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Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon fusion in the standard model.

Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon fusion in the standard model.

Leading-order Feynman diagrams of Higgs boson pair nonresonant production via vector boson fusion in the standard model.

Leading-order Feynman diagrams of Higgs boson pair nonresonant production via vector boson fusion in the standard model.

Leading-order Feynman diagrams of Higgs boson pair nonresonant production via vector boson fusion in the standard model.

Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon fusion with anomalous Higgs boson couplings.

Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon fusion with anomalous Higgs boson couplings.

Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon fusion with anomalous Higgs boson couplings.

The distributions of some of the discriminants included in the DNN training for the single-lepton channel (upper) and the dilepton channel (lower). The distributions are shown after performing a maximum likelihood fit on the data for the variable pictured, using the same set of nuisance parameters (Section~\ref{systematics}) as in the likelihood fit used to extract signal. The variables are from upper left to lower right: the $H_{\mathrm{T}}$ variable, defined as the scalar sum of all selected jets \pt; the invariant mass of the two \Pbottom-tagged jets; the invariant mass of the two leptons; the $p_{\mathrm{T,LD}}^{\text{miss}}$, as defined in Section~~\ref{MET}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of some of the discriminants included in the DNN training for the single-lepton channel (upper) and the dilepton channel (lower). The distributions are shown after performing a maximum likelihood fit on the data for the variable pictured, using the same set of nuisance parameters (Section~\ref{systematics}) as in the likelihood fit used to extract signal. The variables are from upper left to lower right: the $H_{\mathrm{T}}$ variable, defined as the scalar sum of all selected jets \pt; the invariant mass of the two \Pbottom-tagged jets; the invariant mass of the two leptons; the $p_{\mathrm{T,LD}}^{\text{miss}}$, as defined in Section~~\ref{MET}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of some of the discriminants included in the DNN training for the single-lepton channel (upper) and the dilepton channel (lower). The distributions are shown after performing a maximum likelihood fit on the data for the variable pictured, using the same set of nuisance parameters (Section~\ref{systematics}) as in the likelihood fit used to extract signal. The variables are from upper left to lower right: the $H_{\mathrm{T}}$ variable, defined as the scalar sum of all selected jets \pt; the invariant mass of the two \Pbottom-tagged jets; the invariant mass of the two leptons; the $p_{\mathrm{T,LD}}^{\text{miss}}$, as defined in Section~~\ref{MET}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of some of the discriminants included in the DNN training for the single-lepton channel (upper) and the dilepton channel (lower). The distributions are shown after performing a maximum likelihood fit on the data for the variable pictured, using the same set of nuisance parameters (Section~\ref{systematics}) as in the likelihood fit used to extract signal. The variables are from upper left to lower right: the $H_{\mathrm{T}}$ variable, defined as the scalar sum of all selected jets \pt; the invariant mass of the two \Pbottom-tagged jets; the invariant mass of the two leptons; the $p_{\mathrm{T,LD}}^{\text{miss}}$, as defined in Section~~\ref{MET}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Higgs on the lower left and $\PW{+}\text{jets}$ + Other on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Higgs on the lower left and $\PW{+}\text{jets}$ + Other on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Higgs on the lower left and $\PW{+}\text{jets}$ + Other on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Higgs on the lower left and $\PW{+}\text{jets}$ + Other on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Other on the lower left and DY+Multiboson on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Other on the lower left and DY+Multiboson on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Other on the lower left and DY+Multiboson on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the nonresonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, \HH(\VBF) on the upper right, Top+Other on the lower left and DY+Multiboson on the lower right. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to the observed upper limit on its cross section.

The distributions of the DNN discriminants of the resonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, Top+Higgs on the upper right and $\PW{+}\text{jets}$ + Other on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to a cross section of 1\pb.

The distributions of the DNN discriminants of the resonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, Top+Higgs on the upper right and $\PW{+}\text{jets}$ + Other on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to a cross section of 1\pb.

The distributions of the DNN discriminants of the resonant search for each event category for the single-lepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category is shown on the upper left, Top+Higgs on the upper right and $\PW{+}\text{jets}$ + Other on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_SL}. The signal shown is scaled to a cross section of 1\pb.

The distributions of the DNN discriminants of the resonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category divided in bins of HME is shown on the upper left, Top+Other upper right and DY+Multiboson on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to a cross section of 1\pb.

The distributions of the DNN discriminants of the resonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category divided in bins of HME is shown on the upper left, Top+Other upper right and DY+Multiboson on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to a cross section of 1\pb.

The distributions of the DNN discriminants of the resonant search for each event category for the dilepton channel, after performing a maximum likelihood fit to the same distributions in data. The DNN shown corresponds to a scalar resonance with mass 400\GeV. The DNN discriminant for the \HH(\GGF) category divided in bins of HME is shown on the upper left, Top+Other upper right and DY+Multiboson on the lower. The event categories are summarised in Table~\ref{tab:Strategy_scheme_DL}. The signal shown is scaled to a cross section of 1\pb.

Observed and expected 95\% \CL upper limits on the inclusive nonresonant \HH production cross section divided by the SM prediction obtained for both single-lepton and dilepton channels, and from their combination. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL , while the red line shows the SM prediction.

Observed and expected 95\% \CL upper limits on the nonresonant \HH production via vector boson fusion cross section divided by the SM prediction obtained for both single-lepton and dilepton channels, and from their combination. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL, while the red line shows the SM prediction.

Observed and expected 95\% \CL upper limits on the nonresonant \HH production cross section as a function of the Higgs boson self-coupling strength modifier \klambda. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL. All Higgs boson couplings other than $\lambda$ are set to the values predicted by the SM. Overlaid in red is the curve representing the predicted \HH production cross section.

Observed and expected 95\% \CL upper limits on the nonresonant \HH production via \VBF cross section as a function of the effective coupling \CVV. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL. The \GGF contribution in this case is set to the SM expectation. All other Higgs boson couplings are set to the values predicted by the SM. Overlaid in red is the curve representing the predicted \HH production cross section.

Observed and expected 95\% \CL exclusion limits on the nonresonant \HH production cross section as a function of the effective couplings \klambda and \CVV. The blue area is excluded by the observation. The 1 and $2\sigma$ confidence intervals around the expected median exclusion contour are shown as dark and light-grey areas corresponding to 68 and 95\% respectively. The red diamond shows the SM expectation while the fine dashed lines show the theoretical cross section contours. All other Higgs boson couplings are set to the values predicted by the SM.

Observed and expected 95\% \CL exclusion limits on the nonresonant \HH production via \VBF cross section as a function of the effective couplings \CV and \CVV. The blue area is excluded by the observation. The 1 and $2\sigma$ confidence intervals around the expected median exclusion contour are shown as dark and light-grey areas corresponding to 68 and 95\% respectively. The red diamond shows the SM expectation while the fine dashed lines show the theoretical cross section contours. The \GGF contribution in this case is set to the SM expectation. All other Higgs boson couplings are set to the values predicted by the SM.

Observed and expected 95\% \CL exclusion limits on the nonresonant \HH production cross section as a function of the effective couplings \klambda and \ktop. The blue area is excluded by the observation. The 1 and $2\sigma$ confidence intervals around the expected median exclusion contour are shown as dark and light-grey areas corresponding to 68 and 95\% respectively. The red diamond shows the SM expectation while the fine dashed lines show the theoretical cross section contours. All other Higgs boson couplings are set to the values predicted by the SM.

Observed and expected 95\% \CL upper limits on the nonresonant \HH production cross section for two different benchmark scenarios ``JHEP04(2016)01'' and ``JHEP03(2020)91'' from Refs.~\cite{Carvalho_2016,Capozi_2020}. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL.

Observed and expected 95\% CL upper limits on the nonresonant \HH production cross section as a function of the effective coupling \ctwo. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL. All other Higgs boson couplings are set to the values predicted in the SM. Overlaid in red (upper) is the curve representing the predicted \HH production cross section.

Observed and expected 95\% CL exclusion limits on the nonresonant \HH production cross section as a function of the effective couplings \klambda and \ctwo. The blue area is excluded by the observation. The 1 and $2\sigma$ confidence intervals around the expected median exclusion contour are shown as dark and light-grey areas corresponding to 68 and 95\% respectively. The red diamond shows the SM expectation while the fine dashed lines show the theoretical cross section contours. All other Higgs boson couplings are set to the values predicted in the SM.

Observed and expected 95\% CL upper limits on the production of new particles $X$ of spin-0 (upper) and spin-2 (lower) and mass $m_X$ in the range $250 \leq m_X \leq 900\GeV$, which decay to Higgs boson pairs. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL. Theory predictions in benchmark scenarios for bulk radion (upper) and bulk graviton (lower) models are overlaid.

Observed and expected 95\% CL upper limits on the production of new particles $X$ of spin-0 (upper) and spin-2 (lower) and mass $m_X$ in the range $250 \leq m_X \leq 900\GeV$, which decay to Higgs boson pairs. The green and yellow bands show the 1 and $2\sigma$ confidence intervals, corresponding to 68 and 95\% \CL. Theory predictions in benchmark scenarios for bulk radion (upper) and bulk graviton (lower) models are overlaid.