The Higgs width in the SMEFT

  • Ilaria BrivioEmail author
  • Tyler Corbett
  • Michael Trott
Open Access
Regular Article - Theoretical Physics


We calculate the total and partial inclusive Higgs widths at leading order in the Standard Model Effective Field Theory (SMEFT). We report results incorporating SMEFT corrections for two and four body Higgs decays through vector currents in this limit. The narrow width approximation is avoided and all phase space integrals are directly evaluated. We explain why the narrow width approximation fails more significantly in the SMEFT compared to the SM, despite the narrowness of the observed SU(2) × U(1) bosons in both theories. Our results are presented in a manner that allows various input parameter schemes to be used, and they allow the inclusive branching ratios and decay widths of the Higgs to be numerically determined without a Monte Carlo generation of phase space for each Wilson coefficient value chosen.


Effective Field Theories Higgs Physics Precision QED 


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]
    I. Brivio and M. Trott, The Standard Model as an effective field theory, Phys. Rept.793 (2019) 1 [arXiv:1706.08945] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  3. [3]
    J.A. Aguilar-Saavedra, Effective four-fermion operators in top physics: a roadmap, Nucl. Phys.B 843 (2011) 638 [Erratum ibid.B 851 (2011) 443] [arXiv:1008.3562] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  4. [4]
    R. Alonso, H.-M. Chang, E.E. Jenkins, A.V. Manohar and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett.B 734 (2014) 302 [arXiv:1405.0486] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys.B 268 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    CMS collaboration, Measurements of the Higgs boson width and anomalous H V V couplings from on-shell and off-shell production in the four-lepton final state, Phys. Rev.D 99 (2019) 112003 [arXiv:1901.00174] [INSPIRE].ADSGoogle Scholar
  7. [7]
    A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber, Precise predictions for the Higgs-boson decay H → WW/ZZ → 4 leptons, Phys. Rev.D 74 (2006) 013004 [hep-ph/0604011] [INSPIRE].ADSGoogle Scholar
  8. [8]
    N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson signal, JHEP08 (2012) 116 [arXiv:1206.4803] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ production at the LHC, Phys. Rev.D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].ADSGoogle Scholar
  10. [10]
    J.M. Campbell, R.K. Ellis and C. Williams, Bounding the Higgs width at the LHC using full analytic results for gg → e e +μ μ +, JHEP04 (2014) 060 [arXiv:1311.3589] [INSPIRE].
  11. [11]
    S.L. Glashow, Partial-symmetries of weak interactions, Nucl. Phys.22 (1961) 579 [INSPIRE].CrossRefGoogle Scholar
  12. [12]
    S. Weinberg, A model of leptons, Phys. Rev. Lett.19 (1967) 1264 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Salam, Weak and electromagnetic interactions, Conf. Proc.C 680519 (1968) 367 [INSPIRE].Google Scholar
  14. [14]
    B. Grinstein and M.B. Wise, Operator analysis for precision electroweak physics, Phys. Lett.B 265 (1991) 326 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    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, JHEP04 (2014) 159 [arXiv:1312.2014] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    L. Berthier and M. Trott, Towards consistent electroweak precision data constraints in the SMEFT, JHEP05 (2015) 024 [arXiv:1502.02570] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    L. Berthier and M. Trott, Consistent constraints on the Standard Model effective field theory, JHEP02 (2016) 069 [arXiv:1508.05060] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    M. Bjørn and M. Trott, Interpreting W mass measurements in the SMEFT, Phys. Lett.B 762 (2016) 426 [arXiv:1606.06502] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    L. Berthier, M. Bjørn and M. Trott, Incorporating doubly resonant W ±data in a global fit of SMEFT parameters to lift flat directions, JHEP09 (2016) 157 [arXiv:1606.06693] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    I. Brivio and M. Trott, Scheming in the SMEFT... And a reparameterization invariance!, JHEP07 (2017) 148 [Addendum ibid.05 (2018) 136] [arXiv:1701.06424] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools, JHEP12 (2017) 070 [arXiv:1709.06492] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    C. Hays, A. Martin, V. Sanz and J. Setford, On the impact of dimension-eight SMEFT operators on Higgs measurements, JHEP02 (2019) 123 [arXiv:1808.00442] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    S. Descotes-Genon, A. Falkowski, M. Fedele, M. Gonzáalez-Alonso and J. Virto, The CKM parameters in the SMEFT, JHEP05 (2019) 172 [arXiv:1812.08163] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    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].ADSzbMATHCrossRefGoogle Scholar
  25. [25]
    J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, A phenomenological profile of the Higgs boson, Nucl. Phys.B 106 (1976) 292 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-energy theorems for Higgs boson couplings to photons, Sov. J. Nucl. Phys.30 (1979) 711 [Yad. Fiz.30 (1979) 1368] [INSPIRE].Google Scholar
  27. [27]
    L. Bergstrom and G. Hulth, Induced Higgs couplings to neutral bosons in e +e collisions, Nucl. Phys.B 259 (1985) 137 [Erratum ibid.B 276 (1986) 744] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    C. Hartmann and M. Trott, On one-loop corrections in the Standard Model effective field theory; the Γ(h → γ γ) case, JHEP07 (2015) 151 [arXiv:1505.02646] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M. Ghezzi, R. Gomez-Ambrosio, G. Passarino and S. Uccirati, NLO Higgs effective field theory and κ-framework, JHEP07 (2015) 175 [arXiv:1505.03706] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle 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]
    A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho and L. Trifyllis, The decay h → γγ in the Standard-Model effective field theory, JHEP08 (2018) 103 [arXiv:1805.00302] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Dawson and P.P. Giardino, Electroweak corrections to Higgs boson decays to γγ and W +W in Standard Model EFT, Phys. Rev.D 98 (2018) 095005 [arXiv:1807.11504] [INSPIRE].ADSGoogle Scholar
  33. [33]
    H.M. Georgi, S.L. Glashow, M.E. Machacek and D.V. Nanopoulos, Higgs bosons from two gluon annihilation in proton proton collisions, Phys. Rev. Lett.40 (1978) 692 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    J.R. Ellis, M.K. Gaillard, D.V. Nanopoulos and C.T. Sachrajda, Is the mass of the Higgs boson about 10 GeV?, Phys. Lett.B 83 (1979) 339 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    A.V. Manohar and M.B. Wise, Modifications to the properties of the Higgs boson, Phys. Lett.B 636 (2006) 107 [hep-ph/0601212] [INSPIRE].
  36. [36]
    B.A. Kniehl, The Higgs boson decay H → Zgg, Phys. Lett.B 244 (1990) 537 [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    R.N. Cahn, The Higgs boson, Rept. Prog. Phys.52 (1989) 389 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Grau, G. Panchieri and R.J.N. Phillips, Contributions of off-shell top quarks to decay processes, Phys. Lett.B 251 (1990) 293 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    E. Gross, G. Wolf and B.A. Kniehl, Production and decay of the Standard Model Higgs boson LEP-200, Z. Phys.C 63 (1994) 417 [Erratum ibid.C 66 (1995) 321] [hep-ph/9404220] [INSPIRE].ADSGoogle Scholar
  40. [40]
    A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber, Radiative corrections to the semileptonic and hadronic Higgs-boson decays H → WW/ZZ → 4 fermions, JHEP02 (2007) 080 [hep-ph/0611234] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    LHC Higgs Cross Section Working Group collaboration, LHC HXSWG interim recommendations to explore the coupling structure of a Higgs-like particle, arXiv:1209.0040 [INSPIRE].
  42. [42]
    D. Zeppenfeld, R. Kinnunen, A. Nikitenko and E. Richter-Was, Measuring Higgs boson couplings at the CERN LHC, Phys. Rev.D 62 (2000) 013009 [hep-ph/0002036] [INSPIRE].ADSGoogle Scholar
  43. [43]
    M. Dührssen, Prospects for the measurement of Higgs boson coupling parameters in the mass range from 110190 GeV, ATL-PHYS-2003-030, CERN, Geneva, Switzerland (2003) [INSPIRE].
  44. [44]
    M. Dührssen, S. Heinemeyer, H. Logan, D. Rainwater, G. Weiglein and D. Zeppenfeld, Extracting Higgs boson couplings from CERN LHC data, Phys. Rev.D 70 (2004) 113009 [hep-ph/0406323] [INSPIRE].ADSGoogle Scholar
  45. [45]
    R. Lafaye, T. Plehn, M. Rauch, D. Zerwas and M. Dührssen, Measuring the Higgs sector, JHEP08 (2009) 009 [arXiv:0904.3866] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    J.R. Espinosa, C. Grojean, M. Muhlleitner and M. Trott, Fingerprinting Higgs suspects at the LHC, JHEP05 (2012) 097 [arXiv:1202.3697] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    D. Carmi, A. Falkowski, E. Kuflik and T. Volansky, Interpreting LHC Higgs results from natural new physics perspective, JHEP07 (2012) 136 [arXiv:1202.3144] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    A. Azatov, R. Contino and J. Galloway, Model-independent bounds on a light Higgs, JHEP04 (2012) 127 [Erratum ibid.04 (2013) 140] [arXiv:1202.3415] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    T. Hahn, CUBA: a library for multidimensional numerical integration, Comput. Phys. Commun.168 (2005) 78 [hep-ph/0404043] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  50. [50]
    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, JHEP07 (2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    R. Kleiss, W.J. Stirling and S.D. Ellis, A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun.40 (1986) 359 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    E.E. Jenkins, A.V. Manohar and M. Trott, On gauge invariance and minimal coupling, JHEP09 (2013) 063 [arXiv:1305.0017] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922 [INSPIRE].
  54. [54]
    LHC Higgs Cross Section Working Group collaboration, SM Higgs branching ratios and total decay widths,, (2016).
  55. [55]
    A. Bredenstein, A. Denner, S. Dittmaier and M.M. Weber, Precision calculations for the Higgs decays H → ZZ/WW → 4 leptons, Nucl. Phys. Proc. Suppl.160 (2006) 131 [hep-ph/0607060] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    CDF, D0 collaboration, Combination of CDF and D0 W -boson mass measurements, Phys. Rev.D 88 (2013) 052018 [arXiv:1307.7627] [INSPIRE].Google Scholar
  57. [57]
    Particle Data Group collaboration, Review of particle physics, Chin. Phys.C 40 (2016) 100001 [INSPIRE].ADSGoogle Scholar
  58. [58]
    ALEPH, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, SLD Electroweak Group and SLD Heavy Flavour Group collaborations, Precision electroweak measurements on the Z resonance, Phys. Rept.427 (2006) 257 [hep-ex/0509008] [INSPIRE].ADSGoogle Scholar
  59. [59]
    P.J. Mohr, B.N. Taylor and D.B. Newell, CODATA recommended values of the fundamental physical constants: 2010, Rev. Mod. Phys.84 (2012) 1527 [arXiv:1203.5425] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    ATLAS and CMS collaborations, Combined measurement of the Higgs boson mass in pp collisions at \( \sqrt{s}=7 \)and 8 TeV with the ATLAS and CMS experiments, Phys. Rev. Lett.114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    E. Byckling and K. Kajantie, Particle kinematics, University of Jyvaskyla, Jyvaskyla, Finland (1971) [INSPIRE].Google Scholar
  62. [62]
    N. Byers and C.N. Yang, Physical regions in invariant variables for n particles and the phase-space volume element, Rev. Mod. Phys.36 (1964) 595 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Niels Bohr Institute & Discovery CenterUniversity of CopenhagenCopenhagenDenmark
  2. 2.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany

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