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.

Central values and total systematical uncertainties for the unfolded $A_{FB}$ values which takes into account mass bin migration only in muon channel for Born and Dressed leptons. Dressed leptons are constructed by adding 4-vectors of the bare lepton and all real photons coming from the boson/lepton decay within a $\Delta R<$0.1.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Post-fit SR yields of the high-mass channel. The upper panel shows the observed number of events, as well the post-fit background predictions in each region. The bottom panel shows the ratio of the observed data and the total background prediction. The shaded areas correspond to the total statistical and systematic uncertainties obtained after the fit and described in Section 6.

Pre-fit data and background (reweighted $2b$) predictions for each $4b$ SR $E_\text{T}^\text{miss}$ and $m_\text{eff}$ bin of the low-mass channel for the 2016 data-taking period. The bottom panel shows the significance of any differences between the observed $4b$ data and the background prediction. The $1\sigma$ and $2\sigma$ bands are shown in green and yellow, respectively. All systematics are included except the background normalization, which is 2.3%.

Pre-fit data and background (reweighted $2b$) predictions for each $4b$ SR $E_\text{T}^\text{miss}$ and $m_\text{eff}$ bin of the low-mass channel for the 2017 data-taking period. The bottom panel shows the significance of any differences between the observed $4b$ data and the background prediction. The $1\sigma$ and $2\sigma$ bands are shown in green and yellow, respectively. All systematics are included except the background normalization, which is 3.7%.

Pre-fit data and background (reweighted $2b$) predictions for each $4b$ SR $E_\text{T}^\text{miss}$ and $m_\text{eff}$ bin of the low-mass channel for the 2018 data-taking period. The bottom panel shows the significance of any differences between the observed $4b$ data and the background prediction. The $1\sigma$ and $2\sigma$ bands are shown in green and yellow, respectively. All systematics are included except the background normalization, which is 1.8%.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. Results from a previous ATLAS search using 24.3-36.1 fb$^{-1}$ [13] are shown by the solid (observed) and dashed (expected) blue lines. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the 95% CL observed (solid) and expected (dashed) upper limits on $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})$, assuming the theory cross section for higgsino pair production. The higgsinos are assumed to decay as $\tilde{H}\rightarrow h + \tilde{G}$ or $\tilde{H}\rightarrow Z + \tilde{G}$. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the 95% CL observed (solid) and expected (dashed) upper limits on $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})$, assuming the theory cross section for higgsino pair production. The higgsinos are assumed to decay as $\tilde{H}\rightarrow h + \tilde{G}$ or $\tilde{H}\rightarrow Z + \tilde{G}$. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the 95% CL observed (solid) and expected (dashed) upper limits on $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})$, assuming the theory cross section for higgsino pair production. The higgsinos are assumed to decay as $\tilde{H}\rightarrow h + \tilde{G}$ or $\tilde{H}\rightarrow Z + \tilde{G}$. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the 95% CL observed (solid) and expected (dashed) upper limits on $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})$, assuming the theory cross section for higgsino pair production. The higgsinos are assumed to decay as $\tilde{H}\rightarrow h + \tilde{G}$ or $\tilde{H}\rightarrow Z + \tilde{G}$. The phase space above the lines is excluded.

Exclusion limits of the low-mass and high-mass channels. The low-mass channel is used for $m_{\tilde{H}}<250$ GeV while the high-mass channel is used for $m_{\tilde{H}}\ge250$ GeV. The plot shows the 95% CL observed (solid) and expected (dashed) upper limits on $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})$, assuming the theory cross section for higgsino pair production. The higgsinos are assumed to decay as $\tilde{H}\rightarrow h + \tilde{G}$ or $\tilde{H}\rightarrow Z + \tilde{G}$. The phase space above the lines is excluded.

Exclusion limits of the low-mass channel. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the low-mass channel. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the high-mass channel. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Exclusion limits of the high-mass channel. The plot shows the observed (solid) and expected (dashed) 95% CL upper limits on the cross section of higgsino pair production, assuming a higgsino decay branching ratio of $\mathcal{B}(\tilde{H}\rightarrow h + \tilde{G})=100\%$. The theory cross section and its uncertainty are shown by the solid red line and red shading. The bottom panel shows the ratio of the limits to the theory cross section. The phase space above the lines is excluded.

Results of the background-only fit in the low-mass channel discovery region SR_LM_150. Both pre-fit and post-fit values are shown.

Results of the background-only fit in the low-mass channel discovery region SR_LM_300. Both pre-fit and post-fit values are shown.

The experimental efficiency of the low-mass channel for the exclusion and discovery signal regions as a function of higgsino mass. The experimental efficiency is defined as the number of events passing the detector-level event selections divided by the number of events passing the event selections for a perfect detector. The denominator is obtained by implementing particle-level event selections that emulate the detector-level selections. This treats the lack of availability of $b$-jet triggers as an inefficiency.

The particle-level acceptance for the low-mass exclusion and discovery signal regions, shown as a function of higgsino mass. The acceptance is defined as the fraction of signal events passing the particle-level event selection that emulates the detector-level selection. The acceptance calculation considers only those signal events where both higgsinos decay to Higgs bosons.

The experimental efficiency of the high-mass channel discovery regions as a function of higgsino mass. For each higgsino mass, the efficiency is shown for the SR-1 region corresponding to the mass. For masses above 1100 GeV, SR-1-1100 is used. The experimental efficiency is defined as the number of events passing the detector-level event selections divided by the number of events passing the event selections for a perfect detector. The denominator is obtained by implementing particle-level event selections that emulate the detector-level selections. The efficiency calculation considers only those signal events where both higgsinos decay to Higgs bosons.

The particle-level acceptance for the high-mass signal regions, shown as a function of higgsino mass. For each higgsino mass, the acceptance is shown for the SR-1 region corresponding to the mass. For masses above 1100 GeV, SR-1-1100 is used. The acceptance is defined as the fraction of signal events passing the particle-level event selection that emulates the detector-level selection. The acceptance calculation considers only those signal events where both higgsinos decay to Higgs bosons.

Cutflow for the low-mass channel for a representative 130 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 150 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 200 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 250 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 300 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 400 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 500 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 600 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 700 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 800 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 900 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 1000 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the low-mass channel for a representative 1100 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. The $b$-jet cut requires 4 or more $b$-jets with $p_\text{T}>40$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$, with the availability of $b$-jet triggers lowering the luminosity to 126 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 200 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 250 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 300 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 400 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 500 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 600 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 700 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 800 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 900 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1000 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1100 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1200 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1300 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1400 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

Cutflow for the high-mass channel for a representative 1500 GeV signal. The preselection requires 4 or more jets with $p_\text{T}>25$ GeV and 2 or more $b$-jets with $p_\text{T}>25$ GeV. As the samples are generated with $\mathcal{B}(\tilde{H}\rightarrow h\tilde{G})$=50%, $\mathcal{B}(\tilde{H}\rightarrow Z\tilde{G})$=50% to allow for both decays to be studied, the $hh$ events selection is used to select the events where each of the higgsinos decays to a Higgs boson. Expected yields are normalized to a luminosity of 139 fb$^{-1}$. All selections are cumulative, with the exception of the SR cuts, which are each applied separately.

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.

The post-fit BDT score distribution for the direct stau channel, showing the scores for BDT4, before the selections on the BDT score is made. The black arrow depicts the BDT score selection for the SR-BDT. A few example SUSY scenarios targeted by each BDT are overlaid for illustration.

The post-fit kinematic distribution for the Intermediate stau channel, showing the $m_{\mathrm{T}2}$ distribution in SR-C1C1-LM, before the selection on $m_{\mathrm{T}2}$ is made. The black arrow depicts the selection for the signal region. An example SUSY scenario is overlaid for illustration.

The post-fit kinematic distribution for the Intermediate stau channel, showing the $m_{\mathrm{T}2}$ distribution in SR-C1N2OS-LM, before the selection on $m_{\mathrm{T}2}$ is made. The black arrow depicts the selection for the signal region. An example SUSY scenario is overlaid for illustration.

The post-fit kinematic distribution for the Intermediate stau channel, showing the $m_{\mathrm{T}2}$ distribution in SR-C1N2SS-LM, before the selection on $m_{\mathrm{T}2}$ is made. The black arrow depicts the selection for the signal region. An example SUSY scenario is overlaid for illustration.

The post-fit kinematic distribution for the Intermediate $Wh$ channel, showing the $m_{\mathrm{T}2}$ distribution in SR-Wh-LM, before the selection on $m_{\mathrm{T}2}$ is made. The black arrow depicts the selection for the signal region. An example SUSY scenario is overlaid for illustration.

The post-fit kinematic distribution for the Intermediate $Wh$ channel, showing the $m_{\mathrm{Tsum}}$ distribution in SR-Wh-HM, before the selection on $m_{\mathrm{Tsum}}$ is made. The black arrow depicts the selection for the signal region. An example SUSY scenario is overlaid for illustration.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

$+1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

$-1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$ production.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

$+1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

$-1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{L}\tilde{\tau}_{L}$ production.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

$+1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

$-1\sigma$ observed 95\% CL exclusion limits on the simplified models of $\tilde{\tau}_{R}\tilde{\tau}_{R}$ production.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ production decaying via staus.

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ production decaying via staus.

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ production decaying via staus.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ production decaying via staus.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$).

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$).

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$).

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$).

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$) using the OS signal regions.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$) using the OS signal regions.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$) using the SS signal regions.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via staus (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_1^0)$) using the SS signal regions.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$).

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$).

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$).

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$).

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$) using the OS signal regions.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$) using the OS signal regions.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$) using the SS signal regions.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$ (parameterised as $m(\tilde{\chi}_1^{\pm}/\tilde{\chi}_2^0)$ and $m(\tilde{\chi}_2^0)-m(\tilde{\chi}_1^0)$) using the SS signal regions.

Expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$.

$+1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$.

$-1\sigma$ expected 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$.

Observed 95\% CL exclusion limits on the simplified models of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ production decaying via $Wh$.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\tau}_{L}\tilde{\tau}_{L}$.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\tau}_{R}\tilde{\tau}_{R}$.

The best expected signal region used to set limits in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The best expected signal region used to set limits in models of the production of $\tilde{\tau}_{L}\tilde{\tau}_{L}$.

The best expected signal region used to set limits in models of the production of $\tilde{\tau}_{R}\tilde{\tau}_{R}$.

The acceptance $A$ of the direct stau production signal region SR-BDT1 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The efficiency $\epsilon$ of the direct stau production signal region SR-BDT1 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The acceptance $A$ of the direct stau production signal region SR-BDT2 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The efficiency $\epsilon$ of the direct stau production signal region SR-BDT2 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The acceptance $A$ of the direct stau production signal region SR-BDT3 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The efficiency $\epsilon$ of the direct stau production signal region SR-BDT3 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The acceptance $A$ of the direct stau production signal region SR-BDT4 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

The efficiency $\epsilon$ of the direct stau production signal region SR-BDT4 in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$.

Cutflow event yields of the direct stau production SRs in models of the production of $\tilde{\tau}_{L,R}\tilde{\tau}_{L,R}$. All yields correspond to weighted events, so that effects from reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalised to the integrated luminosity of the data sample, $\int L dt = 139$ fb$^{-1}$. The preliminary event reduction is a centralised stage requiring the event to: have at least two hadronically-decaying taus; be selected and matched by the asymmetric ditau trigger (with plateau cuts); have at least two medium taus of opposite sign and have $m_{\mathrm{T2}} > 30$ GeV. Cuts except the BDT score cuts are applied consecutively, while the BDT score cuts are applied one at a time.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$.

The acceptance $A$ of the Intermediate stau signal region SR-C1C1-LM in models of the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1C1-LM in models of the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ decaying via staus.

The acceptance $A$ of the Intermediate stau signal region SR-C1C1-HM in models of the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1C1-HM in models of the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$ decaying via staus.

The acceptance $A$ of the Intermediate stau signal region SR-C1N2OS-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1N2OS-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The acceptance $A$ of the Intermediate stau signal region SR-C1N2SS-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1N2SS-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The acceptance $A$ of the Intermediate stau signal region SR-C1N2OS-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1N2OS-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The acceptance $A$ of the Intermediate stau signal region SR-C1N2SS-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

The efficiency $\epsilon$ of the Intermediate stau signal region SR-C1N2SS-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$ decaying via staus.

Cutflow event yields of the Intermediate stau SRs in models of the production of $\tilde{\chi}_1^{+}\tilde{\chi}_1^{-}$. All yields correspond to weighted events, so that effects from reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalised to the integrated luminosity of the data sample, $\int L dt = 139$ fb$^{-1}$. The preliminary event reduction is a centralised stage requiring the event to: have at least two hadronically-decaying medium taus; be selected and matched by the asymmetric ditau trigger or ditau+MET trigger with offline cuts using HLT threshold values. The different yields of preliminary event reduction are caused by different trigger scale factor.

Cutflow event yields of the Intermediate stau SRs in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^{0}$. All yields correspond to weighted events, so that effects from reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalised to the integrated luminosity of the data sample, $\int L dt = 139$ fb$^{-1}$. The preliminary event reduction is a centralised stage requiring the event to: have at least two hadronically-decaying medium taus; be selected and matched by the asymmetric ditau trigger or ditau+MET trigger with offline cuts using HLT threshold values. The different yields of preliminary event reduction are caused by different trigger scale factor.

Observed upper limit on the signal cross section in fb for the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

The best expected signal region used to set limits in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

The acceptance $A$ of the Intermediate $Wh$ signal region SR-Wh-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

The efficiency $\epsilon$ of the Intermediate $Wh$ signal region SR-Wh-LM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

The acceptance $A$ of the Intermediate $Wh$ signal region SR-Wh-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

The efficiency $\epsilon$ of the Intermediate $Wh$ signal region SR-Wh-HM in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$.

Cutflow event yields of the Intermediate $Wh$ SRs in models of the production of $\tilde{\chi}_1^{\pm}\tilde{\chi}_2^0$ decaying via $Wh$. All yields correspond to weighted events, so that effects from reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalised to the integrated luminosity of the data sample, $\int L dt = 139$ fb$^{-1}$. The preliminary event reduction is a centralised stage requiring the event to: have one single lepton and two hadronically decaying medium taus; be selected and matched by the single lepton trigger with plateau cuts.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 100&nbsp;MeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 10&nbsp;GeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the &mu;DPJ channel (SR_&mu;), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the low E_T^miss caloDPJ channel (SR_c^L), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the high E_T^miss caloDPJ channel (SR_c^H), obtained for the different FRVZ MC signal mass points.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 17&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 50&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 400&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 900&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 2&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 6&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 15&nbsp;GeV.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_&mu; search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^L search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^H search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Summary of the observed and expected 95% CL upper limits on the cross section for $\mathrm{LQ}_{\mathrm{mix}}^{\mathrm{d}}$ pair production as a function of $m_{\mathrm{LQ}_{\mathrm{mix}}^{\mathrm{d}}}$ under the assumptions of B(LQ$\rightarrow t\mu$)=1.

Summary of observed and predicted yields in the four signal region categories. The background prediction is shown after the combined likelihood fit to data under the background-only hypothesis across all control region and signal region categories. The expected signal yields that are obtained by using their theoretical cross sections are also shown with their pre-fit uncertainties, assuming B=1 and $\mu$=1. The "Other" contribution is dominated by $t\bar{t}t\bar{t}$ and $t\bar{t}WW$ in the $3\ell$ SRs, whereas it is dominated by $tWZ$ and $t\bar{t}WW$ in the $4\ell$ SRs. Dashes refer to components that are negligible or not applicable.

Summary of the data, background and signal yields in the four signal region categories. The background prediction is shown before the combined likelihood fit to data. Dashes (--) refer to components that are negligible or not applicable.

Summary of the data and background yields in the seven control region categories. The background prediction is shown before the combined likelihood fit to data. Dashes (--) refer to components that are negligible or not applicable.

Summary of the data and background yields in the seven control region categories. The background prediction is shown after the combined likelihood fit to data under the background-only hypothesis across all control region categories. Dashes (--) refer to components that are negligible or not applicable.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The j+b-jet invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The 2b-jet invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The j+e invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The b-jet+e invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The j+$\gamma$ invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The j+$\mu$ invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The b-jet+$\mu$ invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

Values of $\Delta Z$ for the discovery sensitivity, as defined in the text, as a function of the invariant mass $\textit{m}$. The b-jet+$\gamma$ invariant mass distribution is calculated in the 10 pb AR. Positive percentages indicate improvements in sensitivity. Horizontal dashed lines are drawn at 100% and 200% to guide the eye. The five benchmark BSM models are (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$; (2) a Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a $Z'$ boson decaying to a composite lepton $E$ and $\ell$, with $E \rightarrow Z\ell$; (4) the sequential standard model $W' \rightarrow W Z' \rightarrow \ell\nu q\bar{q}$; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$. The multiple markers shown for the composite-lepton model at the same invariant mass values correspond to different composite lepton ($E$) masses between 0.25 and 3.5 TeV. The center positions of the markers are set to the masses of the corresponding heavy particles.

The 95% CL upper limits on the cross section times acceptance ($A$), efficiency ($\epsilon$), and branching ratio ($B$) for Gaussian-shaped signals with different signal widths. The limits are calculated for events with at least one lepton with pT > 60 GeV in the 10 pb AR. Two width hypotheses are shown; $\sigma X / mX = 0$ and $\sigma X / mX = 0.15$. In both cases, the detector resolution for jets is included in the simulation of signal samples. The $\pm1 \sigma$ and $\pm2 \sigma$ bands around the expected limit are shown for $\sigma X / mX = 0$ signals. Mass points are spaced 5% apart, relative to the preceding point, starting at 0.3 TeV.

Distributions of the anomaly score from the AE for data and five benchmark BSM models. Their legends, from top to bottom, are; (1) charged Higgs boson production in association with a top quark, $tbH^{+}$ with $H^{+} \rightarrow t\bar{b}$, with the $H^{+}$ mass of 2 TeV; (2) a 6 TeV Kaluza-Klein gauge boson, $W_{KK}$, with the SM $W$ boson and a radion $\phi$; (3) a 4 TeV $Z'$ boson decaying to a composite lepton $E$ with a mass of 0.5 TeV; (4) the sequential standard model $W' \rightarrow WZ' \rightarrow \ell\nu q\bar{q}$, with the $W'$ mass of 6.2 TeV and the $Z'$ mass of 6 TeV; (5) a simplified dark-matter model with an axial-vector mediator $Z' \rightarrow q\bar{q}$, where one of the quarks radiates a $W$ boson decaying to $\ell\nu$ with a mass of 6 TeV. The distributions for the BSM models are smoothed to remove fluctuations due to low MC event counts. The vertical lines indicate the start of the three anomaly regions (ARs). The labels of the three ARs indicate the visible cross section for hypothetical processes yielding the same number of events as observed in the 140 $fb^{-1}$ dataset. The AE is applied to preselected events without any requirements on invariant mass distributions.

Invariant mass distributions of $j+Y$ for $M_{jY}$ > 0.3 TeV after preselection along with the fit from Eq.(1). The fit is represented by red lines, and the associated uncertainties are indicated by yellow bands. The lower panels show the bin-by-bin significances of deviations from the fit, calculated as $(d_{\textit{i}} - f_{\textit{i}}) / \delta_{\textit{i}}$, where $d_{\textit{i}}$ is the data yield, $f_{\textit{i}}$ is the fit value, and $\delta_{i}$ is the uncertainty of data in the $\textit{i}$-th bin

Distributions of the anomaly score for data and several anomaly scenarios. The example BSM model (shown with the dashed blue lines) is the sequential standard model $W' \rightarrow WZ' \rightarrow \ell\nu q\bar{q}$. The mass of $W'$ is set to 2.2 TeV and the mass of the $Z'$ is set to 2 TeV. This model leads to the final state of one lepton, two jets, and small missing transverse energy that is similar to the SM backgrounds. The other histograms represent events from the same model with artificial modifications to represent anomalous events; (1) "Anomaly 1" is the case where all jets beyond the second jet ($N_{j}$ > 2) are replaced with photons; (2) "Anomaly 2" is the case where all jets beyond the second jet are replaced with $b$-jets; (3) "Anomaly 3" is the case of low-multiplicity events where all jets beyond the second jet are removed. The histograms are normalized to unit. The left peak near log(Loss) = -9 visible in Anomaly 1 and 2 is from the events without a third jet.