Scotogenic model for co-bimaximal mixing

  • P. M. Ferreira
  • W. Grimus
  • D. Jurčiukonis
  • L. Lavoura
Open Access
Regular Article - Theoretical Physics


We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet η, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle θ 23 = 45° and to a CP -violating phase δ = ±π/2, while the mixing angle θ 13 remains arbitrary. The symmetries consist of softly broken lepton numbers L α (α = e, μ, τ ), a non-standard CP symmetry, and three \( {\mathbb{Z}}_2 \) symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides η, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass 125 GeV, with all the other charged and neutral scalars having much higher masses.


Discrete Symmetries Neutrino Physics 


Open Access

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  1. [1]
    W. Grimus and L. Lavoura, A nonstandard CP transformation leading to maximal atmospheric neutrino mixing, Phys. Lett. B 579 (2004) 113 [hep-ph/0305309] [INSPIRE].
  2. [2]
    M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D.V. Forero, M. Tortola and J.W.F. Valle, Neutrino oscillations refitted, Phys. Rev. D 90 (2014) 093006 [arXiv:1405.7540] [INSPIRE].ADSGoogle Scholar
  4. [4]
    F. Capozzi, G.L. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, Status of three-neutrino oscillation parameters, circa 2013, Phys. Rev. D 89 (2014) 093018 [arXiv:1312.2878] [INSPIRE].ADSGoogle Scholar
  5. [5]
    J. Bergstrom, M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Bayesian global analysis of neutrino oscillation data, JHEP 09 (2015) 200 [arXiv:1507.04366] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    E. Ma, Neutrino Mixing: A 4 Variations, Phys. Lett. B 752 (2016) 198 [arXiv:1510.02501] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    A.S. Joshipura and K.M. Patel, Generalized μ-τ symmetry and discrete subgroups of O(3), Phys. Lett. B 749 (2015) 159 [arXiv:1507.01235] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    H.-J. He, W. Rodejohann and X.-J. Xu, Origin of Constrained Maximal CP-violation in Flavor Symmetry, Phys. Lett. B 751 (2015) 586 [arXiv:1507.03541] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    K. Fukuura, T. Miura, E. Takasugi and M. Yoshimura, Large CP -violation, large mixings of neutrinos and democratic type neutrino mass matrix, Phys. Rev. D 61 (2000) 073002 [hep-ph/9909415] [INSPIRE].
  10. [10]
    T. Miura, E. Takasugi and M. Yoshimura, Large CP -violation, large mixings of neutrinos and the Z 3 symmetry, Phys. Rev. D 63 (2001) 013001 [hep-ph/0003139] [INSPIRE].
  11. [11]
    P.F. Harrison and W.G. Scott, μ-τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].
  12. [12]
    W. Grimus and L. Lavoura, One-loop corrections to the seesaw mechanism in the multi-Higgs-doublet standard model, Phys. Lett. B 546 (2002) 86 [hep-ph/0207229] [INSPIRE].
  13. [13]
    E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].
  14. [14]
    E. Ma, Soft A 4Z 3 symmetry breaking and cobimaximal neutrino mixing, Phys. Lett. B 755 (2016) 348 [arXiv:1601.00138] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    R. Barbieri, L.J. Hall and V.S. Rychkov, Improved naturalness with a heavy Higgs: An alternative road to LHC physics, Phys. Rev. D 74 (2006) 015007 [hep-ph/0603188] [INSPIRE].
  16. [16]
    W. Grimus and L. Lavoura, Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass, J. Phys. G 30 (2004) 73 [hep-ph/0309050] [INSPIRE].
  17. [17]
    L. Lavoura, Real CP-violation in a simple extension of the standard model, Phys. Rev. D 61 (2000) 076003 [hep-ph/9909275] [INSPIRE].
  18. [18]
    A. Masiero and T. Yanagida, Real CP-violation, hep-ph/9812225 [INSPIRE].
  19. [19]
    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].ADSCrossRefzbMATHGoogle Scholar
  20. [20]
    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM, Phys. Rev. D 75 (2007) 035001 [Erratum ibid. D 76 (2007) 039902] [hep-ph/0609018] [INSPIRE].
  21. [21]
    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
  22. [22]
    K. Kannike, Vacuum Stability Conditions From Copositivity Criteria, Eur. Phys. J. C 72 (2012) 2093 [arXiv:1205.3781] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  24. [24]
    ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV, ATLAS-CONF-2015-044 (2015).
  25. [25]
    Z.-z. Xing, H. Zhang and S. Zhou, Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays, Phys. Rev. D 86 (2012) 013013 [arXiv:1112.3112] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • P. M. Ferreira
    • 1
    • 2
  • W. Grimus
    • 3
  • D. Jurčiukonis
    • 4
  • L. Lavoura
    • 5
  1. 1.Instituto Superior de Engenharia de Lisboa — ISELLisboaPortugal
  2. 2.Centro de Física Teórica e Computacional — FCULUniversidade de LisboaLisboaPortugal
  3. 3.Faculty of PhysicsUniversity of ViennaWienAustria
  4. 4.Institute of Theoretical Physics and AstronomyVilnius UniversityVilniusLithuania
  5. 5.CFTP, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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