Acceptance times efficiency as a function of resonant mass for each event selection step in the search for a neutral heavy scalar resonance produced in association with a W boson decaying to a charged lepton and a neutrino.

Acceptance times efficiency as a function of resonant mass for each event selection step in the search for a neutral heavy scalar resonance produced in association with a Z boson decaying to charged leptons.

Acceptance times efficiency as a function of resonant mass for each event selection step in the search for a neutral heavy scalar resonance produced in association with a Z boson decaying to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to neutrinos.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy narrow-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 260 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 300 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to charged leptons.

Acceptance times efficiency as a function of pseudoscalar resonant mass for each event selection step in the search for a neutral heavy large-width pseudoscalar resonance that decays to a 400 GeV scalar resonance and a Z boson, which decays to charged leptons.

Expected and observed 95% CL upper limits on the cross-section of resonant $H\to 4b$ production in association with a W boson. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected and observed 95% CL upper limits on the cross-section of resonant $H\to 4b$ production in association with a W boson. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected and observed 95% CL upper limits on the cross-section of resonant $H\to 4b$ production in association with a Z boson. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected and observed 95% CL upper limits on the cross-section of resonant $H\to 4b$ production in association with a Z boson. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected 95% CL upper limits on the cross-section of a heavy narrow-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected 95% CL upper limits on the cross-section of a heavy narrow-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Observed 95% CL upper limits on the cross-section of a heavy narrow-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Observed 95% CL upper limits on the cross-section of a heavy narrow-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected 95% CL upper limits on the cross-section of a heavy large-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected 95% CL upper limits on the cross-section of a heavy large-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Expected 95% CL upper limits on the cross-section of a heavy large-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Observed 95% CL upper limits on the cross-section of a heavy large-width pseudoscalar resonance decaying to a Z boson and a heavy scalar resonance decaying to $H\to 4b$. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits are shown.

Data and post-fit signal and background from S+B fit for 315 GeV resonant $H\to 4b$ production in association with a W boson.

Data and post-fit signal and background from S+B fit for 315 GeV resonant $H\to 4b$ production in association with a W boson.

Data and post-fit signal and background from S+B fit for 400 GeV resonant $H\to 4b$ production in association with a W boson.

Data and post-fit signal and background from S+B fit for 400 GeV resonant $H\to 4b$ production in association with a W boson.

Data and post-fit signal and background from S+B fit for 550 GeV resonant $H\to 4b$ production in association with a Z boson.

Data and post-fit signal and background from S+B fit for 550 GeV resonant $H\to 4b$ production in association with a Z boson.

Data and post-fit signal and background from S+B fit for 400 GeV resonant $H\to 4b$ production in association with a Z boson.

Data and post-fit signal and background from S+B fit for 400 GeV resonant $H\to 4b$ production in association with a Z boson.

Data and post-fit signal and background from S+B fit for a 790 GeV narrow-width pseudoscalar resonance decaying to a Z boson and a 300 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for a 790 GeV narrow-width pseudoscalar resonance decaying to a Z boson and a 300 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for a 420 GeV large-width pseudoscalar resonance decaying to a Z boson and a 320 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for a 420 GeV large-width pseudoscalar resonance decaying to a Z boson and a 320 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for a 700 GeV large-width pseudoscalar resonance decaying to a Z boson and a 380 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for a 700 GeV large-width pseudoscalar resonance decaying to a Z boson and a 380 GeV scalar resonance decaying to $H\to 4b$.

Data and post-fit signal and background from S+B fit for SM VHH production, with each Higgs boson decaying to $2b$.

Data and post-fit signal and background from S+B fit for SM VHH production, with each Higgs boson decaying to $2b$.

Corrected $m(HH)$ distribution in the resolved $4b$ signal region (dots), after the fit under the background-only hypothesis. The error bars on the $4b$ points represent the Poisson uncertainties corresponding to their event yields. The background model (teal histogram) is shown with its total post-fit uncertainty (gray band). The final bin includes overflow. Representative spin-0 signal hypotheses (dashed, dotted, and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. The bottom panel shows the difference between the $4b$ distribution and the background model, relative to the background model. No significant excess of data relative to the SM background is observed.

Corrected $m(HH)$ distribution in the resolved $4b$ signal region (dots), after the fit under the background-only hypothesis. The error bars on the $4b$ points represent the Poisson uncertainties corresponding to their event yields. The background model (teal histogram) is shown with its total post-fit uncertainty (gray band). The final bin includes overflow. Representative spin-2 signal hypotheses (dashed, dotted, and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. The bottom panel shows the difference between the $4b$ distribution and the background model, relative to the background model. No significant excess of data relative to the SM background is observed.

Cumulative signal acceptance times efficiency as a function of the resonance mass for various selection steps in the boosted channel. The steps up to the $b$-tag categorization are shown for the spin-0.

Cumulative signal acceptance times efficiency as a function of the resonance mass for various selection steps in the boosted channel. The steps up to the $b$-tag categorization are shown for the spin-2.

Cumulative signal acceptance times efficiency as a function of the resonance mass for various selection steps in the boosted channel. The efficiencies of the three b-tag categories are shown for the spin-0 scenario; this efficiency is obtained after the other selection steps including the SR definition. The signal efficiency in the 4b region has a maximum around 1.5 TeV. Above that value the track-jets start to merge together, and for the highest resonance masses the 2b category becomes the most efficient.

Cumulative signal acceptance times efficiency as a function of the resonance mass for various selection steps in the boosted channel. The efficiencies of the three b-tag categories are shown for the spin-2 scenario; this efficiency is obtained after the other selection steps including the SR definition. The signal efficiency in the 4b region has a maximum around 1.5 TeV. Above that value the track-jets start to merge together, and for the highest resonance masses the 2b category becomes the most efficient.

Comparison of the background model (stacked histograms) with data (dots) in the $2b$ validation region. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background uncertainty (gray band) is computed by adding all individual components in quadrature and is not allowed to extend below zero.

Comparison of the background model (stacked histograms) with data (dots) in the $3b$ validation region. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background uncertainty (gray band) is computed by adding all individual components in quadrature and is not allowed to extend below zero.

Comparison of the background model (stacked histograms) with data (dots) in the $4b$ validation region. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background uncertainty (gray band) is computed by adding all individual components in quadrature and is not allowed to extend below zero.

The $m(HH)$ distributions in the boosted $2b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-0 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

The $m(HH)$ distributions in the boosted $2b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-2 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

The $m(HH)$ distributions in the boosted $3b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-0 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

The $m(HH)$ distributions in the boosted $3b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-2 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

The $m(HH)$ distributions in the boosted $4b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-0 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

The $m(HH)$ distributions in the boosted $4b$ signal regions (dots), after the fit under the background-only hypothesis. The error bars on the data points represent the Poisson uncertainties corresponding to their event yields. The background model (stacked histogram) is shown with its total post-fit uncertainty (gray band). The uncertainty bands are defined using an ensemble of curves constructed by sampling a multivariate Gaussian probability density function built from the covariance matrix of the fit. Representative spin-2 signal hypotheses (dashed and dashed-dotted lines) are overlaid, normalized to the overall expected limits on their cross-sections. No significant excess of data relative to the SM background is observed.

Expected (dashed black lines) and observed (solid black lines) 95% CL upper limits on the cross-section of resonant $HH$ production in the spin-0 signal models. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits (colored bands) are shown. Expected limits using each of the resolved and boosted channels individually (dashed colored lines) are shown. The nominal $H\rightarrow b\bar{b}$ branching ratio is taken as 0.582.

Expected (dashed black lines) and observed (solid black lines) 95% CL upper limits on the cross-section of resonant $HH$ production in the spin-2 signal models. The $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty ranges for the expected limits (colored bands) are shown. Expected limits using each of the resolved and boosted channels individually (dashed colored lines) are shown. The theoretical prediction for the bulk RS model with $k/\bar{M}_{\text{Pl}} = 1$ (solid red line) is shown; the decrease below 350 GeV is due to a sharp reduction in the $G^{*}_{\text{KK}} \rightarrow HH$ branching ratio. The nominal $H\rightarrow b\bar{b}$ branching ratio is taken as 0.582.