Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The Higgs boson implications and prospects for future discoveries

Abstract

The Higgs boson, a fundamental scalar boson with mass 125 GeV, was discovered at the Large Hadron Collider (LHC) at CERN in 2012. So far, experiments at the LHC have focused on testing the Higgs boson’s couplings to other elementary particles, precision measurements of the Higgs boson’s properties and an initial investigation of the Higgs boson’s self-interaction and shape of the Higgs potential. The Higgs boson mass of 125 GeV is a remarkable value, meaning that the underlying state of the Universe, the vacuum, sits very close to the border between stable and metastable, which may hint at deeper physics beyond the standard model. The Higgs potential also influences ideas about the cosmological constant, the dark energy that drives the accelerating expansion of the Universe, the mysterious dark matter that comprises about 80% of the matter component in the Universe and a possible phase transition in the early Universe that might be responsible for baryogenesis. A detailed study of the Higgs boson is at the centre of the European Strategy for Particle Physics update. Here we review the current understanding of the Higgs boson and discuss the insights expected from present and future experiments.

Key points

  • The discovery of the Higgs boson was a major milestone in particle physics, confirming the standard model.

  • Direct tests of the couplings of the Higgs boson to fermions confirmed the mechanism that gives mass to the W and Z bosons, thus making the electroweak interaction short range. A recent highlight is the direct observation of the Higgs boson coupling to muons.

  • The observed properties of the Higgs boson put the standard model vacuum intriguingly close to the border between stable and metastable. Further connections to the open questions pertaining to baryogenesis, the nature of dark matter and dark energy and cosmic inflation mean that the Higgs boson is central to our understanding of the Universe.

  • Precision measurements of the Higgs boson to further probe its interactions and possible deeper origin and structure are an essential part of the High-Luminosity Large Hadron Collider programme and were recently identified by the European Strategy for Particle Physics to be the highest priority for the next high-energy collider facility.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: The Higgs potential and its sensitivity to quantum corrections.
Fig. 2: Top quark production in Higgs boson decays.
Fig. 3: Bottom quark production in Higgs boson decays.
Fig. 4: Muon production in Higgs boson decays.
Fig. 5: Summary of measured Higgs boson properties.
Fig. 6: Comparison of the upper limits at 90% CL from direct detection experiments209,210,211,212,213 on the spin-independent weak interacting massive particle (WIMP)-nucleon scattering cross-section σWIMP−N with the observed exclusion limits, assuming Higgs portal scenarios where the 125 GeV Higgs boson decays to a pair of dark matter particles106 with the Higgs boson as the unique link between SM and dark matter particles.
Fig. 7: Vacuum stability and ultraviolet behaviour of the SM.
Fig. 8: 1σ precision reach at the Future Circular Collider (FCC) on the effective Higgs boson couplings to fermions (muons, tau particles, charm quarks, top quarks and b quarks), to vector bosons (W or Z, photons, Zγ and gluons) and the Higgs boson self-coupling in an effective field theory framework.

References

  1. Aad, G. et al. 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, 1–29 (2012).

    Article  ADS  Google Scholar 

  2. Chatrchyan, S. et al. Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30–61 (2012).

    Article  ADS  Google Scholar 

  3. Englert, F. Nobel lecture: the BEH mechanism and its scalar boson. Rev. Mod. Phys. 86, 843 (2014).

    Article  ADS  MATH  Google Scholar 

  4. Higgs, P. W. Nobel lecture: evading the Goldstone theorem. Rev. Mod. Phys. 86, 851 (2014).

    Article  ADS  Google Scholar 

  5. Altarelli, G. Collider physics within the standard model: a primer. Preprint at https://arxiv.org/abs/1303.2842 (2013).

  6. Pokorski, S. Gauge Field Theories 2nd edn (Cambridge Univ. Press, 2000).

  7. Aitchison, I. & Hey, A. Gauge Theories In Particle Physics: A Practical Introduction Vol. 2 Non-Abelian Gauge Theories: QCD and the Electroweak Theory (CRC Press, 2012).

  8. Altarelli, G. The Higgs: so simple yet so unnatural. Phys. Scr. T 158, 014011 (2013).

    Article  ADS  Google Scholar 

  9. Hanneke, D., Fogwell, S. & Gabrielse, G. New measurement of the electron magnetic moment and the fine structure constant. Phys. Rev. Lett. 100, 120801 (2008).

    Article  ADS  Google Scholar 

  10. Parker, R. H., Yu, C., Zhong, W., Estey, B. & Müller, H. Measurement of the fine-structure constant as a test of the standard model. Science 360, 191–195 (2018).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Andreev, V. et al. Improved limit on the electric dipole moment of the electron. Nature 562, 355–360 (2018).

    Article  ADS  Google Scholar 

  12. Frieman, J., Turner, M. & Huterer, D. Dark energy and the accelerating universe. Annu. Rev. Astron. Astrophys. 46, 385–432 (2008).

    Article  ADS  Google Scholar 

  13. Dine, M. & Kusenko, A. The origin of the matter−antimatter asymmetry. Rev. Mod. Phys. 76, 1 (2003).

    Article  ADS  Google Scholar 

  14. Baumann, D. & Peiris, H. V. Cosmological inflation: theory and observations. Adv. Sci. Lett. 2, 105–120 (2009).

    Article  Google Scholar 

  15. Baudis, L. The search for dark matter. Eur. Rev. 26, 70–81 (2018).

    Article  Google Scholar 

  16. Gianotti, F. & Giudice, G. A roadmap for the future. Nat. Phys. 16, 997–998 (2020).

    Article  Google Scholar 

  17. European Strategy Group. 2020 Update of the European Strategy for Particle Physics. CERN https://cds.cern.ch/record/2721370/files/CERN-ESU-015-2020%20Update%20European%20Strategy.pdf (2020).

  18. Higgs, P. W. Broken symmetries, massless particles and gauge fields. Phys. Lett. 12, 132–133 (1964).

    Article  ADS  Google Scholar 

  19. Higgs, P. W. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  20. Higgs, P. W. Spontaneous symmetry breakdown without massless bosons. Phys. Rev. 145, 1156–1163 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  21. Englert, F. & Brout, R. Broken symmetry and the mass of gauge vector mesons. Phys. Rev. Lett. 13, 321–323 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  22. Guralnik, G., Hagen, C. & Kibble, T. Global conservation laws and massless particles. Phys. Rev. Lett. 13, 585–587 (1964).

    Article  ADS  Google Scholar 

  23. Kibble, T. Symmetry breaking in nonAbelian gauge theories. Phys. Rev. 155, 1554–1561 (1967).

    Article  ADS  Google Scholar 

  24. Llewellyn Smith, C. High-energy behavior and gauge symmetry. Phys. Lett. B 46, 233–236 (1973).

    Article  ADS  Google Scholar 

  25. Bell, J. High-energy behavior of tree diagrams in gauge theories. Nucl. Phys. B 60, 427–436 (1973).

    Article  ADS  Google Scholar 

  26. Cornwall, J. M., Levin, D. N. & Tiktopoulos, G. Uniqueness of spontaneously broken gauge theories. Phys. Rev. Lett. 30, 1268–1270 (1973).

    Article  ADS  Google Scholar 

  27. Cornwall, J. M., Levin, D. N. & Tiktopoulos, G. Derivation of gauge invariance from high-energy unitarity bounds on the S matrix. Phys. Rev. D 10, 1145 (1974).

    Article  ADS  Google Scholar 

  28. ’t Hooft, G. Renormalizable Lagrangians for massive Yang−Mills fields. Nucl. Phys. B 35, 167–188 (1971).

    Article  ADS  Google Scholar 

  29. ’t Hooft, G. & Veltman, M. J. G. Regularization and renormalization of gauge fields. Nucl. Phys. B 44, 189–213 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  30. Veltman, M. J. G. Perturbation theory of massive Yang−Mills fields. Nucl. Phys. B 7, 637–650 (1968).

    Article  ADS  Google Scholar 

  31. Anderson, P. W. Plasmons, gauge invariance, and mass. Phys. Rev. 130, 439–442 (1963).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Glashow, S. L. Partial symmetries of weak interactions. Nucl. Phys. 22, 579–588 (1961).

    Article  Google Scholar 

  33. Weinberg, S. A model of leptons. Phys. Rev. Lett. 19, 1264–1266 (1967).

    Article  ADS  Google Scholar 

  34. Salam, A. Weak and electromagnetic interactions. In Proc. 8th Nobel Symp. C680519, 367−377 (1968).

  35. ’t Hooft, G. & Veltman, M. J. G. Regularization and renormalization of gauge fields. Nucl. Phys. B 44, 189–213 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  36. Lykken, J. & Spiropulu, M. The future of the Higgs boson. Phys. Today 66, 28–33 (2013).

    Article  ADS  Google Scholar 

  37. Veltman, M. J. G. Reflections on the Higgs system. CERN-YELLOW-97-05 CERN https://cds.cern.ch/record/2654857?ln=en (1997).

  38. Carr, B. J. & Rees, M. The anthropic principle and the structure of the physical world. Nature 278, 605–612 (1979).

    Article  ADS  Google Scholar 

  39. Chanowitz, M. S. The No-Higgs signal: strong WW scattering at the LHC. Czech. J. Phys. 55, B45–B58 (2005).

    Article  Google Scholar 

  40. Littlewood, P. B. & Varma, C. M. Amplitude collective modes in superconductors and their coupling to charge-density waves. Phys. Rev. B 26, 4883–4893 (1982).

    Article  ADS  Google Scholar 

  41. Sherman, D., Pracht, U. S. & Gorshunov, B. et al. The Higgs mode in disordered superconductors close to a quantum phase transition. Nat. Phys. 11, 188–197 (2015).

    Article  Google Scholar 

  42. Anderson, P. W. Higgs, Anderson and all that. Nat. Phys. 11, 93 (2015).

    Article  Google Scholar 

  43. Shimano, R. & Tsuji, N. Higgs mode in superconductors. Annu. Rev. Condens. Matter Phys. 11, 103–124 (2020).

    Article  Google Scholar 

  44. Pekker, D. & Varma, C. Amplitude/Higgs modes in condensed matter physics. Annu. Rev. Condens. Matter Phys. 6, 269–297 (2015).

    Article  ADS  Google Scholar 

  45. Bruning, O. S. et al. LHC Design Report Vol.1: the LHC Main Ring. CERN https://inspirehep.net/literature/656250 (2004).

  46. Aad, G. et al. The ATLAS experiment at the CERN Large Hadron Collider. J. Instrum. 3, S08003 (2008).

    Article  Google Scholar 

  47. Chatrchyan, S. et al. The CMS experiment at the CERN LHC. J. Instrum. 3, S08004 (2008).

    Google Scholar 

  48. Landau, L. On the angular momentum of a system of two photons. Dokl. Akad. Nauk SSSR 60, 207–209 (1948).

    Google Scholar 

  49. Yang, C.-N. Selection rules for the dematerialization of a particle into two photons. Phys. Rev. 77, 242–245 (1950).

    Article  ADS  MATH  Google Scholar 

  50. Chatrchyan, S. et al. Study of the mass and spin-parity of the Higgs boson candidate via its decays to Z boson pairs. Phys. Rev. Lett. 110, 081803 (2013).

    Article  ADS  Google Scholar 

  51. Khachatryan, V. et al. Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV. Phys. Rev. D 92, 012004 (2015).

    Article  ADS  Google Scholar 

  52. Aad, G. et al. Evidence for the spin-0 nature of the Higgs boson using ATLAS data. Phys. Lett. B 726, 120–144 (2013).

    Article  ADS  Google Scholar 

  53. Dawson, S., Englert, C. & Plehn, T. Higgs physics: it ain’t over till it’s over. Phys. Rep. 816, 1–85 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  54. Heinrich, G. Collider physics at the precision frontier. Phys. Rep. 922, 1–69 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  55. de Florian, D. et al. Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector. Preprint at https://arxiv.org/abs/1610.07922 (2016).

  56. de Blas, J. et al. Higgs Boson studies at future particle colliders. J. High Energy Phys. 2020 (01), 139 (2020).

    Article  Google Scholar 

  57. Alcaraz, J. et al. A combination of preliminary electroweak measurements and constraints on the standard model. Preprint at https://arxiv.org/abs/hep-ex/0612034 (2006).

  58. Aad, G. et al. 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, 191803 (2015).

    Article  ADS  Google Scholar 

  59. Sirunyan, A. M. et al. A measurement of the Higgs boson mass in the diphoton decay channel. Phys. Lett. B 805, 135425 (2020).

    Article  Google Scholar 

  60. Aaboud, M. et al. Measurement of the Higgs boson mass in the H → ZZ* → 4 and H → γγ channels with \(\sqrt{s}=13\) TeV pp collisions using the ATLAS detector. Phys. Lett. B 784, 345–366 (2018).

    Article  ADS  Google Scholar 

  61. d’Enterria, D. On the (Gaussian) maximum at a mass m_H~125 GeV of the product of decay probabilities of the standard model Higgs boson. Preprint at https://arxiv.org/abs/1208.1993 (2012).

  62. Zyla, P. et al. (Particle Data Group). Review of Particle Physics. Prog. Theor. Exp. Phys. 2020, 083C01 (2020).

  63. Aaboud, M. et al. Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector. Phys. Lett. B 784, 173–191 (2018).

    Article  ADS  Google Scholar 

  64. Sirunyan, A. M. et al. Observation of \({\rm{t}}\bar{{\rm{t}}}\)H production. Phys. Rev. Lett. 120, 231801 (2018).

    Article  ADS  Google Scholar 

  65. Sirunyan, A. M. et al. Measurements of \({\rm{t}}\bar{{\rm{t}}}H\) production and the CP structure of the Yukawa interaction between the Higgs boson and top quark in the diphoton decay channel. Phys. Rev. Lett. 125, 061801 (2020).

    Article  Google Scholar 

  66. Aad, G. et al. CP properties of Higgs boson interactions with top quarks in the \(t\bar{t}H\) and tH processes using H → γγ with the ATLAS detector. Phys. Rev. Lett. 125, 061802 (2020).

    Article  ADS  Google Scholar 

  67. Barger, V., Hagiwara, K. & Zheng, Y.-J. Probing the Higgs Yukawa coupling to the top quark at the LHC via single top+Higgs production. Phys. Rev. D 99, 031701 (2019).

    Article  ADS  Google Scholar 

  68. Farina, M., Grojean, C., Maltoni, F., Salvioni, E. & Thamm, A. Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson. J. High Energy Phys. 2013 (05), 022 (2013).

    Google Scholar 

  69. Sirunyan, A. M. et al. Search for associated production of a Higgs boson and a single top quark in proton-proton collisions at \(\sqrt{s}=13\) TeV. Phys. Rev. D 99, 092005 (2019).

    Article  ADS  Google Scholar 

  70. Sirunyan, A. M. et al. Measurement of the Higgs boson production rate in association with top quarks in final states with electrons, muons, and hadronically decaying tau leptons at \(\sqrt{s}=\) 13 TeV. Eur. Phys. J. C 81, 378 (2021).

    Article  ADS  Google Scholar 

  71. Chatrchyan, S. et al. Evidence for the 125 GeV Higgs boson decaying to a pair of τ leptons. J. High Energy Phys. 2014 (05), 104 (2014).

    Article  Google Scholar 

  72. Aad, G. et al. Evidence for the Higgs-boson Yukawa coupling to tau leptons with the ATLAS detector. J. High Energy Phys. 2015 (04), 117 (2015).

    Article  Google Scholar 

  73. Aad, G. et al. 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. J. High Energy Phys. 2016 (08), 045 (2016).

    Article  Google Scholar 

  74. Sirunyan, A. M. et al. Search for the associated production of the Higgs boson and a vector boson in proton-proton collisions at \(\sqrt{s}=\) 13 TeV via Higgs boson decays to τ leptons. J. High Energy Phys. 2019 (06), 093 (2019).

    Article  Google Scholar 

  75. Sirunyan, A. M. et al. Observation of the Higgs boson decay to a pair of τ leptons with the CMS detector. Phys. Lett. B 779, 283–316 (2018).

    Article  ADS  Google Scholar 

  76. Aaboud, M. et al. Cross-section measurements of the Higgs boson decaying into a pair of τ-leptons in proton-proton collisions at \(\sqrt{s}=13\) TeV with the ATLAS detector. Phys. Rev. D 99, 072001 (2019).

    Article  ADS  Google Scholar 

  77. Aaboud, M. et al. Observation of \(H\to b\bar{b}\) decays and VH production with the ATLAS detector. Phys. Lett. B 786, 59–86 (2018).

    Article  ADS  Google Scholar 

  78. Sirunyan, A. M. et al. Observation of Higgs boson decay to bottom quarks. Phys. Rev. Lett. 121, 121801 (2018).

    Article  ADS  Google Scholar 

  79. Sirunyan, A. M. et al. Evidence for Higgs boson decay to a pair of muons. J. High Energy Phys. 2021 (01), 148 (2021).

    Article  Google Scholar 

  80. Aad, G. et al. A search for the dimuon decay of the standard model Higgs boson with the ATLAS detector. Phys. Lett. B 812, 135980 (2021).

    Article  Google Scholar 

  81. Aad, G. et al. Search for the Higgs boson decays H → ee and H → eμ in pp collisions at \(\sqrt{s}=13\) TeV with the ATLAS detector. Phys. Lett. B 801, 135148 (2020).

    Article  Google Scholar 

  82. Khachatryan, V. et al. Search for a standard model-like Higgs boson in the μ+μ and e+e decay channels at the LHC. Phys. Lett. B 744, 184–207 (2015).

    Article  ADS  Google Scholar 

  83. Aaboud, M. et al. Search for the decay of the Higgs boson to charm quarks with the ATLAS experiment. Phys. Rev. Lett. 120, 211802 (2018).

    Article  ADS  Google Scholar 

  84. Sirunyan, A. M. et al. A search for the standard model Higgs boson decaying to charm quarks. J. High Energy Phys. 2020 (03), 131 (2020).

    Google Scholar 

  85. Aaboud, M. et al. Searches for exclusive Higgs and Z boson decays into J/ψγ, ψ(2S)γ, and Υ(nS)γ at \(\sqrt{s}=13\) TeV with the ATLAS detector. Phys. Lett. B 786, 134–155 (2018).

    Article  ADS  Google Scholar 

  86. Aad, G. et al. Search for Higgs and Z boson decays to J/ψγ and Υ(nS)γ with the ATLAS detector. Phys. Rev. Lett. 114, 121801 (2015).

    Article  ADS  Google Scholar 

  87. Sirunyan, A. M. et al. Search for rare decays of Z and Higgs bosons to J/ψ and a photon in proton−proton collisions at \(\sqrt{s}=\) 13 TeV. Eur. Phys. J. C 79, 94 (2019).

    Article  ADS  Google Scholar 

  88. Brivio, I., Goertz, F. & Isidori, G. Probing the charm quark Yukawa coupling in Higgs + charm production. Phys. Rev. Lett. 115, 211801 (2015).

    Article  ADS  Google Scholar 

  89. Cepeda, M. et al. Report from Working Group 2: Higgs physics at the HL-LHC and HE-LHC. CERN Yellow Rep. Monogr. 7, 221–584 (2019).

    Google Scholar 

  90. Aaboud, M. et al. Search for exclusive Higgs and Z boson decays to ϕγ and ργ with the ATLAS detector. J. High Energy Phys. 2018 (07), 127 (2018).

    Article  Google Scholar 

  91. Sirunyan, A. M. et al. Search for decays of the 125 GeV Higgs boson into a Z boson and a ρ or ϕ meson. J. High Energy Phys. 2020 (11), 039 (2020).

    Article  Google Scholar 

  92. Aaboud, M. et al. Search for Higgs and Z boson decays to ϕγ with the ATLAS detector. Phys. Rev. Lett. 117, 111802 (2016).

    Article  ADS  Google Scholar 

  93. Aad, G. et al. Combined measurements of Higgs boson production and decay using up to 80 fb−1 of proton-proton collision data at \(\sqrt{s}=\) 13 TeV collected with the ATLAS experiment. Phys. Rev. D 101, 012002 (2020).

    Article  ADS  Google Scholar 

  94. Sirunyan, A. M. et al. Combined measurements of Higgs boson couplings in proton–proton collisions at \(\sqrt{s}=\,13\,{\rm{Te}}{\rm{V}}\). Eur. Phys. J. C 79, 421 (2019).

    Article  ADS  Google Scholar 

  95. Giudice, G., Grojean, C., Pomarol, A. & Rattazzi, R. The strongly-interacting light Higgs. J. High Energy Phys. 2007 (06), 045 (2007).

    Article  Google Scholar 

  96. Grzadkowski, B., Iskrzynski, M., Misiak, M. & Rosiek, J. Dimension-six terms in the standard model Lagrangian. J. High Energy Phys. 2010 (10), 085 (2010).

    Article  ADS  MATH  Google Scholar 

  97. Ellis, J., Sanz, V. & You, T. Complete Higgs sector constraints on dimension-6 operators. J. High Energy Phys. 2014 (07), 036 (2014).

    Article  Google Scholar 

  98. Falkowski, A. & Riva, F. Model-independent precision constraints on dimension-6 operators. J. High Energy Phys. 2015 (02), 039 (2015).

    Article  Google Scholar 

  99. Dawson, S., Homiller, S. & Lane, S. D. Putting standard model EFT fits to work. Phys. Rev. D 102, 055012 (2020).

    Article  ADS  Google Scholar 

  100. Sirunyan, A. M. et al. Measurements of the Higgs boson width and anomalous HVV couplings from on-shell and off-shell production in the four-lepton final state. Phys. Rev. D 99, 112003 (2019).

    Article  ADS  Google Scholar 

  101. Aaboud, M. et al. Constraints on off-shell Higgs boson production and the Higgs boson total width in ZZ → 4 and ZZ → 22ν final states with the ATLAS detector. Phys. Lett. B 786, 223–244 (2018).

    Article  ADS  Google Scholar 

  102. Arcadi, G., Djouadi, A. & Raidal, M. Dark matter through the Higgs portal. Phys. Rep. 842, 1–180 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  103. Carmona, A., Castellano Ruiz, J. & Neubert, M. A warped scalar portal to fermionic dark matter. Eur. Phys. J. C 81, 58 (2021).

    Article  ADS  Google Scholar 

  104. Sirunyan, A. M. et al. Search for invisible decays of a Higgs boson produced through vector boson fusion in proton−proton collisions at \(\sqrt{s}=\) 13 TeV. Phys. Lett. B 793, 520–551 (2019).

    Article  ADS  Google Scholar 

  105. Aaboud, M. et al. Combination of searches for invisible Higgs boson decays with the ATLAS experiment. Phys. Rev. Lett. 122, 231801 (2019).

    Article  ADS  Google Scholar 

  106. Patt, B. & Wilczek, F. Higgs-field portal into hidden sectors. Preprint at https://arxiv.org/abs/hep-ph/0605188 (2006).

  107. Eboli, O. J. & Zeppenfeld, D. Observing an invisible Higgs boson. Phys. Lett. B 495, 147–154 (2000).

    Article  ADS  Google Scholar 

  108. Fox, P. J., Harnik, R., Kopp, J. & Tsai, Y. Missing energy signatures of dark matter at the LHC. Phys. Rev. D 85, 056011 (2012).

    Article  ADS  Google Scholar 

  109. De Simone, A., Giudice, G. F. & Strumia, A. Benchmarks for dark matter searches at the LHC. J. High Energy Phys. 2014 (06), 081 (2014).

    Article  Google Scholar 

  110. Carena, M., Liu, Z. & Riembau, M. Probing the electroweak phase transition via enhanced di-Higgs boson production. Phys. Rev. D 97, 095032 (2018).

    Article  ADS  Google Scholar 

  111. Aad, G. et al. Combination of searches for Higgs boson pairs in pp collisions at \(\sqrt{s}=\)13 TeV with the ATLAS detector. Phys. Lett. B 800, 135103 (2020).

    Article  Google Scholar 

  112. Sirunyan, A. M. et al. Combination of searches for Higgs boson pair production in proton-proton collisions at \(\sqrt{s}=\) 13 TeV. Phys. Rev. Lett. 122, 121803 (2019).

    Article  ADS  Google Scholar 

  113. Alison, J. et al. Higgs boson potential at colliders: status and perspectives. Rev. Phys. 5, 100045 (2020).

    Article  Google Scholar 

  114. Sirunyan, A. M. et al. Search for nonresonant Higgs boson pair production in final states with two bottom quarks and two photons in proton-proton collisions at \(\sqrt{s}=\) 13 TeV. J. High Energy Phys. 2021 (03), 257 (2021).

    Article  Google Scholar 

  115. Aad, G. et al. Search for the \(HH\to b\bar{b}b\bar{b}\) process via vector-boson fusion production using proton-proton collisions at \(HH\to b\bar{b}b\bar{b}\) TeV with the ATLAS detector. J. High Energy Phys. 2020 (07), 108 (2020).

    Google Scholar 

  116. Di Vita, S., Grojean, C., Panico, G., Riembau, M. & Vantalon, T. A global view on the Higgs self-coupling. J. High Energy Phys. 2017 (09), 069 (2017).

    Article  Google Scholar 

  117. Steggemann, J. Extended scalar sectors. Annu. Rev. Nucl. Part. Sci. 70, 197–223 (2020).

    Article  ADS  Google Scholar 

  118. Brod, J., Haisch, U. & Zupan, J. Constraints on CP-violating Higgs couplings to the third generation. J. High Energy Phys. 2013 (11), 180 (2013).

    Article  ADS  Google Scholar 

  119. Aaboud, M. et al. Measurement of the Higgs boson coupling properties in the H → ZZ* → 4 decay channel at \(\sqrt{s}\) = 13 TeV with the ATLAS detector. J. High Energy Phys. 2018 (03), 095 (2018).

    Article  Google Scholar 

  120. Aad, G. et al. Test of CP invariance in vector-boson fusion production of the Higgs boson using the optimal observable method in the ditau decay channel with the ATLAS detector. Eur. Phys. J. C 76, 658 (2016).

    Article  ADS  Google Scholar 

  121. Sirunyan, A. M. et al. Constraints on anomalous HVV couplings from the production of Higgs bosons decaying to τ lepton pairs. Phys. Rev. D 100, 112002 (2019).

    Article  ADS  Google Scholar 

  122. Berge, S., Bernreuther, W., Niepelt, B. & Spiesberger, H. How to pin down the CP quantum numbers of a Higgs boson in its tau decays at the LHC. Phys. Rev. D 84, 116003 (2011).

    Article  ADS  Google Scholar 

  123. Sirunyan, A. M. et al. Search for production of four top quarks in final states with same-sign or multiple leptons in proton-proton collisions at \(\sqrt{s}=\) 13 TeV. Eur. Phys. J. C 80, 75 (2020).

    Article  ADS  Google Scholar 

  124. Aad, G. et al. Searches for lepton-flavour-violating decays of the Higgs boson in \(\sqrt{s}=13\) TeV pp collisions with the ATLAS detector. Phys. Lett. B 800, 135069 (2020).

    Article  Google Scholar 

  125. Sirunyan, A. M. et al. Search for lepton flavour violating decays of the Higgs boson to μτ and eτ in proton-proton collisions at \(\sqrt{s}=\) 13 TeV. J. High Energy Phys. 2018 (06), 001 (2018).

    Article  Google Scholar 

  126. Slade, E. Towards global fits in EFT’s and new physics implications. Proc. Sci. LHCP2019, 150 (2019).

    Google Scholar 

  127. Ellis, J., Madigan, M., Mimasu, K., Sanz, V. & You, T. Top, Higgs, diboson and electroweak fit to the standard model effective field theory. J. High Energy Phys. 2021 (04), 279 (2021).

    Article  MathSciNet  Google Scholar 

  128. ATLAS Collaboration. Search for top quark decays t → qH with H → γγ using the ATLAS detector. J. High Energy Phys. 2014 (06), 008 (2014).

    Google Scholar 

  129. ATLAS Collaboration. Search for flavour-changing neutral current top quark decays t → Hq in pp collisions at \(\sqrt{s}=8\,{\rm{TeV}}\) with the ATLAS detector. J. High Energy Phys. 2012 (12), 061 (2015).

    ADS  Google Scholar 

  130. ATLAS Collaboration. Search for top quark decays t → qH, with H → γγ, in \(\sqrt{s}=13\,{\rm{TeV}}\) pp collisions using the ATLAS detector. J. High Energy Phys. 2017(10), 129 (2017).

    Google Scholar 

  131. ATLAS Collaboration. Search for flavor-changing neutral currents in top quark decays t → Hc and t → Hu in multilepton final states in proton–proton collisions at \(\sqrt{s}=13\,{\rm{TeV}}\) with the ATLAS detector. Phys. Rev. D 98, 032002 (2018).

    Article  ADS  Google Scholar 

  132. ATLAS Collaboration. Search for top-quark decays t → Hq with 36 fb−1 of pp collision data at \(\sqrt{s}=13\,{\rm{TeV}}\) with the ATLAS detector. J. High Energy Phys. 2019 (05), 123 (2019).

    Google Scholar 

  133. CMS Collaboration. Search for top quark decays via Higgs-boson-mediated flavor-changing neutral currents in pp collisions at \(\sqrt{s}=8\,{\rm{TeV}}\). J. High Energy Phys. 2017 (02), 079 (2017).

    Google Scholar 

  134. CMS Collaboration. Search for the flavor-changing neutral current interactions of the top quark and the Higgs boson which decays into a pair of b quarks at \(\sqrt{s}=13\,{\rm{TeV}}\). J. High Energy Phys. 2018 (06), 102 (2018).

    Google Scholar 

  135. Baak, M. Review of electroweak fits of the SM and beyond, after the Higgs discovery — with Gfitter. Proc. Sci. EPS-HEP2013, 203 (2013).

    Google Scholar 

  136. Degrassi, G. et al. Higgs mass and vacuum stability in the standard model at NNLO. J. High Energy Phys. 2012 (08), 098 (2012).

    Article  Google Scholar 

  137. Buttazzo, D. et al. Investigating the near-criticality of the Higgs boson. J. High Energy Phys. 2013 (12), 089 (2013).

    Article  Google Scholar 

  138. Bezrukov, F., Kalmykov, M. Y., Kniehl, B. A. & Shaposhnikov, M. Higgs boson mass and new physics. J. High Energy Phys. 2012 (10), 140 (2012).

    Article  ADS  Google Scholar 

  139. Alekhin, S., Djouadi, A. & Moch, S. The top quark and Higgs boson masses and the stability of the electroweak vacuum. Phys. Lett. B 716, 214–219 (2012).

    Article  ADS  Google Scholar 

  140. Masina, I. Higgs boson and top quark masses as tests of electroweak vacuum stability. Phys. Rev. D 87, 053001 (2013).

    Article  ADS  Google Scholar 

  141. Hamada, Y., Kawai, H. & Oda, K.-y Bare Higgs mass at Planck scale. Phys. Rev. D 87, 053009 (2013).

    Article  ADS  Google Scholar 

  142. Jegerlehner, F. The standard model as a low-energy effective theory: what is triggering the Higgs mechanism? Acta Phys. Polon. B 45, 1167 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  143. Bednyakov, A., Kniehl, B., Pikelner, A. & Veretin, O. Stability of the electroweak vacuum: gauge independence and advanced precision. Phys. Rev. Lett. 115, 201802 (2015).

    Article  ADS  Google Scholar 

  144. Branchina, V. & Messina, E. Stability, Higgs boson mass and new physics. Phys. Rev. Lett. 111, 241801 (2013).

    Article  ADS  Google Scholar 

  145. Giudice, G. F. Naturally speaking: the naturalness criterion and physics at the LHC. Preprint at https://arxiv.org/abs/0801.2562 (2008).

  146. Wells, J. D. Lectures on Higgs boson physics in the standard model and beyond. Preprint at https://arxiv.org/abs/0909.4541 (2009).

  147. Wess, J. & Zumino, B. A Lagrangian model invariant under supergauge transformations. Phys. Lett. B 49, 52−54 (1974).

    Article  ADS  Google Scholar 

  148. Arkani-Hamed, N., Cohen, A. G. & Georgi, H. Electroweak symmetry breaking from dimensional deconstruction. Phys. Lett. B 513, 232–240 (2001).

    Article  ADS  MATH  Google Scholar 

  149. Arkani-Hamed, N., Cohen, A. G., Katz, E. & Nelson, A. E. The littlest Higgs. J. High Energy Phys. 2002 (07), 034 (2002).

    Article  MathSciNet  Google Scholar 

  150. Chacko, Z., Goh, H.-S. & Harnik, R. The twin Higgs: natural electroweak breaking from mirror symmetry. Phys. Rev. Lett. 96, 231802 (2006).

    Article  ADS  Google Scholar 

  151. Kaplan, D. B. Flavor at SSC energies: a new mechanism for dynamically generated fermion masses. Nucl. Phys. B 365, 259–278 (1991).

    Article  ADS  Google Scholar 

  152. Csaki, C., Grojean, C. & Terning, J. Alternatives to an elementary Higgs. Rev. Mod. Phys. 88, 045001 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  153. Ross, G. G. & Roberts, R. G. Minimal supersymmetric unification predictions. Nucl. Phys. B 377, 571–592 (1992).

    Article  ADS  Google Scholar 

  154. Altarelli, G. The Higgs and the excessive success of the standard model. Frascati Phys. Ser. 58, 102 (2014).

    Google Scholar 

  155. Pokorski, S. Physics beyond the standard model in hadronic collisions. Acta Phys. Polon. B 47, 1767 (2016).

    Article  ADS  Google Scholar 

  156. Ross, G. G. SUSY: Quo vadis? Eur. Phys. J. C 74, 2699 (2014).

    Article  ADS  Google Scholar 

  157. Slavich, P. et al. Higgs-mass predictions in the MSSM and beyond. Preprint at https://arxiv.org/abs/2012.15629 (2020).

  158. Jegerlehner, F. The ‘‘Ether world’’ and elementary particles. Preprint at https://arxiv.org/abs/hep-th/9803021 (1998).

  159. Bjorken, J. Emergent gauge bosons. In Proceedings to the Workshops: What Comes Beyond The Standard Model. Vol. 1, https://doi.org/10.2172/798927 (DOE, 2001) http://www-public.slac.stanford.edu/sciDoc/docMeta.aspx?slacPubNumber=SLAC-PUB-9063.

  160. Forster, D., Nielsen, H. B. & Ninomiya, M. Dynamical stability of local gauge symmetry: creation of light from chaos. Phys. Lett. B 94, 135–140 (1980).

    Article  ADS  Google Scholar 

  161. Giudice, G. F. The dawn of the post-naturalness era. In From My Vast Repertoire ...: Guido Altarelli’s Legacy (eds Levy, A., Forte, S. & Ridolfi, G.) 267−292 (World Scientific, 2019).

  162. Witten, E. Symmetry and emergence. Nat. Phys. 14, 116–119 (2018).

    Article  Google Scholar 

  163. Bass, S. D. Emergent gauge symmetries and particle physics. Prog. Part. Nucl. Phys. 113, 103756 (2020).

    Article  Google Scholar 

  164. Baskaran, G. & Anderson, P. W. Gauge theory of high temperature superconductors and strongly correlated Fermi systems. Phys. Rev. B 37, 580–583 (1988).

    Article  ADS  Google Scholar 

  165. Sachdev, S. Topological order, emergent gauge fields, and Fermi surface reconstruction. Rep. Prog. Phys. 82, 014001 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  166. Affleck, I., Zou, Z., Hsu, T. & Anderson, P. W. SU (2) gauge symmetry of the large-U limit of the Hubbard model. Phys. Rev. B 38, 745–747 (1988).

    Article  ADS  Google Scholar 

  167. Banerjee, D. et al. Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench. Phys. Rev. Lett. 109, 175302 (2012).

    Article  ADS  Google Scholar 

  168. Bañuls, M. C. et al. Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74, 165 (2020).

    Article  ADS  Google Scholar 

  169. Wetterich, C. Gauge symmetry from decoupling. Nucl. Phys. B 915, 135–167 (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  170. Weinberg, S. Essay: half a century of the standard model. Phys. Rev. Lett. 121, 220001 (2018).

    Article  ADS  Google Scholar 

  171. Baha Balantekin, A. & Kayser, B. On the properties of neutrinos. Annu. Rev. Nucl. Part. Sci. 68, 313–338 (2018).

    Article  ADS  Google Scholar 

  172. Weinberg, S. Baryon and lepton nonconserving processes. Phys. Rev. Lett. 43, 1566–1570 (1979).

    Article  ADS  Google Scholar 

  173. Aghanim, N. et al. Planck 2018 results. VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020).

    Article  Google Scholar 

  174. Weinberg, S. The cosmological constant problem. Rev. Mod. Phys. 61, 1–23 (1989).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  175. Wetterich, C. The cosmon model for an asymptotically vanishing time dependent cosmological ‘constant’. Astron. Astrophys. 301, 321–328 (1995).

    ADS  Google Scholar 

  176. Sahni, V. & Starobinsky, A. A. The case for a positive cosmological lambda term. Int. J. Mod. Phys. D 9, 373–444 (2000).

    Article  ADS  Google Scholar 

  177. Peebles, P. J. E. & Ratra, B. The cosmological constant and dark energy. Rev. Mod. Phys. 75, 559–606 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  178. Copeland, E. J., Sami, M. & Tsujikawa, S. Dynamics of dark energy. Int. J. Mod. Phys. D15, 1753–1936 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  179. Straumann, N. Dark energy. Lect. Notes Phys. 721, 327–397 (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  180. Bass, S. D. The cosmological constant puzzle. J. Phys. G38, 043201 (2011).

    Article  ADS  Google Scholar 

  181. Martin, J. Everything you always wanted to know about the cosmological constant problem (but were afraid to ask). C. R. Phys. 13, 566–665 (2012).

    Article  ADS  Google Scholar 

  182. Dvali, G. & Gomez, C. Quantum exclusion of positive cosmological constant? Ann. Phys. 528, 68–73 (2016).

    Article  MathSciNet  Google Scholar 

  183. Laureijs, R. et al. Euclid definition study report. Preprint at https://arxiv.org/abs/1110.3193 (2011).

  184. Altarelli, G. Neutrino 2004: concluding talk. Nucl. Phys. Proc. Suppl. 143, 470–478 (2005).

    Article  ADS  Google Scholar 

  185. Bass, S. D. & Krzysiak, J. The cosmological constant and Higgs mass with emergent gauge symmetries. Acta Phys. Polon. B 51, 1251 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  186. Bass, S. D. & Krzysiak, J. Vacuum energy with mass generation and Higgs bosons. Phys. Lett. B 803, 135351 (2020).

    Article  MathSciNet  Google Scholar 

  187. Trodden, M. Electroweak baryogenesis. Rev. Mod. Phys. 71, 1463–1500 (1999).

    Article  ADS  Google Scholar 

  188. Morrissey, D. E. & Ramsey-Musolf, M. J. Electroweak baryogenesis. New J. Phys. 14, 125003 (2012).

    Article  ADS  Google Scholar 

  189. Servant, G. The serendipity of electroweak baryogenesis. Phil. Trans. R. Soc. Lond. A 376, 20170124 (2018).

    ADS  Google Scholar 

  190. Amaro-Seoane, P. et al. Laser interferometer space antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).

  191. Caprini, C. et al. Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions. J. Cosmol. Astropart. Phys. 2016, 04 (2016).

  192. El-Neaj, Y. A. et al. AEDGE: atomic experiment for dark matter and gravity exploration in space. EPJ Quant. Technol. 7, 6 (2020).

    Article  ADS  Google Scholar 

  193. Bezrukov, F. L. & Shaposhnikov, M. The standard model Higgs boson as the inflaton. Phys. Lett. B 659, 703–706 (2008).

    Article  ADS  Google Scholar 

  194. Jegerlehner, F. Higgs inflation and the cosmological constant. Acta Phys. Polon. B 45, 1215 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  195. Rubio, J. Higgs inflation. Front. Astron. Space Sci. 5, 50 (2019).

    Article  ADS  Google Scholar 

  196. Wetterich, C. Cosmology and the fate of dilatation symmetry. Nucl. Phys. B 302, 668–696 (1988).

    Article  ADS  Google Scholar 

  197. Peebles, P. J. E. & Ratra, B. Cosmology with a time variable cosmological constant. Astrophys. J. Lett. 325, 17 (1988).

    Article  ADS  Google Scholar 

  198. Capozziello, S. & De Laurentis, M. Extended theories of gravity. Phys. Rep. 509, 167–321 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  199. Brüning, O. & Rossi, L. The high-luminosity Large Hadron Collider. Nat. Rev. Phys. 1, 241–243 (2019).

    Article  Google Scholar 

  200. Benedikt, M. & Zimmermann, F. The physics and technology of the Future Circular Collider. Nat. Rev. Phys. 1, 238–240 (2019).

    Article  Google Scholar 

  201. Benedikt, M., Blondel, A., Janot, P., Mangano, M. & Zimmermann, F. Future circular colliders succeeding the LHC. Nat. Phys. 16, 402–407 (2020).

    Article  Google Scholar 

  202. Stapnes, S. The compact linear collider. Nat. Rev. Phys. 1, 235–237 (2019).

    Article  Google Scholar 

  203. Sicking, E. & Ström, R. From precision physics to the energy frontier with the compact linear collider. Nat. Phys. 16, 386–392 (2020).

    Article  Google Scholar 

  204. Michizono, S. The international linear collider. Nat. Rev. Phys. 1, 244–245 (2019).

    Article  Google Scholar 

  205. Lou, X. The circular electron positron collider. Nat. Rev. Phys. 1, 232–234 (2019).

    Article  Google Scholar 

  206. Agostini, M., Benato, G. & Detwiler, J. Discovery probability of next-generation neutrinoless double-β decay experiments. Phys. Rev. D 96, 053001 (2017).

    Article  ADS  Google Scholar 

  207. Caldwell, A., Merle, A., Schulz, O. & Totzauer, M. Global Bayesian analysis of neutrino mass data. Phys. Rev. D 96, 073001 (2017).

    Article  ADS  Google Scholar 

  208. Kusenko, A. Are we on the brink of the Higgs abyss? APS Phys. 8, 108–110 (2015).

    Google Scholar 

  209. Petricca, F. et al. First results on low-mass dark matter from the CRESST-III experiment. J. Phys. Conf. Ser. 1342, 012076 (2020).

    Article  Google Scholar 

  210. Akerib, D. et al. Results from a search for dark matter in the complete LUX exposure. Phys. Rev. Lett. 118, 021303 (2017).

    Article  ADS  Google Scholar 

  211. Cui, X. et al. Dark matter results from 54-ton-day exposure of PandaX-II experiment. Phys. Rev. Lett. 119, 181302 (2017).

    Article  ADS  Google Scholar 

  212. Aprile, E. et al. Dark matter search results from a one ton-year exposure of XENON1T. Phys. Rev. Lett. 121, 111302 (2018).

    Article  ADS  Google Scholar 

  213. Agnes, P. et al. Low-mass dark matter search with the DarkSide-50 experiment. Phys. Rev. Lett. 121, 081307 (2018).

    Article  ADS  Google Scholar 

  214. Kniehl, B. A., Pikelner, A. F. & Veretin, O. L. mr: a C++ library for the matching and running of the standard model parameters. Comput. Phys. Commun. 206, 84–96 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  215. Abada, A. et al. FCC physics opportunities. Eur. Phys. J. C 79, 474 (2019).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

None of the results presented in this review would have been possible without the diligent efforts of all the colleagues from the LHC accelerator group, the ATLAS and CMS experiments, the computing divisions, the theoretical community and many more, who all took part in this fantastic adventure at the energy frontier. Specifically, the authors thank M. Cepeda, F. Jegerlehner and J. Krzysiak for useful discussions during the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Contributions

The authors contributed equally to all aspects of the article.

Corresponding authors

Correspondence to Steven D. Bass, Albert De Roeck or Marumi Kado.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks Fabio Cerutti and the other, anonymous, reviewers for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Glossary

Vacuum expectation value

The matrix element of a field or operator in the vacuum.

Higgs condensate

The Bose−Einstein condensate of Higgs bosons, which forms in the vacuum.

Naturalness

The theoretical idea that dimensionless ratios of mass scales in a physical theory should be of order one. That is, without fine tuning, a mass parameter can only be much smaller than the others if setting it zero increases the symmetry of the theory.

Gauge freedom

With gauge symmetry, we are free to choose the gauge symmetry parameters to make the physics look simplest, with all choices of gauge parameters being physically equivalent and degenerate.

Radiative corrections

Quantum fluctuations in the intermediate state of the particle interactions.

Barn

A unit that quantifies the integrated luminosity. It has the dimension of inverse area, proportional to the amount of proton−proton collisions produced by the Large Hadron Collider (LHC). One femtobarn 1 fb = 10−43 m2.One inverse attobarn 1 ab−1 = 103 fb−1. One inverse femtobarn corresponds to approximately 1014 proton−proton collisions in the LHC.

Signal strength

The ratio of the signal rate divided by the predicted rate for a standard model (SM) Higgs boson at a given mass, denoted by the symbol μS. The closer μS is to one, the more it resembles a SM Higgs boson.

Diphoton channel

(Higgs) particle production with two photons in the final state.

Tree-level interference

A cross term in squaring the amplitude for Higgs boson production, where the Higgs particle is liberated either from a W boson or from a top quark. This is specified to distinguish the loop level interference that occurs in the diphoton decay channel.

Decay channel

A collision final state involving a specific decay mode of the Higgs boson (for example, two photons, four leptons, two vector bosons, two fermions and so on).

Production channel

A collision final state involving a specific production mode of the Higgs boson (for example, gluon fusion, vector boson fusion, associated production with a vector boson, a pair of top quarks and so on).

Drell−Yan di-muon

A process in which a quark from one incoming proton annihilates with an antiquark from the second proton, producing a photon or Z boson that then decays into a μ+μ pair.

Mass shell

Physical particles with the correct energy−momentum relation are called on-shell or on-mass shell; otherwise, they are called off-shell or off-mass shell. Off-shell particles are virtual and can exist in interaction processes.

Trilinear coupling

The interaction vertex involving three Higgs particles (and no others).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Bass, S.D., De Roeck, A. & Kado, M. The Higgs boson implications and prospects for future discoveries. Nat Rev Phys 3, 608–624 (2021). https://doi.org/10.1038/s42254-021-00341-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-021-00341-2

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing