Figure 2: Constraints on the branching fraction of the Higgs boson decaying to invisible particles, as a function of test statistic q, from the CMS collaboration. http://cms-results.web.cern.ch/cms-results/public-results/publications/HIG-17-031/index.html

The BSM models probed by studies of the Higgs boson can generally be classified in three categories: additional BSM Higgs bosons, exotic or rare decays of the SM Higgs boson, and exotic production of the SM Higgs. In the first category, some BSM models, such as supersymmetry (SUSY), extend the Higgs sector to include additional Higgs doublets or triplets. The additional Higgs bosons arising from these added doublets or triplets may be more (or less) massive than the SM Higgs boson, or can be electrically charged, unlike the SM Higgs boson. For example, the minimal supersymmetric SM (MSSM) is a two-Higgs-doublet-model (2HDM), predicting five total Higgs bosons. In particular, in the MSSM, the SM Higgs boson (h) is joined by an additional CP-even Higgs (H), a CP-odd pseudoscalar Higgs (A), and two charged Higgses (H).

We also search directly for additional Higgs bosons, such as the potentially heavy Higgs bosons predicted by the MSSM (H, A). A variety of decay channels are used for such searches, including heavy Higgs boson decays to fermions (A/H → ττ, μμ, bb, tt), vector bosons (A/H → WW, ZZ, γγ), and Higgs boson + vector boson (H → AZ; A → Zh). For instance, Figure 4 depicts the regions of the [mA, tanβ] plane which have been excluded by direct searches for heavy Higgs bosons by the ATLAS collaboration in the “habeus” MSSM (hMSSM) model. Figure 4 also shows the stringent indirect constraints (hashed region) arising from the aforementioned precision measurements of the SM Higgs boson.

 

In addition to neutral, heavy Higgses, searches for charged, heavy Higges have been pursued. The predominant production and decay mechanisms depend on the mass of the H⁺. For example, for higher masses, H⁺ → tb is the dominant decay mode, while H⁺ → τν accesses the full mass range. Figure 5 shows a summary of the charged Higgs results from the CMS collaboration, in terms of constraints on tan β and mH⁺. The complementarity between the H⁺ → tb and H⁺ → τν results, as well as between the direct searches and the indirect constraints (in hashed red), is evident.

 

Figure 5: Observed limits (solid points) from the CMS charged Higgs searches, interpreted as a 95% confidence level exclusion region (hatched area) in the MSSM (mH, tanβ) parameter space, compared to the expected limit assuming only standard model processes (dashed line). The region below the red line is excluded assuming that the observed neutral Higgs boson is the light CP-even 2HDM Higgs boson with a mass of 125±3 GeV. http://cms-results.web.cern.ch/cms-results/public-results/preliminary-results/HIG-18-004/index.html

New physics may also manifest itself by affecting the decays of the SM Higgs boson. BSM physics can enhance rare decays, such as Higgs boson decays to quarkonia (h → J/ψ J/ψ, ΥΥ, J/ψ γ, etc), or induce flavor-changing neutral current decays (t → hq). The SM Higgs boson itself may also be decay to new BSM particles.

As mentioned earlier, measurements of the SM Higgs boson still leave room for such exotic decays.For instance, the next-to-minimal supersymmetric SM (NMSSM) adds a singlet to the MSSM, thus resulting in two more Higgs bosons. The lightest, pseudoscalar Higgs boson (a) in this scenario can be very light (on the order of ~GeV) and thus may have escaped detection. The SM Higgs boson in this case can decay into pairs of these light pseudoscalar particles, which subsequently decay into pairs of SM particles (such as bb, ττ, μμ, γγ). In the case that the pseudoscalar is very low mass (< 10 GeV), the final state particles may be highly boosted, presenting a challenge for particle identification. Figure 6 shows a summary of searches for such decays (h → aa → XXYY) from the CMS collaboration, in terms of the upper limits on the branching fraction as a function of the pseudoscalar mass (m_a).

 

Figure 8: Regions in the (ma, mA) plane excluded by data at 95% CL by the ATLAS mono-object searches and invisible Higgs analyses, in a 2HDM+a model. The dashed grey regions at the top of the figure indicate the region where the width of any of the Higgs bosons exceeds 20% of its mass. https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/EXOT-2017-32/

 

Lastly, the measurement of di-Higgs production (HH) is an important probe of the Higgs boson self-coupling. HH events are predicted by the SM, but are loop-induced and have a very low expected cross section. However, the HH process can be enhanced by BSM physics, in both resonant and nonresonant mechanisms. In the resonant case, HH may be produced through the decay of a massive resonance, such as a spin-2 graviton or a spin-0 radion, which are predicted in models of warped extra spatial dimensions. In the nonresonant case, the HH process may be enhanced through new particles traversing the loops of the HH diagrams. The two Higgs bosons are sought in the typical SM Higgs boson decay channels (eg, bb, γγ, ττ, VV), with the different channels exhibiting varying levels of sensitivity as a function of the resonance mass. Figure 9 shows the 95% confidence level upper limits on the cross-section times branching ratio for producing a graviton, as a function of the graviton mass, combining several analyses from the CMS collaboration. Potential nonresonant enhancements are typically encapsulated in terms of several parameters, such as κ_λ which measures deviations of the Higgs boson tri-linear self coupling (in the SM, κ_λ  = 1). Figure 10 shows the ATLAS Runs 1 and 2 combined constraint on κ_λ  as a profile likelihood scan, combining several HH channels. Although the SM HH process is not expected to be observed at the LHC, in the absence of BSM enhancements, SM HH will be a benchmark channel for the high-luminosity upgrade of the LHC (HL-LHC).

 

 

 

Figure 9: 95% confidence level exclusion limits on the production of a narrow, spin-2 resonance decaying into a pair of Higgs bosons, from the CMS collaboration. http://cms-results.web.cern.ch/cms-results/public-results/publications/HIG-17-030/index.html

 

Figure 10: Profile likelihood scan, in terms of -2 lnΛ(κ_λ), performed as a function of κλ on data from the ATLAS collaboration. The dotted horizontal lines show the ±1σ and ±2σ uncertainties on κ_λ. https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PUBNOTES/ATL-PHYS-PUB-2019-009/

 

The discovery of the Higgs boson has presented us with exciting new paths for resolving the remaining mysteries of the SM. The Higgs boson has opened a door to new explorations of BSM physics at the LHC, through indirect constraints arising from precision measurements of the SM Higgs boson, as well as direct searches for new phenomena. This article has touched upon just a few of those studies, including searches for additional Higgs bosons and interactions of the SM Higgs boson with DM candidate particles. Moreover, the data provided by the upcoming Run 3 of the LHC and the HL-LHC will further aid our exploration of new physics using the Higgs boson.