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.

Distribution of $m_{\mathrm{T},3l}$ in the JNLow SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q2 SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $m_{\mathrm{T},3l}$ in the ZL-CR after the background-only fit.

Distribution of $m_{\mathrm{T},3l}$ in the Fake-CR after the background-only fit.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 DB-CR after the background-only fit.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 RT-CR after the background-only fit.

Expected and observed exclusion limit for the combination of the two- (from Ref. EXOT-2018-33), three- and four-lepton channels, for the type-III seesaw process with the corresponding one- and two-standard-deviation uncertainty bands, showing the 95% CL upper limit on the cross-section.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the three lepton channel for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the four lepton channel for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

Cross-sections of signal Monte Carlo samples for each mass point considered in this analysis. Leading order cross-sections ( $\sigma_{LO}$ ) are computed by the generator and then rescaled to next-to-leading cross-sections ( $\sigma_{NLO+NLL}$ ), with their corresponding uncertainties, using information taken from Refs. C1C1 and N2C1.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZL SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZLVeto SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the JNLow SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0 SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q2 SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZL CR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0-DB CR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0-RT CR. Preselection represents events with at least three leptons.

Expected background yields and observed data after the background-only fit, in the three-lepton CRs and VRs.

Expected background yields and observed data after the background-only fit, in the four-lepton CRs and VRs.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the three and four lepton channels for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

Measured differential cross section with associated uncertainties as a function of $N$($b$-jets). Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate. For the meaning of the bins please refer to the figure.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{j1}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>30\ \mathrm{GeV}}=0)$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Measured differential cross section with associated uncertainties as a function of $m_{jj}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Measured differential cross section with associated uncertainties as a function of $\Delta\phi_{jj}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma}$ in bins of $|y_{\gamma\gamma}|$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Measured differential cross section with associated uncertainties as a function of $\Delta\phi_{jj}$ in the VBF fiducial region. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Observed statistical correlations, evaluated with a bootstrapping technique, between $p_\mathrm{T}^{\gamma\gamma}$, $N_\mathrm{jets}$, $m_{jj}$, $\Delta\phi_{jj}$, and $p_\mathrm{T}^{j1}$

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma}$.

Post-fit correlation matrix for the differential cross section measured as a function of $N_\mathrm{jets}$.

Post-fit correlation matrix for the differential cross section measured as a function of $N$($b$-jets).

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{j1}$.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>30\ \mathrm{GeV}}=0)$.

Post-fit correlation matrix for the differential cross section measured as a function of $m_{jj}$.

Post-fit correlation matrix for the differential cross section measured as a function of $\Delta\phi_{jj}$.

Post-fit correlation matrix for the differential cross section measured as a function of $\Delta\phi_{jj}$ in the VBF fiducial region.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma}$ in bins of $|y_{\gamma\gamma}|$. The bins are the same as in the corresponding plot of the differential cross section.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma1}/m_{\gamma\gamma}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma1}/m_{\gamma\gamma}$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma2}/m_{\gamma\gamma}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma2}/m_{\gamma\gamma}$.

Measured differential cross section with associated uncertainties as a function of $|y_{\gamma\gamma}|$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $|y_{\gamma\gamma}|$.

Measured differential cross section with associated uncertainties as a function of $m_{\gamma\gamma j}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $m_{\gamma\gamma j}$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma j}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma j}$.

Measured differential cross section with associated uncertainties as a function of $H_{T}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $H_{T}$.

Measured differential cross section with associated uncertainties as a function of $\tau_{C,j1}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $\tau_{C,j1}$.

Measured differential cross section with associated uncertainties as a function of $\sum\tau_{C,j}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $\sum\tau_{C,j}$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>40\ \mathrm{GeV}}=0)$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>40\ \mathrm{GeV}}=0)$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>50\ \mathrm{GeV}}=0)$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>50\ \mathrm{GeV}}=0)$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>60\ \mathrm{GeV}}=0)$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma} (N_\mathrm{jets}^{p_T>60\ \mathrm{GeV}}=0)$.

Measured differential cross section with associated uncertainties as a function of $\pi - |\Delta\phi_{\gamma\gamma,jj}|$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $\pi - |\Delta\phi_{\gamma\gamma,jj}|$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma jj}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma jj}$.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma}$ in bins of $p_{T}^{\gamma\gamma j}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma}$ in bins of $p_{T}^{\gamma\gamma j}$. The bins are the same as in the corresponding plot of the differential cross section.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma}$ in bins of $\tau_{C,j1}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma}$ in bins of $\tau_{C,j1}$. The bins are the same as in the corresponding plot of the differential cross section.

Measured differential cross section with associated uncertainties as a function of $(p_{T}^{\gamma1}-p_{T}^{\gamma2})/m_{\gamma\gamma}$ in bins of $(p_{T}^{\gamma1}+p_{T}^{\gamma2})/m_{\gamma\gamma}$. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $(p_{T}^{\gamma1}-p_{T}^{\gamma2})/m_{\gamma\gamma}$ in bins of $(p_{T}^{\gamma1}+p_{T}^{\gamma2})/m_{\gamma\gamma}$. The bins are the same as in the corresponding plot of the differential cross section.

Measured differential cross section with associated uncertainties as a function of $|\eta^*|$ in the VBF fiducial region. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $|\eta^*|$ in the VBF fiducial region.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{\gamma\gamma jj}$ in the VBF fiducial region. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{\gamma\gamma jj}$ in the VBF fiducial region.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{j1}$ in the VBF fiducial region. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{j1}$ in the VBF fiducial region.

Measured differential cross section with associated uncertainties as a function of $p_{T}^{j1}$ in bins of $\Delta\phi_{jj}$ in the VBF fiducial region. Each systematic uncertainty source is fully uncorrelated with the other sources and fully correlated across bins, except for the background modelling systematics for which an uncorrelated treatment across bins is more appropriate.

Post-fit correlation matrix for the differential cross section measured as a function of $p_{T}^{j1}$ in bins of $\Delta\phi_{jj}$ in the VBF fiducial region. The bins are the same as in the corresponding plot of the differential cross section.

Observed yields in the boost_1_ge2J signal region category of the hh channel.

Observed yields in the boost_2 signal region category of the hh channel.

Observed yields in the boost_3 signal region category of the hh channel.

Observed yields in the ttH_0 signal region category of the hh channel.

Observed yields in the ttH_1 signal region category of the hh channel.

Observed yields in the VH_0 signal region category of the hh channel.

Observed yields in the VH_1 signal region category of the hh channel.

Observed yields in the VBF_0 signal region category of the hh channel.

Observed yields in the VBF_1 signal region category of the hh channel.

Observed yields in the boost_0_1J signal region category of the lh channel.

Observed yields in the boost_0_ge2J signal region category of the lh channel.

Observed yields in the boost_1_1J signal region category of the lh channel.

Observed yields in the boost_1_ge2J signal region category of the lh channel.

Observed yields in the boost_2 signal region category of the lh channel.

Observed yields in the boost_3 signal region category of the lh channel.

Observed yields in the VH_0 signal region category of the lh channel.

Observed yields in the VH_1 signal region category of the lh channel.

Observed yields in the VBF_0 signal region category of the lh channel.

Observed yields in the VBF_1 signal region category of the lh channel.

Observed yields in the boost_0_1J signal region category of the ll channel.

Observed yields in the boost_0_ge2J signal region category of the ll channel.

Observed yields in the boost_1_1J signal region category of the ll channel.

Observed yields in the boost_1_ge2J signal region category of the ll channel.

Observed yields in the boost_2 signal region category of the ll channel.

Observed yields in the boost_3 signal region category of the ll channel.

Observed yields in the VH_0 signal region category of the ll channel.

Observed yields in the VH_1 signal region category of the ll channel.

Observed yields in the VBF_0 signal region category of the ll channel.

Observed yields in the VBF_1 signal region category of the ll channel.

Best-fit values and uncertainties for the pp $\rightarrow H\rightarrow\tau\tau$ cross-section measurement and the measurement in the four dominant production modes. All measurements include the branching ratio of $H\rightarrow\tau\tau$ and are performed with true Higgs boson rapidity $|y_{H}|<2.5$. The SM predictions for each region, computed using the inclusive cross-section calculations and the simulated event samples are also shown. The contributions to the total uncertainty in the measurements from statistical (Stat. unc.) or systematic uncertainties (Syst. unc.) are given separately.

The measured correlations between each parameter of interest in the measurement of the cross-sections per production mode

Best-fit values and uncertainties for the $H\rightarrow\tau\tau$ cross-sections, in the reduced stage 1.2 STXS scheme. The EW production mode includes vector-boson fusion and qq$\rightarrow$V($\rightarrow$qq)H processes. All measurements include the branching ratio of $H\rightarrow\tau\tau$ and are performed with true Higgs boson rapidity $|y_{H}|<2.5$. The SM predictions for each region, computed using the inclusive cross-section calculations and the simulated event samples are also shown. The contributions to the total uncertainty in the measurements from statistical (Stat. unc.) or systematic uncertainties (Syst. unc.) are given separately. The asterisk symbol (*) indicates that the criteria for m$_{jj}$ only apply to events with at least two reconstructed jets.

The measured correlations between each pair of parameters of interest in the STXS measurement. The asterisk symbol (*) indicates that the criteria for mjj only apply to events with at least two reconstructed jets.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Ht$ decay ($\Gamma_{T}$ is the $T$-quark width).

Cutflow table listing the number of events passing each criterion for a $T$-quark hypothesis with a mass of 1.6 TeV and $\kappa_{T} = 0.5$. The initial signal event yield is the predicted number of $T$-quark events inclusive in the Higgs-boson and top-quark decays for 139 fb$^{-1}$.

Observed 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Expected 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Wb$ decay ($\Gamma_{T}$ is the $T$-quark width).

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

The efficiency for simulated VBF events to pass each analysis cut.

The efficiency for simulated VH events to pass each analysis cut.

The efficiency for simulated ttH events to pass each analysis cut.

The fractional contribution of each production mode to a given analysis region around the Higgs boson peak, defined as 105 < mJ < 140 GeV. The fraction is given with respect to the total signal yield in the analysis region in question.

Signal acceptance times efficiency within the fiducial volume used in the fiducial region.

Signal acceptance times efficiency for the STXS volumes in the differential measurement. Along with the pTH requirements shown, |yH | < 2 is required. For events with pTH < 300 GeV, the acceptance times efficiency is less than 0.1 × 10−2.

Event yields and associated uncertainties after the global likelihood fit in the pT(H) > 450 GeV fiducial region. The total background yield can differ from the sum of the individual components due to rounding.

Event yields and associated uncertainties after the global likelihood fit of the differential regions. The total background yield can differ from the sum of the individual components due to rounding. The five STXS volumes are labeled pT0–pT4 corresponding to pTH < 300 GeV, 300 – 450 GeV, 450 – 650 GeV, 650 – 1000 GeV, and > 1000 GeV, respectively. The pT0 event yield is constrained to its SM value within the theoretical and experimental uncertainties and free parameters act independently on the remaining four volumes.

The JER for R = 0.2 jets in Pb+Pb collisions as a function of $2|\Psi_2-\phi^{reco}|$ for centrality selections of 0-5%, 5-10%, 10-20%, 20-40% and 40-60%.

The systematic uncertainties in v2 for 20-40% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v2 for 5-10% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v3 for 20-40% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v3 for 5-10% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v4 for 20-40% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v4 for 5-10% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v2 for pT = 71--398 GeV jets as a function of centrality.

The systematic uncertainties in v3 for pT = 71--398 GeV jets as a function of centrality.

The systematic uncertainties in v4 for pT = 71--398 GeV jets as a function of centrality.

Angular distribution of jets as a function of the observed psi2 plane for jets with 71 < pT < 79 GeV in the 10-20% centrality bin.

Angular distribution of jets as a function of the observed psi3 plane for jets with 71 < pT < 79 GeV in the 10-20% centrality bin.

Angular distribution of jets as a function of the observed psi4 plane for jets with 71 < pT < 79 GeV in the 10-20% centrality bin.

The v2 values for R = 0.2 jets as a function of centrality for jets in several pT ranges.

The v2 values for R = 0.2 jets as a function of pT for 0-5%, 5-10%, and 20-40% centrality collisions.

The v2, v3, and v4 as a function of centrality for jets with pT = 71-398 GeV.

The v3 values for R = 0.2 jets as a function of centrality for jets in several pT ranges.

The v4 values for R = 0.2 jets as a function of centrality for jets in several pT ranges.

The v2 as a function of pT for jets in 10-20% centrality collisions.

The v3 as a function of pT for jets in 10-20% centrality collisions.

The v2 as a function of pT for jets in 20-40% centrality collisions.

The v3 as a function of pT for jets in 20-40% centrality collisions.

The v2 for jets in 10-20% centrality collisions.

The v3 for jets in 10-20% centrality collisions.

R2max as a function of pT (filled circles). Also shown is 1 - 4v2/(1+2v2).

R3max as a function of pT (filled circles). Also shown is 1 - 4v3/(1+2v3).

The systematic uncertainties in v2 for 40-60% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v3 for 40-60% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v4 for 40-60% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v2 for 10-20% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v3 for 10-20% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v4 for 10-20% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v2 for 0-5% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v3 for 0-5% centrality Pb+Pb collisions as a function of pT.

The systematic uncertainties in v4 for 0-5% centrality Pb+Pb collisions as a function of pT.

The v2 as a function of pT for jets in 40-60% centrality collisions.

The v2 as a function of pT for jets in 5-10% centrality collisions.

The v2 as a function of pT for jets in 0-5% centrality collisions.

The v3 as a function of pT for jets in 40-60% centrality collisions.

The v3 as a function of pT for jets in 5-10% centrality collisions.

The v3 as a function of pT for jets in 0-5% centrality collisions.

Data from Figure 11a

Model-independent per-channel efficiencies calculated in the fiducial volume of the High Mass channel for the $2e2\mu$ final state.

Model-independent per-channel efficiencies calculated in the fiducial volume of the High Mass channel for the $4e$ final state.

Model-dependent per-channel fiducial region acceptances for the $H\to aa\to 4\mu$ process. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. Both, the Low Mass and the High Mass channel, include $m_X = $ 15 GeV at their signal region's edges, hence the dual entry for $m_X = $ 15 GeV.

Model-dependent per-channel fiducial region acceptances for the $H\to Z_dZ_d\to 4\ell$ process. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. Both, the Low Mass and the High Mass channel, include $m_X = $ 15 GeV at their signal region's edges, hence the dual entry for $m_X = $ 15 GeV.

Model-dependent per-channel fiducial region acceptances for the $H\to Z_dZ_d\to 2e2\mu$ process.

Model-dependent per-channel fiducial region acceptances for the $H\to Z_dZ_d\to 4e$ process.

Upper limits at 95% CL on fiducial cross-sections for the $H\rightarrow XX \rightarrow 4\mu$ process. The step change at $m_X$ = 15 GeV is due to the change in efficiency caused by the change in fiducial phase-space definition. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto.

Upper limits at 95% CL on fiducial cross-sections for the $H\rightarrow XX \rightarrow 4e$ process.

Upper limits at 95% CL on fiducial cross-sections for the $H\rightarrow XX \rightarrow 2e2\mu$ process.

Observed and expected upper limits at 95% CL for the cross section of the $H\to Z_dZ_d\to 4\ell$ process, assuming SM Higgs boson production via the gluon-gluon fusion process. All final states are combined.

Observed and expected upper limits at 95% CL for the cross sections of the $H\to Z_dZ_d\to 4\mu$ processes, assuming SM Higgs boson production via the gluon-gluon fusion process. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. The step changes at $m_{Z_d}= 15 \,\text{GeV}$ are due to the change in selection from the Low Mass to the High Mass analysis.

Observed and expected upper limits at 95% CL for the cross sections of the $H\to aa\to 4\mu$ processes, assuming SM Higgs boson production via the gluon-gluon fusion process. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. The step changes at $m_{Z_d}= 15 \,\text{GeV}$ are due to the change in selection from the Low Mass to the High Mass analysis.

Model-independent efficiencies for the $H\to ZX$ process for the $4\mu$ and $2e2\mu$ final states combined calculated in the $ZX$ fiducial volume.

Model-independent efficiencies for the $H\to ZX$ process for the $4\mu$, $2e2\mu$, $2\mu 2e$, and $4e$ final states combined calculated in the $ZX$ fiducial volume.

Model-independent efficiencies for the $H\to ZX$ process for the $2\mu 2e$, and $4e$ final states combined calculated in the $ZX$ fiducial volume.

Model-dependent per-channel fiducial region acceptances for the $H\to ZZ_d\to 4\ell$ process for the $4\mu$, and $2e2\mu$ final states.

Model-dependent per-channel fiducial region acceptances for the $H\to ZZ_d\to 4\ell$ process for the $4\mu$, $2e2\mu$, $2\mu 2e$, and $4e$ final states.

Model-dependent per-channel fiducial region acceptances for the $H\to ZZ_d\to 4\ell$ process for the $2\mu 2e$, and $4e$ final states.

Per-channel upper limit at 95% CL on the fiducial cross-section for the $H\rightarrow ZX \to 2\ell2e$ process.

Per-channel upper limit at 95% CL on the fiducial cross-section for the $H\rightarrow ZX \to 2\ell2\mu$ process.

Observed and expected upper limits at 95% CL for the cross sections of the $H\to ZZ_d\to 4\ell$ process, assuming SM Higgs~boson production via the gluon-gluon fusion process.

Observed and expected upper limits at 95% CL for the cross sections of the $H\to Za\to 2\ell2\mu$ process, assuming SM Higgs~boson production via the gluon-gluon fusion process.

95% CL upper limits on the cross section times the model-dependent branching ratio divided by the SM Higgs boson production cross section for the $H\rightarrow Z_dZ_d$ process for the benchmark HAHM. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. The step changes at $m_{Z_d}= 15 \,\text{GeV}$ are due to the change in selection from the Low Mass to the High Mass analysis.

95% CL upper limits on the cross section times the model-dependent branching ratio divided by the SM Higgs boson production cross section for the $H\rightarrow aa$ process for the benchmark 2HDM+S model. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. The step changes at $m_{Z_d}= 15 \,\text{GeV}$ are due to the change in selection from the Low Mass to the High Mass analysis.

Upper limit at 95% CL on the effective Higgs mixing parameter $\kappa^\prime=\kappa \, m_H^2 / |m_H^2-m_S^2|$. The regions of 2 GeV to 4.4 GeV, and 8 GeV to 12 GeV are each excluded by the quarkonia veto. The step changes at $m_{Z_d}= 15 \,\text{GeV}$ are due to the change in selection from the Low Mass to the High Mass analysis.

Upper limit at 95% CL on the $Z_d$ kinetic mixing parameter $\epsilon$, assuming the SM Higgs boson production cross section.

Upper limit at 95% CL on the $Z$-$Z_d$ mass mixing parameter $\delta^2 \times \textrm{BR}(Z_d\to \ell\ell)$, assuming the SM Higgs boson production cross section.