Journal of High Energy Physics

, 2019:223 | Cite as

Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw

  • D. M. Barreiros
  • R. G. Felipe
  • F. R. JoaquimEmail author
Open Access
Regular Article - Theoretical Physics


In the framework of the two right-handed neutrino seesaw model, we consider maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and mass matrices, together with the existence of a remnant CP symmetry. Under this premise, we find that several textures are compatible with the most recent data coming from neutrino oscillation and neutrinoless double beta decay experiments. It is shown that, the maximum number of allowed texture zeros in the Dirac Yukawa coupling matrix is two, for an inverted neutrino mass spectrum. In contrast, for Yukawa coupling matrices with just one texture zero, both normal and inverted orderings of neutrino masses are compatible with data. In all cases, the predictions for the low-energy Dirac and Majorana CP-violating phases, and for the effective mass parameter relevant in neutrinoless double-beta decay experiments, are presented and discussed. We also comment on the impact of future experimental improvements in scrutinising texture-zero patterns with a remnant CP symmetry, within the minimal version of the seesaw mechanism considered here.


CP violation Neutrino Physics Beyond Standard Model Discrete Symmetries 


Open Access

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  1. [1]
    P.F. de Salas, D.V. Forero, C.A. Ternes, M. Tortola and J.W.F. Valle, Status of neutrino oscillations 2018: 3σ hint for normal mass ordering and improved CP sensitivity, Phys. Lett. B 782 (2018) 633 [arXiv:1708.01186] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and T. Schwetz, Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP 01 (2017) 087 [arXiv:1611.01514] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    F. Capozzi, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, Neutrino masses and mixings: Status of known and unknown 3ν parameters, Nucl. Phys. B 908 (2016) 218 [arXiv:1601.07777] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    T2K collaboration, Search for CP-violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with 2.2 × 1021 Protons on Target, Phys. Rev. Lett. 121 (2018) 171802 [arXiv:1807.07891] [INSPIRE].
  5. [5]
    NOvA collaboration, New constraints on oscillation parameters from ν e appearance and ν μ disappearance in the NOvA experiment, Phys. Rev. D 98 (2018) 032012 [arXiv:1806.00096] [INSPIRE].
  6. [6]
    S. Dell’Oro, S. Marcocci, M. Viel and F. Vissani, Neutrinoless double beta decay: 2015 review, Adv. High Energy Phys. 2016 (2016) 2162659 [arXiv:1601.07512] [INSPIRE].Google Scholar
  7. [7]
    J.D. Vergados, H. Ejiri and F. Šimkovic, Neutrinoless double beta decay and neutrino mass, Int. J. Mod. Phys. E 25 (2016) 1630007 [arXiv:1612.02924] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Giuliani, The Mid and Long Term Future of Neutrinoless Double Beta Decay, talk at XXVIII International Conference on Neutrino Physics and Astrophysics, Heidelberg, Germany, 4–9 June 2018 [].
  9. [9]
    P. Minkowski, μeγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
  10. [10]
    M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].Google Scholar
  11. [11]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].Google Scholar
  12. [12]
    J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].ADSGoogle Scholar
  13. [13]
    S.L. Glashow, The Future of Elementary Particle Physics, NATO Sci. Ser. B 61 (1980) 687 [INSPIRE].Google Scholar
  14. [14]
    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    G. Ecker, W. Grimus and W. Konetschny, Quark Mass Matrices in Left-right Symmetric Gauge Theories, Nucl. Phys. B 191 (1981) 465 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    G. Ecker, W. Grimus and H. Neufeld, A Standard Form for Generalized CP Transformations, J. Phys. A 20 (1987) L807 [INSPIRE].ADSGoogle Scholar
  17. [17]
    H. Neufeld, W. Grimus and G. Ecker, Generalized CP Invariance, Neutral Flavor Conservation and the Structure of the Mixing Matrix, Int. J. Mod. Phys. A 3 (1988) 603 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    W. Grimus and M.N. Rebelo, Automorphisms in gauge theories and the definition of CP and P, Phys. Rept. 281 (1997) 239 [hep-ph/9506272] [INSPIRE].
  19. [19]
    G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos, CP-odd invariants in models with several Higgs doublets, Phys. Lett. B 614 (2005) 187 [hep-ph/0502118] [INSPIRE].
  20. [20]
    F. Feruglio, C. Hagedorn and R. Ziegler, Lepton Mixing Parameters from Discrete and CP Symmetries, JHEP 07 (2013) 027 [arXiv:1211.5560] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    M. Holthausen, M. Lindner and M.A. Schmidt, CP and Discrete Flavour Symmetries, JHEP 04 (2013) 122 [arXiv:1211.6953] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    I. Girardi, A. Meroni, S.T. Petcov and M. Spinrath, Generalised geometrical CP-violation in a T’ lepton flavour model, JHEP 02 (2014) 050 [arXiv:1312.1966] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP Violation from Finite Groups, Nucl. Phys. B 883 (2014) 267 [arXiv:1402.0507] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    S.F. King and T. Neder, Lepton mixing predictions including Majorana phases from Δ(6n 2) flavour symmetry and generalised CP, Phys. Lett. B 736 (2014) 308 [arXiv:1403.1758] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    G.-J. Ding, S.F. King and T. Neder, Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons, JHEP 12 (2014) 007 [arXiv:1409.8005] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    P. Chen, C.-C. Li and G.-J. Ding, Lepton Flavor Mixing and CP Symmetry, Phys. Rev. D 91 (2015) 033003 [arXiv:1412.8352] [INSPIRE].ADSGoogle Scholar
  27. [27]
    L.L. Everett, T. Garon and A.J. Stuart, A Bottom-Up Approach to Lepton Flavor and CP Symmetries, JHEP 04 (2015) 069 [arXiv:1501.04336] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    G.C. Branco, I. de Medeiros Varzielas and S.F. King, Invariant approach to CP in family symmetry models, Phys. Rev. D 92 (2015) 036007 [arXiv:1502.03105] [INSPIRE].ADSMathSciNetGoogle Scholar
  29. [29]
    P. Ballett, S. Pascoli and J. Turner, Mixing angle and phase correlations from A5 with generalized CP and their prospects for discovery, Phys. Rev. D 92 (2015) 093008 [arXiv:1503.07543] [INSPIRE].ADSGoogle Scholar
  30. [30]
    P. Chen, C.-Y. Yao and G.-J. Ding, Neutrino Mixing from CP Symmetry, Phys. Rev. D 92 (2015) 073002 [arXiv:1507.03419] [INSPIRE].ADSGoogle Scholar
  31. [31]
    I. Girardi, S.T. Petcov, A.J. Stuart and A.V. Titov, Leptonic Dirac CP-violation Predictions from Residual Discrete Symmetries, Nucl. Phys. B 902 (2016) 1 [arXiv:1509.02502] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Classifying CP transformations according to their texture zeros: theory and implications, Phys. Rev. D 94 (2016) 033002 [arXiv:1604.03510] [INSPIRE].ADSGoogle Scholar
  33. [33]
    J.T. Penedo, S.T. Petcov and A.V. Titov, Neutrino mixing and leptonic CP-violation from S 4 flavour and generalised CP symmetries, JHEP 12 (2017) 022 [arXiv:1705.00309] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    I.P. Ivanov, Radiative neutrino masses from order-4 CP symmetry, JHEP 02 (2018) 025 [arXiv:1712.02101] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Samanta, P. Roy and A. Ghosal, Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos, JHEP 06 (2018) 085 [arXiv:1712.06555] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    P. Chen, S. Centelles Chuliá, G.-J. Ding, R. Srivastava and J.W.F. Valle, Neutrino Predictions from Generalized CP Symmetries of Charged Leptons, JHEP 07 (2018) 077 [arXiv:1802.04275] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    C.-C. Li and G.-J. Ding, Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos, Phys. Rev. D 96 (2017) 075005 [arXiv:1701.08508] [INSPIRE].ADSGoogle Scholar
  38. [38]
    J.A. Casas and A. Ibarra, Oscillating neutrinos and μe, γ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [INSPIRE].
  39. [39]
    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].
  40. [40]
    A. Dighe and N. Sahu, Texture zeroes and discrete flavor symmetries in light and heavy Majorana neutrino mass matrices: a bottom-up approach, arXiv:0812.0695 [INSPIRE].
  41. [41]
    B. Adhikary, A. Ghosal and P. Roy, mu tau symmetry, tribimaximal mixing and four zero neutrino Yukawa textures, JHEP 10 (2009) 040 [arXiv:0908.2686] [INSPIRE].
  42. [42]
    S. Dev, S. Gupta and R.R. Gautam, Zero Textures of the Neutrino Mass Matrix from Cyclic Family Symmetry, Phys. Lett. B 701 (2011) 605 [arXiv:1106.3451] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    R. González Felipe and H. Serôdio, Abelian realization of phenomenological two-zero neutrino textures, Nucl. Phys. B 886 (2014) 75 [arXiv:1405.4263] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    L.M. Cebola, D. Emmanuel-Costa and R.G. Felipe, Confronting predictive texture zeros in lepton mass matrices with current data, Phys. Rev. D 92 (2015) 025005 [arXiv:1504.06594] [INSPIRE].ADSGoogle Scholar
  45. [45]
    R. Samanta and A. Ghosal, Probing maximal zero textures with broken cyclic symmetry in inverse seesaw, Nucl. Phys. B 911 (2016) 846 [arXiv:1507.02582] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  46. [46]
    T. Kobayashi, T. Nomura and H. Okada, Predictive neutrino mass textures with origin of flavor symmetries, Phys. Rev. D 98 (2018) 055025 [arXiv:1805.07101] [INSPIRE].ADSGoogle Scholar
  47. [47]
    M.H. Rahat, P. Ramond and B. Xu, Asymmetric tribimaximal texture, Phys. Rev. D 98 (2018) 055030 [arXiv:1805.10684] [INSPIRE].ADSGoogle Scholar
  48. [48]
    N. Nath, μτ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model, arXiv:1808.05062 [INSPIRE].
  49. [49]
    P.H. Frampton, S.L. Glashow and T. Yanagida, Cosmological sign of neutrino CP-violation, Phys. Lett. B 548 (2002) 119 [hep-ph/0208157] [INSPIRE].
  50. [50]
    A. Ibarra and G.G. Ross, Neutrino phenomenology: The Case of two right-handed neutrinos, Phys. Lett. B 591 (2004) 285 [hep-ph/0312138] [INSPIRE].
  51. [51]
    K. Harigaya, M. Ibe and T.T. Yanagida, Seesaw Mechanism with Occam’s Razor, Phys. Rev. D 86 (2012) 013002 [arXiv:1205.2198] [INSPIRE].ADSGoogle Scholar
  52. [52]
    T. Rink and K. Schmitz, Perturbed Yukawa Textures in the Minimal Seesaw Model, JHEP 03 (2017) 158 [arXiv:1611.05857] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    Y. Shimizu, K. Takagi and M. Tanimoto, Towards the minimal seesaw model via CP-violation of neutrinos, JHEP 11 (2017) 201 [arXiv:1709.02136] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    D.M. Barreiros, R.G. Felipe and F.R. Joaquim, Minimal type-I seesaw model with maximally restricted texture zeros, Phys. Rev. D 97 (2018) 115016 [arXiv:1802.04563] [INSPIRE].ADSGoogle Scholar
  55. [55]
    J. Alcaide, J. Salvado and A. Santamaria, Fitting flavour symmetries: the case of two-zero neutrino mass textures, JHEP 07 (2018) 164 [arXiv:1806.06785] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    G.C. Branco, R.G. Felipe and F.R. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012) 515 [arXiv:1111.5332] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    W. Rodejohann and J.W.F. Valle, Symmetrical Parametrizations of the Lepton Mixing Matrix, Phys. Rev. D 84 (2011) 073011 [arXiv:1108.3484] [INSPIRE].ADSGoogle Scholar
  58. [58]
    J. Heeck, Seesaw parametrization for n right-handed neutrinos, Phys. Rev. D 86 (2012) 093023 [arXiv:1207.5521] [INSPIRE].ADSGoogle Scholar
  59. [59]
    A. Ibarra, E. Molinaro and S.T. Petcov, Low Energy Signatures of the TeV Scale See-Saw Mechanism, Phys. Rev. D 84 (2011) 013005 [arXiv:1103.6217] [INSPIRE].ADSGoogle Scholar
  60. [60]
    CUORE collaboration, First Results from CUORE: A Search for Lepton Number Violation via 0νββ Decay of 130 Te, Phys. Rev. Lett. 120 (2018) 132501 [arXiv:1710.07988] [INSPIRE].
  61. [61]
    KamLAND-Zen collaboration, Search for double-beta decay of 136 Xe to excited states of 136 Ba with the KamLAND-Zen experiment, Nucl. Phys. A 946 (2016) 171 [arXiv:1509.03724] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • D. M. Barreiros
    • 1
  • R. G. Felipe
    • 1
    • 2
  • F. R. Joaquim
    • 1
    Email author
  1. 1.CFTP, Departamento de Física, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.Instituto Superior de Engenharia de LisboaLisboaPortugal

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