Journal of High Energy Physics

, 2019:267 | Cite as

Constraints on the quartic Higgs self-coupling from double-Higgs production at future hadron colliders

  • Wojciech Bizoń
  • Ulrich HaischEmail author
  • Luca Rottoli
Open Access
Regular Article - Theoretical Physics


We study the indirect constraints on the quartic Higgs self-coupling that arise from double-Higgs production at future hadron colliders. To this purpose, we calculate the two-loop contributions to the gg → hh amplitudes that involve a modified h4 vertex. Based on our results, we estimate the reach of a pp collider operating at 27 TeV and 100 TeV centre-of-mass energy in constraining the cubic and quartic Higgs self-couplings by measurements of double-Higgs and triple-Higgs production in gluon-fusion.


Beyond Standard Model Higgs Physics Quark Masses and SM Parameters 


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]
    ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
  2. [2]
    C. Anastasiou et al., Higgs boson gluon-fusion production in QCD at three loops, Phys. Rev. Lett. 114 (2015) 212001 [arXiv:1503.06056] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C. Anastasiou et al., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, JHEP 05 (2016) 058 [arXiv:1602.00695] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R. Contino et al., Physics at a 100 TeV pp collider: Higgs and EW symmetry breaking studies, CERN Yellow Rep. (2017) 255 [arXiv:1606.09408] [INSPIRE].
  5. [5]
    S. Borowka et al., Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence, Phys. Rev. Lett. 117 (2016) 012001 [Erratum ibid. 117 (2016) 079901] [arXiv:1604.06447] [INSPIRE].
  6. [6]
    S. Borowka et al., Full top quark mass dependence in Higgs boson pair production at NLO, JHEP 10 (2016) 107 [arXiv:1608.04798] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    G. Heinrich et al., NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers, JHEP 08 (2017) 088 [arXiv:1703.09252] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Grazzini et al., Higgs boson pair production at NNLO with top quark mass effects, JHEP 05 (2018) 059 [arXiv:1803.02463] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    F. Maltoni, E. Vryonidou and M. Zaro, Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO, JHEP 11 (2014) 079 [arXiv:1408.6542] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    F. Goertz, A. Papaefstathiou, L.L. Yang and J. Zurita, Higgs boson pair production in the D = 6 extension of the SM, JHEP 04 (2015) 167 [arXiv:1410.3471] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Azatov, R. Contino, G. Panico and M. Son, Effective field theory analysis of double Higgs boson production via gluon fusion, Phys. Rev. D 92 (2015) 035001 [arXiv:1502.00539] [INSPIRE].ADSGoogle Scholar
  12. [12]
    ATLAS collaboration, Higgs pair production in the H (→ ττ )H (→ b \( \overline{b} \)) channel at the High-Luminosity LHC, ATL-PHYS-PUB-2015-046 (2015).
  13. [13]
    F. Kling, T. Plehn and P. Schichtel, Maximizing the significance in Higgs boson pair analyses, Phys. Rev. D 95 (2017) 035026 [arXiv:1607.07441] [INSPIRE].ADSGoogle Scholar
  14. [14]
    ATLAS collaboration, Projected sensitivity to non-resonant Higgs boson pair production in the b \( \overline{b} \) b \( \overline{b} \) final state using proton–proton collisions at HL-LHC with the ATLAS detector, ATL-PHYS-PUB-2016-024 (2016).
  15. [15]
    S. Di Vita et al., A global view on the Higgs self-coupling, JHEP 09 (2017) 069 [arXiv:1704.01953] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    ATLAS collaboration, Study of the double Higgs production channel H (→ b \( \overline{b} \))H (𝛾𝛾) with the ATLAS experiment at the HL-LHC, ATL-PHYS-PUB-2017-001 (2017).
  17. [17]
    D. Gon¸calves et al., Higgs boson pair production at future hadron colliders: From kinematics to dynamics, Phys. Rev. D 97 (2018) 113004 [arXiv:1802.04319] [INSPIRE].
  18. [18]
    A.J. Barr et al., Higgs self-coupling measurements at a 100 TeV hadron collider, JHEP 02 (2015) 016 [arXiv:1412.7154] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    H.-J. He, J. Ren and W. Yao, Probing new physics of cubic Higgs boson interaction via Higgs pair production at hadron colliders, Phys. Rev. D 93 (2016) 015003 [arXiv:1506.03302] [INSPIRE].ADSGoogle Scholar
  20. [20]
    M.L. Mangano et al., Physics at a 100 TeV pp collider: standard model processes, CERN Yellow Rep. (2017) 1 [arXiv:1607.01831] [INSPIRE].
  21. [21]
    S. Banerjee et al., hh + jet production at 100 TeV, Eur. Phys. J. C 78 (2018) 322 [arXiv:1802.01607] [INSPIRE].
  22. [22]
    J. Chang et al., Higgs-boson-pair production H (→ b \( \overline{b} \))H (𝛾𝛾) from gluon fusion at the HL-LHC and HL-100 TeV hadron collider, arXiv:1804.07130 [INSPIRE].
  23. [23]
    A. Papaefstathiou and K. Sakurai, Triple Higgs boson production at a 100 TeV proton-proton collider, JHEP 02 (2016) 006 [arXiv:1508.06524] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    C.-Y. Chen et al., Probing triple-Higgs productions via 4b2γ decay channel at a 100 TeV hadron collider, Phys. Rev. D 93 (2016) 013007 [arXiv:1510.04013] [INSPIRE].ADSGoogle Scholar
  25. [25]
    B. Fuks, J.H. Kim and S.J. Lee, Probing Higgs self-interactions in proton-proton collisions at a center-of-mass energy of 100 TeV, Phys. Rev. D 93 (2016) 035026 [arXiv:1510.07697] [INSPIRE].ADSGoogle Scholar
  26. [26]
    W. Kilian et al., New physics in multi-Higgs boson final states, JHEP 06 (2017) 145 [arXiv:1702.03554] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    B. Fuks, J.H. Kim and S.J. Lee, Scrutinizing the Higgs quartic coupling at a future 100 TeV proton–proton collider with taus and b-jets, Phys. Lett. B 771 (2017) 354 [arXiv:1704.04298] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    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].
  29. [29]
    M. Gorbahn and U. Haisch, Indirect probes of the trilinear Higgs coupling: gg → h and h → γγ, JHEP 10 (2016) 094 [arXiv:1607.03773] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    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
  31. [31]
    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
  32. [32]
    G. Degrassi, M. Fedele and P.P. Giardino, Constraints on the trilinear Higgs self coupling from precision observables, JHEP 04 (2017) 155 [arXiv:1702.01737] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    G.D. Kribs, A. Maier, H. Rzehak, M. Spannowsky and P. Waite, Electroweak oblique parameters as a probe of the trilinear Higgs boson self-interaction, Phys. Rev. D 95 (2017) 093004 [arXiv:1702.07678] [INSPIRE].ADSGoogle Scholar
  34. [34]
    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
  35. [35]
    S. Di Vita et al., A global view on the Higgs self-coupling at lepton colliders, JHEP 02 (2018) 178 [arXiv:1711.03978] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    F. Maltoni, D. Pagani and X. Zhao, Constraining the Higgs self-couplings at e + e colliders, JHEP 07 (2018) 087 [arXiv:1802.07616] [INSPIRE].Google Scholar
  37. [37]
    T. Liu, K.-F. Lyu, J. Ren and H.X. Zhu, Probing the quartic Higgs boson self-interaction, Phys. Rev. D 98 (2018) 093004 [arXiv:1803.04359] [INSPIRE].ADSGoogle Scholar
  38. [38]
    J. de Blas, M. Chala, M. Pèrez-Victoria and J. Santiago, Observable effects of general new scalar particles, JHEP 04 (2015) 078 [arXiv:1412.8480] [INSPIRE].
  39. [39]
    S. Borowka et al., Probing the scalar potential via double Higgs boson production at hadron colliders, JHEP 04 (2019) 016 [arXiv:1811.12366] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    M. Gorbahn and U. Haisch, Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling, JHEP 04 (2019) 062 [arXiv:1902.05480] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys. B 309 (1988) 282 [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
  43. [43]
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
  44. [44]
    S. Borowka, J. Carter and G. Heinrich, Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0, Comput. Phys. Commun. 184 (2013) 396 [arXiv:1204.4152] [INSPIRE].
  45. [45]
    S. Borowka et al., SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Comput. Phys. Commun. 196 (2015) 470 [arXiv:1502.06595] [INSPIRE].
  46. [46]
    S. Borowka et al., pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, Comput. Phys. Commun. 222 (2018) 313 [arXiv:1703.09692] [INSPIRE].
  47. [47]
    V.A. Smirnov, Applied asymptotic expansions in momenta and masses, Springer Tracts in Modern Physics volume 177, Springer, Germany (2002).Google Scholar
  48. [48]
    M. Steinhauser, MATAD: a program package for the computation of MAssive TADpoles, Comput. Phys. Commun. 134 (2001) 335 [hep-ph/0009029] [INSPIRE].
  49. [49]
    R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
  50. [50]
    O.V. Tarasov, An Algorithm for small momentum expansion of Feynman diagrams, in the proceedings of the Artificial intelligence in high-energy and nuclear physics ’95 – 4th International Workshop On Software Engineering, Artificial Intelligence and Expert Systems, April 3–8, Pisa, Italy (1995), hep-ph/9505277 [INSPIRE].
  51. [51]
    O.V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54 (1996) 6479 [hep-th/9606018] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  52. [52]
    O.V. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses, Nucl. Phys. B 502 (1997) 455 [hep-ph/9703319] [INSPIRE].
  53. [53]
    L. Avdeev, J. Fleischer, S. Mikhailov and O. Tarasov, O(\( \alpha {\alpha}_s^2 \)) correction to the electroweak ρ parameter, Phys. Lett. B 336 (1994) 560 [Erratum ibid. B 349 (1995) 597] [hep-ph/9406363] [INSPIRE].
  54. [54]
    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
  55. [55]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    J.M. Campbell and R.K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. Proc. Suppl. 205-206 (2010) 10 [arXiv:1007.3492] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    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
  60. [60]
    A. Falkowski and R. Rattazzi, Which EFT, arXiv:1902.05936 [INSPIRE].
  61. [61]
    L. Di Luzio, R. Gröber and M. Spannowsky, Maxi-sizing the trilinear Higgs self-coupling: how large could it be?, Eur. Phys. J. C 77 (2017) 788 [arXiv:1704.02311] [INSPIRE].
  62. [62]
    S. Chang and M.A. Luty, The Higgs trilinear coupling and the scale of new physics, arXiv:1902.05556 [INSPIRE].
  63. [63]
    T. Sj¨ostrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
  64. [64]
    T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  65. [65]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].Google Scholar
  67. [67]
    G. Cowan, K. Cranmer, E. Gross and O. Vitells, Asymptotic formulae for likelihood-based tests of new physics, Eur. Phys. J. C 71 (2011) 1554 [Erratum ibid. C 73 (2013) 2501] [arXiv:1007.1727] [INSPIRE].
  68. [68]
    T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institut für Theoretische Teilchenphysik (TTP), KITKarlsruheGermany
  2. 2.Institut für Kernphysik (IKP), KITEggenstein-LeopoldshafenGermany
  3. 3.Max Planck Institute for PhysicsMünchenGermany
  4. 4.Dipartimento di Fisica G. Occhialini, U2Università degli Studi di Milano-BicoccaMilanoItaly
  5. 5.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.
  6. 6.CERN, Theoretical Physics DepartmentGenevaSwitzerland

Personalised recommendations