Stable lepton mass matrices

  • Valerie Domcke
  • Andrea Romanino
Open Access
Regular Article - Theoretical Physics


We study natural lepton mass matrices, obtained assuming the stability of physical flavour observables with respect to the variations of individual matrix elements. We identify all four possible stable neutrino textures from algebraic conditions on their entries. Two of them turn out to be uniquely associated to specific neutrino mass patterns. We then concentrate on the semi-degenerate pattern, corresponding to an overall neutrino mass scale within the reach of future experiments. In this context we show that i) the neutrino and charged lepton mixings and mass matrices are largely constrained by the requirement of stability, ii) naturalness considerations give a mild preference for the Majorana phase most relevant for neutrinoless double-β decay, απ/2, and iii) SU(5) unification allows to extend the implications of stability to the down quark sector. The above considerations would benefit from an experimental determination of the PMNS ratio |U 32 /U 31|, i.e. of the Dirac phase δ.


Neutrino Physics Quark Masses and SM Parameters 


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.H. Frampton and T.W. Kephart, Simple non-Abelian finite flavor groups and fermion masses, Int. J. Mod. Phys. A 10 (1995) 4689 [hep-ph/9409330] [INSPIRE].
  2. [2]
    H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    I. de Medeiros Varzielas and G.G. Ross, SU(3) family symmetry and neutrino bi-tri-maximal mixing, Nucl. Phys. B 733 (2006) 31 [hep-ph/0507176] [INSPIRE].
  5. [5]
    S.F. King, Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification, JHEP 08 (2005) 105 [hep-ph/0506297] [INSPIRE].
  6. [6]
    J. Berger and Y. Grossman, Model of leptons from SO(3) → A 4, JHEP 02 (2010) 071 [arXiv:0910.4392] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  7. [7]
    A. Adulpravitchai, A. Blum and M. Lindner, Non-Abelian discrete groups from the breaking of continuous flavor symmetries, JHEP 09 (2009) 018 [arXiv:0907.2332] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    L. Wolfenstein, Different varieties of massive Dirac neutrinos, Nucl. Phys. B 186 (1981) 147 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. Fukuyama and H. Nishiura, Mass matrix of Majorana neutrinos, hep-ph/9702253 [INSPIRE].
  10. [10]
    D.B. Kaplan, Flavor at SSC energies: a new mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Redi, Leptons in composite MFV, JHEP 09 (2013) 060 [arXiv:1306.1525] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali and J. March-Russell, Neutrino masses from large extra dimensions, Phys. Rev. D 65 (2002) 024032 [hep-ph/9811448] [INSPIRE].
  13. [13]
    N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [INSPIRE].
  14. [14]
    G.R. Dvali and A. Yu. Smirnov, Probing large extra dimensions with neutrinos, Nucl. Phys. B 563 (1999) 63 [hep-ph/9904211] [INSPIRE].
  15. [15]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [INSPIRE].
  16. [16]
    L.J. Hall, H. Murayama and N. Weiner, Neutrino mass anarchy, Phys. Rev. Lett. 84 (2000) 2572 [hep-ph/9911341] [INSPIRE].
  17. [17]
    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
  18. [18]
    D. Marzocca and A. Romanino, Stable fermion mass matrices and the charged lepton contribution to neutrino mixing, JHEP 11 (2014) 159 [arXiv:1409.3760] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    R.D. Peccei and K. Wang, Natural mass matrices, Phys. Rev. D 53 (1996) 2712 [hep-ph/9509242] [INSPIRE].
  20. [20]
    H. Fritzsch and Z.-Z. Xing, Flavor symmetries and the description of flavor mixing, Phys. Lett. B 413 (1997) 396 [hep-ph/9707215] [INSPIRE].
  21. [21]
    G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos, Degenerate and quasidegenerate Majorana neutrinos, Phys. Rev. Lett. 82 (1999) 683 [hep-ph/9810328] [INSPIRE].
  22. [22]
    G. Altarelli and G. Blankenburg, Different SO(10) paths to fermion masses and mixings, JHEP 03 (2011) 133 [arXiv:1012.2697] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  23. [23]
    M. Gupta, P. Fakay, S. Sharma and G. Ahuja, Fermion mass matrices, textures and beyond, Mod. Phys. Lett. A 30 (2015) 1530024 [arXiv:1604.03335] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  24. [24]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  25. [25]
    R. Barbieri and G.F. Giudice, Upper bounds on supersymmetric particle masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S.T. Petcov, On pseudo-Dirac neutrinos, neutrino oscillations and neutrinoless double beta decay, Phys. Lett. B 110 (1982) 245 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C.N. Leung and S.T. Petcov, A comment on the coexistence of Dirac and Majorana massive neutrinos, Phys. Lett. B 125 (1983) 461 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    R. Barbieri, L.J. Hall, D. Tucker-Smith, A. Strumia and N. Weiner, Oscillations of solar and atmospheric neutrinos, JHEP 12 (1998) 017 [hep-ph/9807235] [INSPIRE].
  29. [29]
    G. Altarelli, F. Feruglio and I. Masina, Large neutrino mixing from small quark and lepton mixings, Phys. Lett. B 472 (2000) 382 [hep-ph/9907532] [INSPIRE].
  30. [30]
    G. Altarelli and F. Feruglio, Neutrino masses and mixings: a theoretical perspective, in Neutrino telescopes. Proceedings, 8th International Workshop, vols. 1 and 2, Venice Italy February 23-26 1999 [hep-ph/9905536] [INSPIRE].
  31. [31]
    N. Palanque-Delabrouille et al., Constraint on neutrino masses from SDSS-III/BOSS Lyα forest and other cosmological probes, JCAP 02 (2015) 045 [arXiv:1410.7244] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Topical Conveners collaboration, K.N. Abazajian et al., Neutrino physics from the cosmic microwave background and large scale structure, Astropart. Phys. 63 (2015) 66 [arXiv:1309.5383] [INSPIRE].
  33. [33]
    T. Basse, O.E. Bjaelde, J. Hamann, S. Hannestad and Y.Y.Y. Wong, Dark energy properties from large future galaxy surveys, JCAP 05 (2014) 021 [arXiv:1304.2321] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S.M. Bilenky, S. Pascoli and S.T. Petcov, Majorana neutrinos, neutrino mass spectrum, CP-violation and neutrinoless double beta decay. 1. The three neutrino mixing case, Phys. Rev. D 64 (2001) 053010 [hep-ph/0102265] [INSPIRE].
  35. [35]
    D. Marzocca, S.T. Petcov, A. Romanino and M. Spinrath, Sizeable θ 13 from the charged lepton sector in SU(5), (tri-)bimaximal neutrino mixing and Dirac CP-violation, JHEP 11 (2011) 009 [arXiv:1108.0614] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  36. [36]
    H. Fritzsch and Z.-Z. Xing, On the parametrization of flavor mixing in the standard model, Phys. Rev. D 57 (1998) 594 [hep-ph/9708366] [INSPIRE].
  37. [37]
    F. Feruglio, A. Strumia and F. Vissani, Neutrino oscillations and signals in β and 0ν2β experiments, Nucl. Phys. B 637 (2002) 345 [Addendum ibid. B 659 (2003) 359] [hep-ph/0201291] [INSPIRE].
  38. [38]
    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].MathSciNetCrossRefMATHGoogle Scholar
  39. [39]
    D. Marzocca, S.T. Petcov, A. Romanino and M.C. Sevilla, Nonzero |U e3| from charged lepton corrections and the atmospheric neutrino mixing angle, JHEP 05 (2013) 073 [arXiv:1302.0423] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    KamLAND-Zen collaboration, A. Gando et al., Limit on neutrinoless ββ decay of 136 Xe from the first phase of KamLAND-Zen and comparison with the positive claim in 76 Ge, Phys. Rev. Lett. 110 (2013) 062502 [arXiv:1211.3863] [INSPIRE].
  41. [41]
    S. Dell’Oro, S. Marcocci, M. Viel and F. Vissani, Neutrinoless double beta decay: 2015 review, Adv. High Energy Phys. (2016) 2162659 [arXiv:1601.07512] [INSPIRE].
  42. [42]
    KATRIN collaboration, A. Osipowicz et al., KATRIN: a next generation tritium beta decay experiment with sub-eV sensitivity for the electron neutrino mass. Letter of intent, hep-ex/0109033 [INSPIRE].
  43. [43]
    C. Kraus et al., Final results from phase II of the Mainz neutrino mass search in tritium beta decay, Eur. Phys. J. C 40 (2005) 447 [hep-ex/0412056] [INSPIRE].
  44. [44]
    Troitsk collaboration, V.N. Aseev et al., An upper limit on electron antineutrino mass from Troitsk experiment, Phys. Rev. D 84 (2011) 112003 [arXiv:1108.5034] [INSPIRE].
  45. [45]
    A. Romanino and R. Yakefu, in preparation.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.AstroParticule et Cosmologie (APC)/Paris Centre for Cosmological PhysicsUniversité Paris DiderotParisFrance
  2. 2.SISSA/ISAS and INFNTriesteItaly
  3. 3.ICTPTriesteItaly

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