Two-Higgs leptonic minimal flavour violation

  • F. J. Botella
  • G. C. Branco
  • M. Nebot
  • M. N. RebeloEmail author


We construct extensions of the Standard Model with two Higgs doublets, where there are flavour changing neutral currents both in the quark and leptonic sectors, with their strength fixed by the fermion mixing matrices V CKM and V PMNS. These models are an extension to the leptonic sector of the class of models previously considered by Branco, Grimus and Lavoura, for the quark sector. We consider both the cases of Dirac and Majorana neutrinos and identify the minimal discrete symmetry required in order to implement the models in a natural way.


Higgs Physics Beyond Standard Model Neutrino Physics 


  1. [1]
    G.C. Branco et al., Theory and phenomenology of two-Higgs-doublet models, arXiv:1106.0034 [SPIRES].
  2. [2]
    A. Djouadi, The Higgs sector of supersymmetric theories and the implications for high-energy colliders, Eur. Phys. J. C 59 (2009) 389 [arXiv:0810.2439] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    S. Weinberg, Gauge theory of CP-violation, Phys. Rev. Lett. 37 (1976) 657 [SPIRES].ADSCrossRefGoogle Scholar
  4. [4]
    S.L. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys. Rev. D 15 (1977) 1958 [SPIRES].ADSGoogle Scholar
  5. [5]
    E.A. Paschos, Diagonal neutral currents, Phys. Rev. D 15 (1977) 1966 [SPIRES].ADSGoogle Scholar
  6. [6]
    A. Antaramian, L.J. Hall and A. Rasin, Flavor changing interactions mediated by scalars at the weak scale, Phys. Rev. Lett. 69 (1992) 1871 [hep-ph/9206205] [SPIRES].ADSCrossRefGoogle Scholar
  7. [7]
    L.J. Hall and S. Weinberg, Flavor changing scalar interactions, Phys. Rev. D 48 (1993) 979 [hep-ph/9303241] [SPIRES].ADSGoogle Scholar
  8. [8]
    A.S. Joshipura and S.D. Rindani, Naturally suppressed flavor violations in two Higgs doublet models, Phys. Lett. B 260 (1991) 149 [SPIRES].ADSGoogle Scholar
  9. [9]
    N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [SPIRES].ADSCrossRefGoogle Scholar
  11. [11]
    A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Universal unitarity triangle and physics beyond the standard model, Phys. Lett. B 500 (2001) 161 [hep-ph/0007085] [SPIRES].ADSGoogle Scholar
  12. [12]
    G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavour violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [SPIRES].ADSCrossRefGoogle Scholar
  13. [13]
    V. Cirigliano, B. Grinstein, G. Isidori and M.B. Wise, Minimal flavor violation in the lepton sector, Nucl. Phys. B 728 (2005) 121 [hep-ph/0507001] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    S. Davidson and F. Palorini, Various definitions of minimal flavour violation for leptons, Phys. Lett. B 642 (2006) 72 [hep-ph/0607329] [SPIRES].ADSGoogle Scholar
  15. [15]
    G.C. Branco, A.J. Buras, S. Jager, S. Uhlig and A. Weiler, Another look at minimal lepton flavour violation, l i → l j γ, leptogenesis and the ratio M ν /ΛLFV, JHEP 09 (2007) 004 [hep-ph/0609067] [SPIRES].ADSCrossRefGoogle Scholar
  16. [16]
    M.B. Gavela, T. Hambye, D. Hernandez and P. Hernández, Minimal flavour seesaw models, JHEP 09 (2009) 038 [arXiv:0906.1461] [SPIRES].ADSCrossRefGoogle Scholar
  17. [17]
    G.C. Branco, W. Grimus and L. Lavoura, Relating the scalar flavour changing neutral couplings to the CKM matrix, Phys. Lett. B 380 (1996) 119 [hep-ph/9601383] [SPIRES].ADSGoogle Scholar
  18. [18]
    P. Tuzon and A. Pich, The aligned two-Higgs doublet model, Acta Phys. Polon. Suppl. 3 (2010) 215 [arXiv:1001.0293] [SPIRES].Google Scholar
  19. [19]
    M. Jung, A. Pich and P. Tuzon, Charged-Higgs phenomenology in the aligned two-Higgs-doublet model, JHEP 11 (2010) 003 [arXiv:1006.0470] [SPIRES].ADSCrossRefGoogle Scholar
  20. [20]
    M. Jung, A. Pich and P. Tuzon, The \( \bar{B} \to {X_s}\gamma \) rate and CP asymmetry within the aligned two-Higgs-doublet model, Phys. Rev. D 83 (2011) 074011 [arXiv:1011.5154] [SPIRES].ADSGoogle Scholar
  21. [21]
    F.J. Botella, G.C. Branco and M.N. Rebelo, Minimal flavour violation and multi-Higgs models, Phys. Lett. B 687 (2010) 194 [arXiv:0911.1753] [SPIRES].ADSGoogle Scholar
  22. [22]
    F.J. Botella, M. Nebot and O. Vives, Invariant approach to flavour-dependent CP-violating phases in the MSSM, JHEP 01 (2006) 106 [hep-ph/0407349] [SPIRES].ADSCrossRefGoogle Scholar
  23. [23]
    B. Pontecorvo, Inverse beta processes and nonconservation of lepton charge, Sov. Phys. JETP 7 (1958) 172 [Zh. Eksp. Teor. Fiz. 34 (1957) 247] [SPIRES].Google Scholar
  24. [24]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [SPIRES].ADSzbMATHCrossRefGoogle Scholar
  25. [25]
    B. Pontecorvo, Neutrino experiments and the question of leptonic-charge conservation, Sov. Phys. JETP 26 (1968) 984 [Zh. Eksp. Teor. Fiz. 53 (1967) 1717] [SPIRES].ADSGoogle Scholar
  26. [26]
    T.D. Lee, A theory of spontaneous T violation, Phys. Rev. D 8 (1973) 1226 [SPIRES].ADSGoogle Scholar
  27. [27]
    A.J. Buras, M.V. Carlucci, S. Gori and G. Isidori, Higgs-mediated FCNCs: natural flavour conservation vs. minimal flavour violation, JHEP 10 (2010) 009 [arXiv:1005.5310] [SPIRES].ADSCrossRefGoogle Scholar
  28. [28]
    A.J. Buras, Minimal flavour violation and beyond: towards a flavour code for short distance dynamics, Acta Phys. Polon. B 41 (2010) 2487 [arXiv:1012.1447] [SPIRES].Google Scholar
  29. [29]
    P.M. Ferreira, L. Lavoura and J.P. Silva, Renormalization-group constraints on Yukawa alignment in multi-Higgs-doublet models, Phys. Lett. B 688 (2010) 341 [arXiv:1001.2561] [SPIRES].ADSGoogle Scholar
  30. [30]
    B. Grzadkowski, M. Lindner and S. Theisen, Nonlinear evolution of Yukawa couplings in the double Higgs and supersymmetric extensions of the standard model, Phys. Lett. B 198 (1987) 64 [SPIRES].ADSGoogle Scholar
  31. [31]
    P.M. Ferreira and J.P. Silva, Abelian symmetries in the two-Higgs-doublet model with fermions, Phys. Rev. D 83 (2011) 065026 [arXiv:1012.2874] [SPIRES].ADSGoogle Scholar
  32. [32]
    S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [SPIRES].ADSCrossRefGoogle Scholar
  33. [33]
    W. Grimus and L. Lavoura, Renormalization of the neutrino mass operators in the multi-Higgs-doublet standard model, Eur. Phys. J. C 39 (2005) 219 [hep-ph/0409231] [SPIRES].ADSCrossRefGoogle Scholar
  34. [34]
    R. Alonso, G. Isidori, L. Merlo, L.A. Muñoz and E. Nardi, Minimal flavour violation extensions of the seesaw, JHEP 06 (2011) 037 [arXiv:1103.5461] [SPIRES].ADSCrossRefGoogle Scholar
  35. [35]
    P. Minkowski, μ → eγ at a rate of one out of 1-billion muon decays?, Phys. Lett. B 67 (1977) 421 [SPIRES].ADSGoogle Scholar
  36. [36]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, in Proceedings of the Workshop on the Baryon Number of the Universe and Unified Theories, Tsukuba Japan, 13–14 Feb. 1979 [SPIRES].
  37. [37]
    S.L. Glashow, The future of elementary particle physics, in Quarks and leptons. Cargèse lectures, M. Lévy et al. eds., Plenum, New York U.S.A. (1980) [SPIRES].Google Scholar
  38. [38]
    M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Proceedings of the Supergravity Workshop, Stony Brook, New York U.S.A., 27–28 Sept. 1979 [SPIRES].Google Scholar
  39. [39]
    R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [SPIRES].ADSCrossRefGoogle Scholar
  40. [40]
    G.C. Branco, T. Morozumi, B.M. Nobre and M.N. Rebelo, A bridge between CP-violation at low energies and leptogenesis, Nucl. Phys. B 617 (2001) 475 [hep-ph/0107164] [SPIRES].ADSCrossRefGoogle Scholar
  41. [41]
    J.A. Casas and A. Ibarra, Oscillating neutrinos and μ → e, γ , Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [SPIRES].ADSCrossRefGoogle Scholar
  42. [42]
    M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [SPIRES].ADSGoogle Scholar
  43. [43]
    F.R. Klinkhamer and N.S. Manton, A saddle point solution in the W einberg-Salam theory, Phys. Rev. D 30 (1984) 2212 [SPIRES].ADSGoogle Scholar
  44. [44]
    V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. B 155 (1985) 36 [SPIRES].ADSGoogle Scholar
  45. [45]
    J. Bernabeu, G.C. Branco and M. Gronau, CP restrictions on quark mass matrices, Phys. Lett. B 169 (1986) 243 [SPIRES].ADSGoogle Scholar
  46. [46]
    G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos, CP-odd invariants in models with several Higgs doublets, Phys. Lett. B 614 (2005) 187 [hep-ph/0502118] [SPIRES].ADSGoogle Scholar
  47. [47]
    F. del Aguila and J. Cortes, A new model of weak CP violation, Phys. Lett. B 156 (1985) 243 [SPIRES].ADSGoogle Scholar
  48. [48]
    G.C. Branco and L. Lavoura, On the addition of vector like quarks to the standard model, Nucl. Phys. B 278 (1986) 738 [SPIRES].ADSCrossRefGoogle Scholar
  49. [49]
    F. del Aguila, M.K. Chase and J. Cortes, Vector-like fermion contributions to ε′, Nucl. Phys. B 271 (1986) 61 [SPIRES].ADSGoogle Scholar
  50. [50]
    Y. Nir and D.J. Silverman, Z-mediated flavor changing neutral currents and their implications for CP asymmetries in B 0 decays, Phys. Rev. D 42 (1990) 1477 [SPIRES].ADSGoogle Scholar
  51. [51]
    D. Silverman, Z-mediated \( B - \bar{B} \) mixing and B-meson CP-violating asymmetries in the light of new FCNC bounds, Phys. Rev. D 45 (1992) 1800 [SPIRES].ADSGoogle Scholar
  52. [52]
    G.C. Branco, T. Morozumi, P.A. Parada and M.N. Rebelo, CP asymmetries in B 0 decays in the presence of flavor changing neutral currents, Phys. Rev. D 48 (1993) 1167 [SPIRES].ADSGoogle Scholar
  53. [53]
    V.D. Barger, M.S. Berger and R.J.N. Phillips, Quark singlets: implications and constraints, Phys. Rev. D 52 (1995) 1663 [hep-ph/9503204] [SPIRES].ADSGoogle Scholar
  54. [54]
    M. Gronau and D. London, New physics in CP asymmetries and rare B decays, Phys. Rev. D 55 (1997) 2845 [hep-ph/9608430] [SPIRES].ADSGoogle Scholar
  55. [55]
    F. del Aguila, J.A. Aguilar-Saavedra and G.C. Branco, CP violation from new quarks in the chiral limit, Nucl. Phys. B 510 (1998) 39 [hep-ph/9703410] [SPIRES].ADSGoogle Scholar
  56. [56]
    G. Barenboim, F.J. Botella, G.C. Branco and O. Vives, How sensitive to FCNC can B 0 CP asymmetries be?, Phys. Lett. B 422 (1998) 277 [hep-ph/9709369] [SPIRES].ADSGoogle Scholar
  57. [57]
    G. Barenboim, F.J. Botella and O. Vives, Tree level FCNC in the B system: from CP asymmetries to rare decays, Phys. Rev. D 64 (2001) 015007 [hep-ph/0012197] [SPIRES].ADSGoogle Scholar
  58. [58]
    G. Barenboim, F.J. Botella and O. Vives, Constraining models with vector-like fermions from FCNC in K and B physics, Nucl. Phys. B 613 (2001) 285 [hep-ph/0105306] [SPIRES].ADSCrossRefGoogle Scholar
  59. [59]
    K. Higuchi and K. Yamamoto, Flavor-changing interactions with singlet quarks and their implications for the LHC, Phys. Rev. D 81 (2010) 015009 [arXiv:0911.1175] [SPIRES].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • F. J. Botella
    • 1
  • G. C. Branco
    • 2
  • M. Nebot
    • 1
  • M. N. Rebelo
    • 3
    Email author
  1. 1.Departament de Física Teèrica and IFICUniversitat de València-CSICBurjassotSpain
  2. 2.Departamento de Física and Centro de Física Teórica de Partículas (CFTP)Instituto Superior TécnicoLisboaPortugal
  3. 3.Universidade Técnica de LisboaCentro de Física Teórica de Partículas (CFTP), Instituto Superior TécnicoLisboaPortugal

Personalised recommendations