Normalized differential cross sections, compared with the SM predictions, as a function of the absolute value of pseudorapidity of the subleading jet in transverse momentum. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the invariant mass of the two jets. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the photon's transverse momentum. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the event centrality as defined in Ref.[13] of the paper. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Normalized differential cross sections, compared with the SM predictions, as a function of the Zeppenfeld variable that is defined in Eq.(1) of the paper. The SM predictions are obtained using Madgraph5_aMC@NLO version 2.6.5 at NLO in QCD with PYTHIA version 8.240

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{W}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{HWB}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Negative of twice in the difference in the log-likelihood as a function of $c_{\mathrm{HWB}}$ and $c_{\mathrm{W}}$, based on 138 $\mathrm{fb}^{-1}$ of CMS data at 13 TeV.

Predicted and measured EWK $\gamma\mathrm{jj}$ fiducial cross sections.

Normalized differential distributions of the $\Delta R (\gamma,\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the min. $\Delta R (\gamma,\mathrm{t})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Normalized differential distributions of the min. $\Delta R (\gamma,\mathrm{t})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the $m(\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Normalized differential distributions of the $m(\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the photon $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the photon $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the $\Delta \phi (\ell,\ell)$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the $\Delta \phi (\ell,\ell)$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the ratio between the cross sections of $\mathrm{tt\gamma}$ and $\mathrm{tt}$, as a function of the leading top quark $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the ratio between the cross sections of $\mathrm{tt\gamma}$ and $\mathrm{tt}$, as a function of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the leading top quark $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the leading top quark $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $\Delta R (\gamma,\mathrm{tt})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $\Delta R (\gamma,\mathrm{tt})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the min. $\Delta R (\gamma,\mathrm{t})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the min. $\Delta R (\gamma,\mathrm{t})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $m(\mathrm{tt})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $m(\mathrm{tt})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the photon $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the photon $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $\Delta \phi (\ell,\ell)$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $\Delta \phi (\ell,\ell)$.

Correlation matrix of the total uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading top $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading top $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading lepton $p_{\mathrm{T}}$.

The 95% CL upper limits on the inclusive signal strength $ r = \sigma_{HH} /\sigma_{HH} ^\text{SM} $ for each channel and their combination. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The $ b\overline{b}b\overline{b} $ and $ b\overline{b}WW $ contributions have been combined in order to simplify the presentation of results.

The 95$\%$ CL upper limits on the VBF signal strength $r_{VBF HH} = \sigma_{VBF HH}/\sigma_{VBF HH}^{SM}$ for each channel and their combination. The inner (green) band and the outer (yellow) band indicate the 68 and 95$\%$ CL intervals, respectively, under the background-only hypothesis. Not all of the eight channels are used to extract the combined VBF limit. The contributing channels are indicated in the figure. The b\overline{b}b\overline{b} $ and $ b\overline{b}WW $ contributions have been combined in order to simplify the presentation of results.

The 95$\%$ CL upper limits on the inclusive HH cross section as a function of $\kappa_\lambda$. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section.The inner (green) band and the outer (yellow) band indicate the 68 and 95$\%$ CL intervals, respectively, under the background-only hypothesis. The star shows the limit at the SM value for $\kappa_\lambda$.

The 95$\%$ CL upper limits on the inclusive HH cross section as a function of $\kappa_{2V}$. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH VBF signal cross sections are not considered because here we directly constrain the measured cross section.The inner (green) band and the outer (yellow) band indicate the 68 and 95$\%$ CL intervals, respectively, under the background-only hypothesis. The star shows the limit at the SM value for $\kappa_{2V}$.

The profile likelihood ratio test statistic $-2\Delta\log(L)$ as a function of coupling modifiers $\kappa_\lambda$ for the combination of all channels, when all the other parameters are fixed to their SM values.

The profile likelihood ratio test statistic $-2\Delta\log(L)$ as a function of coupling modifiers $\kappa_{2V}$ for the combination of all channels, when all the other parameters are fixed to their SM values.

The 68 $\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68 $\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ observed CL contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 standard deviation expected contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 standard deviation observed contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The observed best-fit values in the ($\kappa_\lambda$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68 $\%$ expected CL contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68$\%$ expected CL contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 standard deviation expected contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 standard deviation observed contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The observed best-fit values in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68 $\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_t$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68 $\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_t$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_t$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_\lambda$, $\kappa_t$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The observed best-fit values in the ($\kappa_\lambda$, $\kappa_t$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

Upper limits on the HH production cross section at 95$\%$ CL for the two sets of HEFT benchmarks. The theoretical uncertainties in the HH GGF signal cross section are not considered because we directly constrain the measured cross section.

Upper limits on the HH cross section as a function of the $C_2$ coupling modifier. The theoretical uncertainties in the HH GGF signal cross section are not considered because we directly constrain the measured cross section.

The profile likelihood ratio test statistic $-2\Delta\log(L)$ as a function of the $c_2$ coupling modifier.

The 68$\%$CL expected contours of $-2\Delta\log(L)$ in the ($c_2$,$\kappa_t$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 68$\%$CL observed contours of $-2\Delta\log(L)$ in the ($c_2$,$\kappa_t$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 95$\%$CL expected contours of $-2\Delta\log(L)$ in the ($c_2$,$\kappa_t$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 95$\%$CL observed contours of $-2\Delta\log(L)$ in the ($c_2$,$\kappa_t$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 68 $\%$ CL expected contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 68 $\%$ CL observed contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 95 $\%$ CL expected contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) for the combination of all channels when all the other parameters are fixed to their SM value.

The 95 $\%$ CL observed contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) for the combination of all channels when all the other parameters are fixed to their SM value.

The $-2\Delta\log(L)$ scan for the combination of all channels as a function of $|\cos{\alpha}|$ for singlet extensions of the SM with spontaneous $Z_2$ symmetry breaking. The $|\cos{\alpha}|$ is constrained at 95\% CL between 0.79 and 1. The ranges of $|\cos{\alpha}|$ and $\lambda_\text{eff}$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown.

The 95$\%$ CL expected contour of $-2\Delta\log(L)$ in the ($|\cos{\alpha}|$, $\lambda_{eff}$) plane, where $\lambda_{eff}$=$\lambda_\alpha$-$\tan{(\alpha)\frac{m_{2}}{\nu}}$. The ranges of $|\cos{\alpha}|$ and $\lambda_{eff}$ are chosen to guarantee the validity of the models. The excluded regions are to the left of the curves shown.

The 95$\%$ CL observed contour of $-2\Delta\log(L)$ in the ($|\cos{\alpha}|$, $\lambda_{eff}$) plane, where $\lambda_{eff}$=$\lambda_\alpha$-$\tan{(\alpha)\frac{m_{2}}{\nu}}$. The ranges of $|\cos{\alpha}|$ and $\lambda_{eff}$ are chosen to guarantee the validity of the models. The excluded regions are to the left of the curves shown.

The 95% CL expected contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ in the 2HDM-I model. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL observed contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ in the 2HDM-I model. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ for the 2HDM I models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ for the 2HDM II models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ for the 2HDM X models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($m_{H}$, $\tan\beta$) plane for a fixed value of $|\cos(\beta-\alpha)|=0.2$ for the 2HDM Y models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $m_{H}$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $m_{H}$ > 800 GeV for all models considered.

The 95$\%$ CL expected contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ in the 2HDM-I model. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The 95$\%$ CL observed contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ in the 2HDM-I model. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The 95% CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ for the 2HDM I models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The 95% CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ for the 2HDM II models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The 95% CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ for the 2HDM X models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The 95% CL contour of $-2\Delta\log(L)$ for the combination of all channels in the ($|\cos(\beta-\alpha)|$, $\tan\beta$) plane for a fixed value of $m_{H}=1000GeV$ for the 2HDM Y models. In these and all other cases considered in this paper, $m_H$ = $m_A$. The ranges of $|\cos(\beta-\alpha)|$ and $\tan\beta$ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $\tan\beta$ = 0.5 is excluded for $|\cos(\beta-\alpha)|$ > 0.16 and $|\cos(\beta-\alpha)|$ < -0.13 for all models considered.

The $-2\Delta\log(L)$ scan for the combination of all channels as a function of $\xi$ for MCHM$_4$. The range of $\xi$ is chosen to guarantee the validity of the model. At 95% CL, $\xi$ is constrained to be between 0 and 0.45 in MCHM$_4$.

The $-2\Delta\log(L)$ scan for the combination of all channels as a function of $\xi$ for MCHM$_5$. The range of $\xi$ is chosen to guarantee the validity of the model. At 95% CL, $\xi$ is constrained to be between 0 and 0.26 in MCHM$_5$.

Treatment of most important common systematic uncertainties in the S2 scenario.

The expected upper limits at 95% CL on the HH signal strength from the combination of all the considered channels at different integrated luminosities for the S2 scenario.

The expected upper limits at 95% CL on the HH signal strength from the combination of all the considered channels under different assumptions on the systematic uncertainties for an integrated luminosity of 3000fb$^{-1}$ (right).

The expected $-2\Delta\log(L)$ scan as a function of coupling modifier $\kappa_\lambda$ for the combination of all contributing channels, projected to different integrated luminosities. All other parameters are fixed to their SM values.

The expected $-2\Delta\log(L)$ scan as a function of coupling modifier $\kappa_\lambda$ for the combination of all contributing channels, projected under different assumptions on the systematic uncertainties for an integrated luminosity of 3000fb$^{-1}$. All other parameters are fixed to their SM values.

Expected significance for the HH signal projected to 2000 or 3000 fb$^{-1}$ under different assumptions of systematic uncertainties.

The expected signal significance as a function of integrated luminosity for the nominal scenario of systematic uncertainties S2 and for the scenario with statistical uncertainties only.

The expected signal significance as a function of $\kappa_\lambda$ under different assumptions on the systematic uncertainties for an integrated luminosity of 3000fb$^{-1}$.

The 95$\%$ CL upper limits on the inclusive HH signal strenngth as a function of $\kappa_{\lambda}$ coupling modifier. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH VBF signal cross sections are not considered because here we directly constrain the measured cross section.The inner (green) band and the outer (yellow) band indicate the 68 and 95$\%$ CL intervals, respectively, under the background-only hypothesis.

The 95$\%$ CL upper limits on the inclusive HH signal strenngth as a function of $\kappa_{2V}$ coupling modifier. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH VBF signal cross sections are not considered because here we directly constrain the measured cross section.The inner (green) band and the outer (yellow) band indicate the 68 and 95$\%$ CL intervals, respectively, under the background-only hypothesis.

The $-2\Delta\log(L)$ scan as a function of $\kappa_\lambda$ for all channels, when all the other parameters are fixed to their SM value.

The $-2\Delta\log(L)$ scan as a function of $\kappa_{2V}$ for all channels, when all the other parameters are fixed to their SM value.

The $-2\Delta\log(L)$ scan as a function of $\kappa_\lambda$ for all channels, when all the other parameters are fixed to their SM value.

The 95$\%$ CL upper limits on the inclusive HH cross section as a function of $\kappa_\lambda$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section.

The 95$\%$ CL upper limits on the inclusive VBF HH cross section as a function of $\kappa_{2V}$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section.

The 95$\%$ CL upper limits on the inclusive HH signal strength as a function of $\kappa_\lambda$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section.

The 95$\%$ CL upper limits on the inclusive VBF HH signal strength as a function of $\kappa_{2V}$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section.

The best fit value for $\kappa_\lambda$ compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values.

The best fit value for $\kappa_2V$ compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values.

The 68$\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 68$\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL expected contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL observed contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 $\sigma$ expected contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The 5 $\sigma$ observed contours of $-2\Delta\log(L)$ in the ($\kappa_{V}$, $\kappa_{2V}$) plane for the combination of all channels when all the other parameters are fixed to their SM values.

The best-fit values of ($\kappa_{V}$, $\kappa_{2V}$) for the combination of all channels when all the other parameters are fixed to their SM values.

The 95$\%$ CL upper limits on the inclusive VBF HH signal strength as a function of $\kappa_{2V}$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH GGF and VBF signal cross sections are not considered because here we directly constrain the measured cross section. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis.

The $-2\Delta\log(L)$ scan as a function of the $c_2$ coupling modifier for all channels, when all the other parameters are fixed to their SM values.

The 95% CL upper limits on the inclusive HH cross section as a function of the $c_2$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF signal cross sections are not considered because we directly constrain the measured cross section.

The 95% CL upper limits on the inclusive HH signal strength as a function of the $c_2$ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF signal cross sections are considered in this case

The best fit value for the $c_2$ coupling modifier compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values.

The observed 68 $\%$ CL observed contours ($\kappa_\lambda$ =1.0) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_t$) plane for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 68 $\%$ CL observed contours (floating $\kappa_\lambda$) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_t$) plane for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 95 $\%$ CL observed contours ($\kappa_\lambda$ =1.0) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_t$) plane for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 95 $\%$ CL observed contours (floating $\kappa_\lambda$) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_t$) plane for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The best fit values ($\kappa_\lambda$ =1.0) of ($c_2$, $\kappa_t$) for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The best fit values (floating $\kappa_\lambda$) of ($c_2$, $\kappa_t$) for the combination of all channels when $\kappa_t$ is allowed to vary. The range of $\kappa_t$ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 68$\%$ CL cobsevred contours ($\kappa_{t}$ =1.0 (SM)) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 68$\%$ CL cobsevred contours (floating $\kappa_{t}$) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 95$\%$ CL cobsevred contours ($\kappa_{t}$ =1.0 (SM)) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 95$\%$ CL cobsevred contours (floating $\kappa_{t}$) of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The best fit values ($\kappa_{t}$ =1.0 (SM)) of ($c_2$, $\kappa_\lambda$) for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The best fit values (floating $\kappa_{t}$) for ($c_2$, $\kappa_\lambda$) for the combination of all channels when $\kappa_\lambda$ is allowed to vary. The range of $\kappa_\lambda$ is set between -15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values.

The observed 68% CL contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed best fit values in the ($c_2$, $\kappa_\lambda$) plane for the combination of all channels when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}b\bar{b}$ resolved channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed best fit values in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}b\bar{b}$ resolved channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}b\bar{b}$ merged channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed best fit values in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}b\bar{b}$ merged channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}\gamma\gamma$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed best fit values in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}\gamma\gamma$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}W^{+}W^{-}$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The best fit values in in the ($c_2$, $\kappa_\lambda$) plane for the $b\bar{b}W^{+}W^{-}$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in in the ($c_2$, $\kappa_\lambda$) plane for the multilepton channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The best fit values in in the ($c_2$, $\kappa_\lambda$) plane for the multilepton channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The observed 68% CL contours of $-2\Delta\log(L)$ in in the ($c_2$, $\kappa_\lambda$) plane for the $W^{+}W^{-}\gamma\gamma$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

The best fit values in in the ($c_2$, $\kappa_\lambda$) plane for the $W^{+}W^{-}\gamma\gamma$ channel when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $b\bar{b}\tau\tau$ channel are not within the range of the figure.

Signal strength and significance for $\text{t}\overline{\text{t}}\text{Z}(\text{Z}\to\text{b}\overline{\text{b}})$ decays with respect to the standard model expectation of unity.

Signal strength and significance for $\text{t}\overline{\text{t}}\text{Z}(\text{Z}\to\text{c}\overline{\text{c}})$ decays with respect to the standard model expectation of unity.

2D likelihood scans for $\kappa_{b}$ and $\kappa_{c}$ for $\text{t}\overline{\text{t}}\text{H}(\text{H}\to\text{c}\overline{\text{c}})$ and $\text{t}\overline{\text{t}}\text{H}(\text{H}\to\text{b}\overline{\text{b}})$.

Unfolded $R(\rho_{s})$ observable in the 2-to-3 measurement (normalized and divided by bin width). The parton level is defined with two stable top-quarks and a jet with $p_{T}>50$ GeV and $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Impact of systematic uncertainties on the 2-to-3 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-3 unfolded observable.

Unfolded number of events in the 2-to-7measurement (not normalized). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Covariance matrix for statistical and systematic effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Unfolded $R(\rho_{s})$ observable in the 2-to-7 measurement (normalized and divided by bin width). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Impact of systematic uncertainties on the 2-to-7 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-7 unfolded observable.

The 95% CL limits on the cross-section $\sigma(pp \rightarrow Z' \rightarrow \chi \chi$) times branching ratio B in fb with all statistical and systematic uncertainties, for the $R_{\text{inv}}=$0.6 signal points.

Data yield in the PFN signal region.

Yield of data in the ANTELOPE signal region in the binning used for BumpHunter fitting.

Observed profile likelihood as a function of $\sigma\times\mathcal{B}_{H\rightarrow WW^{*}}$ normalised by the SM expectation for the single-channel measurements

Two-dimensional likelihood scan of the measured values of $\sigma_{ZH}\times\mathcal{B}_{H\rightarrow WW^{*}}$ vs. $\sigma_{WH}\times\mathcal{B}_{H\rightarrow WW^{*}}$.

The observed values of the background normalisation factors for the combined 2-POI fit. The uncertainties correspond to the total of all statistical and systematic sources.

Measured cross sections times the $H\rightarrow WW^{*}$ branching ratio for the $p_T^V$ scheme.

Measured cross sections times the $H\rightarrow WW^{*}$ branching ratio for the STXS scheme. Note: the uncertainties of "-0" are due to the confidence interval reaching the minimum allowed value of the POI.

Correlation matrix of the POIs and normalisation factors for the 2-POI inclusive analysis

Correlation matrix of the parameters of interest, normalisation factors and nuissance parameters for the $p_T^V$ scheme

Correlation matrix of the parameters of interest, normalisation factors and nuissance parameters for the STXS scheme

Event data from Z-dominated SR

The combined covariance matrix for the differential cross-section distribution.

Statistical covariance matrix for the differential cross-section distribution.

Statistical covariance matrix for the differential cross-section distribution.

Systematic covariance matrix for the differential cross-section distribution.

Systematic covariance matrix for the differential cross-section distribution.