Invariant mass of the lepton pair plus jet system, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Regression NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Classification NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and various signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The pre-fit background distribution is shown along with three $H\rightarrow Za$ signal hypotheses coming from the pure MC sample ($a\rightarrow q\bar{q}/gg$ inclusively). The background normalization is set equal to that of the data for events passing the preselection and being in the region 100-180 GeV. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty before the fit (assuming all the uncertainties are uncorrelated). The lower panel shows the ratio of the data to the pre-fit background prediction.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and 2.0 GeV signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The background shape and normalization come from the fit to the data. The signal includes only $gg$ decays, its shape comes from the fit, and it is normalized to $\mathcal{B}(H\rightarrow Za)=100\%$. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty after the fit. The lower panel shows the per-bin signal significance, $(N_\text{data}-N_\text{MC})\,\text{\Large{/}}\sqrt{\sigma_\text{data}^2+\sigma_\text{MC}^2}$. The post-fit background uncertainty is calculated from a fit under the background-only hypothesis. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Observed 95$\%$ CL upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a \to gg)=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Observed 95$\%$ confidence level upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a\rightarrow q\bar{q})=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Expected and observed $95\%$ CL limits on the absolute value of the up-type quark coupling parameter $|\zeta_\mathrm{u}|$ for masses of the $A$ boson ranging from $20$ to $90\,\mathrm{GeV}$.

Observed $p_0$ values for the fits on the production cross-section for $gg\rightarrow A$ times the branching ratio for $A$ decaying into two $\tau$-leptons for $A$ boson masses from $20$ to $90\,\mathrm{GeV}$. For the fit on the up-type quark coupling parameter the $p_0$ values agree up to a precision of $O(10^{-5})$.

Distributions of the $\mathrm{NN^{SvsB}}$ output for data and the expected background after the likelihood fit in the $SR_{cQu --}$ signal region. The post-fit background expectations are shown as filled histograms, the combined pre-fit background expectations are shown as dashed lines. The signal distribution using the Wilson coefficient values $c_{tu}^{(1)}=0.04$, $c_{Qu}^{(1)}=0.1$, $c_{Qu}^{(8)}=0.1$ is shown with a dotted line, normalized to the same number of events as the background.

Summary of the observed and predicted number of events in the five 2$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Summary of the observed and predicted number of events in the four 3$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Comparison of the observed limits on the three WCs to the limit obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair [JHEP10(2015)150]. The cross-section limits from that analysis are converted to the limits on the WCs by using the fitted EFT parametrization. The bounds on the WCs are shown at the 68$\%$ CL (solid) and/or 95$\%$ CL (dashed) levels. For the ATLAS Run~1 analysis only the bounds at 95$\%$ CL are available. The vertical bar represents the SM prediction. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$.

Observed lower limits at 95$\%$ confidence level on the scale of new physics $\Lambda$ for Wilson coefficient values of 0.01, 1 and $4\pi^2$. The limits are compared with the limits obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair.

Observed and expected limits at 95$\%$ confidence level on the cross-section of $\sigma(pp \rightarrow tt)$.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(1)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{Qu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

1D-likelihood scan for $c_{tu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(8)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{2\ell3j}$ signal region, which uses the invariant mass of the c-tagged jet and the geometrically closest b-tagged jet, $m_{\mathit{cb}}^{\mathrm{min}\Delta R}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{1\ell6ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{tight}}^{1\ell6ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{2\ell4ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{tight}}^{2\ell4ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Jet multiplicity and tagging criteria for the SRs and CRs in the single-lepton and dilepton channels. All single-lepton regions are defined in the 5-jet-exclusive and 6-jet-inclusive jet selections, all dilepton regions in the 3-jet-exclusive and 4-jet-inclusive jet selections. By construction, $\mathrm{SR}^{2\ell}_{\mathrm{tight}}$ only exists for the 4-jet-inclusive selection. Identical requirements on inclusive and exclusive working points, e.g., one c@22% and one c@11% in the $\mathrm{CR}_1^{1\ell}$, indicate a veto of additional tags at the inclusive working point.

Breakdown of the fiducial $t\bar{t}+{\geq}2c$ and $t\bar{t}+1c$ cross-section uncertainties. Systematic uncertainties are grouped into signal and background modeling, instrumental, and MC statistics categories. The table lists the fractional uncertainty in the measured cross-sections in percent and is estimated from the covariance matrix of the profile likelihood fit, following EPJC 84 (2024) 593. Individual groups of uncertainties can be added in quadrature to obtain the total uncertainty. JES and JER denote the jet energy scale and resolution uncertainties, respectively. The fractional uncertainties in the fitted $t\bar{t}+{\geq}1c$ and $t\bar{t}+\text{light}$ normalization factors are included in the data statistics category. For presentation purposes, all uncertainties are symmetrized.

Measured fiducial cross-section values in comparison with various NLO+PS predictions. The uncertainties in the predictions include independent and simultaneous variations of the $\mu_R$ and $\mu_F$ scales and uncertainties in the choice of the PDF set, but no uncertainties in the parton shower or hadronization. The uncertainties in the measured values include all statistical and systematic uncertainties. For presentation purposes, the quoted measurement and prediction uncertainties are symmetrized.

Measured and predicted values for the $t\bar{t}+{\geq}1b$, $t\bar{t}+{\geq}2c$, and $t\bar{t}+1c$ cross-sections and for the cross-section ratios of these processes to total $t\bar{t}+\text{jets}$ production. The quoted uncertainties in the measurements include statistical and systematic uncertainties. The predictions are taken from the nominal setup using inclusive $t\bar{t}$ Powheg+Pythia8 predictions for the $t\bar{t}+{\geq}2c$, $t\bar{t}+1c$, and $t\bar{t}+\text{light}$ processes, and $t\bar{t}+b\bar{b}$ Powheg+Pythia8 predictions for the $t\bar{t}+{\geq}1b$ process. The first use the 5FS, the latter the 4FS, where the $b$-quarks are treated as massive particles and are included in the matrix element calculation. The uncertainties in the predictions include independent and simultaneous variations of the $\mu_R$ and $\mu_F$ scales and uncertainties in the choice of the PDF set.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+{\geq}2c$ cross-section measurement. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+1c$ cross-section measurement. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+{\geq}2c$ ratio to total $t\bar{t}+\text{jets}$ production. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+1c$ ratio to total $t\bar{t}+\text{jets}$ production. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Efficiencies and rejection rates for the $b$- and $c$-jet tagging working points of the $b/c$-tagger, as well as the selection cuts on the discriminants, $\mathcal{D}_b'$ and $\mathcal{D}_c'$ that define the tagging bins. The primes indicate that a standard logistic function is applied to the discriminants. The b@70% and c@22% working points are inclusive of their respective tighter working points. The values were estimated from single-lepton and dilepton $t\bar{t}$ events simulated with Powheg + Pythia 8.

Efficiencies and rejection rates for the $b$- and $c$-jet tagging working points of the $b/c$-tagger, as well as the selection cuts on the discriminants, $\mathcal{D}_b'$ and $\mathcal{D}_c'$ that define the tagging bins. The primes indicate that a standard logistic function is applied to the discriminants. The b@70% and c@22% working points are inclusive of their respective tighter working points. The values were estimated from single-lepton and dilepton $t\bar{t}$ events simulated with Powheg + Pythia 8.

Pre-fit event yields in the twelve single-lepton and dilepton control regions (CRs) of the analysis. The quoted uncertainties include both statistical and systematic components, but all normalization factors are fixed to their pre-fit values with no uncertainties. All uncertainties are assumed to be uncorrelated. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Pre-fit event yields in the seven signal regions (SRs) of the analysis. The quoted uncertainties include both statistical and systematic components, but all normalization factors are fixed to their pre-fit values with no uncertainties. All uncertainties are assumed to be uncorrelated. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Post-fit event yields in the twelve single-lepton and dilepton control regions (CRs) of the analysis. The quoted uncertainties include both statistical and systematic components, and post-fit correlations between uncertainties are taken into account. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Post-fit event yields in the seven signal regions (SRs) of the analysis. The quoted uncertainties include both statistical and systematic components, and post-fit correlations between uncertainties are taken into account. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

The cutflow table for $N1$ and $N2$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 0.1 pb. The abbreviations used in the table are, SC = Same Charge, SF = Same Flavor.

The cutflow table for $N3$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 10 pb. The abbreviations used in the table are, SS = Same Charge, SF = Same Flavor.

Expected and observed upper limits on the strength of HNL mixing with electron neutrinos

Expected and observed upper limits on the strength of HNL mixing with muon neutrinos

Expected and observed upper limits on the strength of HNL mixing with tau neutrinos

Expected and observed exclusion limits at 95% CL for $\sigma_{\mathrm{VBF}}(H_{5}^{\pm\pm}) \times \mathcal{B}(H_{5}^{\pm\pm} \to W^{\pm}W^{\pm})$ as a function of $m_{\mathrm{H_5}}$. The inner (outer) band represents the $68\%$ ($95\%$) confidence interval around the median expected limit.

Expected and observed exclusion limits at 95% CL for $\sin \theta_{{\mathrm{H}}}$ as a function of $m_{\mathrm{H_5}}$. The inner (outer) band represents the $68\%$ ($95\%$) confidence interval around the median expected limit. The exclusion limits are shown up to $m_{\mathrm{H_5}} = 1500$ GeV. The limits obtained separately in the $H_{5}^{\pm} \to W^{\pm}Z$ and $H_{5}^{\pm\pm} \to W^{\pm}W^{\pm}$ channels are also shown for comparison. The hatched region covers the parameter space where the intrinsic widths of the $H_{5}^{\pm}$ and $H_{5}^{\pm\pm}$ bosons would be larger than $10\%$ of $m_{\mathrm{H_5}}$ and is disfavoured in the GM model.

Signal selection efficiency times acceptance for charged Higgs boson with masses between $60\,$GeV to $168\,$GeV. The efficiency times acceptance drops at high masses rapidly due to the low momentum of the $b$-quark produced together with the charged Higgs boson. For the $168\,$GeV mass point the efficiency times acceptance is larger than for the $160\,$GeV mass point due to having a higher probability that the top quark, which decays into the charged Higgs boson and a $b$-quark, is off-shell.

Best fit values of $\mu_{t\bar{t}}$ and $f_{\mathrm{HF}}$ parameters at charged Higgs masses between $60\,$GeV and $168\,$GeV.

Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as a function of c&tau; for a selection of models targeted in the CalR+W channel for (a) WALP models and (b) WHS models with a SM Higgs boson mediator.

Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as a function of c&tau; for a selection of models targeted in the CalR+W channel for (a) WALP models and (b) WHS models with a SM Higgs boson mediator.

Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as a function of c&tau; for a variety of models probed by the CalR+Z channel for (a) ZALP models, (b) ZHS models with the SM Higgs boson as a mediator, and (c) HZZ_d models.

Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as a function of c&tau; for a variety of models probed by the CalR+Z channel for (a) ZALP models, (b) ZHS models with the SM Higgs boson as a mediator, and (c) HZZ_d models.

Observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on the cross-section times branching fraction as a function of c&tau; for a variety of models probed by the CalR+Z channel for (a) ZALP models, (b) ZHS models with the SM Higgs boson as a mediator, and (c) HZZ_d models.

Summary of the observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on C_G as a function of C_W for a variety of ALP mass hypotheses probed by the CalR+R and Cal+Z channels for (a) WALP and (b) ZALP models.

Summary of the observed (solid line) and expected (dashed line) upper limits at the 95&percnt; CL on C_G as a function of C_W for a variety of ALP mass hypotheses probed by the CalR+R and Cal+Z channels for (a) WALP and (b) ZALP models.

Regions in the ALP mass versus its coupling to gluons scaled by the ALP energy scale g_agg=4C_G/f_a excluded at 95&percnt; CL, for C_W=1, C_W=0.5, C_W=0.3 and C_W=0.15, in the (a) WALP and (b) ZALP models. The contours are obtained by interpolating between the exclusions for different LLP masses considered in the analysis, taking the logical union of the regions excluded for each mass.

Regions in the ALP mass versus its coupling to gluons scaled by the ALP energy scale g_agg=4C_G/f_a excluded at 95&percnt; CL, for C_W=1, C_W=0.5, C_W=0.3 and C_W=0.15, in the (a) WALP and (b) ZALP models. The contours are obtained by interpolating between the exclusions for different LLP masses considered in the analysis, taking the logical union of the regions excluded for each mass.

Signal efficiencies as a function of c&tau; for HS signals in the CalR+2J channel for samples with mediator masses (a) below 400 GeV and (b) equal to or above 400 GeV. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for HS signals in the CalR+2J channel for samples with mediator masses (a) below 400 GeV and (b) equal to or above 400 GeV. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for WALP and WHS signals in the CalR+W channel for (a) the WALP selection, (b) the CalR+W low-E_T selection and (c) the CalR+W high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for WALP and WHS signals in the CalR+W channel for (a) the WALP selection, (b) the CalR+W low-E_T selection and (c) the CalR+W high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for WALP and WHS signals in the CalR+W channel for (a) the WALP selection, (b) the CalR+W low-E_T selection and (c) the CalR+W high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for ZALP, HZZ_d and ZHS signals in the CalR+Z channel for (a, b) the CalR+Z low-E_T selection and (c, d) the CalR+Z high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for ZALP, HZZ_d and ZHS signals in the CalR+Z channel for (a, b) the CalR+Z low-E_T selection and (c, d) the CalR+Z high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for ZALP, HZZ_d and ZHS signals in the CalR+Z channel for (a, b) the CalR+Z low-E_T selection and (c, d) the CalR+Z high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

Signal efficiencies as a function of c&tau; for ZALP, HZZ_d and ZHS signals in the CalR+Z channel for (a, b) the CalR+Z low-E_T selection and (c, d) the CalR+Z high-E_T selection. The extrapolation of efficiencies to new mean LLP lifetimes is done via the event reweighting procedure. Only statistical uncertainties are shown.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed black line) and observed (solid line) upper limits on the cross-section times branching fraction in the CalR+2J channel for the benchmark HS models with mass pairs (m_&Phi;, m_S) (a) (60, 16), (b) (125, 35), (c) (125, 55), (d) (200, 50), (e) (400, 100), (f) (600, 150), (g) (600, 275), (h) (1000, 275), and (i) (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) upper limits on the cross-section times branching fraction in the WHS channel for the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (60, 5) and (60, 15), (b) (200, 50) and (200, 80), (c) (400, 100) and (400, 175), (d) (600, 50), (600, 150), and (600, 275), (e) (1000, 50), (1000, 275), and (1000, 475) GeV

95&percnt; CL expected (dashed line) and observed (solid line) upper limits on the cross-section times branching fraction in the WHS channel for the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (60, 5) and (60, 15), (b) (200, 50) and (200, 80), (c) (400, 100) and (400, 175), (d) (600, 50), (600, 150), and (600, 275), (e) (1000, 50), (1000, 275), and (1000, 475) GeV

95&percnt; CL expected (dashed line) and observed (solid line) upper limits on the cross-section times branching fraction in the WHS channel for the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (60, 5) and (60, 15), (b) (200, 50) and (200, 80), (c) (400, 100) and (400, 175), (d) (600, 50), (600, 150), and (600, 275), (e) (1000, 50), (1000, 275), and (1000, 475) GeV

95&percnt; CL expected (dashed line) and observed (solid line) upper limits on the cross-section times branching fraction in the WHS channel for the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (60, 5) and (60, 15), (b) (200, 50) and (200, 80), (c) (400, 100) and (400, 175), (d) (600, 50), (600, 150), and (600, 275), (e) (1000, 50), (1000, 275), and (1000, 475) GeV

95&percnt; CL expected (dashed line) and observed (solid line) upper limits on the cross-section times branching fraction in the WHS channel for the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (60, 5) and (60, 15), (b) (200, 50) and (200, 80), (c) (400, 100) and (400, 175), (d) (600, 50), (600, 150), and (600, 275), (e) (1000, 50), (1000, 275), and (1000, 475) GeV

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (125, 16), (b) (600, 150) GeV, and the WALP selection for WALP models with (c) m_ALP = 1 GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (125, 16), (b) (600, 150) GeV, and the WALP selection for WALP models with (c) m_ALP = 1 GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the low-E_T WHS selection for benchmark WHS models with mass pairs (m_&Phi;, m_S) (a) (125, 16), (b) (600, 150) GeV, and the WALP selection for WALP models with (c) m_ALP = 1 GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

95&percnt; CL expected (dashed line) and observed (solid line) limits on the branching fraction in the CalR+Z channel for benchmark HZZ_d models with mass pairs (m_&Phi;, m_{Z_d}) (a) (400, 100) and (400, 200), (b) (600, 150) and (600, 400). The ZHS sample is shown for masses (m_&Phi;, m_S) in GeV: (c) (200, 50) and (200, 80), (d) (400, 100) and (400, 175), (e) (600, 50), (600, 150) and (600, 275), (f) (1000, 50), (1000, 275) and (1000, 475) GeV.

The pNN input variable visible transverse momentum $p_{\mathrm{T}}^{\mathrm{vis}}(\mu\tau_{\mathrm{had}})$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

The pNN input variable transverse mass $m_{\mathrm{T}}(\mu,E_{\mathrm{T}}^{\mathrm{miss}})$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

The pNN input variable MMC mass $m^{\mathrm{MMC}}(bb\tau\tau)$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

Mass distribution of the $\tau^+\tau^-$ system for each of the generated MC signal mass points for the $\mu\tau_{\mathrm{h}}$ category. All distributions are normalized assuming $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=10\%$.

Mass distribution of the $\tau^+\tau^-$ system for each of the generated MC signal mass points for the $e\mu$ category. All distributions are normalized assuming $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=10\%$.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\mu$, $1b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($\mu\tau_{\mathrm{had}}$,$2b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\mu$,$1B$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\tau_{\mathrm{had}}$,$2b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The observed (solid) 95% C.L. upper limits on $(\sigma(H)/\sigma_{\mathrm{SM}}(H)) \mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)$ as a function of $m_a$ and the expected (dashed) limits under the background-only hypothesis when combining all categories. The inner green and outer yellow shaded bands show the $\pm 1\sigma$ and $\pm 2\sigma$ uncertainties of the expected limits.

The observed (solid) 95% C.L. upper limits on $(\sigma(H)/\sigma_{\mathrm{SM}}(H)) \mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)$ as a function of $m_a$ and the expected (dashed) limits under the background-only hypothesis when considering different categories based on the heavy-flavor objects separately. When the category is not used for a mass hypothesis, the limit is listed as zero.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed and expected 95&percnt; CL upper limits on the signal strength for the inclusive ggF HH production from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. When deriving the limit on &mu;_ggF^HH (&mu;_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected 95&percnt; CL upper limits on the signal strength for the VBF HH production from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. When deriving the limit on &mu;_ggF^HH (&mu;_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected upper limits at 95&percnt; CL on the inclusive ggF and VBF HH production cross-section from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. The Higgs boson mass is set to 125&nbsp;GeV when deriving the predicted SM cross-section (red band). The expected limits, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, are calculated under the assumption of no Higgs boson pair production and with all NPs profiled to the observed data.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed (solid lines) and expected (dashed lines) 95&percnt; CL exclusion limits on the HH production cross-sections of (a) the inclusive ggF and VBF processes as a function of &kappa;_&lambda;, for the bb&#772;&gamma;&gamma; (purple), bb&#772;&tau;⁺&tau;^- (green), multilepton (cyan), bb&#772;bb&#772; (blue) and bb&#772;&#8467;&#8467;+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no HH production. The red line shows the theory prediction for the ggF and VBF HH production cross-section as a function of &kappa;_&lambda;. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed (solid lines) and expected (dashed lines) 95&percnt; CL exclusion limits on the HH production cross-sections of the VBF process as a function of &kappa;_2V, for the bb&#772;&gamma;&gamma; (purple), bb&#772;&tau;⁺&tau;^- (green), multilepton (cyan), bb&#772;bb&#772; (blue) and bb&#772;&#8467;&#8467;+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no VBF HH production. The ggF HH production cross-section is assumed to be as predicted by the SM. The ggF HH production cross-section is assumed to be as predicted by the SM. The red line shows the predicted VBF HH cross-section as a function of &kappa;_2V. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Observed and expected 95&percnt; CL combined upper limits on the cross-section for the SM and seven BSM HEFT benchmarks (arXiv:2304.01968 [hep-ph]) in the ggF process, describing representative signal kinematics and m_HH shape features obtained by varying multiple HEFT coefficients. The expected limits from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma; and bb&#772;bb&#772; decay channels are presented as well. Theoretical predictions, estimated using specific sets of coefficient values defined in the benchmarks, are shown as red cross dots.