Littlest mu-tau seesaw

  • Stephen F. King
  • Ye-Ling ZhouEmail author
Open Access
Regular Article - Theoretical Physics


We propose a μτ reflection symmetric Littlest Seesaw (μτ -LSS) model. In this model the two mass parameters of the LSS model are fixed to be in a special ratio by symmetry, so that the resulting neutrino mass matrix in the flavour basis (after the seesaw mechanism has been applied) satisfies μτ reflection symmetry and has only one free adjustable parameter, namely an overall free mass scale. However the physical low energy predictions of the neutrino masses and lepton mixing angles and CP phases are subject to renormalisation group (RG) corrections, which introduces further parameters. Although the high energy model is rather complicated, involving (S4 × U(1))2 and supersymmetry, with many flavons and driving fields, the low energy neutrino mass matrix has ultimate simplicity.


Discrete Symmetries Neutrino Physics Renormalization Group Solar and Atmospheric Neutrinos 


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]
    Z.-z. Xing and S. Zhou, Neutrinos in particle physics, astronomy and cosmology, Springer-Verlag, Berlin Heidelberg (2011) [INSPIRE].
  2. [2]
    S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
  3. [3]
    S.F. King, Models of Neutrino Mass, Mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
  4. [4]
    F. Capozzi, E. Lisi, A. Marrone and A. Palazzo, Current unknowns in the three neutrino framework, Prog. Part. Nucl. Phys. 102 (2018) 48 [arXiv:1804.09678] [INSPIRE].CrossRefGoogle Scholar
  5. [5]
    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].
  6. [6]
    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].CrossRefGoogle Scholar
  7. [7]
    Z.-z. Xing and Z.-h. Zhao, A review of μ-τ flavor symmetry in neutrino physics, Rept. Prog. Phys. 79 (2016) 076201 [arXiv:1512.04207] [INSPIRE].
  8. [8]
    P. Minkowski, μeγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. 67B (1977) 421 [INSPIRE].
  9. [9]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [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].
  11. [11]
    S.L. Glashow, The Future of Elementary Particle Physics, NATO Sci. Ser. B 61 (1980) 687 [INSPIRE].
  12. [12]
    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].CrossRefzbMATHGoogle Scholar
  13. [13]
    S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].
  14. [14]
    S.F. King, Constructing the large mixing angle MNS matrix in seesaw models with right-handed neutrino dominance, JHEP 09 (2002) 011 [hep-ph/0204360] [INSPIRE].
  15. [15]
    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].
  16. [16]
    M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
  17. [17]
    W.-l. Guo and Z.-z. Xing, Calculable CP-violating phases in the minimal seesaw model of leptogenesis and neutrino mixing, Phys. Lett. B 583 (2004) 163 [hep-ph/0310326] [INSPIRE].
  18. [18]
    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].
  19. [19]
    J.-w. Mei and Z.-z. Xing, Radiative corrections to neutrino mixing and CP-violation in the minimal seesaw model with leptogenesis, Phys. Rev. D 69 (2004) 073003 [hep-ph/0312167] [INSPIRE].
  20. [20]
    W.-l. Guo, Z.-z. Xing and S. Zhou, Neutrino Masses, Lepton Flavor Mixing and Leptogenesis in the Minimal Seesaw Model, Int. J. Mod. Phys. E 16 (2007) 1 [hep-ph/0612033] [INSPIRE].
  21. [21]
    S. Antusch, P. Di Bari, D.A. Jones and S.F. King, Leptogenesis in the Two Right-Handed Neutrino Model Revisited, Phys. Rev. D 86 (2012) 023516 [arXiv:1107.6002] [INSPIRE].
  22. [22]
    K. Harigaya, M. Ibe and T.T. Yanagida, Seesaw Mechanism with Occams Razor, Phys. Rev. D 86 (2012) 013002 [arXiv:1205.2198] [INSPIRE].
  23. [23]
    J. Zhang and S. Zhou, A Further Study of the Frampton-Glashow-Yanagida Model for Neutrino Masses, Flavor Mixing and Baryon Number Asymmetry, JHEP 09 (2015) 065 [arXiv:1505.04858] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    S.F. King, Minimal predictive see-saw model with normal neutrino mass hierarchy, JHEP 07 (2013) 137 [arXiv:1304.6264] [INSPIRE].CrossRefGoogle Scholar
  25. [25]
    F. Björkeroth and S.F. King, Testing constrained sequential dominance models of neutrinos, J. Phys. G 42 (2015) 125002 [arXiv:1412.6996] [INSPIRE].
  26. [26]
    S.F. King, Littlest Seesaw, JHEP 02 (2016) 085 [arXiv:1512.07531] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    F. Björkeroth, F.J. de Anda, I. de Medeiros Varzielas and S.F. King, Towards a complete A 4 × SU(5) SUSY GUT, JHEP 06 (2015) 141 [arXiv:1503.03306] [INSPIRE].
  28. [28]
    F. Björkeroth, F.J. de Anda, I. de Medeiros Varzielas and S.F. King, Leptogenesis in minimal predictive seesaw models, JHEP 10 (2015) 104 [arXiv:1505.05504] [INSPIRE].CrossRefGoogle Scholar
  29. [29]
    S.F. King and C. Luhn, Littlest Seesaw model from S 4 × U(1), JHEP 09 (2016) 023 [arXiv:1607.05276] [INSPIRE].
  30. [30]
    P. Ballett, S.F. King, S. Pascoli, N.W. Prouse and T. Wang, Precision neutrino experiments vs the Littlest Seesaw, JHEP 03 (2017) 110 [arXiv:1612.01999] [INSPIRE].CrossRefGoogle Scholar
  31. [31]
    S.F. King and C.C. Nishi, Mu-tau symmetry and the Littlest Seesaw, Phys. Lett. B 785 (2018) 391 [arXiv:1807.00023] [INSPIRE].
  32. [32]
    Z.-z. Xing and S. Zhou, Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis, Phys. Lett. B 653 (2007) 278 [hep-ph/0607302] [INSPIRE].
  33. [33]
    C.H. Albright and W. Rodejohann, Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing, Eur. Phys. J. C 62 (2009) 599 [arXiv:0812.0436] [INSPIRE].
  34. [34]
    C.H. Albright, A. Dueck and W. Rodejohann, Possible Alternatives to Tri-bimaximal Mixing, Eur. Phys. J. C 70 (2010) 1099 [arXiv:1004.2798] [INSPIRE].
  35. [35]
    X.-G. He and A. Zee, Minimal Modification to Tri-bimaximal Mixing, Phys. Rev. D 84 (2011) 053004 [arXiv:1106.4359] [INSPIRE].
  36. [36]
    W. Rodejohann and H. Zhang, Simple two Parameter Description of Lepton Mixing, Phys. Rev. D 86 (2012) 093008 [arXiv:1207.1225] [INSPIRE].
  37. [37]
    I. de Medeiros Varzielas and L. Lavoura, Flavour models for T M 1 lepton mixing, J. Phys. G 40 (2013) 085002 [arXiv:1212.3247] [INSPIRE].
  38. [38]
    W. Grimus, Discrete symmetries, roots of unity and lepton mixing, J. Phys. G 40 (2013) 075008 [arXiv:1301.0495] [INSPIRE].
  39. [39]
    P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [INSPIRE].
  40. [40]
    K.S. Babu, C.N. Leung and J.T. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223] [INSPIRE].
  41. [41]
    J.R. Ellis and S. Lola, Can neutrinos be degenerate in mass?, Phys. Lett. B 458 (1999) 310 [hep-ph/9904279] [INSPIRE].
  42. [42]
    H. Fritzsch and Z.-z. Xing, Mass and flavor mixing schemes of quarks and leptons, Prog. Part. Nucl. Phys. 45 (2000) 1 [hep-ph/9912358] [INSPIRE].
  43. [43]
    Z.-z. Xing, Democratic neutrino mixing and radiative corrections, Phys. Rev. D 63 (2001) 057301 [hep-ph/0011217] [INSPIRE].
  44. [44]
    Y.-L. Zhou, μ-τ reflection symmetry and radiative corrections, arXiv:1409.8600 [INSPIRE].
  45. [45]
    C. Hagedorn, S.F. King and C. Luhn, A SUSY GUT of Flavour with S 4 × SU(5) to NLO, JHEP 06 (2010) 048 [arXiv:1003.4249] [INSPIRE].
  46. [46]
    C. Hagedorn, S.F. King and C. Luhn, SUSY S 4 × SU(5) revisited, Phys. Lett. B 717 (2012) 207 [arXiv:1205.3114] [INSPIRE].
  47. [47]
    G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S 4 models of leptons, JHEP 05 (2013) 084 [arXiv:1303.6180] [INSPIRE].
  48. [48]
    F. Feruglio, C. Hagedorn and R. Ziegler, A realistic pattern of lepton mixing and masses from S 4 and CP, Eur. Phys. J. C 74 (2014) 2753 [arXiv:1303.7178] [INSPIRE].
  49. [49]
    F. Bazzocchi, L. Merlo and S. Morisi, Fermion Masses and Mixings in a S 4 -based Model, Nucl. Phys. B 816 (2009) 204 [arXiv:0901.2086] [INSPIRE].
  50. [50]
    G.-J. Ding and Y.-L. Zhou, Dirac Neutrinos with S 4 Flavor Symmetry in Warped Extra Dimensions, Nucl. Phys. B 876 (2013) 418 [arXiv:1304.2645] [INSPIRE].
  51. [51]
    I. de Medeiros Varzielas, T. Neder and Y.-L. Zhou, Effective alignments as building blocks of flavor models, Phys. Rev. D 97 (2018) 115033 [arXiv:1711.05716] [INSPIRE].
  52. [52]
    T. Morozumi, H. Okane, H. Sakamoto, Y. Shimizu, K. Takagi and H. Umeeda, Phenomenological Aspects of Possible Vacua of a Neutrino Flavor Model, Chin. Phys. C 42 (2018) 023102 [arXiv:1707.04028] [INSPIRE].

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Physics and AstronomyUniversity of SouthamptonSouthamptonUnited Kingdom

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