The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The geometric signal acceptance as a function of $c\tau$. The acceptance is shown for four different LLP mass hypotheses: 7, 15, 40, and 55 GeV. The acceptance is defined by requiring at least 1 LLP to decay in the region defined as 400 cm $< |z| <$ 1100 cm, $r < $ 695.5 cm, and $|\eta| <$ 2.4.

Distribution of $m_{T}(W)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

Summary of the one-dimensional intervals at 68 and 95% CL.

Summary of the one-dimensional intervals at 68 and 95% CL.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

The measured single-differential cross sections in leading jet transverse momenta for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading lepton transverse momenta for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured double-differential cross sections as functions of $m_{\mathrm{jj}}$ and $|\Delta\eta_{\mathrm{jj}}|$ for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in photon transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading jet transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading lepton transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured double-differential cross sections as functions of $m_{\mathrm{jj}}$ and $|\Delta\eta_{\mathrm{jj}}|$ for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The expected and observed limits on the aQGC parameters at 95% confidence level. The last column presents the scattering energy values for which the amplitude would violate unitarity for the observed value of the aQGC parameter. All coupling parameter limits are set in TeV$^{-4}$, whereas the unitarity bounds are in TeV.

Differential cross sections as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Differential cross sections as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events.

Area normalized distribution as function of Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events

Response matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events.

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Distribution of the transverse momentum of the diphoton system for the $\mathrm{Z}\gamma\gamma$ muon channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons for the $\mathrm{W}\gamma\gamma$ electron channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons for the $\mathrm{Z}\gamma\gamma$ electron channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

The measured $\mathrm{W}\gamma\gamma$ and $\mathrm{Z}\gamma\gamma$ fiducial cross sections and corresponding theoretical predictions from MadGraph5_aMC@NLO. The measured yields in the electron and muon channels are extrapolated to a common fiducial phase space determined from simulated signal events at the generated particle level. Generated particles are considered stable if their mean decay length is larger than $1\,\mathrm{cm}$. Generated leptons are required to have a $\mathrm{p}_\mathrm{t}>15\,\mathrm{GeV}$ and $|\eta|<2.5$. The momenta of photons in a cone of $\Delta R=0.1$, the same cone size as the one applied to reconstructed data, are added to the charged lepton momentum to correct for final-state radiation. Generated photons are required to have $\mathrm{p}_\mathrm{t}>15\,\mathrm{GeV}$ and $|\eta|<2.5$. Additionally, the candidate photons are required to have no selected leptons or photons in a cone of radius $\Delta R=0.4$ and no other stable particles, apart from photons and neutrinos, in a cone of radius $\Delta R=0.1$. Events are then selected in the $\mathrm{W}\gamma\gamma$ channel by requiring exactly one electron (muon) with $\mathrm{p}_\mathrm{t}>30\,\mathrm{GeV}$ and at least two photons with $\mathrm{p}_\mathrm{t}>20\,\mathrm{GeV}$. Events are selected in the $\mathrm{Z}\gamma\gamma$ channel by requiring two electrons (muons), at least one of them with $\mathrm{p}_\mathrm{t}>30\,\mathrm{GeV}$, and not less than two photons, each of them with $\mathrm{p}_\mathrm{t}>20\,\mathrm{GeV}$. Additionally, the invariant mass of the dilepton system is required to be $m_{\ell\ell}>55\,\mathrm{GeV}$.

Expected and observed 95% confidence level intervals for the different anomalous couplings parameters in both the $\ell\nu\gamma\gamma$ and $\ell\ell\gamma\gamma$ channels. All parameters are fixed to their SM values except the one that is fitted. No unitarity regularisation scheme is applied. Intervals with a NAN value are not measured in the corresponding channels.

95% CL observed upper limits on the Yukawa couplings

The product of acceptance and selection efficiency within the fiducial region for the VBF $\mathrm{H}^{\pm\pm}\rightarrow\mathrm{W}^{\pm}\mathrm{W}^{\pm}\rightarrow 2\ell 2v$ and $\mathrm{H}^{\pm}\rightarrow\mathrm{W}^{\pm}\mathrm{Z}\rightarrow 3\ell v$ processes, as a function of $m_{\mathrm{H}_{5}}$. The combination of the statistical and systematic uncertainties is shown. The theoretical uncertainties in the acceptance are also included.

Expected and observed exclusion limits at 95\% confidence level for $\sigma_\mathrm{VBF}(\mathrm{H}^{\pm\pm}) \mathcal{B}(\mathrm{H}^{\pm\pm} \rightarrow \mathrm{W}^{\pm}\mathrm{W}^{\pm})$ as functions of $m_{\mathrm{H}^{\pm\pm}}$. The contribution of the $\mathrm{H}^{\pm}$ boson signal is set to zero for the derivation of the exclusion limits on the $\sigma_\mathrm{VBF}(\mathrm{H}^{\pm\pm}) \mathcal{B}(\mathrm{H}^{\pm\pm} \rightarrow \mathrm{W}^{\pm}\mathrm{W}^{\pm})$. Values above the curves are excluded.

Expected and observed exclusion limits at 95\% confidence level for $\sigma_\mathrm{VBF}(\mathrm{H}^{\pm}) \mathcal{B}(\mathrm{H}^{\pm} \rightarrow \mathrm{W}^{\pm}\mathrm{Z})$ as functions of $m_{\mathrm{H}^{\pm}}$. The contribution of the $\mathrm{H}^{\pm\pm}$ boson signal is set to zero for the derivation of the exclusion limits on the $\sigma_\mathrm{VBF}(\mathrm{H}^{\pm}) \mathcal{B}(\mathrm{H}^{\pm} \rightarrow \mathrm{W}^{\pm}\mathrm{Z})$. Values above the curves are excluded.

Expected and observed exclusion limits at 95\% confidence level for $s_{\mathrm{H}}$ as functions of $m_{\mathrm{H}_{5}}$ in the Georgi-Machacek model. Values above the curves are excluded. The exclusion limits for $s_{\mathrm{H}}$ are shown up to $m_{\mathrm{H}_{5}}=2000$ GeV, given the low sensitivity in the Georgi-Machacek model for values above that mass.

Covariance matrix for all the bins used in Figure 4. The covariance matrix from the background-only fit is shown.

Observed and expected correlations between the parameters in the production mode signal strength fit.

Results of the maximal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

The observed and expected impacts from the various sources of systematic uncertainty on the per-production mode signal strengths. The expected impacts are derived using an asimov dataset.

Observed and expected correlations between the parameters in the STXS stage 1.2 maximal merging fit.

Results of the maximal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

Results of the minimal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

Observed and expected correlations between the parameters in the STXS stage 1.2 maximal merging fit.

Observed and expected correlations between the parameters in the STXS stage 1.2 minimal merging fit.

Results of the minimal merging scheme STXS fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

Observed likelihood surface.

Observed and expected correlations between the parameters in the STXS stage 1.2 minimal merging fit.

Expected likelihood surface.

Observed likelihood surface.

Observed likelihood surface.

Expected likelihood surface.

Expected likelihood surface.

Observed likelihood surface.

Results of the STXS stage 0 fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

Expected likelihood surface.

Observed and expected correlations between the parameters in the STXS stage 0 fit.

Results of the STXS stage 0 fit. The best fit cross sections are shown together with the respective 68% C.L. intervals. The uncertainty is decomposed into the systematic and statistical components. The expected uncertainties on the fitted parameters are given in brackets. Also listed are the SM predictions for the cross sections and the theoretical uncertainty in those predictions.

Observed likelihood surface.

Observed and expected correlations between the parameters in the STXS stage 0 fit.

Expected likelihood surface.

Observed likelihood surface.

Observed likelihood surface.

Expected likelihood surface.

Expected likelihood surface.

Observed likelihood surface.

Expected likelihood surface.