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Renormalization group invariants in neutrino sector

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Abstract

We show renormalization group invariants in neutrino sector. These are found from a simple analytical discussion of Majorana mass matrix for light neutrinos. There are four invariants, which are ratios among elements of the mass matrix. They are independent of neutrino mass ordering and a parameterization of mixing matrix for the lepton sector. We also investigate two running parameters of renormalization group equations, which can directly show neutrino mass matrix at the high energy scale.

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References

  1. Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  2. B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Sov. Phys. JETP 26 (1968) 984 [Zh. Eksp. Teor. Fiz. 53 (1967) 1717] [INSPIRE].

  3. T2K collaboration, K. Abe et al., Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].

    Article  ADS  Google Scholar 

  4. MINOS collaboration, P. Adamson et al., Improved search for muon-neutrino to electron-neutrino oscillations in MINOS, Phys. Rev. Lett. 107 (2011) 181802 [arXiv:1108.0015] [INSPIRE].

    Article  ADS  Google Scholar 

  5. DOUBLE-CHOOZ collaboration, Y. Abe et al., Indication for the disappearance of reactor electron antineutrinos in the Double CHOOZ experiment, Phys. Rev. Lett. 108 (2012) 131801 [arXiv:1112.6353] [INSPIRE].

    Article  ADS  Google Scholar 

  6. DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].

    Article  ADS  Google Scholar 

  7. RENO collaboration, J. Ahn et al., Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].

    Article  ADS  Google Scholar 

  8. D. Forero, M. Tortola and J. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].

    ADS  Google Scholar 

  9. G. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE].

    ADS  Google Scholar 

  10. M. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].

    Article  ADS  Google Scholar 

  11. P. Minkowski, μeγ at a rate of one out of 1-billion muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].

    Article  ADS  Google Scholar 

  12. T. Yanagida, Horizontal symmetry and masses of neutrinos, in Proceedings of the Workshop on Unified Theories and Baryon Number in the Universe, O. Sawada and A. Sugamoto eds., KEK report 79-18, Japan (1979) [INSPIRE].

  13. M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman eds., North Holland, Amsterdam The Netherlands (1979) [arXiv:1306.4669] [INSPIRE].

  14. R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].

    Article  ADS  Google Scholar 

  15. J. Schechter and J. Valle, Neutrino masses in SU(2) × U(1) theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].

    ADS  Google Scholar 

  16. J. Schechter and J. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25 (1982) 774 [INSPIRE].

    ADS  Google Scholar 

  17. P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [INSPIRE].

    Article  ADS  Google Scholar 

  18. K. Babu, C.N. Leung and J.T. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223] [INSPIRE].

    Article  ADS  Google Scholar 

  19. J.R. Ellis and S. Lola, Can neutrinos be degenerate in mass?, Phys. Lett. B 458 (1999) 310 [hep-ph/9904279] [INSPIRE].

    Article  ADS  Google Scholar 

  20. N. Haba, N. Okamura and M. Sugiura, The renormalization group analysis of the large lepton flavor mixing and the neutrino mass, Prog. Theor. Phys. 103 (2000) 367 [hep-ph/9810471] [INSPIRE].

  21. N. Haba, Y. Matsui, N. Okamura and M. Sugiura, The effect of Majorana phase in degenerate neutrinos, Prog. Theor. Phys. 103 (2000) 145 [hep-ph/9908429] [INSPIRE].

    Article  ADS  Google Scholar 

  22. N. Haba, Y. Matsui and N. Okamura, Analytic solutions to the RG equations of the neutrino physical parameters, Prog. Theor. Phys. 103 (2000) 807 [hep-ph/9911481] [INSPIRE].

    Article  ADS  Google Scholar 

  23. N. Haba, Y. Matsui and N. Okamura, The effects of Majorana phases in three generation neutrinos, Eur. Phys. J. C 17 (2000) 513 [hep-ph/0005075] [INSPIRE].

    Article  ADS  Google Scholar 

  24. N. Haba, Y. Matsui, N. Okamura and T. Suzuki, Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?, Phys. Lett. B 489 (2000) 184 [hep-ph/0005064] [INSPIRE].

    Article  ADS  Google Scholar 

  25. S. Antusch, J. Kersten, M. Lindner and M. Ratz, Running neutrino masses, mixings and CP phases: analytical results and phenomenological consequences, Nucl. Phys. B 674 (2003) 401 [hep-ph/0305273] [INSPIRE].

    Article  ADS  Google Scholar 

  26. S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].

    Article  ADS  Google Scholar 

  27. J.-W. Mei, Running neutrino masses, leptonic mixing angles and CP-violating phases: from M Z to ΛGUT, Phys. Rev. D 71 (2005) 073012 [hep-ph/0502015] [INSPIRE].

    ADS  Google Scholar 

  28. J.-W. Mei and Z.-Z. Xing, Radiative corrections to democratic lepton mixing, Phys. Lett. B 623 (2005) 227 [hep-ph/0506304] [INSPIRE].

    Article  ADS  Google Scholar 

  29. S. Luo, J.-W. Mei and Z.-Z. Xing, Radiative generation of leptonic CP-violation, Phys. Rev. D 72 (2005) 053014 [hep-ph/0507065] [INSPIRE].

    ADS  Google Scholar 

  30. S. Ray, W. Rodejohann and M.A. Schmidt, Lower bounds on the smallest lepton mixing angle, Phys. Rev. D 83 (2011) 033002 [arXiv:1010.1206] [INSPIRE].

    ADS  Google Scholar 

  31. S. Luo and Z.-Z. Xing, Impacts of the observed θ 13 on the running behaviors of Dirac and Majorana neutrino mixing angles and CP-violating phases, Phys. Rev. D 86 (2012) 073003 [arXiv:1203.3118] [INSPIRE].

    ADS  Google Scholar 

  32. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  33. N. Haba and N. Okamura, Stability of the lepton-flavor mixing matrix against quantum corrections, Eur. Phys. J. C 14 (2000) 347 [hep-ph/9906481] [INSPIRE].

    Article  ADS  Google Scholar 

  34. N. Haba and R. Takahashi, Grand unification of flavor mixings, Europhys. Lett. 100 (2012) 31001 [arXiv:1206.2793] [INSPIRE].

    Article  ADS  Google Scholar 

  35. N. Haba, K. Kaneta and R. Takahashi, Stability of leptonic self-complementarity, Europhys. Lett. 101 (2013) 11001 [arXiv:1209.1522] [INSPIRE].

    Article  ADS  Google Scholar 

  36. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].

    Article  ADS  Google Scholar 

  37. R. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett. B 644 (2007) 59 [hep-ph/0608111] [INSPIRE].

  38. Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].

  39. WMAP collaboration, C. Bennett et al., Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: final maps and results, arXiv:1212.5225 [INSPIRE].

  40. Planck collaboration, P. Ade et al., Planck 2013 results. XV. CMB power spectra and likelihood, arXiv:1303.5075 [INSPIRE].

  41. N. Haba and R. Takahashi, Constraints on neutrino mass ordering and degeneracy from Planck and neutrino-less double beta decay, arXiv:1305.0147 [INSPIRE].

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Correspondence to Ryo Takahashi.

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ArXiv ePrint: 1306.1375

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Haba, N., Takahashi, R. Renormalization group invariants in neutrino sector. J. High Energ. Phys. 2013, 123 (2013). https://doi.org/10.1007/JHEP08(2013)123

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  • DOI: https://doi.org/10.1007/JHEP08(2013)123

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