Lepton mixing and the charged-lepton mass ratios

  • Darius Jurčiukonis
  • Luís Lavoura
Open Access
Regular Article - Theoretical Physics


We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CP -breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.


Phenomenological Models 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    P. Minkowski, μeγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
  2. [2]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, in Proceedings of the workshop on unified theory and baryon number in the universe, Tsukuba, Japan (1979), O. Sawata and A. Sugamoto eds., KEK report 79-18, Tsukuba (1979) [INSPIRE].
  3. [3]
    S.L. Glashow, The future of elementary particle physics, in Quarks and leptons, proceedings of the advanced study institute, Cargèse, Corsica, (1979), M. Lévy et al. eds., Plenum, New York (1980) [INSPIRE].
  4. [4]
    M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Supergravity, D.Z. Freedman and F. van Nieuwenhuizen eds., North Holland, Amsterdam (1979) [INSPIRE].
  5. [5]
    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    W. Grimus and L. Lavoura, Softly broken lepton numbers and maximal neutrino mixing, JHEP 07 (2001) 045 [hep-ph/0105212] [INSPIRE].
  7. [7]
    W. Grimus and L. Lavoura, Softly broken lepton numbers: An Approach to maximal neutrino mixing, Acta Phys. Polon. B 32 (2001) 3719 [hep-ph/0110041] [INSPIRE].
  8. [8]
    W. Grimus and L. Lavoura, Leptogenesis in seesaw models with a twofold degenerate neutrino Dirac mass matrix, J. Phys. G 30 (2004) 1073 [hep-ph/0311362] [INSPIRE].
  9. [9]
    Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  10. [10]
    S.F. King, Unified Models of Neutrinos, Flavour and CP-violation, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino Mass and Mixing: from Theory to Experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
  12. [12]
    G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    P.H. Frampton, S.L. Glashow and D. Marfatia, Zeroes of the neutrino mass matrix, Phys. Lett. B 536 (2002) 79 [hep-ph/0201008] [INSPIRE].
  14. [14]
    P.F. de Salas, D.V. Forero, C.A. Ternes, M. Tórtola and J.W.F. Valle, Status of neutrino oscillations 2017, arXiv:1708.01186 [INSPIRE].
  15. [15]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
  16. [16]
    R. Emami et al., Evidence of Neutrino Enhanced Clustering in a Complete Sample of Sloan Survey Clusters, Implyingm ν = 0.11 ± 0.03 eV, arXiv:1711.05210 [INSPIRE].
  17. [17]
    J.M. Lamprea and E. Peinado, Seesaw scale discrete dark matter and two-zero texture Majorana neutrino mass matrices, Phys. Rev. D 94 (2016) 055007 [arXiv:1603.02190] [INSPIRE].
  18. [18]
    W. Grimus, A.S. Joshipura, L. Lavoura and M. Tanimoto, Symmetry realization of texture zeros, Eur. Phys. J. C 36 (2004) 227 [hep-ph/0405016] [INSPIRE].
  19. [19]
    P.M. Ferreira, W. Grimus, D. Jurciukonis and L. Lavoura, Scotogenic model for co-bimaximal mixing, JHEP 07 (2016) 010 [arXiv:1604.07777] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, A Precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [arXiv:0711.4022] [INSPIRE].
  21. [21]
    K. Kannike, Vacuum Stability Conditions From Copositivity Criteria, Eur. Phys. J. C 72 (2012) 2093 [arXiv:1205.3781] [INSPIRE].
  22. [22]
    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    L. Lavoura and D. Jurčiukonis, Unitarity bounds and the allowed Higgs masses and couplings in a general 2HDM, in preparation.Google Scholar
  24. [24]
    M.P. Bento, H.E. Haber, J.C. Romão and J.P. Silva, Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095 [arXiv:1708.09408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Institute of Theoretical Physics and AstronomyUniversity of VilniusVilniusLithuania
  2. 2.Instituto Superior Técnico, CFTPUniversidade de LisboaLisboaPortugal

Personalised recommendations