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Covert symmetries in the neutrino mass matrix

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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.

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  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].

  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)Hgauge 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, JHEP07 (2011) 012 [arXiv:1103.2915] [INSPIRE].

  18. [18]

    J.R. Espinosa, C.S. Fong and E. Nardi, Yukawa hierarchies from spontaneous breaking of the SU (3)L× SU(3)Rflavour symmetry?, JHEP02 (2013) 137 [arXiv:1211.6428] [INSPIRE].

  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].

  22. [22]

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

  23. [23]

    Y. Reyimuaji and A. Romanino, Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?, JHEP03 (2018) 067 [arXiv:1801.10530] [INSPIRE].

  24. [24]

    F. Björkeroth, L. Di Luzio, F. Mescia and E. Nardi, U(1) flavour symmetries as Peccei-Quinn symmetries, JHEP02 (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, δCPand the mass ordering, JHEP01 (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].

  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, JCAP06 (2017) 029 [arXiv:1703.03425] [INSPIRE].

  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].

  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, JHEP07 (2018) 164 [arXiv:1806.06785] [INSPIRE].

  34. [34]

    M. Singh, G. Ahuja and M. Gupta, Revisiting the texture zero neutrino mass matrices, PTEP2016 (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, JHEP09 (2011) 083 [arXiv:1108.4534] [INSPIRE].

  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].

  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, JHEP03 (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].

  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].

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Correspondence to Enrico Nardi.

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ArXiv ePrint: 1910.00576

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Björkeroth, F., Di Luzio, L., Mescia, F. et al. Covert symmetries in the neutrino mass matrix. J. High Energ. Phys. 2020, 66 (2020).

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  • Global Symmetries
  • Neutrino Physics
  • Beyond Standard Model