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.

Experimental uncertainties affecting transfer factors in the analysis that is used to estimate the W background in the signal region (SR). The number of W boson events are denoted as $W_{SR}$ for the SR and in analogy as $W_{\mu\nu}$ ($W_{e\nu}$) for the single-muon (single-electron) control region (CR).

Uncertainties assigned to the simulation based processes in SR and CRs.

Uncertainties assigned to the simulation based processes in SR and CRs.

Cross sections (fb) at large Z $p_{T}$ values in the Z -> $\ell\ell$ and Z -> $\nu\nu$ channels, and their combination. The theoretical predictions from Madgraph at NLO in QCD and corrected to NLO in electroweak using the NNPDF 3.0 are also reported. With the exception of the largest Z $p_{T}$ bin, the statistical uncertainties in the measurements are much smaller than the systematic uncertainties. Both measurements and predictions correspond to $\sigma \mathcal{B}(Z -> \ell\ell)$, where $\sigma$ is the total fiducial cross section, $\mathcal{B}$ is the branching fraction, and $\ell$ is a charged lepton. The $Z -> \nu\nu$ measurement corresponds to $\sigma \mathcal{B}(Z -> \ell\ell)/\mathcal{B}(Z -> \nu\nu)$.

Cross sections (fb) at large Z $p_{T}$ values in the Z -> $\ell\ell$ and Z -> $\nu\nu$ channels, and their combination. The theoretical predictions from Madgraph at NLO in QCD and corrected to NLO in electroweak using the NNPDF 3.0 are also reported. With the exception of the largest Z $p_{T}$ bin, the statistical uncertainties in the measurements are much smaller than the systematic uncertainties. Both measurements and predictions correspond to $\sigma \mathcal{B}(Z -> \ell\ell)$, where $\sigma$ is the total fiducial cross section, $\mathcal{B}$ is the branching fraction, and $\ell$ is a charged lepton. The $Z -> \nu\nu$ measurement corresponds to $\sigma \mathcal{B}(Z -> \ell\ell)/\mathcal{B}(Z -> \nu\nu)$.

Cross sections normalized to the total cross section measurements at high Z $p_{T}$ values in the Z -> $\ell\ell$ and Z -> $\nu\nu$ channels, and in their combination. The uncertainty includes both statistical and systematic uncertainties.

Cross sections normalized to the total cross section measurements at high Z $p_{T}$ values in the Z -> $\ell\ell$ and Z -> $\nu\nu$ channels, and in their combination. The uncertainty includes both statistical and systematic uncertainties.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on charged leptons.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on charged leptons.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on charged leptons.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on charged leptons.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on neutrinos.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on neutrinos.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on neutrinos.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on neutrinos.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

The relative statistical and systematic uncertainties from various sources for the absolute cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

The relative statistical and systematic uncertainties from various sources for the relative cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

Cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

Cross section measurements in bins of Z $p_{T}$ on neutrinos and charged leptons.

Measured fiducial cross sections for the $\mathrm{W}^\pm_{\mathrm{L}}\mathrm{W}^\pm_{\mathrm{L}}$ and $\mathrm{W}^\pm_{\mathrm{X}}\mathrm{W}^\pm_{\mathrm{T}}$ processes, and for the $\mathrm{W}^\pm_{\mathrm{L}}\mathrm{W}^\pm_{\mathrm{X}}$ and $\mathrm{W}^\pm_{\mathrm{T}}\mathrm{W}^\pm_{\mathrm{T}}$ processes for the helicity eigenstates defined in the parton-parton center-of-mass frame. The combination of the statistical and systematic uncertainties is shown. $\mathcal{B}$ is the branching fraction for $\mathrm{W}\mathrm{W} \rightarrow \ell \nu \ell' \nu$. The fiducial region is defined by requiring two same-sign leptons with $p_{T}>20$, $|\eta|<2.5$, and $m_{ll}>20$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$. The jets at generator level are clustered from stable particles, excluding neutrinos, using the anti-kt clustering algorithm with R = 0.4, and are required to have $p_{T}>50$ and $|\eta|<4.7$. The jets within $\Delta R<0.4$ of the selected charged leptons are not included. The theoretical predictions including the $\mathcal{O}(\alpha_{s}\alpha^6)$ and $\mathcal{O}(\alpha^7)$ corrections to the \MGvATNLO LO cross sections, as described in arXiv:2009.09429, are also shown. The theoretical uncertainties include statistical, PDF, and LO scale uncertainties.

Expected and observed yields from the standard model processeses in the WW signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

Expected and observed yields from the standard model processeses in the WW signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

Expected and observed yields from the standard model processeses in the WW signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

Expected and observed yields from the standard model processeses in the WZ signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

Expected and observed yields from the standard model processeses in the WZ signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

Expected and observed yields from the standard model processeses in the WZ signal region. The combination of the statistical and systematic uncertainties are shown. The predicted yields are shown with their best-fit normalizations from the simultaneous fit.

The measured inclusive fiducial cross section measurements. The WW fiducial region is defined by requiring two same-sign leptons with $p_{T}>20$, $|\eta|<2.5$, and $m_{ll}>20$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$. The jets at generator level are clustered from stable particles, excluding neutrinos, using the anti-kt clustering algorithm with R = 0.4, and are required to have $p_{T}>50$ and $|\eta|<4.7$. The jets within $\Delta R<0.4$ of the selected charged leptons are not included. The WZ fiducial region is defined by requiring three leptons with $p_{T}>20$, $|\eta|<2.5$, a pair of opposite charge same-flavor lepton pair with $|m_{ll}-m_{Z}|<15$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$.

The measured inclusive fiducial cross section measurements. The WW fiducial region is defined by requiring two same-sign leptons with $p_{T}>20$, $|\eta|<2.5$, and $m_{ll}>20$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$. The jets at generator level are clustered from stable particles, excluding neutrinos, using the anti-kt clustering algorithm with R = 0.4, and are required to have $p_{T}>50$ and $|\eta|<4.7$. The jets within $\Delta R<0.4$ of the selected charged leptons are not included. The WZ fiducial region is defined by requiring three leptons with $p_{T}>20$, $|\eta|<2.5$, a pair of opposite charge same-flavor lepton pair with $|m_{ll}-m_{Z}|<15$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$.

The measured inclusive fiducial cross section measurements. The WW fiducial region is defined by requiring two same-sign leptons with $p_{T}>20$, $|\eta|<2.5$, and $m_{ll}>20$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$. The jets at generator level are clustered from stable particles, excluding neutrinos, using the anti-kt clustering algorithm with R = 0.4, and are required to have $p_{T}>50$ and $|\eta|<4.7$. The jets within $\Delta R<0.4$ of the selected charged leptons are not included. The WZ fiducial region is defined by requiring three leptons with $p_{T}>20$, $|\eta|<2.5$, a pair of opposite charge same-flavor lepton pair with $|m_{ll}-m_{Z}|<15$, and two jets with $m_{jj}>500$ and $|\Delta \eta_{jj}|>2.5$.

Distributions of $m_{jj}$ in the WW signal region.

Distributions of $m_{jj}$ in the WW signal region.

Distributions of $m_{jj}$ in the WW signal region.

Distributions of $m_{ll}$ in the WW signal region.

Distributions of $m_{ll}$ in the WW signal region.

Distributions of $m_{ll}$ in the WW signal region.

Distributions of $m_{jj}$ in the WZ signal region.

Distributions of $m_{jj}$ in the WZ signal region.

Distributions of $m_{jj}$ in the WZ signal region.

Distributions of BDT score in the WZ signal region.

Distributions of BDT score in the WZ signal region.

Distributions of BDT score in the WZ signal region.

Absolute WW cross section in $m_{jj}$ bins.

Absolute WW cross section in $m_{jj}$ bins.

Absolute WW cross section in $m_{jj}$ bins.

Normalized WW cross section in $m_{jj}$ bins.

Normalized WW cross section in $m_{jj}$ bins.

Normalized WW cross section in $m_{jj}$ bins.

Absolute WW cross section in $m_{ll}$ bins.

Absolute WW cross section in $m_{ll}$ bins.

Absolute WW cross section in $m_{ll}$ bins.

Normalized WW cross section in $m_{ll}$ bins.

Normalized WW cross section in $m_{ll}$ bins.

Normalized WW cross section in $m_{ll}$ bins.

Absolute WW cross section in $p_{T}^{l max}$ bins.

Absolute WW cross section in $p_{T}^{l max}$ bins.

Absolute WW cross section in $p_{T}^{l max}$ bins.

Normalized WW cross section in $p_{T}^{l max}$ bins.

Normalized WW cross section in $p_{T}^{l max}$ bins.

Normalized WW cross section in $p_{T}^{l max}$ bins.

Absolute WZ cross section in $m_{jj}$ bins.

Absolute WZ cross section in $m_{jj}$ bins.

Absolute WZ cross section in $m_{jj}$ bins.

Normalized WZ cross section in $m_{jj}$ bins.

Normalized WZ cross section in $m_{jj}$ bins.

Normalized WZ cross section in $m_{jj}$ bins.

Distributions of $m_{T}^{WW}$ in the WW signal region.

Distributions of $m_{T}^{WW}$ in the WW signal region.

Distributions of $m_{T}^{WW}$ in the WW signal region.

Distributions of $m_{T}^{WZ}$ in the WZ signal region.

Distributions of $m_{T}^{WZ}$ in the WZ signal region.

Distributions of $m_{T}^{WZ}$ in the WZ signal region.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic, obtained without using any unitarization procedure.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic, obtained without using any unitarization procedure.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic, obtained without using any unitarization procedure.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic by cutting the EFT expansion at the unitarity limit.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic by cutting the EFT expansion at the unitarity limit.

Observed and expected lower and upper 95\% confidence level limits in TeV$^{-4}$ on the parameters of the quartic by cutting the EFT expansion at the unitarity limit.