This Letter presents results from a combination of searches for Higgs boson pair production using 126$-$140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. At 95% confidence level (CL), the upper limit on the production rate is 2.9 times the standard model (SM) prediction, with an expected limit of 2.4 assuming no Higgs boson pair production. Constraints on the Higgs boson self-coupling modifier $\kappa_{\lambda}=\lambda_{HHH}/\lambda_{HHH}^\mathrm{SM}$, and the quartic $HHVV$ coupling modifier $\kappa_{2V}=g_{HHVV}/g_{HHVV}^\mathrm{SM}$, are derived individually, fixing the other parameter to its SM value. The observed 95% CL intervals are $-1.2 < \kappa_{\lambda} < 7.2$ and $0.6 < \kappa_{2V} < 1.5$, respectively, while the expected intervals are $-1.6 < \kappa_{\lambda} < 7.2$ and $0.4 < \kappa_{2V} < 1.6$ in the SM case. Constraints obtained for several interaction parameters within Higgs effective field theory are the strongest to date, offering insights into potential deviations from SM predictions.
Observed and expected 95% CL upper limits on the signal strength for inclusive ggF HH and VBF HH production from the bb̄τ<sup>+</sup>τ<sup>-</sup>, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E<sub>T</sub><sup>miss</sup> decay channels, and their statistical combination. The predicted SM cross-section assumes m<sub>H</sub> = 125 GeV. The expected limit, along with its associated ±1σ and ±2σ bands, is calculated for the assumption of no HH production and with all NPs profiled to the observed data.
Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}b\bar{b}$.
Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\tau\tau$.
Constraints on the Higgs boson self-coupling are set by combining double-Higgs boson analyses in the $b\bar{b}b\bar{b}$, $b\bar{b}\tau^+\tau^-$ and $b\bar{b} \gamma \gamma$ decay channels with single-Higgs boson analyses targeting the $\gamma \gamma$, $ZZ^*$, $WW^*$, $\tau^+ \tau^-$ and $b\bar{b}$ decay channels. The data used in these analyses were recorded by the ATLAS detector at the LHC in proton$-$proton collisions at $\sqrt{s}=13$ TeV and correspond to an integrated luminosity of 126$-$139 fb$^{-1}$. The combination of the double-Higgs analyses sets an upper limit of $\mu_{HH} < 2.4$ at 95% confidence level on the double-Higgs production cross-section normalised to its Standard Model prediction. Combining the single-Higgs and double-Higgs analyses, with the assumption that new physics affects only the Higgs boson self-coupling ($\lambda_{HHH}$), values outside the interval $-0.4< \kappa_{\lambda}=(\lambda_{HHH}/\lambda_{HHH}^{\textrm{SM}})< 6.3$ are excluded at 95% confidence level. The combined single-Higgs and double-Higgs analyses provide results with fewer assumptions, by adding in the fit more coupling modifiers introduced to account for the Higgs boson interactions with the other Standard Model particles. In this relaxed scenario, the constraint becomes $-1.4 < \kappa_{\lambda} < 6.1$ at 95% CL.
Observed and expected 95% CL upper limits on the signal strength for double-Higgs production from the bbbb, bb$\tau\tau$ and bb$\gamma\gamma$ decay channels, and their statistical combination. The value $m_H$ = 125.09 GeV is assumed when deriving the predicted SM cross-section. The expected limit and the corresponding error bands are derived assuming the absence of the HH process and with all nuisance parameters profiled to the observed data.
Observed and expected 95% CL exclusion limits on the production cross-sections of the combined ggF HH and VBF HH processes as a function of $\kappa_\lambda$, for the three double-Higgs search channels and their combination. The expected limits assume no HH production. The red line shows the theory prediction for the combined ggF HH and VBF HH cross-section as a function of $\kappa_\lambda$ where all parameters and couplings are set to their SM values except for $\kappa_\lambda$. The band surrounding the red cross-section lines indicate the theoretical uncertainty of the predicted cross-section.
Observed and expected 95% CL exclusion limits on the production cross-sections of the VBF HH process as a function of $\kappa_{2V}$, for the three double-Higgs search channels and their combination. The expected limits assume no VBF HH production. The red line shows the predicted VBF HH cross-section as a function of $\kappa_{2V}$. The bands surrounding the red cross-section lines indicate the theoretical uncertainty of the predicted cross-section. The uncertainty band is smaller than the width of the plotted line.
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