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.

Two-dimensional distribution of the invariant mass $m_{DV}$ and the track multiplicity in the High-pT jet SR for observed data events

Two-dimensional distribution of the invariant mass $m_{DV}$ and the track multiplicity in the High-pT jet SR for expected signal events in the strong gluino pair pair production model with m(gluino)=1.8 TeV, m(chi0)=0.2 TeV, tau(chi0)=0.1 ns

Two-dimensional distribution of the invariant mass $m_{DV}$ and the track multiplicity in the Trackless jet SR for observed data events

Two-dimensional distribution of the invariant mass $m_{DV}$ and the track multiplicity in the Trackless jet SR for expected signal events in the electroweak pair production model

Expected exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Observed exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in electroweakino pair production models

Expected exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Observed exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.4 TeV

Exclusion limits at 95% CL on the production cross section in the electroweak pair production model.

Exclusion limits at 95% CL on the production cross section in the strong gluino pair production models and m(gluino)=2.4 TeV

Expected exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Observed exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.0 TeV

Expected exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Observed exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the neutralino in strong gluino pair production models and m(gluino)=2.2 TeV

Expected exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Observed exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=50 GeV

Expected exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Expected (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Expected (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Observed exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Observed (+1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Observed (-1 sigma) exclusion limits at 95% CL on the lifetime and mass of the gluino in strong gluino pair production models and m(chi0)=450 GeV

Expected exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Expected (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Expected (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Observed exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Observed (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Observed (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.01 ns

Expected exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Expected (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Expected (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Observed exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Observed (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Observed (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=0.1 ns

Expected exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Expected (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Expected (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Observed exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Observed (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Observed (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=1 ns

Expected exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Expected (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Expected (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Observed exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Observed (+1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Observed (-1 sigma) exclusion limits at 95% CL on the mass of the gluino and neutralino in strong gluino pair production models and tau(chi0)=10 ns

Exclusion limits at 95% CL on the production cross section in the strong gluino pair production models and m($ ilde{\chi}^0_1$)=1.25 TeV

Acceptance cutflow for the High-pT SR for representative points in the strong gluino pair production model. See additional resources for more information.

Acceptance cutflow for the Trackless SR for representative points in the electroweak pair production model. See additional resources for more information.

Acceptance cutflow for the Trackless SR for representative points in the electroweak pair production model with heavy-flavor quarks final state. See additional resources for more information.

Acceptance cutflow for the High-pT SR for representative points in the electroweak pair production model with heavy-flavor quarks final state. See additional resources for more information.

Reinterpretation Material: Event-level Efficiency for HighPt SR selections, R < 1150 mm

Reinterpretation Material: Event-level Efficiency for HighPt SR selections, R [1150, 3870] mm

Reinterpretation Material: Event-level Efficiency for HighPt SR selections, R > 3870 mm

Reinterpretation Material: Event-level Efficiency for Trackless SR selections, R < 1150 mm

Reinterpretation Material: Event-level Efficiency for Trackless SR selections, R [1150, 3870] mm

Reinterpretation Material: Event-level Efficiency for Trackless SR selections, R > 3870 mm

Reinterpretation Material: Vertex-level Efficiency for R < 22 mm

Reinterpretation Material: Vertex-level Efficiency for R [22, 25] mm

Reinterpretation Material: Vertex-level Efficiency for R [25, 29] mm

Reinterpretation Material: Vertex-level Efficiency for R [29, 38] mm

Reinterpretation Material: Vertex-level Efficiency for R [38, 46] mm

Reinterpretation Material: Vertex-level Efficiency for R [46, 73] mm

Reinterpretation Material: Vertex-level Efficiency for R [73, 84] mm

Reinterpretation Material: Vertex-level Efficiency for R [84, 111] mm

Reinterpretation Material: Vertex-level Efficiency for R [111, 120] mm

Reinterpretation Material: Vertex-level Efficiency for R [120, 145] mm

Reinterpretation Material: Vertex-level Efficiency for R [145, 180] mm

Reinterpretation Material: Vertex-level Efficiency for R [180, 300] mm

Cutflow (acceptance x efficiency) for the High-pT SR for representative points in the strong gluino pair production model. See additional resources for more information.

Cutflow (acceptance x efficiency) for the Trackless SR for representative points in the electroweak pair production model. See additional resources for more information.

Cutflow (acceptance x efficiency) for the Trackless SR for representative points in the electroweak pair production model with heavy-flavor quarks. See additional resources for more information.

Cutflow (acceptance x efficiency) for the High-pT SR for representative points in the electroweak pair production model with heavy-flavor quarks. See additional resources for more information.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions.In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon--gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.

Expected exclusion limits at 95% CL from Fig 7(a) for $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(a) for $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Observed exclusion limits at 95% CL from Fig 7(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Positive one $\sigma$ observed exclusion limits at 95% CL from Fig 7(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Negative one $\sigma$ observed exclusion limits at 95% CL from Fig 7(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Expected exclusion limits at 95% CL from Fig 7(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Observed exclusion limits at 95% CL from Fig 7(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Positive one $\sigma$ observed exclusion limits at 95% CL from Fig 7(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Negative one $\sigma$ observed exclusion limits at 95% CL from Fig 7(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Expected exclusion limits at 95% CL from Fig 7(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Observed exclusion limits at 95% CL from Fig 7(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Positive one $\sigma$ observed exclusion limits at 95% CL from Fig 7(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Negative one $\sigma$ observed exclusion limits at 95% CL from Fig 7(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Expected exclusion limits at 95% CL from Fig 7(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Observed exclusion limits at 95% CL from Fig 7(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Positive one $\sigma$ observed exclusion limits at 95% CL from Fig 7(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Negative one $\sigma$ observed exclusion limits at 95% CL from Fig 7(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Expected exclusion limits at 95% CL from Fig 7(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Observed exclusion limits at 95% CL from Fig 7(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Positive one $\sigma$ observed exclusion limits at 95% CL from Fig 7(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Negative one $\sigma$ observed exclusion limits at 95% CL from Fig 7(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Expected exclusion limits at 95% CL from Fig 7(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

One $\sigma$ band of expected exclusion limits at 95% CL from Fig 7(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

N-1 distribution for $m_{\mathrm{eff}}$of observed data and expected background in SRGGWZ-H.

N-1 distribution for $E_{\mathrm{T}}^{\mathrm{miss}}$of observed data and expected background in SRGGSlep-M.

N-1 distribution for $\sum{p_{\mathrm{T}}^\mathrm{jet}}$of observed data and expected background in SRUDD-ge2b.

N-1 distribution for $m_{\mathrm{eff}}$of observed data and expected background in SRLQD.

N-1 distribution for $m_{\mathrm{eff}}$of observed data and expected background in SRSSWZ-H.

N-1 distribution for $m_{\mathrm{eff}}$of observed data and expected background in SRSSSlep-H(loose).

Signal acceptance for SRGGWZ-H signal region from Fig 10(c) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGWZ-H signal region from Fig 15(c) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRGGWZ-M signal region from Fig 10(b) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGWZ-M signal region from Fig 15(b) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRGGWZ-L signal region from Fig 10(a) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGWZ-L signal region from Fig 15(a) in a SUSY scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRGGSlep-L signal region from Fig 12(a) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGSlep-L signal region from Fig 17(a) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRGGSlep-M signal region from Fig 12(b) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGSlep-M signal region from Fig 17(b) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRGGSlep-H signal region from Fig 12(c) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRGGSlep-H signal region from Fig 17(c) in a SUSY scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRUDD-1b signal region from Fig 14(b) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal efficiency for SRUDD-1b signal region from Fig 19(b) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal acceptance for SRUDD-2b signal region from Fig 14(c) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal efficiency for SRUDD-2b signal region from Fig 19(c) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal acceptance for SRUDD-ge2b signal region from Fig 14(d) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal efficiency for SRUDD-ge2b signal region from Fig 19(d) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal acceptance for SRUDD-ge3b signal region from Fig 14(e) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal efficiency for SRUDD-ge3b signal region from Fig 19(e) in a SUSY scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Signal acceptance for SRLQD signal region from Fig 14(a) in a SUSY scenario where direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Signal efficiency for SRLQD signal region from Fig 19(a) in a SUSY scenario where direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Signal acceptance for SRSSWZ-L signal region from Fig 11(a) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSWZ-L signal region from Fig 16(a) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSWZ-ML signal region from Fig 11(b) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSWZ-ML signal region from Fig 16(b) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSWZ-MH signal region from Fig 11(c) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSWZ-MH signal region from Fig 16(c) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSWZ-H signal region from Fig 11(d) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSWZ-H signal region from Fig 16(d) in a SUSY scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSSlep-H signal region from Fig 13(d) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSSlep-H signal region from Fig 18(d) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSSlep-MH signal region from Fig 13(c) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSSlep-MH signal region from Fig 18(c) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSSlep-L signal region from Fig 13(a) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSSlep-L signal region from Fig 18(a) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSSlep-ML signal region from Fig 13(b) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSSlep-ML signal region from Fig 18(b) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal acceptance for SRSSSlep-H(loose) signal region from Fig 13(e) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Signal efficiency for SRSSSlep-H(loose) signal region from Fig 18(e) in a SUSY scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGWZ-H in a susy scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1400 GeV, $m(\tilde{\chi_{1}^{0}})$ = 1000 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGWZ-M in a susy scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1400 GeV, $m(\tilde{\chi_{1}^{0}})$ = 1000 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGWZ-L in a susy scenario where $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1400 GeV, $m(\tilde{\chi_{1}^{0}})$ = 1000 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGSlep-L in a susy scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 2000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 500 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGSlep-M in a susy scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 2000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 500 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRGGSlep-H in a susy scenario where $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 2000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 500 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRUDD-1b in a susy scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1600 GeV, $m(\tilde{t})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRUDD-2b in a susy scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1600 GeV, $m(\tilde{t})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRUDD-ge2b in a susy scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1600 GeV, $m(\tilde{t})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRUDD-ge3b in a susy scenario where $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 1600 GeV, $m(\tilde{t})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRLQD in a susy scenario where direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$. The masses of the superpartners involved in the process are set to $m(\tilde{g})$ = 2200 GeV, $m(\tilde{\chi_{1}^{0}})$ = 1870 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSWZ-L in a susy scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 800 GeV, $m(\tilde{\chi_{1}^{0}})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSWZ-ML in a susy scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 800 GeV, $m(\tilde{\chi_{1}^{0}})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSWZ-MH in a susy scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 800 GeV, $m(\tilde{\chi_{1}^{0}})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSWZ-H in a susy scenario where $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 800 GeV, $m(\tilde{\chi_{1}^{0}})$ = 600 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSSlep-H in a susy scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 1000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 800 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSSlep-MH in a susy scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 1000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 800 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSSlep-L in a susy scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 1000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 800 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSSlep-ML in a susy scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 1000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 800 GeV. Only statistical uncertainties are shown.

Number of signal events expected for 139 fb$^{-1}$ at different stages of the event selection for the signal region SRSSSlep-H(loose) in a susy scenario where $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$. The masses of the superpartners involved in the process are set to $m(\tilde{q})$ = 1000 GeV, $m(\tilde{\chi_{1}^{0}})$ = 800 GeV. Only statistical uncertainties are shown.

Cross-section upper limits at 95% CL from Fig1(a) for $\tilde{g}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Cross-section upper limits at 95% CL from Fig1(c) for $\tilde{g}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

Cross-section upper limits at 95% CL from Fig1(f) for $\tilde{g}$ decays into anti-top and $\tilde{t}$ and $\tilde{t}$ decays via a non-zero RPV coupling $\lambda''$

Cross-section upper limits at 95% CL from Fig1(e) for direct $\tilde{\chi_{1}^{0}}$ decay into SM leptons and quarks via a non-zero RPV coupling $\lambda'$

Cross-section upper limits at 95% CL from Fig1(b) for $\tilde{q}$ decays into SM gauge bosons and $\tilde{\chi}^{0}_{1}$

Cross-section upper limits at 95% CL from Fig1(d) for $\tilde{q}$ decays into sleptons and subsequently to SM leptons and $\tilde{\chi}^{0}_{1}$

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

Predicted and observed yields as a function of $m_{4\ell}$ in the VBS-Suppressed region. Overflow events are included in the last bin of the distribution.

Relative systematic uncertainties in the unfolded differential cross section for 4ljj production in the VBS-Enhanced region as a function of m_{jj}

Relative systematic uncertainties in the unfolded differential cross section for 4ljj production in the VBS-Enhanced region as a function of m_{4\ell}

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $m_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $m_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $m_{4\ell}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $m_{4\ell}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $ p_{T,4l}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $ p_{T,4l}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $\Delta\phi_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $\Delta\phi_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $|\Delta y_{jj}|$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $|\Delta y_{jj}|$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $cos(\theta^{*}_{12})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $cos(\theta^{*}_{12})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $cos(\theta^{*}_{34})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $cos(\theta^{*}_{34})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $p_{T,jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $p_{T,jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $p_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $p_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $S_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $S_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Statistical correlation between different bins of the unfolded cross-section for all the measured observables in the VBS-Enhanced region.

Statistical correlation between different bins of the unfolded cross-section for all the measured observables in the VBS-Suppressed region.

Distribution of $m_{\mathrm{JJ}}$ in the SR (black points) compared to the background-only expectation, where the shape is derived from the CR and the normalisation is fitted in the SR.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model A, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model B, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d} = 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model C, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d}= 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model D, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Relative efficiency (in %) of each stage of the analysis selection with respect to the previous one for models A through D and $m_{Z^\prime}=2.5$ TeV. Approximately 90000 events were generated per signal mass hypothesis.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $q\bar{q}\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $gg\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the WMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-0 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $q\bar{q} \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The jet mass distribution of large-$R$ jets originating from the hadronic decay of $W$ and $Z$ bosons produced from the decay of BSM bosons with mass $m_X = 2000$ GeV. The decays simulated are for the production models $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ with a spin-1 resonance $X^{\pm}$ and $gg\to X^0 \to Z\gamma$ with a spin-0 resonance $X^{0}$.

The photon $E_{T}$ selection criteria as a function of resonance mass for D2 categories. Selections for four different signal channels are shown together.

The photon $E_{T}$ selection criteria as a function of resonance mass for ZMASS or WMASS categories. Selections for four different signal channels are shown together.

Events in bins of the $E_{miss}^T$ in the SR.

Parametrization of the $A_{X}$ factor, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level, as function of $m_{X}$ obtained from the narrow width simulated signal samples produced in gluon fusion.

The correction factor, $C_{X}$, defined as the ratio between the number of reconstructed signal events passing the analysis cuts and the number of signal events at the particle level generated within the fiducial volume, and acceptance correction factor, $A_{X}$, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level. Both are computed for NWA spin-0 models as a function of $m_{X}$.

Effect of event selections on a scalar MC signal sample generated for $m_{X}$ = 15 GeV and on the data. For the MC sample, the efficiencies are shown after applying event weights and a truth level filter that requires two photons with $p^{\gamma\gamma}_{T}>40$ GeV; for the data, the absolute yields are shown. The initial yields for data include a trigger preselection that is the OR of a list of single photon and diphoton triggers. The "2 $loose$ photons" step includes the kinematic acceptance cuts.

Parameterization of the Double Sided Crystal Ball function parameters describing the scalar mass resolution model as a function of $m_{X}$ [GeV].