NLO electroweak corrections in extended Higgs sectors with RECOLA2

  • Ansgar Denner
  • Jean-Nicolas Lang
  • Sandro Uccirati
Open Access
Regular Article - Theoretical Physics


We present the computer code RECOLA2 along with the first NLO electroweak corrections to Higgs production in vector-boson fusion and updated results for Higgs strahlung in the Two-Higgs-Doublet Model and Higgs-Singlet extension of the Standard Model. A fully automated procedure for the generation of tree-level and one-loop matrix elements in general models, including renormalization, is presented. We discuss the application of the Background-Field Method to the extended models. Numerical results for NLO electroweak cross sections are presented for different renormalization schemes in the Two-Higgs-Doublet Model and the Higgs-Singlet extension of the Standard Model. Finally, we present distributions for the production of a heavy Higgs boson.


NLO Computations Phenomenological Models 


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]
    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].
  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]
    S. Kallweit, J.M. Lindert, P. Maierhöfer, S. Pozzorini and M. Schönherr, NLO electroweak automation and precise predictions for W +multijet production at the LHC, JHEP 04 (2015) 012 [arXiv:1412.5157] [INSPIRE].CrossRefGoogle Scholar
  4. [4]
    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].CrossRefADSGoogle Scholar
  5. [5]
    G. Cullen et al., GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond, Eur. Phys. J. C 74 (2014) 3001 [arXiv:1404.7096] [INSPIRE].
  6. [6]
    M. Chiesa, N. Greiner and F. Tramontano, Automation of electroweak corrections for LHC processes, J. Phys. G 43 (2016) 013002 [arXiv:1507.08579] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
  8. [8]
    C. Groß, T. Hahn, S. Heinemeyer, F. von der Pahlen, H. Rzehak and C. Schappacher, New developments in FormCalc 8.4, arXiv:1407.0235 [INSPIRE].
  9. [9]
    S. Actis, A. Denner, L. Hofer, A. Scharf and S. Uccirati, Recursive generation of one-loop amplitudes in the Standard Model, JHEP 04 (2013) 037 [arXiv:1211.6316] [INSPIRE].CrossRefADSGoogle Scholar
  10. [10]
    S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf and S. Uccirati, RECOLA: REcursive Computation of One-Loop Amplitudes, Comput. Phys. Commun. 214 (2017) 140 [arXiv:1605.01090] [INSPIRE].CrossRefADSGoogle Scholar
  11. [11]
    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].
  12. [12]
    F. Staub, SARAH 4: a tool for (not only SUSY) model builders, Comput. Phys. Commun. 185 (2014) 1773 [arXiv:1309.7223] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  13. [13]
    C. Degrande, Automatic evaluation of UV and R 2 terms for beyond the Standard Model Lagrangians: a proof-of-principle, Comput. Phys. Commun. 197 (2015) 239 [arXiv:1406.3030] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  14. [14]
    C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer and T. Reiter, UFO — the Universal FeynRules Output, Comput. Phys. Commun. 183 (2012) 1201 [arXiv:1108.2040] [INSPIRE].CrossRefADSGoogle Scholar
  15. [15]
    R. Hamberg, W.L. van Neerven and T. Matsuura, A complete calculation of the order α s correction to the Drell-Yan K factor, Nucl. Phys. B 359 (1991) 343 [Erratum ibid. B 644 (2002) 403] [INSPIRE].
  16. [16]
    O. Brein, A. Djouadi and R. Harlander, NNLO QCD corrections to the Higgs-strahlung processes at hadron colliders, Phys. Lett. B 579 (2004) 149 [hep-ph/0307206] [INSPIRE].
  17. [17]
    O. Brein, R. Harlander, M. Wiesemann and T. Zirke, Top-quark mediated effects in hadronic Higgs-strahlung, Eur. Phys. J. C 72 (2012) 1868 [arXiv:1111.0761] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    G. Ferrera, M. Grazzini and F. Tramontano, Associated W H production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107 (2011) 152003 [arXiv:1107.1164] [INSPIRE].CrossRefADSGoogle Scholar
  19. [19]
    G. Ferrera, M. Grazzini and F. Tramontano, Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, Phys. Lett. B 740 (2015) 51 [arXiv:1407.4747] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    M.L. Ciccolini, S. Dittmaier and M. Krämer, Electroweak radiative corrections to associated WH and ZH production at hadron colliders, Phys. Rev. D 68 (2003) 073003 [hep-ph/0306234] [INSPIRE].
  21. [21]
    A. Denner, S. Dittmaier, S. Kallweit and A. Mück, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, JHEP 03 (2012) 075 [arXiv:1112.5142] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  22. [22]
    R.V. Harlander, S. Liebler and T. Zirke, Higgs strahlung at the Large Hadron Collider in the 2-Higgs-doublet model, JHEP 02 (2014) 023 [arXiv:1307.8122] [INSPIRE].CrossRefADSGoogle Scholar
  23. [23]
    A. Denner, L. Jenniches, J.-N. Lang and C. Sturm, Gauge-independent \( \overline{M\ S} \) renormalization in the 2HDM, JHEP 09 (2016) 115 [arXiv:1607.07352] [INSPIRE].
  24. [24]
    F. Maltoni, K. Mawatari and M. Zaro, Higgs characterisation via vector-boson fusion and associated production: NLO and parton-shower effects, Eur. Phys. J. C 74 (2014) 2710 [arXiv:1311.1829] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    T. Han, G. Valencia and S. Willenbrock, Structure function approach to vector boson scattering in pp collisions, Phys. Rev. Lett. 69 (1992) 3274 [hep-ph/9206246] [INSPIRE].
  26. [26]
    P. Bolzoni, F. Maltoni, S.-O. Moch and M. Zaro, Higgs production via vector-boson fusion at NNLO in QCD, Phys. Rev. Lett. 105 (2010) 011801 [arXiv:1003.4451] [INSPIRE].CrossRefADSGoogle Scholar
  27. [27]
    P. Bolzoni, F. Maltoni, S.-O. Moch and M. Zaro, Vector boson fusion at NNLO in QCD: SM Higgs and beyond, Phys. Rev. D 85 (2012) 035002 [arXiv:1109.3717] [INSPIRE].ADSGoogle Scholar
  28. [28]
    T. Figy, C. Oleari and D. Zeppenfeld, Next-to-leading order jet distributions for Higgs boson production via weak boson fusion, Phys. Rev. D 68 (2003) 073005 [hep-ph/0306109] [INSPIRE].
  29. [29]
    M. Ciccolini, A. Denner and S. Dittmaier, Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC, Phys. Rev. D 77 (2008) 013002 [arXiv:0710.4749] [INSPIRE].ADSGoogle Scholar
  30. [30]
    M. Ciccolini, A. Denner and S. Dittmaier, Strong and electroweak corrections to the production of Higgs + 2 jets via weak interactions at the LHC, Phys. Rev. Lett. 99 (2007) 161803 [arXiv:0707.0381] [INSPIRE].CrossRefADSGoogle Scholar
  31. [31]
    M. Cacciari, F.A. Dreyer, A. Karlberg, G.P. Salam and G. Zanderighi, Fully differential vector-boson-fusion Higgs production at next-to-next-to-leading order, Phys. Rev. Lett. 115 (2015) 082002 [arXiv:1506.02660] [INSPIRE].CrossRefADSGoogle Scholar
  32. [32]
    F.A. Dreyer and A. Karlberg, Vector-boson fusion Higgs production at three loops in QCD, Phys. Rev. Lett. 117 (2016) 072001 [arXiv:1606.00840] [INSPIRE].CrossRefADSGoogle Scholar
  33. [33]
    S. Frixione, P. Torrielli and M. Zaro, Higgs production through vector-boson fusion at the NLO matched with parton showers, Phys. Lett. B 726 (2013) 273 [arXiv:1304.7927] [INSPIRE].CrossRefADSGoogle Scholar
  34. [34]
    M. Rauch and S. Plätzer, Parton-shower effects in vector-boson-fusion processes, PoS(DIS2016)076 [arXiv:1607.00159] [INSPIRE].
  35. [35]
    D. Goncalves, T. Plehn and J.M. Thompson, Weak boson fusion at 100 TeV, Phys. Rev. D 95 (2017) 095011 [arXiv:1702.05098] [INSPIRE].ADSGoogle Scholar
  36. [36]
    T. Figy, S. Palmer and G. Weiglein, Higgs production via weak boson fusion in the Standard Model and the MSSM, JHEP 02 (2012) 105 [arXiv:1012.4789] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  37. [37]
  38. [38]
    J. Campbell, K. Ellis and C. Williams, MCFM — Monte Carlo for FeMtobarn processes,
  39. [39]
    A. Denner, S. Dittmaier, S. Kallweit and A. Mück, HAWK 2.0: a Monte Carlo program for Higgs production in vector-boson fusion and Higgs strahlung at hadron colliders, Comput. Phys. Commun. 195 (2015) 161 [arXiv:1412.5390] [INSPIRE].
  40. [40]
    O. Brein, R.V. Harlander and T.J.E. Zirke, vh@nnlo — Higgs strahlung at hadron colliders, Comput. Phys. Commun. 184 (2013) 998 [arXiv:1210.5347] [INSPIRE].
  41. [41]
    F.J. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75 (1949) 1736 [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  42. [42]
    J.S. Schwinger, On the Green’s functions of quantized fields. 1, Proc. Nat. Acad. Sci. 37 (1951) 452 [INSPIRE].
  43. [43]
    J.S. Schwinger, On the Green’s functions of quantized fields. 2, Proc. Nat. Acad. Sci. 37 (1951) 455 [INSPIRE].
  44. [44]
    A. Kanaki and C.G. Papadopoulos, HELAC: a package to compute electroweak helicity amplitudes, Comput. Phys. Commun. 132 (2000) 306 [hep-ph/0002082] [INSPIRE].
  45. [45]
    A. van Hameren, Multi-gluon one-loop amplitudes using tensor integrals, JHEP 07 (2009) 088 [arXiv:0905.1005] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  46. [46]
    A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations, Comput. Phys. Commun. 212 (2017) 220 [arXiv:1604.06792] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    F.A. Berends and W.T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    F. Caravaglios and M. Moretti, An algorithm to compute Born scattering amplitudes without Feynman graphs, Phys. Lett. B 358 (1995) 332 [hep-ph/9507237] [INSPIRE].
  49. [49]
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
  50. [50]
    A. Meurer et al., SymPy: symbolic computing in python, PeerJ Comp. Sci. 3 (2017) e103.CrossRefGoogle Scholar
  51. [51]
    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
  52. [52]
    G. Ossola, C.G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  53. [53]
    P. Draggiotis, M.V. Garzelli, C.G. Papadopoulos and R. Pittau, Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  54. [54]
    M.V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the electroweak 1-loop amplitudes, JHEP 01 (2010) 040 [Erratum ibid. 10 (2010) 097] [arXiv:0910.3130] [INSPIRE].
  55. [55]
    S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
  56. [56]
    S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
  57. [57]
    S. Dittmaier, A general approach to photon radiation off fermions, Nucl. Phys. B 565 (2000) 69 [hep-ph/9904440] [INSPIRE].
  58. [58]
    S. Dittmaier, A. Kabelschacht and T. Kasprzik, Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables, Nucl. Phys. B 800 (2008) 146 [arXiv:0802.1405] [INSPIRE].CrossRefADSGoogle Scholar
  59. [59]
    J.F. Gunion and H.E. Haber, The CP conserving two Higgs doublet model: the approach to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010] [INSPIRE].
  60. [60]
    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].CrossRefADSGoogle Scholar
  61. [61]
    R.M. Schabinger and J.D. Wells, A minimal spontaneously broken hidden sector and its impact on Higgs boson physics at the Large Hadron Collider, Phys. Rev. D 72 (2005) 093007 [hep-ph/0509209] [INSPIRE].
  62. [62]
    B. Patt and F. Wilczek, Higgs-field portal into hidden sectors, hep-ph/0605188 [INSPIRE].
  63. [63]
    M. Bowen, Y. Cui and J.D. Wells, Narrow trans-TeV Higgs bosons and Hhh decays: two LHC search paths for a hidden sector Higgs boson, JHEP 03 (2007) 036 [hep-ph/0701035] [INSPIRE].
  64. [64]
    G.M. Pruna and T. Robens, Higgs singlet extension parameter space in the light of the LHC discovery, Phys. Rev. D 88 (2013) 115012 [arXiv:1303.1150] [INSPIRE].ADSGoogle Scholar
  65. [65]
    T. Robens and T. Stefaniak, Status of the Higgs singlet extension of the Standard Model after LHC run 1, Eur. Phys. J. C 75 (2015) 104 [arXiv:1501.02234] [INSPIRE].CrossRefADSGoogle Scholar
  66. [66]
    T. Robens and T. Stefaniak, LHC benchmark scenarios for the real Higgs singlet extension of the Standard Model, Eur. Phys. J. C 76 (2016) 268 [arXiv:1601.07880] [INSPIRE].CrossRefADSGoogle Scholar
  67. [67]
    G. Chalons, D. Lopez-Val, T. Robens and T. Stefaniak, The Higgs singlet extension at LHC run 2, PoS(ICHEP2016)1180 [arXiv:1611.03007] [INSPIRE].
  68. [68]
    S.L. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE].ADSGoogle Scholar
  69. [69]
    E.A. Paschos, Diagonal neutral currents, Phys. Rev. D 15 (1977) 1966 [INSPIRE].ADSGoogle Scholar
  70. [70]
    B.S. DeWitt, Theory of radiative corrections for non-Abelian gauge fields, Phys. Rev. Lett. 12 (1964) 742 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  71. [71]
    B.S. DeWitt, Quantum theory of gravity 2. The manifestly covariant theory, Phys. Rev. 162 (1967) 1195 [INSPIRE].
  72. [72]
    L.F. Abbott, Introduction to the background field method, Acta Phys. Polon. B 13 (1982) 33 [INSPIRE].MathSciNetGoogle Scholar
  73. [73]
    J.P. Bornsen and A.E.M. van de Ven, Three loop Yang-Mills β-function via the covariant background field method, Nucl. Phys. B 657 (2003) 257 [hep-th/0211246] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  74. [74]
    L.F. Abbott, M.T. Grisaru and R.K. Schaefer, The background field method and the S matrix, Nucl. Phys. B 229 (1983) 372 [INSPIRE].CrossRefADSGoogle Scholar
  75. [75]
    A. Denner, G. Weiglein and S. Dittmaier, Application of the background field method to the electroweak Standard Model, Nucl. Phys. B 440 (1995) 95 [hep-ph/9410338] [INSPIRE].
  76. [76]
    A. Sirlin, Radiative corrections in the SU(2)L × U(1) theory: a simple renormalization framework, Phys. Rev. D 22 (1980) 971 [INSPIRE].ADSGoogle Scholar
  77. [77]
    W.J. Marciano and A. Sirlin, Radiative corrections to neutrino induced neutral-current phenomena in the SU(2)L × U(1) theory, Phys. Rev. D 22 (1980) 2695 [Erratum ibid. D 31 (1985) 213] [INSPIRE].
  78. [78]
    A. Sirlin and W.J. Marciano, Radiative corrections to ν μ + Nμ + X and their effect on the determination of ρ 2 and sin2 θ W , Nucl. Phys. B 189 (1981) 442 [INSPIRE].CrossRefADSGoogle Scholar
  79. [79]
    A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Predictions for all processes e + e → 4 fermions +γ, Nucl. Phys. B 560 (1999) 33 [hep-ph/9904472] [INSPIRE].
  80. [80]
    A. Denner, S. Dittmaier, M. Roth and L.H. Wieders, Electroweak corrections to charged-current e + e → 4 fermion processes: technical details and further results, Nucl. Phys. B 724 (2005) 247 [Erratum ibid. B 854 (2012) 504] [hep-ph/0505042] [INSPIRE].
  81. [81]
    A. Denner and S. Dittmaier, The complex-mass scheme for perturbative calculations with unstable particles, Nucl. Phys. Proc. Suppl. 160 (2006) 22 [hep-ph/0605312] [INSPIRE].
  82. [82]
    J. Fleischer and F. Jegerlehner, Radiative corrections to Higgs decays in the extended Weinberg-Salam model, Phys. Rev. D 23 (1981) 2001 [INSPIRE].ADSGoogle Scholar
  83. [83]
    M. Krause, R. Lorenz, M. Mühlleitner, R. Santos and H. Ziesche, Gauge-independent renormalization of the 2-Higgs-doublet model, JHEP 09 (2016) 143 [arXiv:1605.04853] [INSPIRE].CrossRefADSGoogle Scholar
  84. [84]
    Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  85. [85]
    LHC Higgs Cross section Working Group collaboration, D. de Florian et al., Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922 [INSPIRE].
  86. [86]
    L. Altenkamp, S. Dittmaier and H. Rzehak, Renormalization schemes for the two-Higgs-doublet model and applications to hW W/ZZ → 4 fermions, arXiv:1704.02645 [INSPIRE].
  87. [87]
    P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  88. [88]
    S. Actis, A. Ferroglia, G. Passarino, M. Passera, Ch. Sturm and S. Uccirati, GraphShot, a Form package for automatic generation and manipulation of one- and two-loop Feynman diagrams, unpublished.Google Scholar
  89. [89]
    CMS collaboration, Search for the Standard Model Higgs boson produced in association with a W or a Z boson and decaying to bottom quarks, Phys. Rev. D 89 (2014) 012003 [arXiv:1310.3687] [INSPIRE].
  90. [90]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].CrossRefADSGoogle Scholar
  91. [91]
    NNPDF collaboration, R.D. Ball et al., Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
  92. [92]
    LHC Higgs Cross section Working Group collaboration, I. Low et al., Beyond the Standard Model predictions,, accessed 29 June 2016.
  93. [93]
    J. Baglio, O. Eberhardt, U. Nierste and M. Wiebusch, Benchmarks for Higgs pair production and heavy Higgs boson searches in the two-Higgs-doublet model of type II, Phys. Rev. D 90 (2014) 015008 [arXiv:1403.1264] [INSPIRE].ADSGoogle Scholar
  94. [94]
    F. Bojarski, G. Chalons, D. Lopez-Val and T. Robens, Heavy to light Higgs boson decays at NLO in the singlet extension of the Standard Model, JHEP 02 (2016) 147 [arXiv:1511.08120] [INSPIRE].CrossRefADSGoogle Scholar
  95. [95]
    J.R. Espinosa and I. Navarro, Scale independent mixing angles, Phys. Rev. D 66 (2002) 016004 [hep-ph/0109126] [INSPIRE].
  96. [96]
    J.R. Espinosa and Y. Yamada, Scale independent and gauge independent mixing angles for scalar particles, Phys. Rev. D 67 (2003) 036003 [hep-ph/0207351] [INSPIRE].
  97. [97]
    A. Denner, G. Weiglein and S. Dittmaier, Gauge invariance of Green functions: background field method versus pinch technique, Phys. Lett. B 333 (1994) 420 [hep-ph/9406204] [INSPIRE].
  98. [98]
    D. Binosi, Electroweak pinch technique to all orders, J. Phys. G 30 (2004) 1021 [hep-ph/0401182] [INSPIRE].
  99. [99]
    J.M. Cornwall, Dynamical mass generation in continuum QCD, Phys. Rev. D 26 (1982) 1453 [INSPIRE].ADSGoogle Scholar
  100. [100]
    J.M. Cornwall and J. Papavassiliou, Gauge-invariant three gluon vertex in QCD, Phys. Rev. D 40 (1989) 3474 [INSPIRE].ADSGoogle Scholar
  101. [101]
    S. Kanemura, M. Kikuchi, K. Sakurai and K. Yagyu, Gauge invariant one-loop corrections to Higgs boson couplings in non-minimal Higgs models, arXiv:1705.05399 [INSPIRE].
  102. [102]
    A. Freitas and D. Stöckinger, Gauge dependence and renormalization of tan β in the MSSM, Phys. Rev. D 66 (2002) 095014 [hep-ph/0205281] [INSPIRE].
  103. [103]
    J. Brehmer, A. Freitas, D. Lopez-Val and T. Plehn, Pushing Higgs effective theory to its limits, Phys. Rev. D 93 (2016) 075014 [arXiv:1510.03443] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Ansgar Denner
    • 1
  • Jean-Nicolas Lang
    • 1
  • Sandro Uccirati
    • 2
  1. 1.Institut für Theoretische Physik und AstrophysikJulius-Maximilians-Universität WürzburgWürzburgGermany
  2. 2.Department of PhysicsUniversity of TorinoTorinoItaly

Personalised recommendations