Journal of High Energy Physics

, 2016:145 | Cite as

Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes

  • Silvia Pascoli
  • Ye-Ling Zhou
Open Access
Regular Article - Theoretical Physics


In leptonic flavour models with discrete flavour symmetries, couplings between flavons and leptons can result in special flavour structures after they gain vacuum expectation values. At the same time, they can also contribute to the other lepton-flavour-violating processes. We study the flavon-induced LFV 3-body charged lepton decays and radiative decays and we take as example the A 4 discrete symmetry. In A 4 models, a Z 3 residual symmetry roughly holds in the charged lepton sector for the realisation of tri-bimaximal mixing at leading order. The only processes allowed by this symmetry are τ μ + e e , e + μ μ , and the other 3-body and all radiative decays are suppressed by small Z 3-breaking effects. These processes also depend on the representation the flavon is in, whether pseudo-real (case i) or complex (case ii). We calculate the decay rates for all processes for each case and derive their strong connection with lepton flavour mixing. In case i, sum rules for the branching ratios of these processes are obtained, with typical examples Br(τ μ + e e ) ≈ Br(τ e + μ μ ) and Br(τ e γ) ≈ Br(τ μ γ). In case ii, we observe that the mixing between two Z 3-covariant flavons plays an important role. All processes are suppressed by charged lepton masses and current experimental con- straints allow the electroweak scale and the flavon masses to be around hundreds of GeV. Our discussion can be generalised in other flavour models with different flavour symmetries.


Discrete Symmetries Neutrino Physics Effective field theories Beyond Standard Model 


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]
    Super-Kamiokande collaboration, S. Fukuda et al., Solar B-8 and hep neutrino measurements from 1258 days of Super-Kamiokande data, Phys. Rev. Lett. 86 (2001) 5651 [hep-ex/0103032] [INSPIRE].
  2. [2]
    SNO collaboration, Q.R. Ahmad et al., Measurement of the rate of ν e + dp + p + e interactions produced by 8 B solar neutrinos at the Sudbury Neutrino Observatory, Phys. Rev. Lett. 87 (2001) 071301 [nucl-ex/0106015] [INSPIRE].
  3. [3]
    SNO collaboration, Q.R. Ahmad et al., Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89 (2002) 011301 [nucl-ex/0204008] [INSPIRE].
  4. [4]
    Super-Kamiokande collaboration, Y. Fukuda et al., Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].
  5. [5]
    K2K collaboration, M.H. Ahn et al., Indications of neutrino oscillation in a 250 KM long baseline experiment, Phys. Rev. Lett. 90 (2003) 041801 [hep-ex/0212007] [INSPIRE].
  6. [6]
    T2K collaboration, K. Abe et al., Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].
  7. [7]
    KamLAND collaboration, K. Eguchi et al., First results from KamLAND: Evidence for reactor anti-neutrino disappearance, Phys. Rev. Lett. 90 (2003) 021802 [hep-ex/0212021] [INSPIRE].
  8. [8]
    Daya Bay collaboration, F.P. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
  9. [9]
    RENO collaboration, J.K. Ahn et al., Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
  10. [10]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    B. Pontecorvo, Neutrino Experiments and the Problem of Conservation of Leptonic Charge, Sov. Phys. JETP 26 (1968) 984 [Zh. Eksp. Teor. Fiz. 53 (1967) 1717] [INSPIRE].
  12. [12]
    Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  13. [13]
    M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    J. Bergstrom, M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Bayesian global analysis of neutrino oscillation data, JHEP 09 (2015) 200 [arXiv:1507.04366] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    E. Ma and G. Rajasekaran, Softly broken A 4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].ADSGoogle Scholar
  16. [16]
    R.N. Mohapatra, M.K. Parida and G. Rajasekaran, High scale mixing unification and large neutrino mixing angles, Phys. Rev. D 69 (2004) 053007 [hep-ph/0301234] [INSPIRE].ADSGoogle Scholar
  17. [17]
    L.L. Everett and A.J. Stuart, Icosahedral (A(5)) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing, Phys. Rev. D 79 (2009) 085005 [arXiv:0812.1057] [INSPIRE].ADSGoogle Scholar
  18. [18]
    G.-J. Ding and Y.-L. Zhou, Lepton mixing parameters from Δ(48) family symmetry and generalised CP, JHEP 06 (2014) 023 [arXiv:1404.0592] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    G.-J. Ding and Y.-L. Zhou, Predicting lepton flavor mixing from Δ(48) and generalized CP symmetries, Chin. Phys. C 39 (2015) 021001 [arXiv:1312.5222] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    R. de Adelhart Toorop, F. Feruglio and C. Hagedorn, Discrete Flavour Symmetries in Light of T2K, Phys. Lett. B 703 (2011) 447 [arXiv:1107.3486] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    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
  22. [22]
    P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    Z.-z. Xing, Nearly tri bimaximal neutrino mixing and CP-violation, Phys. Lett. B 533 (2002) 85 [hep-ph/0204049] [INSPIRE].
  24. [24]
    P.F. Harrison and W.G. Scott, Symmetries and generalizations of tri - bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [INSPIRE].ADSGoogle Scholar
  25. [25]
    X.G. He and A. Zee, Some simple mixing and mass matrices for neutrinos, Phys. Lett. B 560 (2003) 87 [hep-ph/0301092] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A 4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    I.K. Cooper, S.F. King and C. Luhn, A 4 × SU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing, JHEP 06 (2012) 130 [arXiv:1203.1324] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    G. Altarelli, F. Feruglio and L. Merlo, Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries, Fortsch. Phys. 61 (2013) 507 [arXiv:1205.5133] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  30. [30]
    Y. BenTov, X.-G. He and A. Zee, An A 4 × Z 4 model for neutrino mixing, JHEP 12 (2012) 093 [arXiv:1208.1062] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    M.-C. Chen, J. Huang, J.-M. O’Bryan, A.M. Wijangco and F. Yu, Compatibility of θ 13 and the Type I Seesaw Model with A 4 Symmetry, JHEP 02 (2013) 021 [arXiv:1210.6982] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    N. Memenga, W. Rodejohann and H. Zhang, A 4 flavor symmetry model for Dirac neutrinos and sizable U e3, Phys. Rev. D 87 (2013) 053021 [arXiv:1301.2963] [INSPIRE].ADSGoogle Scholar
  33. [33]
    C.S. Lam, The Unique Horizontal Symmetry of Leptons, Phys. Rev. D 78 (2008) 073015 [arXiv:0809.1185] [INSPIRE].ADSGoogle Scholar
  34. [34]
    F. Bazzocchi and S. Morisi, S 4 as a natural flavor symmetry for lepton mixing, Phys. Rev. D 80 (2009) 096005 [arXiv:0811.0345] [INSPIRE].ADSGoogle Scholar
  35. [35]
    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].ADSCrossRefMATHGoogle Scholar
  36. [36]
    F. Bazzocchi, L. Merlo and S. Morisi, Phenomenological Consequences of See-Saw in S 4 Based Models, Phys. Rev. D 80 (2009) 053003 [arXiv:0902.2849] [INSPIRE].ADSGoogle Scholar
  37. [37]
    C. Hagedorn, S.F. King and C. Luhn, SUSY S 4× SU(5) revisited, Phys. Lett. B 717 (2012) 207 [arXiv:1205.3114] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    R. Krishnan, P.F. Harrison and W.G. Scott, Simplest Neutrino Mixing from S 4 Symmetry, JHEP 04 (2013) 087 [arXiv:1211.2000] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    F. Vissani, A Study of the scenario with nearly degenerate Majorana neutrinos, hep-ph/9708483 [INSPIRE].
  40. [40]
    V.D. Barger, S. Pakvasa, T.J. Weiler and K. Whisnant, Bimaximal mixing of three neutrinos, Phys. Lett. B 437 (1998) 107 [hep-ph/9806387] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    G. Altarelli, F. Feruglio and L. Merlo, Revisiting Bimaximal Neutrino Mixing in a Model with S 4 Discrete Symmetry, JHEP 05 (2009) 020 [arXiv:0903.1940] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    R. de Adelhart Toorop, F. Bazzocchi and L. Merlo, The Interplay Between GUT and Flavour Symmetries in a Pati-Salam ×S 4 Model, JHEP 08 (2010) 001 [arXiv:1003.4502] [INSPIRE].CrossRefMATHGoogle Scholar
  43. [43]
    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].ADSCrossRefMATHGoogle Scholar
  44. [44]
    D. Meloni, Bimaximal mixing and large θ 13 in a SUSY SU(5) model based on S 4, JHEP 10 (2011) 010 [arXiv:1107.0221] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  45. [45]
    Z.-h. Zhao, Understanding for flavor physics in the lepton sector, Phys. Rev. D 86 (2012) 096010 [arXiv:1207.2545] [INSPIRE].ADSGoogle Scholar
  46. [46]
    Y. Kajiyama, M. Raidal and A. Strumia, The Golden ratio prediction for the solar neutrino mixing, Phys. Rev. D 76 (2007) 117301 [arXiv:0705.4559] [INSPIRE].ADSGoogle Scholar
  47. [47]
    F. Feruglio and A. Paris, The Golden Ratio Prediction for the Solar Angle from a Natural Model with A 5 Flavour Symmetry, JHEP 03 (2011) 101 [arXiv:1101.0393] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  48. [48]
    G.-J. Ding, L.L. Everett and A.J. Stuart, Golden Ratio Neutrino Mixing and A 5 Flavor Symmetry, Nucl. Phys. B 857 (2012) 219 [arXiv:1110.1688] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  49. [49]
    J. Gehrlein, J.P. Oppermann, D. Schäfer and M. Spinrath, An SU(5) × A 5 golden ratio flavour model, Nucl. Phys. B 890 (2014) 539 [arXiv:1410.2057] [INSPIRE].ADSMATHGoogle Scholar
  50. [50]
    I. de Medeiros Varzielas and L. Lavoura, Golden ratio lepton mixing and nonzero reactor angle with A 5, J. Phys. G 41 (2014) 055005 [arXiv:1312.0215] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    S. Pascoli and Y.-L. Zhou, The role of flavon cross couplings in leptonic flavour mixing, JHEP 06 (2016) 073 [arXiv:1604.00925] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    G.-J. Ding, TFH Mixing Patterns, Large θ 13 and Δ(96) Flavor Symmetry, Nucl. Phys. B 862 (2012) 1 [arXiv:1201.3279] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  53. [53]
    S.F. King, C. Luhn and A.J. Stuart, A Grand Δ(96) × SU(5) Flavour Model, Nucl. Phys. B 867 (2013) 203 [arXiv:1207.5741] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  54. [54]
    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
  55. [55]
    S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino Mass and Mixing: from Theory to Experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    R. de Adelhart Toorop, F. Bazzocchi, L. Merlo and A. Paris, Constraining Flavour Symmetries At The EW Scale I: the A 4 Higgs Potential, JHEP 03 (2011) 035 [Erratum ibid. 01 (2013) 098] [arXiv:1012.1791] [INSPIRE].
  57. [57]
    R. de Adelhart Toorop, F. Bazzocchi, L. Merlo and A. Paris, Constraining Flavour Symmetries At The EW Scale II: The Fermion Processes, JHEP 03 (2011) 040 [arXiv:1012.2091] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  58. [58]
    A. Degee, I.P. Ivanov and V. Keus, Geometric minimization of highly symmetric potentials, JHEP 02 (2013) 125 [arXiv:1211.4989] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  59. [59]
    M. Holthausen, M. Lindner and M.A. Schmidt, Lepton flavor at the electroweak scale: A complete A 4 model, Phys. Rev. D 87 (2013) 033006 [arXiv:1211.5143] [INSPIRE].ADSGoogle Scholar
  60. [60]
    V. Keus, S.F. King and S. Moretti, Three-Higgs-doublet models: symmetries, potentials and Higgs boson masses, JHEP 01 (2014) 052 [arXiv:1310.8253] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    J. Heeck, M. Holthausen, W. Rodejohann and Y. Shimizu, Higgsμτ in Abelian and non-Abelian flavor symmetry models, Nucl. Phys. B 896 (2015) 281 [arXiv:1412.3671] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  62. [62]
    I. de Medeiros Varzielas, O. Fischer and V. Maurer, \( {\mathbb{A}}_4 \) symmetry at colliders and in the universe, JHEP 08 (2015) 080 [arXiv:1504.03955] [INSPIRE].CrossRefGoogle Scholar
  63. [63]
    L. Lavoura and H. Kuhbock, A 4 model for the quark mass matrices, Eur. Phys. J. C 55 (2008) 303 [arXiv:0711.0670] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    S. Morisi and E. Peinado, An A 4 model for lepton masses and mixings, Phys. Rev. D 80 (2009) 113011 [arXiv:0910.4389] [INSPIRE].ADSGoogle Scholar
  65. [65]
    A.E. Carcamo Hernandez, I. de Medeiros Varzielas, S.G. Kovalenko, H. Päs and I. Schmidt, Lepton masses and mixings in an A 4 multi-Higgs model with a radiative seesaw mechanism, Phys. Rev. D 88 (2013) 076014 [arXiv:1307.6499] [INSPIRE].ADSGoogle Scholar
  66. [66]
    R. González Felipe, I.P. Ivanov, C.C. Nishi, H. Serôdio and J.P. Silva, Constraining multi-Higgs flavour models, Eur. Phys. J. C 74 (2014) 2953 [arXiv:1401.5807] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    E. Ma, Quark and Lepton Flavor Triality, Phys. Rev. D 82 (2010) 037301 [arXiv:1006.3524] [INSPIRE].ADSGoogle Scholar
  68. [68]
    Y. Muramatsu, T. Nomura and Y. Shimizu, Mass limit for light flavon with residual Z 3 symmetry, JHEP 03 (2016) 192 [arXiv:1601.04788] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    T. Kobayashi, Y. Omura, F. Takayama and D. Yasuhara, Study of lepton flavor violation in flavor symmetric models for lepton sector, JHEP 10 (2015) 042 [arXiv:1505.07636] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    K. Hayasaka et al., Search for Lepton Flavor Violating Tau Decays into Three Leptons with 719 Million Produced Tau+Tau- Pairs, Phys. Lett. B 687 (2010) 139 [arXiv:1001.3221] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    BaBar collaboration, B. Aubert et al., Searches for Lepton Flavor Violation in the Decays τ ±e ± γ and τ ±μ ± γ, Phys. Rev. Lett. 104 (2010) 021802 [arXiv:0908.2381] [INSPIRE].
  72. [72]
    SINDRUM collaboration, U. Bellgardt et al., Search for the Decay μ +e + e + e , Nucl. Phys. B 299 (1988) 1 [INSPIRE].
  73. [73]
    MEG collaboration, A.M. Baldini et al., Search for the lepton flavour violating decay μ + → e+ γ with the full dataset of the MEG experiment, Eur. Phys. J. C 76 (2016) 434 [arXiv:1605.05081] [INSPIRE].
  74. [74]
    MEG II collaboration, S. Ogawa, Upgrade of liquid xenon calorimeter in MEG experiment with VUV sensitive MPPCs, PoS(FPCP2015)063.
  75. [75]
    F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo, Lepton Flavour Violation in Models with A 4 Flavour Symmetry, Nucl. Phys. B 809 (2009) 218 [arXiv:0807.3160] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  76. [76]
    B. He, T.P. Cheng and L.-F. Li, A Less suppressed μeγ loop amplitude and extra dimension theories, Phys. Lett. B 553 (2003) 277 [hep-ph/0209175] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    L. Lavoura, General formulae for f(1) → f(2)γ, Eur. Phys. J. C 29 (2003) 191 [hep-ph/0302221] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    G. Blankenburg, J. Ellis and G. Isidori, Flavour-Changing Decays of a 125 GeV Higgs-like Particle, Phys. Lett. B 712 (2012) 386 [arXiv:1202.5704] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Institute for Particle Physics Phenomenology, Department of PhysicsDurham UniversityDurhamUnited Kingdom

Personalised recommendations