys. Rev. D 17, 2369 (1978)

    Article  ADS  Google Scholar 

  16. S.P. Mikheev, A.Y. Smirnov, Yad. Fiz. 42, 1441 (1985)

    ADS  Google Scholar 

  17. S.P. Mikheev, A.Y. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985)

    Google Scholar 

  18. Particle Data Group, W.-M. Yao et al., J. Phys. G: Nucl. Part. Phys. 33, 1 (2006)

    Article  ADS  Google Scholar 

  19. H. Minako, K. Yee, O. Naotoshi, T. Tatsu, YITP 05-52, 73P (2006) [arXiv:hep-ph/0602115]

    Google Scholar 

  20. L.-L. Chau, W.-Y. Keung, Phys. Rev. Lett. 53, 1802 (1984)

    Article  ADS  Google Scholar 

  21. H. Harari, M. Leurer, Phys. Lett. B 181, 123 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  22. H. Fritzsch, J. Plankl, Phys. Rev. D 35, 1732 (1987)

    Article  ADS  Google Scholar 

  23. F.J. Botella, L.-L. Chao, Phys. Lett. B 168, 97 (1986)

    Article  ADS  Google Scholar 

  24. SNO Collaboration, B. Aharmin et al., nucl-ex/0502021

  25. KamLAND Collaboration, T. Araki et al., Phys. Rev. Lett. 94, 081801 (2005)

    Article  ADS  Google Scholar 

  26. Y. Suzuki, presented at the XXII Int. Symp. on Lepton and Photon Interactions at High Energies (Lepton–Photon 2005), Uppsala, Sweden, July 2005

  27. Chooz Collaboration, C. Bemporad, Nucl. Phys. Proc. Suppl. 77, 159 (1999)

    Article  ADS  Google Scholar 

  28. L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983)

    Article  ADS  Google Scholar 

  29. Z.Z. Xing, Phys. Lett. B 533, 85 (2002)

    Article  ADS  Google Scholar 

  30. J.D. Bjorken, P.F. Harrison, W.G. Scott, Phys. Rev. D 74, 073012 (2006)

    Article  ADS  Google Scholar 

  31. A. Datta, L. Everett, P. Ramond, Phys. Lett. B 620, 42 (2005)

    Article  ADS  Google Scholar 

  32. S. Antush, S.F. King, Phys. Lett. B 631, 42 (2005)

    ADS  Google Scholar 

  33. G. Altarelli, F. Feruglio, Y. Lin, Nucl. Phys. B 775, 31 (2007)

    Article  MATH  ADS  Google Scholar 

  34. E. Ma, Mod. Phys. Lett. A 22, 101 (2007)

    Article  MATH  ADS  Google Scholar 

  35. S.F. King, arXiv:0710.0530 [hep-ph]

  36. N. Li, B.Q. Ma, Phys. Rev. D 71, 017302 (2005)

    Article  ADS  Google Scholar 

  37. G. Dattoli, K. Zhukovsky, Eur. Phys. J. C 50, 817 (2007)

    Article  ADS  Google Scholar 

  38. G. Dattoli, K. Zhukovsky, Eur. Phys. J. C 52, 591 (2007)

    Article  ADS  Google Scholar 

  39. G. Dattoli, E. Sabia, A. Torre, Nuovo Cim. A 109, 1425 (1996)

    Article  ADS  Google Scholar 

  40. H. Goldstein, Classical Mechanics (Addison-Wesley, Cambridge, MA, 1950), p. 399

    Google Scholar 

  41. H. Minakata, A.Y. Smirnov, Phys. Rev. D 70, 073009 (2004)

    Article  ADS  Google Scholar 

  42. M. Raidal, Phys. Rev. Lett. 93, 161801 (2004)

    Article  ADS  Google Scholar 

  43. M. Fukugita, T. Yanagida, Phys. Lett. B 174, 45 (1986)

    Article  ADS  Google Scholar 

  44. V. Kusmin, V. Rubakov, M. Shaposnikov, Phys. Lett. B 155, 36 (1985)

    Article  ADS  Google Scholar 

  45. S. Pascoli, S. Petcov, W. Rodejohann, Phys. Rev. D 68, 093007 (2003)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Gruppo Fisica Teorica e Matematica Applicata Unita Tecnico Scientifica Tecnologie Fisiche Avanzante (FIS-MAT), ENEA – Centro Ricerche Frascati, Via Enrico Fermi 45, 00044, Frascati, Rome, Italy

    G. Dattoli

  2. Dept. of Optics and Spectroscopy, Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, 119991, Russia

    K.V. Zhukovsky

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  1. G. Dattoli
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  2. K.V. Zhukovsky
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Correspondence to K.V. Zhukovsky.

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Dattoli, G., Zhukovsky, K. Neutrino mixing and the exponential form of the Pontecorvo–Maki–Nakagawa–Sakata matrix. Eur. Phys. J. C 55, 547–552 (2008). https://doi.org/10.1140/epjc/s10052-008-0620-8

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  • DOI: https://doi.org/10.1140/epjc/s10052-008-0620-8

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