| : Trilinear coupling : Box diagram |
| : The Feynman diagrams for the dominant gluon--gluon fusion production processes. In the SM, the (a) trilinear coupling process, (b) box diagram, and the destructive interference between the two processes, contribute to the total cross-section. In the figure, \klambda{} represents the Higgs boson trilinear coupling modifier. The quark content in the diagram is dominated by the top-quark contribution due to the large top-quark Yukawa coupling to the Higgs boson. The corresponding coupling strength modifier is denoted by $\kappa_t$. : Caption not extracted |
| : Trilinear coupling : $HHVV$ vertex |
| : $VVH$ Production mode : The VBF production of Higgs boson pairs via (a) the trilinear coupling, (b) the $HHVV$ vertex, and (c) the $VVH$ production mode. In the figure, $\kappa_V$ and $\kappa_{2V}$ denote the $HVV$ and $HHVV$ coupling strength modifiers. |
| : Caption not extracted |
| : |
| : : BDT score distributions for simulated ggF and VBF $HH\to\bbyy$ signal events and simulated background events from nonresonant $\gamma\gamma$ + jets and singly produced Higgs bosons decaying into $\gamma\gamma$ for the \protect\subref{fig:BDT_LM} low and \protect\subref{fig:BDT_HM} high mass regions. The data in the $m_{\gamma\gamma}$ sidebands, which are not expected to be populated by single nor double Higgs boson events, are also shown compared with the $\gamma\gamma$ + jets sample. The latter comprises the majority of the nonresonant diphoton background and is used in the training of the BDT. All distributions are normalised to unity. The vertical dashed lines correspond to the thresholds used to define the event categories. Events with a BDT score between 0 and the lowest threshold (thick dashed line) are discarded. Events satisfying the lowest threshold are categorised as Low Mass $i$, $i = 1..4$ (High Mass $i$, $i = 1..3$), with a higher category index $i$ corresponding to higher BDT scores and more signal-like events. |
| : Low Mass 1 |
| : Low Mass 2 : Low Mass 3 |
| : Low Mass 4 : High Mass 1 |
| : High Mass 2 : High Mass 3 |
| : Comparison between the diphoton invariant mass distribution in data (points with error bars) and the background-only fit (solid line) for the four low mass (a--d) and three high mass (e--g) categories of the $HH\to\bbyy$ search. In each of the regions, a higher category index corresponds to higher BDT scores and more signal-like events. The solid line peaks near 125~\GeV are due to single Higgs boson production. : Caption not extracted |
| : Caption not extracted |
| : Caption not extracted |
| : |
| : Observed (solid line) and expected (dashed line) value of $-2\ln\Lambda$ as a function of (a) $\kappa_{\lambda}$ and (b) $\kappa_{2V}$, when all other coupling modifiers (including, respectively, \kvv or \kl) are fixed to their SM predictions. : Caption not extracted |
| Likelihood contours at 68\% (solid line) and 95\% (dashed line) CL in the $(\kl, \kvv)$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross. |
| : |
| : : Likelihood contours at 68\% (solid line) and 95\% (dashed line) CL in the (a) $c_{gghh}$ versus $c_{hhh}$ and (b) $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the best-fit value is denoted by the cross. |
| The observed (filled circles) and expected (hollow circles) 95\% CL upper limits on the $HH$ ggF production cross-section in the SM and for seven HEFT benchmark points defined in Ref.~\cite{Alasfar:2023xpc}. The expected constraints are obtained from a background hypothesis with $\sigma_{HH} =0$. The predicted cross-sections of each of the models under consideration are shown by the crosses. Benchmarks where the filled circles are below the crosses are excluded. The inner and outer shaded bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The contribution from VBF production to the total $HH$ production cross-section is neglected. |
| Likelihood contours at 68\% (solid line) and 95\% (dashed line) CL in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the best-fit value is denoted by the cross. |