Charming CP violation and dipole operators from RS flavor anarchy

  • Cédric DelaunayEmail author
  • Jernej F. Kamenik
  • Gilad Perez
  • Lisa Randall
Open Access


Recently the LHCb collaboration reported evidence for direct CP violation in charm decays. The value is sufficiently large that either substantially enhanced Standard Model contributions or non-Standard Model physics is required to explain it. In the latter case only a limited number of possibilities would be consistent with other existing flavor-changing constraints. We show that warped extra dimensional models that explain the quark spectrum through flavor anarchy can naturally give rise to contributions of the size required to explain the the LHCb result. The D meson asymmetry arises through a sizable CP-violating contribution to a chromomagnetic dipole operator. This happens naturally without introducing inconsistencies with existing constraints in the up quark sector. We discuss some subtleties in the loop calculation that are similar to those in Higgs to γγ. Loop-induced dipole operators in warped scenarios and their composite analogs exhibit non-trivial dependence on the Higgs profile, with the contributions monotonically decreasing when the Higgs is pushed away from the IR brane. We show that the size of the dipole operator quickly saturates as the Higgs profile approaches the IR brane, implying small dependence on the precise details of the Higgs profile when it is quasi IR localized. We also explain why the calculation of the coefficient of the lowest dimension 5D operator is guaranteed to be finite. This is true not only in the charm sector but also with other radiative processes such as electric dipole moments, b, ϵ /ϵ K and μ. We furthermore discuss the interpretation of this contribution within the framework of partial compositeness in four dimensions and highlight some qualitative differences between the generic result of composite models and that obtained for dynamics that reproduces the warped scenario.


Phenomenology of Field Theories in Higher Dimensions 


  1. [1]
    LHCb collaboration, A search for time-integrated CP violation in D 0h h + decays, talk presented at HCP2011, November 14–18, Paris, France (2011), LHCb-CONF-2011-061.
  2. [2]
    LHCb collaboration, Evidence for CP-violation in time-integrated D 0h h + decay rates, Phys. Rev. Lett. 108 (2012) 111602 [arXiv:1112.0938] [INSPIRE].CrossRefGoogle Scholar
  3. [3]
    CDF collaboration, Improved measurement of the difference between time integrated CP asymmetries in D 0k + K and D 0π + π decays at CDF, CDF Public Note 10784 (2012).Google Scholar
  4. [4]
    CDF collaboration, Measurement of CP-violating asymmetries in D 0π + π and D 0K + K decays at CDF, Phys. Rev. D 85 (2012) 012009 [arXiv:1111.5023] [INSPIRE].Google Scholar
  5. [5]
    Belle collaboration, M. Staric et al., Measurement of CP asymmetry in Cabibbo suppressed D 0 decays, Phys. Lett. B 670 (2008) 190 [arXiv:0807.0148] [INSPIRE].ADSGoogle Scholar
  6. [6]
    BaBar collaboration, B. Aubert et al., Search for CP-violation in the decays D 0K K + and D 0π π +, Phys. Rev. Lett. 100 (2008) 061803 [arXiv:0709.2715] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    Heavy Flavor Averaging Group collaboration, D. Asner et al., Averages of b-hadron, c-hadron and τ-lepton Properties, arXiv:1010.1589 [INSPIRE].
  8. [8]
    G. D’Ambrosio, G. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    A.L. Kagan, G. Perez, T. Volansky and J. Zupan, General minimal flavor violation, Phys. Rev. D 80 (2009) 076002 [arXiv:0903.1794] [INSPIRE].ADSGoogle Scholar
  10. [10]
    Y. Grossman, A.L. Kagan and Y. Nir, New physics and CP-violation in singly Cabibbo suppressed D decays, Phys. Rev. D 75 (2007) 036008 [hep-ph/0609178] [INSPIRE].ADSGoogle Scholar
  11. [11]
    M. Golden and B. Grinstein, Enhanced CP-violations in hadronic charm decays, Phys. Lett. B 222 (1989) 501 [INSPIRE].ADSGoogle Scholar
  12. [12]
    J. Brod, A.L. Kagan and J. Zupan, Size of direct CP-violation in singly Cabibbo-suppressed D decays, Phys. Rev. D 86 (2012) 014023 [arXiv:1111.5000] [INSPIRE].ADSGoogle Scholar
  13. [13]
    D. Pirtskhalava and P. Uttayarat, CP violation and flavor Su(3) breaking in D-meson decays, Phys. Lett. B 712 (2012) 81 [arXiv:1112.5451] [INSPIRE].ADSGoogle Scholar
  14. [14]
    H.-Y. Cheng and C.-W. Chiang, Direct CP-violation in two-body hadronic charmed meson decays, Phys. Rev. D 85 (2012) 034036 [Erratum ibid. D 85 (2012) 079903] [arXiv:1201.0785] [INSPIRE].
  15. [15]
    B. Bhattacharya, M. Gronau and J.L. Rosner, CP asymmetries in singly-Cabibbo-suppressed D decays to two pseudoscalar mesons, Phys. Rev. D 85 (2012) 054014 [arXiv:1201.2351] [INSPIRE].ADSGoogle Scholar
  16. [16]
    T. Feldmann, S. Nandi and A. Soni, Repercussions of flavour symmetry breaking on CP-violation in D-meson decays, JHEP 06 (2012) 007 [arXiv:1202.3795] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    H.-n. Li, C.-D. Lu and F.-S. Yu, Branching ratios and direct CP asymmetries in Dpp decays, Phys. Rev. D 86 (2012) 036012 [arXiv:1203.3120] [INSPIRE].ADSGoogle Scholar
  18. [18]
    E. Franco, S. Mishima and L. Silvestrini, The standard model confronts CP-violation in D 0π + π and D 0K + K , JHEP 05 (2012) 140 [arXiv:1203.3131] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. Brod, Y. Grossman, A.L. Kagan and J. Zupan, A consistent picture for large penguins in Dπ + π , K + K , JHEP 10 (2012) 161 [arXiv:1203.6659] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Isidori, J.F. Kamenik, Z. Ligeti and G. Perez, Implications of the LHCb evidence for charm CP-violation, Phys. Lett. B 711 (2012) 46 [arXiv:1111.4987] [INSPIRE].ADSGoogle Scholar
  21. [21]
    G.F. Giudice, G. Isidori and P. Paradisi, Direct CP-violation in charm and flavor mixing beyond the SM, JHEP 04 (2012) 060 [arXiv:1201.6204] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSGoogle Scholar
  24. [24]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  25. [25]
    W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    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] [INSPIRE].ADSGoogle Scholar
  28. [28]
    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    K. Agashe, G. Perez and A. Soni, Flavor structure of warped extra dimension models, Phys. Rev. D 71 (2005) 016002 [hep-ph/0408134] [INSPIRE].ADSGoogle Scholar
  30. [30]
    K. Agashe, G. Perez and A. Soni, B-factory signals for a warped extra dimension, Phys. Rev. Lett. 93 (2004) 201804 [hep-ph/0406101] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    S.J. Huber, Flavor violation and warped geometry, Nucl. Phys. B 666 (2003) 269 [hep-ph/0303183] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    C. Csáki, A. Falkowski and A. Weiler, The flavor of the composite pseudo-goldstone Higgs, JHEP 09 (2008) 008 [arXiv:0804.1954] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    K. Agashe, A. Azatov and L. Zhu, Flavor violation tests of warped/composite SM in the two-site approach, Phys. Rev. D 79 (2009) 056006 [arXiv:0810.1016] [INSPIRE].ADSGoogle Scholar
  34. [34]
    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] [INSPIRE].ADSGoogle Scholar
  35. [35]
    R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudo-Goldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    G. Isidori, Y. Nir and G. Perez, Flavor physics constraints for physics beyond the standard model, Ann. Rev. Nucl. Part. Sci. 60 (2010) 355 [arXiv:1002.0900] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    B. Keren-Zur et al., On partial compositeness and the CP asymmetry in charm decays, Nucl. Phys. B 867 (2013) 429 [arXiv:1205.5803] [INSPIRE].Google Scholar
  38. [38]
    F. Goertz, U. Haisch and M. Neubert, Bounds on warped extra dimensions from a standard model-like Higgs boson, Phys. Lett. B 713 (2012) 23 [arXiv:1112.5099] [INSPIRE].ADSGoogle Scholar
  39. [39]
    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
  40. [40]
    M. Carena, S. Casagrande, F. Goertz, U. Haisch and M. Neubert, Higgs production in a warped extra dimension, JHEP 08 (2012) 156 [arXiv:1204.0008] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    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
  42. [42]
    S.M. Barr, Solving the strong CP problem without the Peccei-Quinn symmetry, Phys. Rev. Lett. 53 (1984) 329 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    A.E. Nelson, Naturally weak CP-violation, Phys. Lett. B 136 (1984) 387 [INSPIRE].ADSGoogle Scholar
  44. [44]
    M. Blanke, B. Shakya, P. Tanedo and Y. Tsai, The birds and the Bs in RS: The btosγ penguin in a warped extra dimension, JHEP 08 (2012) 038 [arXiv:1203.6650] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    A.L. Fitzpatrick, G. Perez and L. Randall, Flavor anarchy in a Randall-Sundrum model with 5D minimal flavor violation and a low Kaluza-Klein scale, Phys. Rev. Lett. 100 (2008) 171604 [arXiv:0710.1869] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    C. Csáki, G. Perez, Z. Surujon and A. Weiler, Flavor alignment via shining in RS, Phys. Rev. D 81 (2010) 075025 [arXiv:0907.0474] [INSPIRE].ADSGoogle Scholar
  47. [47]
    O. Gedalia, Y. Grossman, Y. Nir and G. Perez, Lessons from recent measurements of D 0-D 0 mixing, Phys. Rev. D 80 (2009) 055024 [arXiv:0906.1879] [INSPIRE].ADSGoogle Scholar
  48. [48]
    C. Csáki, Y. Grossman, P. Tanedo and Y. Tsai, Warped penguin diagrams, Phys. Rev. D 83 (2011) 073002 [arXiv:1004.2037] [INSPIRE].ADSGoogle Scholar
  49. [49]
    P. Gambino and J.F. Kamenik, Lepton energy moments in semileptonic charm decays, Nucl. Phys. B 840 (2010) 424 [arXiv:1004.0114] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    G. Burdman and I. Shipsey, \( {D^0}-{{\overline{D}}^0} \) mixing and rare charm decays, Ann. Rev. Nucl. Part. Sci. 53 (2003) 431 [hep-ph/0310076] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    G. Isidori and J.F. Kamenik, Shedding light on CP-violation in the charm system via DVγ decays, Phys. Rev. Lett. 109 (2012) 171801 [arXiv:1205.3164] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    S. Fajfer, S. Prelovsek and P. Singer, Resonant and nonresonant contributions to the weak DV lepton + lepton decays, Phys. Rev. D 58 (1998) 094038 [hep-ph/9805461] [INSPIRE].ADSGoogle Scholar
  53. [53]
    G. Burdman, E. Golowich, J.L. Hewett and S. Pakvasa, Rare charm decays in the standard model and beyond, Phys. Rev. D 66 (2002) 014009 [hep-ph/0112235] [INSPIRE].ADSGoogle Scholar
  54. [54]
    S. Fajfer and S. Prelovsek, Effects of littlest Higgs model in rare D meson decays, Phys. Rev. D 73 (2006) 054026 [hep-ph/0511048] [INSPIRE].ADSGoogle Scholar
  55. [55]
    DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    RENO collaboration, J. Ahn et al., Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    G. Perez and L. Randall, Natural neutrino masses and mixings from warped geometry, JHEP 01 (2009) 077 [arXiv:0805.4652] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    K. Agashe, A.E. Blechman and F. Petriello, Probing the Randall-Sundrum geometric origin of flavor with lepton flavor violation, Phys. Rev. D 74 (2006) 053011 [hep-ph/0606021] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  • Cédric Delaunay
    • 1
    Email author
  • Jernej F. Kamenik
    • 2
    • 3
  • Gilad Perez
    • 1
    • 4
  • Lisa Randall
    • 5
  1. 1.CERN, Theoretical PhysicsGeneva 23Switzerland
  2. 2.J. Stefan InstituteLjubljanaSlovenia
  3. 3.Department of PhysicsUniversity of LjubljanaLjubljanaSlovenia
  4. 4.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael
  5. 5.Department of PhysicsHarvard UniversityCambridgeU.S.A.

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