Higgs pair production

Higgs boson pair production, also known as di-Higgs production (HH), is a process in particle physics regarding the self-interactions of the Higgs boson. This process is essential for testing the structure of the Higgs potential and the mechanism of electroweak symmetry breaking (EWSB).

Total cross sections at the LO and NLO in QCD for HH production channels, at the LHC as a function of the self-interaction coupling λ.

Motivation

After the Higgs boson was discovered in 2012, ^{[2] [3]} research efforts focused on exploring its interactions with other particles. While many of these couplings have been measured, ^{[4] [5]} the Higgs boson's self-coupling remains unmeasured. ^{[1] [6]} The shape of the Higgs potential in the Standard Model (SM) includes both trilinear and quartic self-couplings, which are key to understanding the nature of the Higgs field and EWSB.

The Higgs potential in the SM is described as: ^[7]

${\displaystyle V_{\text{H}}={\frac {1}{2}}{m_{\text{H}}}^{2}H^{2}+\lambda _{\text{HHH}}H^{3}+\lambda _{\text{HHHH}}H^{4}}$

where ${\displaystyle m_{\text{H}}}$ is the Higgs boson mass, and ${\displaystyle \lambda _{\text{HHH}}}$ and ${\displaystyle \lambda _{\text{HHHH}}}$ are the trilinear and quartic self-couplings. Precise measurements of these parameters could also indicate the presence of beyond the Standard Model (BSM) physics.

Total cross sections at the NLO in QCD for the six largest HH production channels at pp colliders. The thickness of the lines corresponds to the scale and PDF uncertainties added linearly.

Production mechanisms at the LHC

At the Large Hadron Collider (LHC), Higgs boson pairs can be produced through several mechanisms:

• Gluon–gluon fusion (ggF), the dominant production mode, proceeds via heavy quark loops (primarily top quarks) and involves both box and triangle Feynman diagrams. Interference between these diagrams plays a significant role.
• Vector boson fusion (VBF), where Higgs bosons are radiated from virtual W or Z bosons exchanged between quarks.
• Associated production with top quark pairs (ttHH) or vector bosons (VHH), which become more relevant at higher center-of-mass energies.

Each mechanism provides different sensitivity to the Higgs self-coupling. For example, the triangle diagram in ggF directly involves the trilinear coupling.

Decay channels

Higgs boson pairs can decay through various channels. The most studied final states include:^{[ citation needed ]}

• HH → bbbb: Has the highest branching fraction (~34%) but suffers from large QCD background.
• HH → bbγγ: Low branching fraction (~0.3%) but excellent mass resolution due to clean photon identification.
• HH → bbτ⁺τ⁻: Offers a good compromise between signal rate and background contamination (~7.3% branching ratio).

The choice of decay mode affects the sensitivity of LHC experiments to the HH signal.

Experimental status

Higgs boson pair production has not yet been observed at the LHC. The Standard Model predicts a small cross-section for non-resonant HH production via gluon–gluon fusion, approximately 31 fb at a center-of-mass energy of 13 TeV. This small rate, coupled with large backgrounds in most decay channels, makes the search experimentally challenging. ^[8]

Higgs self-coupling constraints

The Higgs self-coupling ${\displaystyle \lambda _{\text{HHH}}}$ directly affects the triangle diagram in gluon fusion production. Experimental results place constraints on this coupling by measuring deviations in the total cross-section and kinematic distributions. Current constraints from global combinations of decay channels show that the self-coupling value ${\displaystyle \kappa _{\lambda }=\lambda _{\text{HHH}}/\lambda _{\text{HHH}}^{\text{SM}}}$ is within experimental error of the SM value. ^{[8] : fig.9}

Future prospects

The upcoming High Luminosity Large Hadron Collider (HL-LHC), expected to deliver up to 3 ab⁻¹ of data at √s = 14 TeV, will significantly improve the sensitivity to HH production. Projections suggest:

• A ~3σ evidence for non-resonant HH production in the SM,
• A measurement of ${\displaystyle \kappa _{\lambda }}$ with ~50% precision,
• Discovery potential in certain BSM scenarios (e.g., enhanced self-coupling or new resonances decaying to HH).

Dedicated studies have been performed for each decay mode, indicating that the bbγγ and bbτ⁺τ⁻ channels will remain key to achieving maximal sensitivity. Additionally, future colliders such as the FCC-hh (100 TeV), CLIC, or a muon collider would dramatically extend the sensitivity, possibly allowing for percent-level precision on ${\displaystyle \lambda _{\text{HHH}}}$.

Resonant searches

Searches for heavy particles decaying into Higgs boson pairs (resonant HH production) are also ongoing. Such signals could arise from new scalar bosons or Kaluza–Klein gravitons in BSM models. Mass ranges from a few hundred GeV to several TeV have been explored, with no significant excess observed so far.

See also

• Electroweak symmetry breaking
• Standard Model
• Effective field theory

References

1. Frederix, R.; Frixione, S.; Hirschi, V.; Maltoni, F.; Mattelaer, O.; Torrielli, P.; Vryonidou, E.; Zaro, M. (2014-05-01). "Higgs pair production at the LHC with NLO and parton-shower effects". Physics Letters B. 732: 142–149. doi:10.1016/j.physletb.2014.03.026. ISSN   0370-2693.
2. Aad, G.; Abajyan, T.; Abbott, B.; Abdallah, J.; Abdel Khalek, S.; Abdelalim, A. A.; Abdinov, O.; Aben, R.; Abi, B.; Abolins, M.; AbouZeid, O. S.; Abramowicz, H.; Abreu, H.; Acharya, B. S.; Adamczyk, L. (2012-09-17). "Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC". Physics Letters B. 716 (1): 1–29. doi:10.1016/j.physletb.2012.08.020. ISSN   0370-2693.
3. Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Aguilo, E.; Bergauer, T.; Dragicevic, M.; Erö, J.; Fabjan, C.; Friedl, M.; Frühwirth, R.; Ghete, V. M.; Hammer, J.; Hoch, M. (2012-09-17). "Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC". Physics Letters B. 716 (1): 30–61. doi:10.1016/j.physletb.2012.08.021. ISSN   0370-2693.
4. Tumasyan, A.; Adam, W.; Andrejkovic, J. W.; Bergauer, T.; Chatterjee, S.; Damanakis, K.; Dragicevic, M.; Del Valle, A. Escalante; Hussain, P. S.; Jeitler, M.; Krammer, N.; Lechner, L.; Liko, D.; Mikulec, I.; Paulitsch, P. (July 2022). "A portrait of the Higgs boson by the CMS experiment ten years after the discovery". Nature. 607 (7917): 60–68. doi:10.1038/s41586-022-04892-x. ISSN   1476-4687. PMC   9259501 .
5. Aad, G.; Abbott, B.; Abbott, D. C.; Abeling, K.; Abidi, S. H.; Aboulhorma, A.; Abramowicz, H.; Abreu, H.; Abulaiti, Y.; Abusleme Hoffman, A. C.; Acharya, B. S.; Achkar, B.; Adam, L.; Bourdarios, C. Adam; Adamczyk, L. (July 2022). "A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery". Nature. 607 (7917): 52–59. doi:10.1038/s41586-022-04893-w. ISSN   1476-4687. PMC   9259483 .
6. Micco, Biagio Di; Gouzevitch, Maxime; Mazzitelli, Javier; Vernieri, Caterina (2020-11-01). "Higgs boson potential at colliders: Status and perspectives". Reviews in Physics. 5: 100045. doi:10.1016/j.revip.2020.100045. ISSN   2405-4283.
7. Higgs, Peter W. (1966-05-27). "Spontaneous Symmetry Breakdown without Massless Bosons". Physical Review. 145 (4): 1156–1163. doi:10.1103/PhysRev.145.1156.
8. The CMS Collaboration; Tumasyan, A.; Adam, W.; Andrejkovic, J. W.; Bergauer, T.; Chatterjee, S.; Damanakis, K.; Dragicevic, M.; Del Valle, A. Escalante; Hussain, P. S.; Jeitler, M.; Krammer, N.; Lechner, L.; Liko, D.; Mikulec, I. (2022-07-07). "A portrait of the Higgs boson by the CMS experiment ten years after the discovery". Nature. 607 (7917): 60–68. doi:10.1038/s41586-022-04892-x. ISSN   0028-0836. PMC   9259501 .