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Matching of gauge invariant dimension-six operators for bs and bc transitions

  • Jason Aebischer
  • Andreas Crivellin
  • Matteo Fael
  • Christoph Greub
Open Access
Regular Article - Theoretical Physics

Abstract

New physics realized above the electroweak scale can be encoded in a model independent way in the Wilson coefficients of higher dimensional operators which are in-variant under the Standard Model gauge group. In this article, we study the matching of the SU(3) C × SU(2) L × U(1) Y gauge invariant dimension-six operators on the standard B physics Hamiltonian relevant for bs and bc transitions. The matching is performed at the electroweak scale (after spontaneous symmetry breaking) by integrating out the top quark, W , Z and the Higgs particle. We first carry out the matching of the dimension-six operators that give a contribution at tree level to the low energy Hamiltonian. In a second step, we identify those gauge invariant operators that do not enter bs transitions already at tree level, but can give relevant one-loop matching effects.

Keywords

Effective field theories Heavy Quark Physics Beyond Standard Model 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
  2. [2]
    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].
  3. [3]
    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].
  4. [4]
    T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].
  5. [5]
    S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  8. [8]
    S. Weinberg, The quantum theory of fields. Vol. 1: foundations, Cambridge University Press, Cambridge U.K. (1995) [INSPIRE]
  9. [9]
    S. Fajfer, J.F. Kamenik and I. Nisandzic, On the \( B\to {D}^{\ast}\tau\ {\overline{\nu}}_{\tau } \) sensitivity to new physics, Phys. Rev. D 85 (2012) 094025 [arXiv:1203.2654] [INSPIRE].ADSGoogle Scholar
  10. [10]
    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].
  11. [11]
    T. Hurth, F. Mahmoudi and S. Neshatpour, Global fits to bsℓℓ data and signs for lepton non-universality, JHEP 12 (2014) 053 [arXiv:1410.4545] [INSPIRE].CrossRefADSGoogle Scholar
  12. [12]
    W. Altmannshofer and D.M. Straub, New physics in bs transitions after LHC run 1, Eur. Phys. J. C 75 (2015) 382 [arXiv:1411.3161] [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, Global analysis of bsℓℓ anomalies, arXiv:1510.04239 [INSPIRE].
  14. [14]
    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
  15. [15]
    R. Gauld, F. Goertz and U. Haisch, On minimal Z explanations of the BK μ + μ anomaly, Phys. Rev. D 89 (2014) 015005 [arXiv:1308.1959] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A.J. Buras and J. Girrbach, Left-handed Z and Z FCNC quark couplings facing new b + μ data, JHEP 12 (2013) 009 [arXiv:1309.2466] [INSPIRE].
  17. [17]
    R. Gauld, F. Goertz and U. Haisch, An explicit Z -boson explanation of the BK μ + μ anomaly, JHEP 01 (2014) 069 [arXiv:1310.1082] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    A.J. Buras, F. De Fazio and J. Girrbach, 331 models facing new b + μ data, JHEP 02 (2014) 112 [arXiv:1311.6729] [INSPIRE].
  19. [19]
    W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Quark flavor transitions in L μ -L τ models, Phys. Rev. D 89 (2014) 095033 [arXiv:1403.1269] [INSPIRE].ADSGoogle Scholar
  20. [20]
    B. Gripaios, M. Nardecchia and S.A. Renner, Composite leptoquarks and anomalies in B-meson decays, JHEP 05 (2015) 006 [arXiv:1412.1791] [INSPIRE].CrossRefADSGoogle Scholar
  21. [21]
    A. Crivellin, G. D’Ambrosio and J. Heeck, Explaining hμ ± τ , BK μ + μ and B + μ /BKe + e in a two-Higgs-doublet model with gauged L μ -L τ, Phys. Rev. Lett. 114 (2015) 151801 [arXiv:1501.00993] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    A. Crivellin, G. D’Ambrosio and J. Heeck, Addressing the LHC flavor anomalies with horizontal gauge symmetries, Phys. Rev. D 91 (2015) 075006 [arXiv:1503.03477] [INSPIRE].ADSGoogle Scholar
  23. [23]
    D. Bečirević, S. Fajfer and N. Košnik, Lepton flavor nonuniversality in bsℓ + processes, Phys. Rev. D 92 (2015) 014016 [arXiv:1503.09024] [INSPIRE].ADSGoogle Scholar
  24. [24]
    C. Niehoff, P. Stangl and D.M. Straub, Violation of lepton flavour universality in composite Higgs models, Phys. Lett. B 747 (2015) 182 [arXiv:1503.03865] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    I. de Medeiros Varzielas and G. Hiller, Clues for flavor from rare lepton and quark decays, JHEP 06 (2015) 072 [arXiv:1503.01084] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    D. Aristizabal Sierra, F. Staub and A. Vicente, Shedding light on the bs anomalies with a dark sector, Phys. Rev. D 92 (2015) 015001 [arXiv:1503.06077] [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Celis, J. Fuentes-Martin, M. Jung and H. Serodio, Family nonuniversal Z models with protected flavor-changing interactions, Phys. Rev. D 92 (2015) 015007 [arXiv:1505.03079] [INSPIRE].ADSGoogle Scholar
  28. [28]
    S. Sahoo and R. Mohanta, Leptoquark effects on \( b\to s\nu \overline{\nu} \) and BKl + l decay processes, New J. Phys. 18 (2016) 013032 [arXiv:1509.06248] [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    G. Bélanger, C. Delaunay and S. Westhoff, A dark matter relic from muon anomalies, Phys. Rev. D 92 (2015) 055021 [arXiv:1507.06660] [INSPIRE].ADSGoogle Scholar
  30. [30]
    A. Falkowski, M. Nardecchia and R. Ziegler, Lepton flavor non-universality in B-meson decays from a U(2) flavor model, JHEP 11 (2015) 173 [arXiv:1509.01249] [INSPIRE].CrossRefADSGoogle Scholar
  31. [31]
    B. Grinstein and J. Martin Camalich, Weak decays of unstable b-mesons, Phys. Rev. Lett. 116 (2016) 141801 [arXiv:1509.05049] [INSPIRE].
  32. [32]
    B. Gripaios, M. Nardecchia and S.A. Renner, Linear flavour violation and anomalies in B physics, arXiv:1509.05020 [INSPIRE].
  33. [33]
    A. Carmona and F. Goertz, Lepton flavor and non-universality from minimal composite Higgs setups, arXiv:1510.07658 [INSPIRE].
  34. [34]
    M. Bauer and M. Neubert, One leptoquark to rule them all: a minimal explanation for R D(∗) , R K and (g − 2)μ, Phys. Rev. Lett. 116 (2016) 141802 [arXiv:1511.01900] [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    S. Fajfer and N. Košnik, Vector leptoquark resolution of R K and R D(∗) puzzles, Phys. Lett. B 755 (2016) 270 [arXiv:1511.06024] [INSPIRE].
  36. [36]
    A. Crivellin, C. Greub and A. Kokulu, Explaining BDτ ν, BD τ ν and Bτ ν in a 2HDM of type-III, Phys. Rev. D 86 (2012) 054014 [arXiv:1206.2634] [INSPIRE].ADSGoogle Scholar
  37. [37]
    A. Datta, M. Duraisamy and D. Ghosh, Diagnosing new physics in bcτ ν τ decays in the light of the recent BaBar result, Phys. Rev. D 86 (2012) 034027 [arXiv:1206.3760] [INSPIRE].ADSGoogle Scholar
  38. [38]
    A. Celis, M. Jung, X.-Q. Li and A. Pich, Sensitivity to charged scalars in BD (∗) τ ν τ and Bτν τ decays, JHEP 01 (2013) 054 [arXiv:1210.8443] [INSPIRE].
  39. [39]
    A. Crivellin, A. Kokulu and C. Greub, Flavor-phenomenology of two-Higgs-doublet models with generic Yukawa structure, Phys. Rev. D 87 (2013) 094031 [arXiv:1303.5877] [INSPIRE].ADSGoogle Scholar
  40. [40]
    X.-Q. Li, Y.-D. Yang and X.-B. Yuan, Exclusive radiative B-meson decays within minimal flavor-violating two-Higgs-doublet models, Phys. Rev. D 89 (2014) 054024 [arXiv:1311.2786] [INSPIRE].ADSGoogle Scholar
  41. [41]
    G. Faisel, Charged Higgs contribution to \( {\overline{B}}_s\to \phi {\pi}^0 \) and \( {\overline{B}}_s\to \phi {\rho}^0 \), Phys. Lett. B 731 (2014) 279 [arXiv:1311.0740] [INSPIRE].CrossRefADSGoogle Scholar
  42. [42]
    M. Atoui, V. Morénas, D. Bečirevic and F. Sanfilippo, B sD s ℓν near zero recoil in and beyond the standard model, Eur. Phys. J. C 74 (2014) 2861 [arXiv:1310.5238] [INSPIRE].CrossRefADSGoogle Scholar
  43. [43]
    Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, Testing leptoquark models in \( \overline{B}\to {D^{\Big(}}^{\ast \Big)}\tau \overline{\nu} \), Phys. Rev. D 88 (2013)094012 [arXiv:1309.0301] [INSPIRE].
  44. [44]
    I. Doršner, S. Fajfer, N. Košnik and I. Nišandžić, Minimally flavored colored scalar in \( \overline{B}\to {D^{\Big(}}^{\ast \Big)}\tau \overline{\nu} \) and the mass matrices constraints, JHEP 11(2013)084 [arXiv:1306.6493] [INSPIRE].
  45. [45]
    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
  46. [46]
    A. Crivellin, J. Heeck and P. Stoffer, A perturbed lepton-specific two-Higgs-doublet model facing experimental hints for physics beyond the standard model, Phys. Rev. Lett. 116 (2016) 081801 [arXiv:1507.07567] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    M. Freytsis, Z. Ligeti and J.T. Ruderman, Flavor models for \( \overline{B}\to {D^{\Big(}}^{\ast \Big)}\tau\ \overline{\nu} \), Phys. Rev. D 92 (2015) 054018 [arXiv:1506.08896] [INSPIRE].
  48. [48]
    G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].
  49. [49]
    A.J. Buras, Weak Hamiltonian, CP-violation and rare decays, in Probing the standard model of particle interactions. Proceedings, Summer School in Theoretical Physics, NATO Advanced Study Institute, 68th session, Les Houches France July 28-September 5 1997, pg. 281 [hep-ph/9806471] [INSPIRE].
  50. [50]
    A. Crivellin, S. Najjari and J. Rosiek, Lepton flavor violation in the standard model with general dimension-six operators, JHEP 04 (2014) 167 [arXiv:1312.0634] [INSPIRE].CrossRefADSGoogle Scholar
  51. [51]
    A. Crivellin, M. Hoferichter and M. Procura, Improved predictions for μe conversion in nuclei and Higgs-induced lepton flavor violation, Phys. Rev. D 89 (2014) 093024 [arXiv:1404.7134] [INSPIRE].ADSGoogle Scholar
  52. [52]
    G.M. Pruna and A. Signer, The μeγ decay in a systematic effective field theory approach with dimension 6 operators, JHEP 10 (2014) 014 [arXiv:1408.3565] [INSPIRE].CrossRefADSGoogle Scholar
  53. [53]
    B.M. Dassinger, T. Feldmann, T. Mannel and S. Turczyk, Model-independent analysis of lepton flavour violating τ decays, JHEP 10 (2007) 039 [arXiv:0707.0988] [INSPIRE].CrossRefADSGoogle Scholar
  54. [54]
    B. Bhattacharya, A. Datta, D. London and S. Shivashankara, Simultaneous explanation of the R K and R(D (∗)) puzzles, Phys. Lett. B 742 (2015) 370 [arXiv:1412.7164] [INSPIRE].CrossRefADSGoogle Scholar
  55. [55]
    R. Alonso, B. Grinstein and J. Martin Camalich, Lepton universality violation and lepton flavor conservation in B-meson decays, JHEP 10 (2015) 184 [arXiv:1505.05164] [INSPIRE].CrossRefADSGoogle Scholar
  56. [56]
    L. Calibbi, A. Crivellin and T. Ota, Effective field theory approach to bsℓℓ (′) , \( B\to {K^{\Big(}}^{\ast \Big)}\nu \overline{\nu} \) and BD (∗) τ ν with third generation couplings, Phys. Rev. Lett. 115 (2015) 181801 [arXiv:1506.02661] [INSPIRE].CrossRefADSGoogle Scholar
  57. [57]
    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].CrossRefADSGoogle Scholar
  58. [58]
    A.J. Buras, J. Girrbach-Noe, C. Niehoff and D.M. Straub, \( B\to {K^{\Big(}}^{\ast \Big)}\nu \overline{\nu} \) decays in the standard model and beyond, JHEP 02 (2015) 184 [arXiv:1409.4557] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  59. [59]
    M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective Hamiltonians, Nucl. Phys. B 523 (1998)501 [hep-ph/9711402] [INSPIRE].
  60. [60]
    A.J. Buras, M. Misiak and J. Urban, Two loop QCD anomalous dimensions of flavor changing four quark operators within and beyond the standard model, Nucl. Phys. B 586 (2000)397 [hep-ph/0005183] [INSPIRE].
  61. [61]
    F. Borzumati and C. Greub, 2HDMs predictions for \( \overline{B}\to {X}_s\gamma \) in NLO QCD, Phys. Rev. D 58 (1998) 074004 [hep-ph/9802391] [INSPIRE].
  62. [62]
    F. Borzumati, C. Greub, T. Hurth and D. Wyler, Gluino contribution to radiative B decays: organization of QCD corrections and leading order results, Phys. Rev. D 62 (2000) 075005 [hep-ph/9911245] [INSPIRE].
  63. [63]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators I: formalism and λ dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  64. [64]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators II: Yukawa dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].CrossRefADSGoogle Scholar
  65. [65]
    R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators III: gauge coupling dependence and phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].CrossRefADSGoogle Scholar
  66. [66]
    C. Bobeth and U. Haisch, Anomalous triple gauge couplings from B-meson and kaon observables, JHEP 09 (2015) 018 [arXiv:1503.04829] [INSPIRE].CrossRefGoogle Scholar
  67. [67]
    G. Blankenburg, J. Ellis and G. Isidori, Flavour-changing decays of a 125 GeV Higgs-like particle, Phys. Lett. B 712 (2012) 386 [arXiv:1202.5704] [INSPIRE].CrossRefADSGoogle Scholar
  68. [68]
    S. Davidson and P. Verdier, LHC sensitivity to the decay hτ ± mu , Phys. Rev. D 86 (2012) 111701 [arXiv:1211.1248] [INSPIRE].
  69. [69]
    D. Becirevic et al., \( {B}_d-{\overline{B}}_d \) mixing and the B dJ/ψK s asymmetry in general SUSY models, Nucl. Phys. B 634 (2002) 105 [hep-ph/0112303] [INSPIRE].
  70. [70]
    M.B. Voloshin, Bound on V + A admixture in the bc current from inclusive versus exclusive semileptonic decays of B mesons, Mod. Phys. Lett. A 12 (1997) 1823 [hep-ph/9704278] [INSPIRE].
  71. [71]
    B.M. Dassinger, R. Feger and T. Mannel, Testing the left-handedness of the bc transition, Phys. Rev. D 75 (2007) 095007 [hep-ph/0701054] [INSPIRE].
  72. [72]
    C.-H. Chen and S.-H. Nam, Left-right mixing on leptonic and semileptonic bu decays, Phys. Lett. B 666 (2008) 462 [arXiv:0807.0896] [INSPIRE].CrossRefADSGoogle Scholar
  73. [73]
    B. Dassinger, R. Feger and T. Mannel, Complete Michel parameter analysis of inclusive semileptonic bc transition, Phys. Rev. D 79 (2009) 075015 [arXiv:0803.3561] [INSPIRE].ADSGoogle Scholar
  74. [74]
    A. Crivellin, Effects of right-handed charged currents on the determinations of |V ub| and |V cb|, Phys. Rev. D 81 (2010) 031301 [arXiv:0907.2461] [INSPIRE].ADSGoogle Scholar
  75. [75]
    V. Cirigliano, J. Jenkins and M. Gonzalez-Alonso, Semileptonic decays of light quarks beyond the standard model, Nucl. Phys. B 830 (2010) 95 [arXiv:0908.1754] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  76. [76]
    X.-G. He, J. Tandean and G. Valencia, Probing new physics in charm couplings with FCNC, Phys. Rev. D 80 (2009) 035021 [arXiv:0904.2301] [INSPIRE].ADSGoogle Scholar
  77. [77]
    A.J. Buras, K. Gemmler and G. Isidori, Quark flavour mixing with right-handed currents: an effective theory approach, Nucl. Phys. B 843 (2011) 107 [arXiv:1007.1993] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  78. [78]
    R. Feger, T. Mannel, V. Klose, H. Lacker and T. Luck, Limit on a right-handed admixture to the weak bc current from semileptonic decays, Phys. Rev. D 82 (2010) 073002 [arXiv:1003.4022] [INSPIRE].ADSGoogle Scholar
  79. [79]
    A. Crivellin and S. Pokorski, Can the differences in the determinations of V ub and V cb be explained by new physics?, Phys. Rev. Lett. 114 (2015) 011802 [arXiv:1407.1320] [INSPIRE].CrossRefADSGoogle Scholar
  80. [80]
    F.U. Bernlochner, Z. Ligeti and S. Turczyk, New ways to search for right-handed current in \( B\to \rho \ell \overline{\nu} \) decay, Phys. Rev. D 90 (2014)094003 [arXiv:1408.2516] [INSPIRE].
  81. [81]
    J. Brod, A. Greljo, E. Stamou and P. Uttayarat, Probing anomalous \( t\overline{t}Z \) interactions with rare meson decays, JHEP 02 (2015) 141 [arXiv:1408.0792] [INSPIRE].CrossRefADSGoogle Scholar
  82. [82]
    B. Grzadkowski and M. Misiak, Anomalous W tb coupling effects in the weak radiative B-meson decay, Phys. Rev. D 78 (2008) 077501 [Erratum ibid. D 84 (2011) 059903] [arXiv:0802.1413] [INSPIRE].
  83. [83]
    J. Drobnak, S. Fajfer and J.F. Kamenik, Probing anomalous tW b interactions with rare B decays, Nucl. Phys. B 855 (2012) 82 [arXiv:1109.2357] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  84. [84]
    A. Crivellin and L. Mercolli, BX d γ and constraints on new physics, Phys. Rev. D 84 (2011) 114005 [arXiv:1106.5499] [INSPIRE].
  85. [85]
    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].CrossRefADSGoogle Scholar
  86. [86]
    M. Czakon, P. Fiedler, T. Huber, M. Misiak, T. Schutzmeier and M. Steinhauser, The (Q 7 , Q 1,2) contribution to \( \overline{B}\to {X}_s\gamma \) at O(α s2), JHEP 04 (2015) 168 [arXiv:1503.01791] [INSPIRE].CrossRefADSGoogle Scholar
  87. [87]
    P.L. Cho and M. Misiak, bsγ decay in SU(2)L × SU(2)R × U(1) extensions of the standard model, Phys. Rev. D 49 (1994) 5894 [hep-ph/9310332] [INSPIRE].
  88. [88]
    C. Bernardo et al., Studying the W tb vertex structure using recent LHC results, Phys. Rev. D 90 (2014)113007 [arXiv:1408.7063] [INSPIRE].
  89. [89]
    ATLAS collaboration, Search for anomalous couplings in the W tb vertex from the measurement of double differential angular decay rates of single top quarks produced in the t-channel with the ATLAS detector, JHEP 04 (2016) 023 [arXiv:1510.03764] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Jason Aebischer
    • 1
  • Andreas Crivellin
    • 2
  • Matteo Fael
    • 1
  • Christoph Greub
    • 1
  1. 1.Albert Einstein Center for Fundamental PhysicsInstitute for Theoretical Physics, University of BernBernSwitzerland
  2. 2.CERN, Theory DivisionGeneva 23Switzerland

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