Journal of High Energy Physics

, 2012:100 | Cite as

The effective Lagrangian for bulk fermions

Article

Abstract

We compute the dimension 6 effective Lagrangian arising from the tree level integration of an arbitrary number of bulk fermions in models with warped extra dimensions. The coefficients of the effective operators are written in terms of simple integrals of the metric and are valid for arbitrary warp factors, with or without an infrared brane, and for a general Higgs profile. All relevant tree level fermion effects in electroweak and flavor observables can be computed using this effective Lagrangian.

Keywords

Heavy Quark Physics Field Theories in Higher Dimensions 

References

  1. [1]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    R. Rattazzi and A. Zaffaroni, Comments on the holographic picture of the Randall-Sundrum model, JHEP 04 (2001) 021 [hep-th/0012248] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    M. Pérez-Victoria, Randall-Sundrum models and the regularized AdS/CFT correspondence, JHEP 05 (2001) 064 [hep-th/0105048] [INSPIRE].CrossRefGoogle Scholar
  6. [6]
    S.J. Huber, C.-A. Lee and Q. Shafi, Kaluza-Klein excitations of W and Z at the LHC?, Phys. Lett. B 531 (2002) 112 [hep-ph/0111465] [INSPIRE].ADSGoogle Scholar
  7. [7]
    C. Csáki, J. Erlich and J. Terning, The effective Lagrangian in the Randall-Sundrum model and electroweak physics, Phys. Rev. D 66 (2002) 064021 [hep-ph/0203034] [INSPIRE].ADSGoogle Scholar
  8. [8]
    M.S. Carena, A. Delgado, E. Ponton, T.M. Tait and C. Wagner, Precision electroweak data and unification of couplings in warped extra dimensions, Phys. Rev. D 68 (2003) 035010 [hep-ph/0305188] [INSPIRE].ADSGoogle Scholar
  9. [9]
    K. Agashe, A. Delgado, M.J. May and R. Sundrum, RS1, custodial isospin and precision tests, JHEP 08 (2003) 050 [hep-ph/0308036] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M.S. Carena, E. Ponton, J. Santiago and C.E. Wagner, Light Kaluza Klein states in Randall-Sundrum models with custodial SU(2), Nucl. Phys. B 759 (2006) 202 [hep-ph/0607106] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    M.S. Carena, E. Ponton, J. Santiago and C. Wagner, Electroweak constraints on warped models with custodial symmetry, Phys. Rev. D 76 (2007) 035006 [hep-ph/0701055] [INSPIRE].ADSGoogle Scholar
  12. [12]
    A.D. Medina, N.R. Shah and C.E. Wagner, Gauge-Higgs unification and radiative electroweak symmetry breaking in warped extra dimensions, Phys. Rev. D 76 (2007) 095010 [arXiv:0706.1281] [INSPIRE].ADSGoogle Scholar
  13. [13]
    A. Falkowski and M. Pérez-Victoria, Electroweak breaking on a soft wall, JHEP 12 (2008) 107 [arXiv:0806.1737] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Bouchart and G. Moreau, The precision electroweak data in warped extra-dimension models, Nucl. Phys. B 810 (2009) 66 [arXiv:0807.4461] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, Flavor physics in the Randall-Sundrum model: I. Theoretical setup and electroweak precision tests, JHEP 10 (2008) 094 [arXiv:0807.4937] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    B. Batell, T. Gherghetta and D. Sword, The soft-wall standard model, Phys. Rev. D 78 (2008) 116011 [arXiv:0808.3977] [INSPIRE].ADSGoogle Scholar
  17. [17]
    M.E. Albrecht, M. Blanke, A.J. Buras, B. Duling and K. Gemmler, Electroweak and flavour structure of a warped extra dimension with custodial protection, JHEP 09 (2009) 064 [arXiv:0903.2415] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    A. Carmona, E. Ponton and J. Santiago, Phenomenology of non-custodial warped models, arXiv:1107.1500 [INSPIRE].
  19. [19]
    K. Agashe, R. Contino and A. Pomarol, The minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    K. Agashe and R. Contino, The minimal composite Higgs model and electroweak precision tests, Nucl. Phys. B 742 (2006) 59 [hep-ph/0510164] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A custodial symmetry for \( Zb\overline b \), Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [INSPIRE].ADSGoogle Scholar
  22. [22]
    J.A. Cabrer, G. von Gersdorff and M. Quirós, Warped electroweak breaking without custodial symmetry, Phys. Lett. B 697 (2011) 208 [arXiv:1011.2205] [INSPIRE].ADSGoogle Scholar
  23. [23]
    J.A. Cabrer, G. von Gersdorff and M. Quirós, Suppressing electroweak precision observables in 5D warped models, JHEP 05 (2011) 083 [arXiv:1103.1388] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J.A. Cabrer, G. von Gersdorff and M. Quirós, Improving naturalness in warped models with a heavy bulk Higgs boson, Phys. Rev. D 84 (2011) 035024 [arXiv:1104.3149] [INSPIRE].ADSGoogle Scholar
  25. [25]
    F. del Aguila, M. Pérez-Victoria and J. Santiago, Effective description of quark mixing, Phys. Lett. B 492 (2000) 98 [hep-ph/0007160] [INSPIRE].ADSGoogle Scholar
  26. [26]
    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] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    F. del Aguila, J. de Blas and M. Pérez-Victoria, Effects of new leptons in electroweak precision data, Phys. Rev. D 78 (2008) 013010 [arXiv:0803.4008] [INSPIRE].ADSGoogle Scholar
  28. [28]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    A.J. Buras, C. Grojean, S. Pokorski and R. Ziegler, FCNC effects in a minimal theory of fermion masses, JHEP 08 (2011) 028 [arXiv:1105.3725] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    C. Csáki, Y. Grossman, P. Tanedo and Y. Tsai, Warped penguin diagrams, Phys. Rev. D 83 (2011) 073002 [arXiv:1004.2037] [INSPIRE].ADSGoogle Scholar
  31. [31]
    A. Azatov, M. Toharia and L. Zhu, Higgs production from gluon fusion in warped extra dimensions, Phys. Rev. D 82 (2010) 056004 [arXiv:1006.5939] [INSPIRE].ADSGoogle Scholar
  32. [32]
    H. Davoudiasl, S. Gopalakrishna, E. Ponton and J. Santiago, Warped 5-dimensional models: phenomenological status and experimental prospects, New J. Phys. 12 (2010) 075011 [arXiv:0908.1968] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    C. Csáki, C. Grojean, H. Murayama, L. Pilo and J. Terning, Gauge theories on an interval: unitarity without a Higgs, Phys. Rev. D 69 (2004) 055006 [hep-ph/0305237] [INSPIRE].ADSGoogle Scholar
  34. [34]
    G. Cacciapaglia, C. Csáki, G. Marandella and J. Terning, A new custodian for a realistic Higgsless model, Phys. Rev. D 75 (2007) 015003 [hep-ph/0607146] [INSPIRE].ADSGoogle Scholar
  35. [35]
    N. Arkani-Hamed, L.J. Hall, Y. Nomura, D. Tucker-Smith and N. Weiner, Finite radiative electroweak symmetry breaking from the bulk, Nucl. Phys. B 605 (2001) 81 [hep-ph/0102090] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M.S. Carena, A. Delgado, E. Ponton, T.M. Tait and C. Wagner, Warped fermions and precision tests, Phys. Rev. D 71 (2005) 015010 [hep-ph/0410344] [INSPIRE].ADSGoogle Scholar
  37. [37]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Azatov, M. Toharia and L. Zhu, Higgs mediated FCNCs in warped extra dimensions, Phys. Rev. D 80 (2009) 035016 [arXiv:0906.1990] [INSPIRE].ADSGoogle Scholar
  39. [39]
    S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, Flavor physics in the Randall-Sundrum model: I. Theoretical setup and electroweak precision tests, JHEP 10 (2008) 094 [arXiv:0807.4937] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, The custodial Randall-Sundrum model: from precision tests to Higgs physics, JHEP 09 (2010) 014 [arXiv:1005.4315] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    F. del Aguila, M. Pérez-Victoria and J. Santiago, Bulk fields with general brane kinetic terms, JHEP 02 (2003) 051 [hep-th/0302023] [INSPIRE].CrossRefGoogle Scholar
  43. [43]
    F. del Aguila, M. Pérez-Victoria and J. Santiago, Discrete regularisation of localised kinetic terms, Nucl. Phys. Proc. Suppl. 135 (2004) 295 [hep-ph/0410082] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    F. del Aguila, M. Pérez-Victoria and J. Santiago, Effective description of brane terms in extra dimensions, JHEP 10 (2006) 056 [hep-ph/0601222] [INSPIRE].CrossRefGoogle Scholar
  45. [45]
    B. Batell, T. Gherghetta and D. Sword, The soft-wall standard model, Phys. Rev. D 78 (2008) 116011 [arXiv:0808.3977] [INSPIRE].ADSGoogle Scholar
  46. [46]
    A. Delgado and D. Diego, Fermion mass hierarchy from the soft wall, Phys. Rev. D 80 (2009) 024030 [arXiv:0905.1095] [INSPIRE].ADSGoogle Scholar
  47. [47]
    S. Mert Aybat and J. Santiago, Bulk fermions in warped models with a soft wall, Phys. Rev. D 80 (2009) 035005 [arXiv:0905.3032] [INSPIRE].ADSGoogle Scholar
  48. [48]
    S. Aybat and J. Santiago, Bulk fermions in soft wall models, AIP Conf. Proc. 1200 (2010) 611 [arXiv:0909.3999] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    T. Gherghetta and D. Sword, Fermion flavor in soft-wall AdS, Phys. Rev. D 80 (2009) 065015 [arXiv:0907.3523] [INSPIRE].ADSGoogle Scholar
  50. [50]
    M. Atkins and S.J. Huber, Suppressing lepton flavour violation in a soft-wall extra dimension, Phys. Rev. D 82 (2010) 056007 [arXiv:1002.5044] [INSPIRE].ADSGoogle Scholar
  51. [51]
    P.R. Archer, S.J. Huber and S. Jager, Flavour physics in the soft wall model, JHEP 12 (2011) 101 [arXiv:1108.1433] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    J.A. Cabrer, G. von Gersdorff and M. Quirós, Flavor phenomenology in general 5D warped spaces, arXiv:1110.3324 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.CAFPE and Departamento de Física Teórica y del CosmosUniversidad de GranadaGranadaSpain

Personalised recommendations