5.9 Combination with Other Decay Channels

The results of the search presented here have been combined with other Higgs pair searches carried out by the CMS collaboration for other decay channels for the same data collection period at \(\sqrt{13}\ \textrm{TeV}\). For the combination, another three decay modes are considered in addition to the \(\textrm{b}\bar{\textrm{b}}\textrm{b}\bar{\textrm{b}}\), where one the Higgs decays to a \(\textrm{b}\bar{\textrm{b}}\) pair where the other decays into \(\gamma\gamma\), \(\tau\bar{\tau}\) or a pair or vector bosons, respectively. Combined upper limits where obtained by considering the product of the likelihoods, which depend on the HH cross section and several nuisance parameters. Some sources of uncertainty that are correlated between different channels, such as the luminosity or b-tagging uncertainty, where modelled using the same nuisance parameters in each individual likelihood. More details on the combination procedure are included in the following CMS Public Analysis Note [185].

The 95% C.L. upper limits for the Higgs pair non-resonant production cross section \(\sigma(\textrm{pp} \rightarrow \textrm{HH})\) from the \(\textrm{pp} \rightarrow \textrm{HH} \rightarrow \textrm{b}\bar{\textrm{b}}\textrm{b}\bar{\textrm{b}}\) can be compared with those obtained by the other searches in Figure 5.18. In the same figure, the upper limits for the combination of the four decay modes are also shown. The combination results are statistically compatible with the SM background contribution. An median expected limit of \(12.8\) times the SM expectation is obtained from the combination. The combined observed upper limit is \(22.2\) times the SM expectation, which is well-within the expected variation under the background only hypothesis. Analogously to what was done in Section 5.8, upper limits are also obtained for the cross section times branching ratio of Higgs pair production processes in the EFT framework, varying \(\kappa_\lambda\) in the range \([-20,20]\), while assuming that \(\kappa_\textrm{t}=1\) and the rest of the couplings are zero. This results are shown graphically in Figure 5.19; values for the anomalous self-coupling \(\kappa_\lambda\) in the range \(-11.8 < \kappa_\lambda < 18.8\) are not excluded by the data (\(-7.1 < \kappa_\lambda < 13.6\) was the expected interval). The aforementioned results make this combination analysis the most sensitive search to date at the LHC for non-resonant HH production. Substantial improvements can be expected due to the extensions of each analysis to the full Run II dataset.

Figure 5.18: Observed and expected \(\sigma(\textrm{pp} \rightarrow \textrm{HH})\) cross section limits relative to the SM for the combination of searches for Higgs boson pair production at 95% CL for values of \(\kappa_\lambda\) in the [-20,20] range, assuming \(\kappa_\textrm{t} = 1\). The inner green band and the outer yellow bands correspond to the range of percentiles around the median that contain the 68% and 95% times the upper limit under the background-only hypothesis. Figure adapted from [185].

Figure 5.19: Observed and expected \(\sigma(\textrm{pp} \rightarrow \textrm{HH})\) cross section limits for the combination of searches for Higgs boson pair production at 95% CL for values of \(\kappa_\lambda\) in the [-20,20] range, assuming \(\kappa_\textrm{t} = 1\). The inner green band and the outer yellow bands correspond to the range of percentiles around the median that contain the 68% and 95% times the upper limit under the background-only hypothesis. The anomalous couplings theoretical prediction with \(\kappa_\textrm{t} = 1\) is also shown in red colour. Figure adapted from [185].