Observed (solid line) and expected (dashed line) 95\% CL limits on the product of the production cross section times the branching ratio of a narrow width spin-0 resonance $X$ produced via gluon-gluon initial states decaying to a $Z$ boson and a photon, $\sigma(pp\to X)\cdot\mathcal{B}(X\to Z\gamma)$, as a function of the resonance mass $m_{X}$. Observed (expected) results are derived from ensemble tests for $m_{X}>1850 (900)$~\GeV. The green and yellow solid bands correspond to the $\pm1\sigma$ and $\pm2\sigma$ intervals for the expected upper limits. The limits in the $m_{X}$ ranges from 220 GeV to 3400 GeV and are obtained from the combined $ee\gamma$ and $\mu\mu\gamma$ channels.

Observed (solid line) and expected (dashed line) 95\% CL limits on the product of the production cross section times the branching ratio of a narrow width spin-2 resonance $X$ produced via gluon-gluon initial states decaying to a $Z$ boson and a photon, $\sigma(pp\to X)\cdot\mathcal{B}(X\to Z\gamma)$, as a function of the resonance mass $m_{X}$. Observed (expected) results are derived from ensemble tests for $m_{X}>1850 (900)$~\GeV. The green and yellow solid bands correspond to the $\pm1\sigma$ and $\pm2\sigma$ intervals for the expected upper limit respectively. The limits in the $m_{X}$ ranges from 220 GeV to 3400 GeV and are obtained from the combined $ee\gamma$ and $\mu\mu\gamma$ channels..

Observed (solid line) and expected (dashed line) 95\% CL limits on the product of the production cross section times the branching ratio of a narrow width spin-2 resonance $X$ produced via $q\bar{q}$ initial states decaying to a $Z$ boson and a photon, $\sigma(pp\to X)\cdot\mathcal{B}(X\to Z\gamma)$, as a function of the resonance mass $m_{X}$. Observed (expected) results are derived from ensemble tests for $m_{X}>1850 (900)$~\GeV. The green and yellow solid bands correspond to the $\pm1\sigma$ and $\pm2\sigma$ intervals for the expected upper limit respectively. The limits in the $m_{X}$ ranges from 220 GeV to 3400 GeV and are obtained from the combined $ee\gamma$ and $\mu\mu\gamma$ channels.

Distribution (events/100 GeV) of the reconstructed $m_{tb}$ for data and backgrounds in the 0-lepton channel's the signal region 3 after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Distribution (events/100 GeV) of the reconstructed $m_{tb}$ for data and backgrounds in the 0-lepton channel's validation region before the fit to data. The systematics uncertainty is shown for the pre-fit background sum, including the background statistical uncertainty. The individual background components are obtained before the fit, too. There is also the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j2b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j2b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b control region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b control region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b validation region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b validation region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=0.5. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=1.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=2.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=0.5. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=1.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=2.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

95% CL limits on the coupling value ($g^{\prime}/g$) and the $W^{\prime}$-boson mass for left-handed $W^{\prime}$-boson couplings. The area above the line is excluded.

95% CL limits on the coupling value ($g^{\prime}/g$) and the $W^{\prime}$-boson mass for right-handed $W^{\prime}$-boson couplings. The area above the line is excluded.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

Observed and expected upper limits at 95% CL on the production cross-section times branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 50 GeV

Observed and expected upper limits at 95% CL on the production cross-section times branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 60 GeV

Observed and expected upper limits at 95% CL on the production cross-section times branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 70 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 20 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 30 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 40 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 50 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 60 GeV

Observed 90% CL upper limits on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 70 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 20 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 30 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 40 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 50 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 60 GeV

Observed 90% CL upper limits on $\epsilon^{2}$, assuming of $\alpha_{D}=0.1$, as a function of $m_{A'}$ at dark Higgs boson mass of 70 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 20 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 30 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 40 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 50 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 60 GeV

Observed and expected upper limits at 95% CL on the branching fraction as a function of $m_{A'}$ at dark Higgs boson mass of 70 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 20 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 30 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 40 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 50 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 60 GeV

Observed and expected upper limits at 95% CL on $\alpha_{D}\epsilon^{2}$ as a function of $m_{A'}$ at dark Higgs boson mass of 70 GeV

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.

Expected and observed 95% CL for the 1SFH mu Majorana model.

Expected and observed 95% CL for the 2QDH NH Dirac model.

Expected and observed 95% CL for the 2QDH NH Majorana model.

Expected and observed 95% CL for the 2QDH IH Dirac model.

Expected and observed 95% CL for the 2QDH IH Majorana model.

Cutflow for six simulated signal channels showing the weighted number of expected events based on the single-flavour mixing model in the Majorana limit. Each column uses the generated signal sample with the mass hypothesis $m_N = 10$ GeV and proper decay length $c\tau_N = 10$ mm.

Cutflow for the six channels in data showing the number of events passing each successive signal selection for Majorana HNLs.

The event selection efficiency for each mass-lifetime point in all six studied channels. Shown is the fraction of the produced MC simulation events that pass all signal region selections. An entry of 0 indicates no events were selected.

The dominant signal uncertainty is due to differences in reconstruction of displaced vertices and tracks between data and MC. This is evaluated by comparing $K^{0}_{S} \rightarrow \pi^+\pi^-$ event yields in the VR and in MC produced with Pythia8.186 in bins of $p_\mathrm{T}$ and $r_\mathrm{DV}$. The data/MC ratio is normalized to the bin nearest the IP where the tracking and vertexing reconstruction algorithms are expected to be most robust. The symmetrized difference from 1.0 is applied to each signal vertex as a per-event systematic variation.

Expected and observed yields in the different analysis regions (prefit) for the 1SFH e Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 1SFH e Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 1SFH e Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 1SFH e Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 1SFH u Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 1SFH u Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 1SFH u Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 1SFH u Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 2QDH (NH) Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 2QDH (NH) Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 2QDH (NH) Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 2QDH (NH) Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 2QDH (IH) Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 2QDH (IH) Dirac model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (prefit) for the 2QDH (IH) Majorana model (10 GeV, 10mm).

Expected and observed yields in the different analysis regions (postfit) for the 2QDH (IH) Majorana model (10 GeV, 10mm).

The total displaced vertexing efficiency as a function of $r_{DV}$ for the custom configuration used in this analysis. The definition of the secondary vertex efficiency can be found in defined in \cite{ATL-PHYS-PUB-2019-013}. The efficiency is shown for $\mu-\mu\mu$, $\mu-\mu e$ and $\mu-ee$ signals with $m_N=10$~GeV and $c\tau_N=10$~mm.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Background-only fit to the observed numbers of events (black points) as a function of the diphoton invariant mass $m_{\gamma\gamma}$.

Expected and observed 95% CL upper limits on the signal fiducial cross section $\sigma_{\textrm{fid}}$, assuming 100% branching ratio for ALP decay into two photons, as a function of the hypothetical ALP mass $m_{\textrm{X}}$. The 1$\sigma$ and 2$\sigma$ confidence intervals are shown by the coloured bands.

Expected and observed 95% CL upper limits on the the ALP coupling constant, assuming 100% branching ratio for ALP decay into two photons, as a function of the hypothetical ALP mass $m_{\textrm{X}}$. The 1$\sigma$ and 2$\sigma$ confidence intervals are shown by the coloured bands. Contours of the ALP natural width $\Gamma$ are illustrated by the smooth blue solid lines.

Fiducial region acceptance of signal events for coupling constant f$^{-1}=0.05$ TeV$^{-1}$. EL, SD, and DD stand for the exclusive, single-dissociative, and double-dissociative processes. The acceptances are parameterised as $p_0 + p^{i}_{1} e^{p_{2}^{i} m_{\textrm{X}}} + p_{3}^{i} e^{p_{4}^{i} m_{\textrm{X}}} $ , where $i$ specifies the process type, exclusive, single-dissociative, or double-dissociative.

Correction factors $A_{\textrm{X}}/A_{0}$ and $C_{\textrm{X}}$ for the exclusive signal events with ALP coupling constant f$^{-1}$=0.05 TeV$^{-1}$, where acceptance $A_{\textrm{X}}$ and efficiency $C_{\textrm{X}}$ are defined in arXiv:2102.13405. $A_{\textrm{X}}$/$A_{0}$ and $C_{\textrm{X}}$ are parameterised as $p_0 + p^{i}_{1} e^{p_{2}^{i} m_{\textrm{X}}} + p_{3}^{i} e^{p_{4}^{i} m_{\textrm{X}}}$, where $i$ specifies the process type.

Simulated ALP signal cutflow for $m_{\rm{X}}$=300 GeV and $m_{\rm{X}}$=1200 GeV. The yields are normalized to a luminosity of 14.6 fb$^{-1}$. Selections are applied for each side after the selection on acoplanarity. The union of the sets of selected events is taken finally.

The reconstruction efficiency for caloDPJs produced by the decay of &gamma;_d into e⁺e^- or qq&#772;. The reconstruction efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as a function of their transverse momentum in events where the &gamma;_d L_xy is between 2&nbsp;m and 4&nbsp;m.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d+X and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_2&mu;^ggF, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d+X is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d+X and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_c+&mu;^ggF, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d+X is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d+X and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_2c^ggF, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d+X is larger than unity.

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

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d+X and WH selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_c+&mu;^WH, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d+X is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d+X and WH selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_2c^WH, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d+X is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_2&mu;^ggF, assuming a HAHM signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_c+&mu;^ggF, assuming a HAHM signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d is larger than unity.

Observed 95% CL upper limits on the branching ratio (B) for the decay H&rarr;&nbsp;2&gamma;_d and ggF selection, for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson. The limits are shown for the SR_2c^ggF, assuming a HAHM signal model. The hatched band denotes the region in which the branching ratio of H&rarr;&nbsp;2&gamma;_d is larger than unity.

The CalRatio 2015--2016 trigger efficiency for the decay of &gamma;_d in e⁺e^- or qq&#772;. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse decay length L_xy.

The CalRatio 2015--2016 trigger efficiency for the decay of &gamma;_d in e⁺e^- or qq&#772;. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse momentum, in events where the &gamma;_d L_xy is between 2&nbsp;m and 4&nbsp;m.

The CalRatio 2017--2018 trigger efficiency for the decay of &gamma;_d in e⁺e^- or qq&#772;. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse decay length L_xy.

The CalRatio 2017--2018 trigger efficiency for the decay of &gamma;_d in e⁺e^- or qq&#772;. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse momentum, in events where the &gamma;_d L_xy is between 2&nbsp;m and 4&nbsp;m.

The narrow-scan 2015--2016 trigger efficiency for the decay of &gamma;_d in &mu;⁺&mu;^-. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse decay length L_xy.

The narrow-scan 2015--2016 trigger efficiency for the decay of &gamma;_d in &mu;⁺&mu;^-. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse momentum, in events where the &gamma;_d L_xy is below 6&nbsp;m.

The narrow-scan 2017--2018 trigger efficiency for the decay of &gamma;_d in &mu;⁺&mu;^-. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse decay length L_xy.

The narrow-scan 2017--2018 trigger efficiency for the decay of &gamma;_d in &mu;⁺&mu;^-. The trigger efficiency is shown for &gamma;_d with 0&lt;|&eta;|&lt;1.1 as function of the transverse momentum, in events where the &gamma;_d L_xy is below 6&nbsp;m.

Efficiency of the cosmic-ray tagger as function of the &gamma;_d transverse decay length. The efficiency is calculated accepting the &mu;DPJs for which the cosmic-ray tagger score is &gt; 0.2 for each associated MS-only track.

Efficiency of the cosmic-ray tagger as function of the &gamma;_d transverse momentum. The efficiency is calculated accepting the &mu;DPJs for which the cosmic-ray tagger score is &gt; 0.2 for each associated MS-only track.

Efficiency of the QCD tagger as function of the &gamma;_d transverse decay length. The efficiency is calculated accepting the caloDPJs for which the QCD tagger score is &gt; 0.5.

Efficiency of the QCD tagger as function of the &gamma;_d transverse momentum. The efficiency is calculated accepting the caloDPJs for which the QCD tagger score is &gt; 0.5.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_2&mu;^ggF.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_c+&mu;^ggF.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_2c^ggF.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_c^WH.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_2c^WH.

The extrapolated acceptance times efficiencies as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the SR_c+&mu;^WH.

The extrapolated acceptance times efficiencies for SR_2&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_c+&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_2c;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;2&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_2&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the HAHM H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the ggF channel.

The extrapolated acceptance times efficiencies for SR_c+&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the HAHM H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the ggF channel.

The extrapolated acceptance times efficiencies for SR_2c;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the HAHM H&rarr;&nbsp;2&gamma;_d+X process and a SM Higgs boson for the ggF channel.

The extrapolated acceptance times efficiencies for SR_2&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_c+&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_2c;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a Higgs-like scalar with a mass of 800&nbsp;GeV. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_2&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a SM Higgs boson. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_c+&mu;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a SM Higgs boson. The coloured bands represent the MC statistical uncertainties.

The extrapolated acceptance times efficiencies for SR_2c;^ggF, as a function of the &gamma;_d mean proper lifetime c&tau; for the FRVZ pp &rarr; H&rarr;&nbsp;4&gamma;_d+X process and a SM Higgs boson. The coloured bands represent the MC statistical uncertainties.

Observed limits at the 95% CL on the branching ratio (B), obtained from the SR_2&mu;^ggF, for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X, for different &gamma;_d masses and a 125 GeV Higgs boson. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the branching ratio (B), obtained from the SR_c+&mu;^ggF, for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X, for different &gamma;_d masses and a 125 GeV Higgs boson. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the branching ratio (B), obtained from the SR_2c^ggF, for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X, for different &gamma;_d masses and a 125 GeV Higgs boson. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section, obtained from the SR_2&mu;^ggF, for the process pp &rarr; H&rarr;&nbsp;2&gamma;_d+X, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section, obtained from the SR_c+&mu;^ggF, for the process pp &rarr; H&rarr;&nbsp;2&gamma;_d+X, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section, obtained from the SR_2c^ggF, for the process pp &rarr; H&rarr;&nbsp;2&gamma;_d+X and ggF selection, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X and ggF selection, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown for the 2&mu; search channel, assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X and ggF selection, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown for the c+&mu; search channel, assuming an FRVZ signal model.

Observed limits at the 95% CL on the cross section for the process pp &rarr; H&rarr;&nbsp;4&gamma;_d+X and ggF selection, for different &gamma;_d masses and a Higgs-like scalar with a mass of 800&nbsp;GeV. The limits are shown for the 2c search channel, assuming an FRVZ signal model.

95% CL exclusion limits on $\mathcal{B}(H\rightarrow aa \rightarrow b\bar{b}b\bar{b})$ for $m_a = 45$ GeV.

95% CL exclusion limits on $\mathcal{B}(H\rightarrow aa \rightarrow b\bar{b}b\bar{b})$ for $m_a = 55$ GeV.

The fraction of $a$ boson decays matched to reconstructed displaced vertices passing all vertex selections in signal MC.

The extrapolated signal selection efficiency as a function of $c\tau_{a}$.

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.