FCNC effects in a minimal theory of fermion masses


As a minimal theory of fermion masses we extend the SM by heavy vectorlike fermions, with flavor-anarchical Yukawa couplings, that mix with chiral fermions such that small SM Yukawa couplings arise from small mixing angles. This model can be regarded as an effective description of the fermionic sector of a large class of existing flavor models and thus might serve as a useful reference frame for a further understanding of flavor hierarchies in the SM. Already such a minimal framework gives rise to FCNC effects through exchange of massive SM bosons whose couplings to the light fermions get modified by the mixing. We derive general formulae for these corrections and discuss the bounds on the heavy fermion masses. Particularly stringent bounds, in a few TeV range, come from the corrections to the Z couplings.


  1. [1]

    C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [SPIRES].

    Article  ADS  Google Scholar 

  2. [2]

    Y. Nir and N. Seiberg, Should squarks be degenerate?, Phys. Lett. B 309 (1993) 337 [hep-ph/9304307] [SPIRES].

    ADS  Google Scholar 

  3. [3]

    M. Leurer, Y. Nir and N. Seiberg, Mass matrix models: The Sequel, Nucl. Phys. B 420 (1994) 468 [hep-ph/9310320] [SPIRES].

    Article  ADS  Google Scholar 

  4. [4]

    L.E. Ibáñez and G.G. Ross, Fermion masses and mixing angles from gauge symmetries, Phys. Lett. B 332 (1994) 100 [hep-ph/9403338] [SPIRES].

    ADS  Google Scholar 

  5. [5]

    N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [SPIRES].

    ADS  Google Scholar 

  6. [6]

    Y. Grossman and M. Neubert, Neutrino masses and mixings in non-factorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  7. [7]

    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  8. [8]

    S.J. Huber and Q. Shafi, Fermion Masses, Mixings and Proton Decay in a Randall-Sundrum Model, Phys. Lett. B 498 (2001) 256 [hep-ph/0010195] [SPIRES].

    ADS  Google Scholar 

  9. [9]

    S. Davidson, G. Isidori and S. Uhlig, Solving the flavour problem with hierarchical fermion wave functions, Phys. Lett. B 663 (2008) 73 [arXiv:0711.3376] [SPIRES].

    ADS  Google Scholar 

  10. [10]

    H. Georgi, A.E. Nelson and A. Manohar, On The Proposition That All Fermions Are Created Equal, Phys. Lett. B 126 (1983) 169 [SPIRES].

    ADS  Google Scholar 

  11. [11]

    D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [SPIRES].

    Article  ADS  Google Scholar 

  12. [12]

    A.E. Nelson and M.J. Strassler, Suppressing flavor anarchy, JHEP 09 (2000) 030 [hep-ph/0006251] [SPIRES].

    Article  ADS  Google Scholar 

  13. [13]

    D. Poland and D. Simmons-Duffin, Superconformal Flavor Simplified, JHEP 05 (2010) 079 [arXiv:0910.4585] [SPIRES].

    Article  ADS  Google Scholar 

  14. [14]

    K.S. Babu and S. Nandi, Natural fermion mass hierarchy and new signals for the Higgs boson, Phys. Rev. D 62 (2000) 033002 [hep-ph/9907213] [SPIRES].

    ADS  Google Scholar 

  15. [15]

    G.F. Giudice and O. Lebedev, Higgs-dependent Yukawa couplings, Phys. Lett. B 665 (2008) 79 [arXiv:0804.1753] [SPIRES].

    ADS  Google Scholar 

  16. [16]

    K. Agashe and R. Contino, Composite Higgs-Mediated FCNC, Phys. Rev. D 80 (2009) 075016 [arXiv:0906.1542] [SPIRES].

    ADS  Google Scholar 

  17. [17]

    A. Azatov, M. Toharia and L. Zhu, Higgs Mediated FCNC’s in Warped Extra Dimensions, Phys. Rev. D 80 (2009) 035016 [arXiv:0906.1990] [SPIRES].

    ADS  Google Scholar 

  18. [18]

    A.J. Buras, C. Grojean, S. Pokorski and R. Ziegler, in preparation.

  19. [19]

    F. del Aguila and J. Santiago, Universality limits on bulk fermions, Phys. Lett. B 493 (2000) 175 [hep-ph/0008143] [SPIRES].

    ADS  Google Scholar 

  20. [20]

    F. del Aguila, M. Pérez-Victoria and J. Santiago, Effective description of quark mixing, Phys. Lett. B 492 (2000) 98 [hep-ph/0007160] [SPIRES].

    ADS  Google Scholar 

  21. [21]

    F. del Aguila, M. Pérez-Victoria and J. Santiago, Observable contributions of new exotic quarks to quark mixing, JHEP 09 (2000) 011 [hep-ph/0007316] [SPIRES].

    Article  Google Scholar 

  22. [22]

    A.J. Buras, B. Duling and S. Gori, The Impact of Kaluza-Klein Fermions on Standard Model Fermion Couplings in a RS Model with Custodial Protection, JHEP 09 (2009) 076 [arXiv:0905.2318] [SPIRES].

    Article  ADS  Google Scholar 

  23. [23]

    Z.-z. Xing, H. Zhang and S. Zhou, Updated Values of Running Quark and Lepton Masses, Phys. Rev. D 77 (2008) 113016 [arXiv:0712.1419] [SPIRES].

    ADS  Google Scholar 

  24. [24]

    UTfit collaboration, M. Bona et al., Model-independent constraints onF = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [SPIRES].

    Article  ADS  Google Scholar 

  25. [25]

    G. Isidori, Y. Nir and G. Perez, Flavor Physics Constraints for Physics Beyond the Standard Model, arXiv:1002.0900 [SPIRES].

  26. [26]

    G. Isidori and R. Unterdorfer, On the short-distance constraints from K(L, S) → μ + μ , JHEP 01 (2004) 009 [hep-ph/0311084] [SPIRES].

    Article  ADS  Google Scholar 

  27. [27]

    K. Agashe, A. Delgado, M.J. May and R. Sundrum, RS1, custodial isospin and precision tests, JHEP 08 (2003) 050 [hep-ph/0308036] [SPIRES].

    Article  ADS  Google Scholar 

  28. [28]

    K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A custodial symmetry for Z b anti-b, Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [SPIRES].

    ADS  Google Scholar 

  29. [29]

    M.S. Carena, E. Ponton, J. Santiago and C.E.M. Wagner, Electroweak constraints on warped models with custodial symmetry, Phys. Rev. D 76 (2007) 035006 [hep-ph/0701055] [SPIRES].

    ADS  Google Scholar 

  30. [30]

    ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group and SLD Heavy Flavour Group collaboration, Precision electroweak measurements on the Z resonance, Phys. Rept. 427 (2006) 257 [hep-ex/0509008] [SPIRES].

    ADS  Google Scholar 

  31. [31]

    R. Contino, T. Kramer, M. Son and R. Sundrum, Warped/Composite Phenomenology Simplified, JHEP 05 (2007) 074 [hep-ph/0612180] [SPIRES].

    Article  ADS  Google Scholar 

  32. [32]

    K. Agashe, G. Perez and A. Soni, Flavor structure of warped extra dimension models, Phys. Rev. D 71 (2005) 016002 [hep-ph/0408134] [SPIRES].

    ADS  Google Scholar 

  33. [33]

    C. Csáki, A. Falkowski and A. Weiler, The Flavor of the Composite Pseudo-Goldstone Higgs, JHEP 09 (2008) 008 [arXiv:0804.1954] [SPIRES].

    Article  ADS  Google Scholar 

  34. [34]

    M. Blanke, A.J. Buras, B. Duling, S. Gori and A. Weiler, ∆F = 2 Observables and Fine-Tuning in a Warped Extra Dimension with Custodial Protection, JHEP 03 (2009) 001 [arXiv:0809.1073] [SPIRES].

    Article  ADS  Google Scholar 

  35. [35]

    M. Blanke, A.J. Buras, B. Duling, K. Gemmler and S. Gori, Rare K and B Decays in a Warped Extra Dimension with Custodial Protection, JHEP 03 (2009) 108 [arXiv:0812.3803] [SPIRES].

    Article  ADS  Google Scholar 

  36. [36]

    M. Bauer, S. Casagrande, U. Haisch and M. Neubert, Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes, JHEP 09 (2010) 017 [arXiv:0912.1625] [SPIRES].

    Article  ADS  Google Scholar 

  37. [37]

    O. Gedalia, G. Isidori and G. Perez, Combining Direct & Indirect Kaon CP-violation to Constrain the Warped KK Scale, Phys. Lett. B 682 (2009) 200 [arXiv:0905.3264] [SPIRES].

    ADS  Google Scholar 

  38. [38]

    R. Contino and A. Pomarol, Holography for fermions, JHEP 11 (2004) 058 [hep-th/0406257] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  39. [39]

    D.B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [SPIRES].

    ADS  Google Scholar 

  40. [40]

    D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs Scalars, Phys. Lett. B 136 (1984) 187 [SPIRES].

    ADS  Google Scholar 

  41. [41]

    H. Georgi and D.B. Kaplan, Composite Higgs and Custodial SU(2), Phys. Lett. B 145 (1984) 216 [SPIRES].

    ADS  Google Scholar 

  42. [42]

    H. Georgi, D.B. Kaplan and P. Galison, Calculation of the composite Higgs mass, Phys. Lett. B 143 (1984) 152 [SPIRES].

    ADS  Google Scholar 

  43. [43]

    M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys. B 254 (1985) 299 [SPIRES].

    Article  ADS  Google Scholar 

  44. [44]

    G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [SPIRES].

    Article  ADS  Google Scholar 

  45. [45]

    C. Csáki, C. Grojean, L. Pilo and J. Terning, Towards a realistic model of Higgsless electroweak symmetry breaking, Phys. Rev. Lett. 92 (2004) 101802 [hep-ph/0308038] [SPIRES].

    Article  ADS  Google Scholar 

  46. [46]

    R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudo-Goldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [SPIRES].

    Article  ADS  Google Scholar 

  47. [47]

    K. Agashe, R. Contino and A. Pomarol, The Minimal Composite Higgs Model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [SPIRES].

    Article  ADS  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Christophe Grojean.

Rights and permissions

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Cite this article

Buras, A.J., Grojean, C., Pokorski, S. et al. FCNC effects in a minimal theory of fermion masses. J. High Energ. Phys. 2011, 28 (2011). https://doi.org/10.1007/JHEP08(2011)028

Download citation


  • Beyond Standard Model
  • Quark Masses and SM Parameters
  • Rare Decays