Covert symmetries in the neutrino mass matrix

Abstract

The flavour neutrino puzzle is often addressed by considering neutrino mass matrices m with a certain number of vanishing entries (mij = 0 for some values of the indices), since a reduction in the number of free parameters increases the predictive power. Symmetries that can enforce textures zero can also enforce a more general type of conditions f(mij) = 0 with f some function of the matrix elements mij. In this case m can have all entries non-vanishing with no reduction in its predictive power. We classify all generation-dependent U(1) symmetries which, in the presence of two leptonic Higgs doublets, can reduce the number of independent high-energy parameters of type-I seesaw to the minimum number compatible with non-vanishing neutrino mixings and CP violation. These symmetries are broken above the scale where the effective operator is generated and can thus remain covert, in the sense that no explicit evidence of the symmetry can be read off the neutrino mass matrix, and different symmetries can give rise to the same low-energy structure. We find that only two cases are viable: one yields a structure with two zero-textures already considered in the literature, the other has no zero-textures and has never been considered before. It predicts normal ordering, a lightest neutrino mass 10 meV, a Dirac phase δ\( \frac{3\pi }{2} \) and definite values for the Majorana phases.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    C.D. Froggatt and H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    M. Leurer, Y. Nir and N. Seiberg, Mass matrix models, Nucl. Phys. B 398 (1993) 319 [hep-ph/9212278] [INSPIRE].

  3. [3]

    M. Leurer, Y. Nir and N. Seiberg, Mass matrix models: the sequel, Nucl. Phys. B 420 (1994) 468 [hep-ph/9310320] [INSPIRE].

  4. [4]

    M. Dine, R.G. Leigh and A. Kagan, Flavor symmetries and the problem of squark degeneracy, Phys. Rev. D 48 (1993) 4269 [hep-ph/9304299] [INSPIRE].

  5. [5]

    L.E. Ibáñez and G.G. Ross, Fermion masses and mixing angles from gauge symmetries, Phys. Lett. B 332 (1994) 100 [hep-ph/9403338] [INSPIRE].

  6. [6]

    T. Banks, Y. Grossman, E. Nardi and Y. Nir, Supersymmetry without R-parity and without lepton number, Phys. Rev. D 52 (1995) 5319 [hep-ph/9505248] [INSPIRE].

  7. [7]

    E. Dudas, C. Grojean, S. Pokorski and C.A. Savoy, Abelian flavor symmetries in supersymmetric models, Nucl. Phys. B 481 (1996) 85 [hep-ph/9606383] [INSPIRE].

  8. [8]

    N. Irges, S. Lavignac and P. Ramond, Predictions from an anomalous U(1) model of Yukawa hierarchies, Phys. Rev. D 58 (1998) 035003 [hep-ph/9802334] [INSPIRE].

  9. [9]

    J.M. Mira, E. Nardi and D.A. Restrepo, Nonanomalous horizontal U(1)H gauge model of flavor, Phys. Rev. D 62 (2000) 016002 [hep-ph/9911212] [INSPIRE].

  10. [10]

    J.K. Elwood, N. Irges and P. Ramond, Family symmetry and neutrino mixing, Phys. Rev. Lett. 81 (1998) 5064 [hep-ph/9807228] [INSPIRE].

  11. [11]

    A. Pomarol and D. Tommasini, Horizontal symmetries for the supersymmetric flavor problem, Nucl. Phys. B 466 (1996) 3 [hep-ph/9507462] [INSPIRE].

  12. [12]

    R. Barbieri, G.R. Dvali and L.J. Hall, Predictions from a U(2) flavor symmetry in supersymmetric theories, Phys. Lett. B 377 (1996) 76 [hep-ph/9512388] [INSPIRE].

  13. [13]

    R. Barbieri, L.J. Hall, S. Raby and A. Romanino, Unified theories with U(2) flavor symmetry, Nucl. Phys. B 493 (1997) 3 [hep-ph/9610449] [INSPIRE].

  14. [14]

    R. Barbieri, L.J. Hall and A. Romanino, Consequences of a U(2) flavor symmetry, Phys. Lett. B 401 (1997) 47 [hep-ph/9702315] [INSPIRE].

  15. [15]

    C.D. Carone and L.J. Hall, Neutrino physics from a U(2) flavor symmetry, Phys. Rev. D 56 (1997) 4198 [hep-ph/9702430] [INSPIRE].

  16. [16]

    E. Nardi, Naturally large Yukawa hierarchies, Phys. Rev. D 84 (2011) 036008 [arXiv:1105.1770] [INSPIRE].

  17. [17]

    R. Alonso, M.B. Gavela, L. Merlo and S. Rigolin, On the scalar potential of minimal flavour violation, JHEP 07 (2011) 012 [arXiv:1103.2915] [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    J.R. Espinosa, C.S. Fong and E. Nardi, Yukawa hierarchies from spontaneous breaking of the SU (3)L × SU(3)R flavour symmetry?, JHEP 02 (2013) 137 [arXiv:1211.6428] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  19. [19]

    C.S. Fong and E. Nardi, Quark masses, mixings and CP-violation from spontaneous breaking of flavor SU(3)3 , Phys. Rev. D 89 (2014) 036008 [arXiv:1307.4412] [INSPIRE].

  20. [20]

    L.F. Duque, D.A. Gutierrez, E. Nardi and J. Norena, Fermion mass hierarchy and non-hierarchical mass ratios in SU(5) × U(1)F, Phys. Rev. D 78 (2008) 035003 [arXiv:0804.2865] [INSPIRE].

  21. [21]

    F. Wang and Y.-X. Li, Generalized Froggatt-Nielsen mechanism, Eur. Phys. J. C 71 (2011) 1803 [arXiv:1103.6017] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    E. Nardi, D. Restrepo and M. Velasquez, Neutrino masses in SU(5) × U(1)F with adjoint flavons, Eur. Phys. J. C 72 (2012) 1941 [arXiv:1108.0722] [INSPIRE].

    ADS  Article  Google Scholar 

  23. [23]

    Y. Reyimuaji and A. Romanino, Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?, JHEP 03 (2018) 067 [arXiv:1801.10530] [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    F. Björkeroth, L. Di Luzio, F. Mescia and E. Nardi, U(1) flavour symmetries as Peccei-Quinn symmetries, JHEP 02 (2019) 133 [arXiv:1811.09637] [INSPIRE].

  25. [25]

    E. Ma, Pathways to naturally small neutrino masses, Phys. Rev. Lett. 81 (1998) 1171 [hep-ph/9805219] [INSPIRE].

  26. [26]

    I. Esteban et al., Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of θ23, δCP and the mass ordering, JHEP 01 (2019) 106 [arXiv:1811.05487] [INSPIRE].

  27. [27]

    P.F. de Salas et al., 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].

    ADS  Article  Google Scholar 

  28. [28]

    Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].

  29. [29]

    F. Capozzi et al., Global constraints on absolute neutrino masses and their ordering, Phys. Rev. D 95 (2017) 096014 [arXiv:1703.04471] [INSPIRE].

  30. [30]

    F. Simpson, R. Jimenez, C. Pena-Garay and L. Verde, Strong Bayesian evidence for the normal neutrino hierarchy, JCAP 06 (2017) 029 [arXiv:1703.03425] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    P. F. De Salas et al., Neutrino mass ordering from oscillations and beyond: 2018 status and future prospects, Front. Astron. Space Sci. 5 (2018) 36 [arXiv:1806.11051].

    ADS  Article  Google Scholar 

  32. [32]

    M. Singh, Testing texture two zero neutrino mass matrices under current experimental scenario, arXiv:1909.01552 [INSPIRE].

  33. [33]

    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].

    ADS  Article  Google Scholar 

  34. [34]

    M. Singh, G. Ahuja and M. Gupta, Revisiting the texture zero neutrino mass matrices, PTEP 2016 (2016) 123B08 [arXiv:1603.08083] [INSPIRE].

  35. [35]

    S. Zhou, Update on two-zero textures of the Majorana neutrino mass matrix in light of recent T2K, Super-Kamiokande and NOνA results, Chin. Phys. C 40 (2016) 033102 [arXiv:1509.05300] [INSPIRE].

  36. [36]

    T. Kitabayashi and M. Yasuè, Formulas for flavor neutrino masses and their application to texture two zeros, Phys. Rev. D 93 (2016) 053012 [arXiv:1512.00913] [INSPIRE].

  37. [37]

    H. Fritzsch, Z.-z. Xing and S. Zhou, Two-zero textures of the Majorana neutrino mass matrix and current experimental tests, JHEP 09 (2011) 083 [arXiv:1108.4534] [INSPIRE].

    ADS  Article  Google Scholar 

  38. [38]

    D. Meloni and G. Blankenburg, Fine-tuning and naturalness issues in the two-zero neutrino mass textures, Nucl. Phys. B 867 (2013) 749 [arXiv:1204.2706] [INSPIRE].

    ADS  MATH  Google Scholar 

  39. [39]

    S. Dev, S. Kumar, S. Verma and S. Gupta, Phenomenology of two-texture zero neutrino mass matrices, Phys. Rev. D 76 (2007) 013002 [hep-ph/0612102] [INSPIRE].

  40. [40]

    W.-l. Guo and Z.-z. Xing, Implications of the KamLAND measurement on the lepton flavor mixing matrix and the neutrino mass matrix, Phys. Rev. D 67 (2003) 053002 [hep-ph/0212142] [INSPIRE].

  41. [41]

    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].

  42. [42]

    R. Barbieri, T. Hambye and A. Romanino, Natural relations among physical observables in the neutrino mass matrix, JHEP 03 (2003) 017 [hep-ph/0302118] [INSPIRE].

  43. [43]

    J.F. Nieves and P.B. Pal, Minimal rephasing invariant CP violating parameters with Dirac and Majorana fermions, Phys. Rev. D 36 (1987) 315 [INSPIRE].

    ADS  Google Scholar 

  44. [44]

    U. Sarkar and S.K. Singh, CP violation in neutrino mass matrix, Nucl. Phys. B 771 (2007) 28 [hep-ph/0608030] [INSPIRE].

  45. [45]

    Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].

Download references

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

Author information

Affiliations

Authors

Corresponding author

Correspondence to Enrico Nardi.

Additional information

ArXiv ePrint: 1910.00576

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Björkeroth, F., Di Luzio, L., Mescia, F. et al. Covert symmetries in the neutrino mass matrix. J. High Energ. Phys. 2020, 66 (2020). https://doi.org/10.1007/JHEP02(2020)066

Download citation

Keywords

  • Global Symmetries
  • Neutrino Physics
  • Beyond Standard Model