Dimension-six electroweak top-loop effects in Higgs production and decay

  • Eleni Vryonidou
  • Cen ZhangEmail author
Open Access
Regular Article - Theoretical Physics


We study the next-to-leading order electroweak corrections to Higgs processes from dimension-six top-quark operators in the Standard Model Effective Field Theory approach. We consider the major production channels, including W H, ZH, and VBF production at the LHC, and ZH, VBF production at future lepton colliders, as well as the major decay channels including H → γγ, γZ, W lν, Zll, \( b\overline{b} \), μμ, ττ . The results show that within the current constraints, top-quark operators can shift the signal strength of the loop-induced processes, i.e. H → γγ, γZ, by factors of \( \sim \mathcal{O}(1)-\mathcal{O}(10) \), and that of the tree-level processes, i.e. all remaining production and decay channels, by ∼ 5 − 10% at the LHC, and up to ∼ 15% at future lepton colliders. This implies that essentially all Higgs channels have started to become sensitive to top-quark couplings, and in particular, Higgs observables at high luminosity LHC as well as future lepton colliders, even below the \( t\overline{t} \) threshold, will improve our knowledge of top-quark couplings. We derive the sensitivities of Higgs measurements to top-quark operators at the high luminosity LHC, using projections for both inclusive and differential measurements. We conclude that treating the dimension-six top-quark sector and the Higgs/electroweak sector separately may not continue to be a good strategy. A global analysis combining Higgs and top-quark measurements is desirable, and our calculation and implementation provide an automatic and realistic simulation tool for this purpose.


Heavy Quark Physics Higgs Physics Effective Field Theories Beyond Standard Model 


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.


  1. [1]
    S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C.N. Leung, S.T. Love and S. Rao, Low-energy manifestations of a new interaction scale: operator analysis, Z. Phys. C 31 (1986) 433 [INSPIRE].ADSGoogle Scholar
  4. [4]
    A. Buckley et al., Global fit of top quark effective theory to data, Phys. Rev. D 92 (2015) 091501 [arXiv:1506.08845] [INSPIRE].ADSGoogle Scholar
  5. [5]
    A. Buckley et al., Constraining top quark effective theory in the LHC run II era, JHEP 04 (2016) 015 [arXiv:1512.03360] [INSPIRE].ADSGoogle Scholar
  6. [6]
    V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Constraining the top-Higgs sector of the Standard Model effective field theory, Phys. Rev. D 94 (2016) 034031 [arXiv:1605.04311] [INSPIRE].ADSGoogle Scholar
  7. [7]
    M.P. Rosello and M. Vos, Constraints on four-fermion interactions from the tt charge asymmetry at hadron colliders, Eur. Phys. J. C 76 (2016) 200 [arXiv:1512.07542] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J. de Blas, M. Chala and J. Santiago, Renormalization group constraints on new top interactions from electroweak precision data, JHEP 09 (2015) 189 [arXiv:1507.00757] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S. Alioli, V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Right-handed charged currents in the era of the Large Hadron Collider, JHEP 05 (2017) 086 [arXiv:1703.04751] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    C. Bernardo et al., Studying the W tb vertex structure using recent LHC results, Phys. Rev. D 90 (2014) 113007 [arXiv:1408.7063] [INSPIRE].ADSGoogle Scholar
  11. [11]
    A. Tonero and R. Rosenfeld, Dipole-induced anomalous top quark couplings at the LHC, Phys. Rev. D 90 (2014) 017701 [arXiv:1404.2581] [INSPIRE].ADSGoogle Scholar
  12. [12]
    Q.-H. Cao, B. Yan, J.-H. Yu and C. Zhang, A general analysis of W tb anomalous couplings, Chin. Phys. C 41 (2017) 063101 [arXiv:1504.03785] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Jung, P. Ko, Y.W. Yoon and C. Yu, Renormalization group-induced phenomena of top pairs from four-quark effective operators, JHEP 08 (2014) 120 [arXiv:1406.4570] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Zhang, N. Greiner and S. Willenbrock, Constraints on non-standard top quark couplings, Phys. Rev. D 86 (2012) 014024 [arXiv:1201.6670] [INSPIRE].ADSGoogle Scholar
  15. [15]
    N. Greiner, S. Willenbrock and C. Zhang, Effective field theory for nonstandard top quark couplings, Phys. Lett. B 704 (2011) 218 [arXiv:1104.3122] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    T. Corbett, O.J.P. Eboli, J. Gonzalez-Fraile and M.C. Gonzalez-Garcia, Robust determination of the Higgs couplings: power to the data, Phys. Rev. D 87 (2013) 015022 [arXiv:1211.4580] [INSPIRE].ADSGoogle Scholar
  17. [17]
    A. Butter, O.J.P. Éboli, J. Gonzalez-Fraile, M.C. Gonzalez-Garcia, T. Plehn and M. Rauch, The gauge-Higgs legacy of the LHC run I, JHEP 07 (2016) 152 [arXiv:1604.03105] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    C. Englert, R. Kogler, H. Schulz and M. Spannowsky, Higgs coupling measurements at the LHC, Eur. Phys. J. C 76 (2016) 393 [arXiv:1511.05170] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Falkowski, M. Gonzalez-Alonso, A. Greljo and D. Marzocca, Global constraints on anomalous triple gauge couplings in effective field theory approach, Phys. Rev. Lett. 116 (2016) 011801 [arXiv:1508.00581] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    A. Falkowski and F. Riva, Model-independent precision constraints on dimension-6 operators, JHEP 02 (2015) 039 [arXiv:1411.0669] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J. Ellis, V. Sanz and T. You, Complete Higgs sector constraints on dimension-6 operators, JHEP 07 (2014) 036 [arXiv:1404.3667] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    J. Ellis, V. Sanz and T. You, The effective Standard Model after LHC run I, JHEP 03 (2015) 157 [arXiv:1410.7703] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    J. Ellis, C.W. Murphy, V. Sanz and T. You, Updated global SMEFT fit to Higgs, diboson and electroweak data, JHEP 06 (2018) 146 [arXiv:1803.03252] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    C. Degrande, J.M. Gerard, C. Grojean, F. Maltoni and G. Servant, Probing top-Higgs non-standard interactions at the LHC, JHEP 07 (2012) 036 [Erratum ibid. 03 (2013) 032] [arXiv:1205.1065] [INSPIRE].
  25. [25]
    N. Deutschmann, C. Duhr, F. Maltoni and E. Vryonidou, Gluon-fusion Higgs production in the Standard Model effective field theory, JHEP 12 (2017) 063 [Erratum ibid. 02 (2018) 159] [arXiv:1708.00460] [INSPIRE].
  26. [26]
    O. Bessidskaia Bylund, F. Maltoni, I. Tsinikos, E. Vryonidou and C. Zhang, Probing top quark neutral couplings in the Standard Model effective field theory at NLO in QCD, JHEP 05 (2016) 052 [arXiv:1601.08193] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C. Englert, R. Rosenfeld, M. Spannowsky and A. Tonero, New physics and signal-background interference in associated ppHZ production, EPL 114 (2016) 31001 [arXiv:1603.05304] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    F. Maltoni, E. Vryonidou and C. Zhang, Higgs production in association with a top-antitop pair in the Standard Model effective field theory at NLO in QCD, JHEP 10 (2016) 123 [arXiv:1607.05330] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    C. Hartmann and M. Trott, On one-loop corrections in the Standard Model effective field theory; the Γ(hγ γ) case, JHEP 07 (2015) 151 [arXiv:1505.02646] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    C. Hartmann and M. Trott, Higgs decay to two photons at one loop in the Standard Model effective field theory, Phys. Rev. Lett. 115 (2015) 191801 [arXiv:1507.03568] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Ghezzi, R. Gomez-Ambrosio, G. Passarino and S. Uccirati, NLO Higgs effective field theory and κ-framework, JHEP 07 (2015) 175 [arXiv:1505.03706] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S. Dawson and P.P. Giardino, Higgs decays to ZZ and Zγ in the Standard Model effective field theory: an NLO analysis, Phys. Rev. D 97 (2018) 093003 [arXiv:1801.01136] [INSPIRE].ADSGoogle Scholar
  33. [33]
    R. Gauld, B.D. Pecjak and D.J. Scott, One-loop corrections to \( h\to b\overline{b} \) and \( h\to \tau \overline{\tau} \) decays in the Standard Model dimension-6 EFT: four-fermion operators and the large-m t limit, JHEP 05 (2016) 080 [arXiv:1512.02508] [INSPIRE].
  34. [34]
    K. Mimasu, V. Sanz and C. Williams, Higher order QCD predictions for associated Higgs production with anomalous couplings to gauge bosons, JHEP 08 (2016) 039 [arXiv:1512.02572] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    C. Degrande, B. Fuks, K. Mawatari, K. Mimasu and V. Sanz, Electroweak Higgs boson production in the Standard Model effective field theory beyond leading order in QCD, Eur. Phys. J. C 77 (2017) 262 [arXiv:1609.04833] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    C. Zhang, Automating predictions for Standard Model effective field theory in MadGraph5 aMC@NLO, PoS(RADCOR2015)101 [arXiv:1601.03994] [INSPIRE].
  38. [38]
    C. Degrande, F. Maltoni, J. Wang and C. Zhang, Automatic computations at next-to-leading order in QCD for top-quark flavor-changing neutral processes, Phys. Rev. D 91 (2015) 034024 [arXiv:1412.5594] [INSPIRE].ADSGoogle Scholar
  39. [39]
    D. Buarque Franzosi and C. Zhang, Probing the top-quark chromomagnetic dipole moment at next-to-leading order in QCD, Phys. Rev. D 91 (2015) 114010 [arXiv:1503.08841] [INSPIRE].ADSGoogle Scholar
  40. [40]
    C. Zhang, Single top production at next-to-leading order in the Standard Model effective field theory, Phys. Rev. Lett. 116 (2016) 162002 [arXiv:1601.06163] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    C. Degrande, F. Maltoni, K. Mimasu, E. Vryonidou and C. Zhang, Single-top associated production with a Z or H boson at the LHC: the SMEFT interpretation, submitted to JHEP (2018) [arXiv:1804.07773] [INSPIRE].
  42. [42]
    M. McCullough, An indirect model-dependent probe of the Higgs self-coupling, Phys. Rev. D 90 (2014) 015001 [Erratum ibid. D 92 (2015) 039903] [arXiv:1312.3322] [INSPIRE].
  43. [43]
    M. Gorbahn and U. Haisch, Indirect probes of the trilinear Higgs coupling: ggh and hγγ, JHEP 10 (2016) 094 [arXiv:1607.03773] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    G. Degrassi, P.P. Giardino, F. Maltoni and D. Pagani, Probing the Higgs self coupling via single Higgs production at the LHC, JHEP 12 (2016) 080 [arXiv:1607.04251] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    W. Bizon, M. Gorbahn, U. Haisch and G. Zanderighi, Constraints on the trilinear Higgs coupling from vector boson fusion and associated Higgs production at the LHC, JHEP 07 (2017) 083 [arXiv:1610.05771] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    S. Di Vita, C. Grojean, G. Panico, M. Riembau and T. Vantalon, A global view on the Higgs self-coupling, JHEP 09 (2017) 069 [arXiv:1704.01953] [INSPIRE].CrossRefGoogle Scholar
  47. [47]
    CEPC-SPPC Study Group collaboration, CEPC-SPPC preliminary conceptual design report. 1. Physics and detector, tech. rep. IHEP-CEPC-DR-2015-01, (2015) [IHEP-TH-2015-01] [IHEP-EP-2015-01] [INSPIRE].
  48. [48]
    TLEP Design Study Working Group collaboration, M. Bicer et al., First look at the physics case of TLEP, JHEP 01 (2014) 164 [arXiv:1308.6176] [INSPIRE].
  49. [49]
    H. Baer et al., The International Linear Collider technical design report — volume 2: physics, arXiv:1306.6352 [INSPIRE].
  50. [50]
    CLICdp and CLIC collaborations, M.J. Boland et al., Updated baseline for a staged Compact Linear Collider, arXiv:1608.07537 [INSPIRE].
  51. [51]
    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].ADSCrossRefzbMATHGoogle Scholar
  52. [52]
    Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  53. [53]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    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].ADSCrossRefGoogle Scholar
  55. [55]
    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].ADSCrossRefGoogle Scholar
  56. [56]
    J.D. Wells and Z. Zhang, Effective theories of universal theories, JHEP 01 (2016) 123 [arXiv:1510.08462] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    K. Hagiwara, S. Ishihara, R. Szalapski and D. Zeppenfeld, Low-energy effects of new interactions in the electroweak boson sector, Phys. Rev. D 48 (1993) 2182 [INSPIRE].ADSGoogle Scholar
  58. [58]
    C. Grojean, W. Skiba and J. Terning, Disguising the oblique parameters, Phys. Rev. D 73 (2006) 075008 [hep-ph/0602154] [INSPIRE].
  59. [59]
    I. Brivio and M. Trott, Scheming in the SMEFT. . . And a reparameterization invariance!, JHEP 07 (2017) 148 [arXiv:1701.06424] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 — a complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
  61. [61]
    O. Mattelaer, On the maximal use of Monte Carlo samples: re-weighting events at NLO accuracy, Eur. Phys. J. C 76 (2016) 674 [arXiv:1607.00763] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek and K. Suxho, Feynman rules for the Standard Model effective field theory in R ξ -gauges, JHEP 06 (2017) 143 [arXiv:1704.03888] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
  64. [64]
    R. Mertig, M. Böhm and A. Denner, FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    V. Shtabovenko, R. Mertig and F. Orellana, New developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
  66. [66]
    D. Kreimer, The γ 5 problem and anomalies: a Clifford algebra approach, Phys. Lett. B 237 (1990) 59 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    J.G. Korner, D. Kreimer and K. Schilcher, A practicable γ 5 scheme in dimensional regularization, Z. Phys. C 54 (1992) 503 [INSPIRE].ADSGoogle Scholar
  68. [68]
    D. Kreimer, The role of γ 5 in dimensional regularization, hep-ph/9401354 [INSPIRE].
  69. [69]
    H.-S. Shao, Y.-J. Zhang and K.-T. Chao, Feynman rules for the rational part of the Standard Model one-loop amplitudes in the ’t Hooft-Veltman γ 5 scheme, JHEP 09 (2011) 048 [arXiv:1106.5030] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  70. [70]
    T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].
  71. [71]
    A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].ADSGoogle Scholar
  72. [72]
    M. Ruan, Status & updates from CEPC simulation — detector optimization, in Presentation at the High Energy Physics Conference, 201701hep/HEP_20170124_Manqi_Ruan.pdf, IAS HKUST, Hong Kong, 24 January 2017.
  73. [73]
    A. Blondel, Summary FCC-ee experiments, in Presentation at the FCC week, 99-Blondel-FCC-ee-summary-Berlin.pdf, Berlin, Germany, 2 June 2017.
  74. [74]
    K. Fujii et al., Physics case for the International Linear Collider, arXiv:1506.05992 [INSPIRE].
  75. [75]
    T. Barklow et al., ILC operating scenarios, arXiv:1506.07830 [INSPIRE].
  76. [76]
    G. Durieux, Precision constraints on the top-quark effective field theory at future lepton colliders, PoS(DIS2017)088 [arXiv:1708.09849] [INSPIRE].
  77. [77]
    G. Durieux, M. Perelló, M. Vos and C. Zhang, Global and optimal probes for the top-quark effective field theory at future lepton colliders, arXiv:1807.02121 [INSPIRE].
  78. [78]
    Y. Jiang and M. Trott, On the non-minimal character of the SMEFT, Phys. Lett. B 770 (2017)108 [arXiv:1612.02040] [INSPIRE].
  79. [79]
    CMS collaboration, Search for the associated production of a Higgs boson with a top quark pair in final states with a τ lepton at \( \sqrt{s}=13 \) TeV, CMS-PAS-HIG-17-003, CERN, Geneva, Switzerland, (2017).
  80. [80]
    CMS collaboration, Search for Higgs boson production in association with top quarks in multilepton final states at \( \sqrt{s}=13 \) TeV, CMS-PAS-HIG-17-004, CERN, Geneva, Switzerland, (2017).
  81. [81]
    ATLAS collaboration, Evidence for the associated production of the Higgs boson and a top quark pair with the ATLAS detector, Phys. Rev. D 97 (2018) 072003 [arXiv:1712.08891] [INSPIRE].
  82. [82]
    ATLAS collaboration, Search for the Standard Model Higgs boson produced in association with top quarks and decaying into a \( b\overline{b} \) pair in pp collisions at \( \sqrt{s}=13 \) TeV with the ATLAS detector, Phys. Rev. D 97 (2018) 072016 [arXiv:1712.08895] [INSPIRE].
  83. [83]
    F. Maltoni, D. Pagani, A. Shivaji and X. Zhao, Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC, Eur. Phys. J. C 77 (2017) 887 [arXiv:1709.08649] [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    ATLAS collaboration, Prospects for the study of the Higgs boson in the V H(bb) channel at HL-LHC, ATL-PHYS-PUB-2014-011, CERN, Geneva, Switzerland, (2014).
  85. [85]
    ATLAS collaboration, Update of the prospects for the HZγ search at the High-Luminosity LHC, ATL-PHYS-PUB-2014-006, CERN, Geneva, Switzerland, (2014).
  86. [86]
    G. Durieux, C. Grojean, J. Gu and K. Wang, The leptonic future of the Higgs, JHEP 09 (2017) 014 [arXiv:1704.02333] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.CERN, Theoretical Physics DepartmentGeneva 23Switzerland
  2. 2.Institute of High Energy Physics and School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingP.R. China

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