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Impact of warped extra dimensions on the dipole coefficients in b transitions

  • Raoul Malm
  • Matthias Neubert
  • Christoph Schmell
Open Access
Regular Article - Theoretical Physics

Abstract

We calculate the electro- and chromomagnetic dipole coefficients C 7γ,8g and \( {\tilde{C}}_{7\gamma, 8g} \) in the context of the minimal Randall-Sundrum (RS) model with a Higgs sector localized on the IR brane using the five-dimensional (5D) approach, where the coefficients are expressed in terms of integrals over 5D propagators. Since we keep the full dependence on the Yukawa matrices, the integral expressions are formally valid to all orders in v 2/M KK 2 . In addition we relate our results to the expressions obtained in the Kaluza-Klein (KK) decomposed theory and show the consistency in both pictures analytically and numerically, which presents a non-trivial cross-check. In Feynman-’t Hooft gauge, the dominant corrections from virtual KK modes arise from the scalar parts of the W ±-boson penguin diagrams, including the contributions from the scalar component of the 5D gauge-boson field and from the charged Goldstone bosons in the Higgs sector. The size of the KK corrections depends on the parameter y *, which sets the upper bound for the anarchic 5D Yukawa matrices. We find that for y * ≳ 1 the KK corrections are proportional to y 2 . We discuss the phenomenological implications of our results for the branching ratio \( \mathrm{B}\mathrm{r}\left(\overline{B}\to {X}_s\gamma \right) \), the time-dependent CP asymmetry S K ∗ γ , the direct CP asymmetry A CP b →  and the CP asymmetry difference ΔA CP b →  . We can derive a lower bound on the first KK gluon resonance of 3.8 TeV for y * = 3, requiring that at least 10% of the RS parameter space covers the experimental 2σ error margins. We further discuss the branching ratio \( \mathrm{B}\mathrm{r}\left(\overline{B}\to {X}_s{l}^{+}{l}^{-}\right) \) and compare our predictions for C 7γ,9,10 and \( {\tilde{C}}_{7\gamma, 9,10} \) with phenomenological results derived from model-independent analyses.

Keywords

Phenomenology of Field Theories in Higher Dimensions 

Notes

Open Access

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References

  1. [1]
    ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
  2. [2]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
  3. [3]
    L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    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].ADSCrossRefGoogle Scholar
  7. [7]
    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
  8. [8]
    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
  9. [9]
    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
  10. [10]
    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].ADSCrossRefMATHGoogle Scholar
  11. [11]
    M. Blanke, A.J. Buras, B. Duling, S. Gori and A. Weiler, ΔF = 2 observables and fine-tuning in a warped extra dimension with custodial protection, JHEP 03 (2009) 001 [arXiv:0809.1073] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    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].ADSCrossRefMATHGoogle Scholar
  14. [14]
    U. Haisch, \( \overline{B}\to {X}_s\gamma \) : standard model and beyond, arXiv:0805.2141 [INSPIRE].
  15. [15]
    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
  16. [16]
    C. Csáki, Y. Grossman, P. Tanedo and Y. Tsai, Warped penguin diagrams, Phys. Rev. D 83 (2011) 073002 [arXiv:1004.2037] [INSPIRE].ADSGoogle Scholar
  17. [17]
    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
  18. [18]
    C. Schmell, Hunting for warped extra-dimensions using loop-induced processes, Doctoral Thesis, Johannes Gutenberg University Mainz, Mainz Germany (2015).Google Scholar
  19. [19]
    P. Biancofiore, P. Colangelo and F. De Fazio, Rare semileptonic BK * + decays in RS c model, Phys. Rev. D 89 (2014) 095018 [arXiv:1403.2944] [INSPIRE].ADSGoogle Scholar
  20. [20]
    M. Beneke, P. Moch and J. Rohrwild, Lepton flavour violation in RS models with a brane- or nearly brane-localized Higgs, arXiv:1508.01705 [INSPIRE].
  21. [21]
    M. Carena, A. Delgado, E. Ponton, T.M.P. Tait and C.E.M. Wagner, Warped fermions and precision tests, Phys. Rev. D 71 (2005) 015010 [hep-ph/0410344] [INSPIRE].ADSGoogle Scholar
  22. [22]
    Gfitter Group collaboration, M. Baak et al., The global electroweak fit at NNLO and prospects for the LHC and ILC, Eur. Phys. J. C 74 (2014) 3046 [arXiv:1407.3792] [INSPIRE].
  23. [23]
    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
  24. [24]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    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].ADSCrossRefGoogle Scholar
  26. [26]
    M. Bauer, R. Malm and M. Neubert, A solution to the flavor problem of warped extra-dimension models, Phys. Rev. Lett. 108 (2012) 081603 [arXiv:1110.0471] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    R. Malm, M. Neubert and C. Schmell, Higgs couplings and phenomenology in a warped extra dimension, JHEP 02 (2015) 008 [arXiv:1408.4456] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    J. Hahn, C. Hörner, R. Malm, M. Neubert, K. Novotny and C. Schmell, Higgs decay into two photons at the boundary of a warped extra dimension, Eur. Phys. J. C 74 (2014) 2857 [arXiv:1312.5731] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    R. Malm, M. Neubert, K. Novotny and C. Schmell, 5D perspective on Higgs production at the boundary of a warped extra dimension, JHEP 01 (2014) 173 [arXiv:1303.5702] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    K. Agashe, A. Azatov, Y. Cui, L. Randall and M. Son, Warped dipole completed, with a tower of Higgs bosons, JHEP 06 (2015) 196 [arXiv:1412.6468] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    C. Delaunay, J.F. Kamenik, G. Perez and L. Randall, Charming CP-violation and dipole operators from RS flavor anarchy, JHEP 01 (2013) 027 [arXiv:1207.0474] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    L. Randall and M.D. Schwartz, Quantum field theory and unification in AdS 5, JHEP 11 (2001) 003 [hep-th/0108114] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    M. Puchwein and Z. Kunszt, Radiative corrections with 5D mixed position/momentum space propagators, Annals Phys. 311 (2004) 288 [hep-th/0309069] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  34. [34]
    R. Contino and A. Pomarol, Holography for fermions, JHEP 11 (2004) 058 [hep-th/0406257] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    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].ADSCrossRefMATHGoogle Scholar
  36. [36]
    A. Djouadi and G. Moreau, Higgs production at the LHC in warped extra-dimensional models, Phys. Lett. B 660 (2008) 67 [arXiv:0707.3800] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    A. Falkowski, Pseudo-Goldstone Higgs production via gluon fusion, Phys. Rev. D 77 (2008) 055018 [arXiv:0711.0828] [INSPIRE].ADSGoogle Scholar
  38. [38]
    G. Cacciapaglia, A. Deandrea and J. Llodra-Perez, Higgsγγ beyond the standard model, JHEP 06 (2009) 054 [arXiv:0901.0927] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    G. Bhattacharyya and T.S. Ray, Probing warped extra dimension via ggh and hγγ at LHC, Phys. Lett. B 675 (2009) 222 [arXiv:0902.1893] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    C. Bouchart and G. Moreau, Higgs boson phenomenology and VEV shift in the RS scenario, Phys. Rev. D 80 (2009) 095022 [arXiv:0909.4812] [INSPIRE].ADSGoogle Scholar
  41. [41]
    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
  42. [42]
    A. Azatov and J. Galloway, Light custodians and Higgs physics in composite models, Phys. Rev. D 85 (2012) 055013 [arXiv:1110.5646] [INSPIRE].ADSGoogle Scholar
  43. [43]
    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].ADSCrossRefGoogle Scholar
  44. [44]
    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
  45. [45]
    P.R. Archer, M. Carena, A. Carmona and M. Neubert, Higgs production and decay in models of a warped extra dimension with a bulk Higgs, JHEP 01 (2015) 060 [arXiv:1408.5406] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    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
  47. [47]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  48. [48]
    M. Beneke, P. Dey and J. Rohrwild, The muon anomalous magnetic moment in the Randall-Sundrum model, JHEP 08 (2013) 010 [arXiv:1209.5897] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    P. Moch and J. Rohrwild, (g − 2)μ in the custodially protected RS model, J. Phys. G 41 (2014) 105005 [arXiv:1405.5385] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    M. Beneke, P. Moch and J. Rohrwild, Muon anomalous magnetic moment and penguin loops in warped extra dimensions, Int. J. Mod. Phys. A 29 (2014) 1444011 [arXiv:1404.7157] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  51. [51]
    A.J. Buras, L. Merlo and E. Stamou, The impact of flavour changing neutral gauge bosons on \( \overline{B}\to {X}_s\gamma \), JHEP 08 (2011) 124 [arXiv:1105.5146] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  52. [52]
    P. Gambino and M. Misiak, Quark mass effects in \( \overline{B}\to {X}_s\gamma \), Nucl. Phys. B 611 (2001) 338 [hep-ph/0104034] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    M. Misiak and M. Steinhauser, NNLO QCD corrections to the \( \overline{B}\to {X}_s\gamma \) matrix elements using interpolation in m c, Nucl. Phys. B 764 (2007) 62 [hep-ph/0609241] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    Heavy Flavor Averaging Group (HFAG) collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2014, arXiv:1412.7515 [INSPIRE].
  55. [55]
    M. Misiak et al., Updated NNLO QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A.L. Kagan and M. Neubert, Direct CP-violation in BX s γ decays as a signature of new physics, Phys. Rev. D 58 (1998) 094012 [hep-ph/9803368] [INSPIRE].ADSGoogle Scholar
  57. [57]
    M. Benzke, S.J. Lee, M. Neubert and G. Paz, Factorization at subleading power and irreducible uncertainties in \( \overline{B}\to {X}_s\gamma \) decay, JHEP 08 (2010) 099 [arXiv:1003.5012] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  58. [58]
    ATLAS collaboration, A search for \( t\overline{t} \) resonances in the lepton plus jets final state with ATLAS using 14 fb−1 of pp collisions at \( \sqrt{s}=8 \) TeV, ATLAS-CONF-2013-052, CERN, Geneva Switzerland (2013).
  59. [59]
    CMS collaboration, Search for \( t\overline{t} \) resonances in semileptonic final state, CMS-PAS-B2G-12-006, CERN, Geneva Switzerland (2012).
  60. [60]
    Belle collaboration, M. Iwasaki et al., Improved measurement of the electroweak penguin process BX s + , Phys. Rev. D 72 (2005) 092005 [hep-ex/0503044] [INSPIRE].
  61. [61]
    BaBar collaboration, J.P. Lees et al., Measurement of the BX s + branching fraction and search for direct CP-violation from a sum of exclusive final states, Phys. Rev. Lett. 112 (2014) 211802 [arXiv:1312.5364] [INSPIRE].
  62. [62]
    T. Huber, T. Hurth and E. Lunghi, Inclusive \( \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} \) : complete angular analysis and a thorough study of collinear photons, JHEP 06 (2015) 176 [arXiv:1503.04849] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    D. Guetta and E. Nardi, Searching for new physics in rare Bτ decays, Phys. Rev. D 58 (1998) 012001 [hep-ph/9707371] [INSPIRE].ADSGoogle Scholar
  64. [64]
    A.J. Buras, Weak Hamiltonian, CP-violation and rare decays, hep-ph/9806471 [INSPIRE].
  65. [65]
    S. Descotes-Genon, D. Ghosh, J. Matias and M. Ramon, Exploring new physics in the C 7 ‐ C 7 plane, JHEP 06 (2011) 099 [arXiv:1104.3342] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  66. [66]
    P. Ball and R. Zwicky, Time-dependent CP asymmetry in BK *γ as a (quasi) null test of the standard model, Phys. Lett. B 642 (2006) 478 [hep-ph/0609037] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    W. Altmannshofer, P. Paradisi and D.M. Straub, Model-independent constraints on new physics in bs transitions, JHEP 04 (2012) 008 [arXiv:1111.1257] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].
  69. [69]
    M. Benzke, S.J. Lee, M. Neubert and G. Paz, Long-distance dominance of the CP asymmetry in BX s,d + γ decays, Phys. Rev. Lett. 106 (2011) 141801 [arXiv:1012.3167] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    LHCb collaboration, Angular analysis of the B 0K *0 μ + μ decay, LHCb-CONF-2015-002, CERN, Geneva Switzerland (2015) [CERN-LHCb-CONF-2015-002].
  71. [71]
    S. Descotes-Genon, J. Matias and J. Virto, Understanding the BK * μ + μ anomaly, Phys. Rev. D 88 (2013) 074002 [arXiv:1307.5683] [INSPIRE].ADSGoogle Scholar
  72. [72]
    W. Altmannshofer and D.M. Straub, New physics in BK * μμ?, Eur. Phys. J. C 73 (2013) 2646 [arXiv:1308.1501] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    F. Beaujean, C. Bobeth and D. van Dyk, Comprehensive Bayesian analysis of rare (semi)leptonic and radiative B decays, Eur. Phys. J. C 74 (2014) 2897 [Erratum ibid. C 74 (2014) 3179] [arXiv:1310.2478] [INSPIRE].
  74. [74]
    T. Hurth and F. Mahmoudi, On the LHCb anomaly in BK * + , JHEP 04 (2014) 097 [arXiv:1312.5267] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    R. Alonso, B. Grinstein and J. Martin Camalich, SU(2) × U(1) gauge invariance and the shape of new physics in rare B decays, Phys. Rev. Lett. 113 (2014) 241802 [arXiv:1407.7044] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    G. Hiller and M. Schmaltz, R K and future bsℓℓ physics beyond the standard model opportunities, Phys. Rev. D 90 (2014) 054014 [arXiv:1408.1627] [INSPIRE].ADSGoogle Scholar
  77. [77]
    D. Ghosh, M. Nardecchia and S.A. Renner, Hint of lepton flavour non-universality in B meson decays, JHEP 12 (2014) 131 [arXiv:1408.4097] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    W. Altmannshofer and D.M. Straub, Implications of bs measurements, arXiv:1503.06199 [INSPIRE].
  79. [79]
    P. Moch and J. Rohrwild, \( \overline{B}\to {X}_s\gamma \) with a warped bulk Higgs, Nucl. Phys. B 902 (2016) 142 [arXiv:1509.04643] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Raoul Malm
    • 1
  • Matthias Neubert
    • 1
    • 2
    • 3
  • Christoph Schmell
    • 1
  1. 1.PRISMA Cluster of Excellence & Mainz Institute for Theoretical PhysicsJohannes Gutenberg UniversityMainzGermany
  2. 2.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany
  3. 3.Department of Physics, LEPPCornell UniversityIthacaU.S.A.

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