The three- and four-Higgs couplings in the general two-Higgs-doublet model

  • D. JurčiukonisEmail author
  • L. Lavoura
Open Access
Regular Article - Theoretical Physics


We apply the unitarity bounds and the bounded-from-below (BFB) bounds to the most general scalar potential of the two-Higgs-doublet model (2HDM). We do this in the Higgs basis, i.e. in the basis for the scalar doublets where only one doublet has vacuum expectation value. In this way we obtain bounds on the scalar masses and couplings that are valid for all 2HDMs. We compare those bounds to the analogous bounds that we have obtained for other simple extensions of the Standard Model (SM), namely the 2HDM extended by one scalar singlet and the extension of the SM through two scalar singlets.


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]
    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].
  2. [2]
    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].
  3. [3]
    I.P. Ivanov, Building and testing models with extended Higgs sectors, Prog. Part. Nucl. Phys. 95 (2017) 160 [arXiv:1702.03776] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  5. [5]
    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].
  6. [6]
    L. Wu, J.M. Yang, C.-P. Yuan and M. Zhang, Higgs self-coupling in the MSSM and NMSSM after the LHC Run 1, Phys. Lett. B 747 (2015) 378 [arXiv:1504.06932] [INSPIRE].
  7. [7]
    L. Bian and N. Chen, Higgs pair productions in the CP-violating two-Higgs-doublet model, JHEP 09 (2016) 069 [arXiv:1607.02703] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    N. Chakrabarty and B. Mukhopadhyaya, High-scale validity of a two Higgs doublet scenario: predicting collider signals, Phys. Rev. D 96 (2017) 035028 [arXiv:1702.08268] [INSPIRE].
  9. [9]
    N.F. Bell, G. Busoni and I.W. Sanderson, Self-consistent Dark Matter Simplified Models with an s-channel scalar mediator, JCAP 03 (2017) 015 [arXiv:1612.03475] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    N.F. Bell, G. Busoni and I.W. Sanderson, Two Higgs Doublet Dark Matter Portal, JCAP 01 (2018) 015 [arXiv:1710.10764] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Bauer, U. Haisch and F. Kahlhoefer, Simplified dark matter models with two Higgs doublets: I. Pseudoscalar mediators, JHEP 05 (2017) 138 [arXiv:1701.07427] [INSPIRE].
  12. [12]
    C.-F. Chang, X.-G. He and J. Tandean, Two-Higgs-Doublet-Portal Dark-Matter Models in Light of Direct Search and LHC Data, JHEP 04 (2017) 107 [arXiv:1702.02924] [INSPIRE].ADSGoogle Scholar
  13. [13]
    M. Gorbahn and U. Haisch, Indirect probes of the trilinear Higgs coupling: ggh and hγγ, JHEP 10 (2016) 094 [arXiv:1607.03773] [INSPIRE].
  14. [14]
    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
  15. [15]
    ATLAS collaboration, Search for pair production of Higgs bosons in the bbbb final state using protonproton collisions at \( \sqrt{s}=13 \) TeV with the ATLAS detector, ATLAS-CONF-2016-049.
  16. [16]
    S.D. Rindani and B. Singh, Indirect measurement of triple-Higgs coupling at an electron-positron collider with polarized beams, arXiv:1805.03417 [INSPIRE].
  17. [17]
    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].
  18. [18]
    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
  19. [19]
    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
  20. [20]
    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].
  21. [21]
    D. Jurčiukonis and L. Lavoura, Lepton mixing and the charged-lepton mass ratios, JHEP 03 (2018) 152 [arXiv:1712.04292] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Gonçalo, Latest Higgs results from ATLAS, talk at The Workshop on Multi-Higgs Models, Lisbon, Portugal, 4-7 September 2018 [].
  23. [23]
    P. Silva, Latest from CMS on the exploration of the Higgs sector, talk at The Workshop on Multi-Higgs Models, Lisbon, Portugal, 4-7 September 2018 [].
  24. [24]
    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
  25. [25]
    T. Plehn and M. Rauch, The quartic Higgs coupling at hadron colliders, Phys. Rev. D 72 (2005) 053008 [hep-ph/0507321] [INSPIRE].
  26. [26]
    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].
  27. [27]
    A. Abada, D. Ghaffor and S. Nasri, A Two-Singlet Model for Light Cold Dark Matter, Phys. Rev. D 83 (2011) 095021 [arXiv:1101.0365] [INSPIRE].
  28. [28]
    A. Ahriche, A. Arhrib and S. Nasri, Higgs Phenomenology in the Two-Singlet Model, JHEP 02 (2014) 042 [arXiv:1309.5615] [INSPIRE].
  29. [29]
    B. Grzadkowski and D. Huang, Spontaneous CP -Violating Electroweak Baryogenesis and Dark Matter from a Complex Singlet Scalar, JHEP 08 (2018) 135 [arXiv:1807.06987] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    A. Arhrib and M. Maniatis, The two-real-singlet Dark Matter model, arXiv:1807.03554 [INSPIRE].
  31. [31]
    M.D. Goodsell and F. Staub, Unitarity constraints on general scalar couplings with SARAH, Eur. Phys. J. C 78 (2018) 649 [arXiv:1805.07306] [INSPIRE].
  32. [32]
    M.D. Goodsell and F. Staub, Improved unitarity constraints in Two-Higgs-Doublet-Models, arXiv:1805.07310 [INSPIRE].
  33. [33]
    M.P. Bento, H.E. Haber, J.C. Romão and J.P. Silva, Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095 [arXiv:1708.09408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    K. Kannike, Vacuum Stability Conditions From Copositivity Criteria, Eur. Phys. J. C 72 (2012) 2093 [arXiv:1205.3781] [INSPIRE].
  35. [35]
    K.P. Hadeler, On Copositive Matrices, Linear Algebra Appl. 49 (1983) 79.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, A Precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [arXiv:0711.4022] [INSPIRE].
  37. [37]
    M. Maniatis, A. von Manteuffel, O. Nachtmann and F. Nagel, Stability and symmetry breaking in the general two-Higgs-doublet model, Eur. Phys. J. C 48 (2006) 805 [hep-ph/0605184] [INSPIRE].
  38. [38]
    I.F. Ginzburg and I.P. Ivanov, Tree-level unitarity constraints in the most general 2HDM, Phys. Rev. D 72 (2005) 115010 [hep-ph/0508020] [INSPIRE].
  39. [39]
    S. Kanemura and K. Yagyu, Unitarity bound in the most general two Higgs doublet model, Phys. Lett. B 751 (2015) 289 [arXiv:1509.06060] [INSPIRE].
  40. [40]
    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM, Phys. Rev. D 75 (2007) 035001 [Erratum ibid. D 76 (2007) 039902] [hep-ph/0609018] [INSPIRE].
  41. [41]
    I.P. Ivanov and J.P. Silva, Tree-level metastability bounds for the most general two Higgs doublet model, Phys. Rev. D 92 (2015) 055017 [arXiv:1507.05100] [INSPIRE].
  42. [42]
    N.G. Deshpande and E. Ma, Pattern of Symmetry Breaking with Two Higgs Doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].
  43. [43]
    K.G. Klimenko, On Necessary and Sufficient Conditions for Some Higgs Potentials to Be Bounded From Below, Theor. Math. Phys. 62 (1985) 58 [INSPIRE].CrossRefGoogle Scholar
  44. [44]
    P.M. Ferreira, R. Santos and A. Barroso, Stability of the tree-level vacuum in two Higgs doublet models against charge or CP spontaneous violation, Phys. Lett. B 603 (2004) 219 [Erratum ibid. B 629 (2005) 114] [hep-ph/0406231] [INSPIRE].
  45. [45]
    F. Staub, Reopen parameter regions in Two-Higgs Doublet Models, Phys. Lett. B 776 (2018) 407 [arXiv:1705.03677] [INSPIRE].
  46. [46]
    L. Lavoura and J.P. Silva, Fundamental CP-violating quantities in a SU(2) × U(1) model with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph/9404276] [INSPIRE].
  47. [47]
    A. Arhrib, Phenomenology of 2HDM with a real singlet, talk at The Workshop on Multi-Higgs Models, Lisbon, Portugal, 4-7 September 2018 [].
  48. [48]
    I.P. Ivanov, M. Köpke and M. Mühlleitner, Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials, Eur. Phys. J. C 78 (2018) 413 [arXiv:1802.07976] [INSPIRE].
  49. [49]
    G.T. Gilber, Positive definite matrices and Sylvester’s criterion, Am. Math. Monthly 98 (1991) 44.MathSciNetCrossRefGoogle Scholar
  50. [50]
    X.-J. Xu, Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential, Phys. Rev. D 95 (2017) 115019 [arXiv:1705.08965] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Institute of Theoretical Physics and AstronomyUniversity of VilniusVilniusLithuania
  2. 2.Instituto Superior Técnico, CFTPUniversidade de LisboaLisboaPortugal

Personalised recommendations