Covariances $c_{ij}$ for the highest ranked systematic uncertainties in the energy asymmetry measurement differential in $\theta_j$.

Definition of the fiducial phase space with lepton candidate ($\ell$), hadronic top candidate ($j_h$), leptonic top candidate ($j_l$) and associated jet candidate ($j_a$).

Bounds on individual Wilson coefficients $C($TeV$/\Lambda)^2$ from the energy asymmetry, obtained from a combined fit to its values in all three $\theta_j$ bins.

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

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

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

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

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

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

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

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

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

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

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

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

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.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.16 < $\alpha$ < 0.18.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.18 < $\alpha$ < 0.20.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.20 < $\alpha$ < 0.22.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.22 < $\alpha$ < 0.24.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.24 < $\alpha$ < 0.26.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.26 < $\alpha$ < 0.28.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.28 < $\alpha$ < 0.30.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.30 < $\alpha$ < 0.32.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.32 < $\alpha$ < 0.34.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.10 < $\alpha$ < 0.12.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.12 < $\alpha$ < 0.14.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.14 < $\alpha$ < 0.16.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.16 < $\alpha$ < 0.18.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.18 < $\alpha$ < 0.20.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.20 < $\alpha$ < 0.22.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.22 < $\alpha$ < 0.24.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.24 < $\alpha$ < 0.26.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.26 < $\alpha$ < 0.28.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.28 < $\alpha$ < 0.30.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.30 < $\alpha$ < 0.32.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The product of the analysis acceptance and selection efficiency for all analysis selection criteria is shown as a function of $m_Y$ and $m_{X}/m_{Y}$.

The cross-section of the signal samples is shown as a function of $m_Y$ and $m_{X}/m_{Y}$.

Absolute differential cross-section as a function of $p_T^{t,l}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $p_T^{t,l}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $m^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $m^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $y^{t,h}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $y^{t,h}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $y^{t,l}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $y^{t,l}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $y^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $y^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $H_T^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $H_T^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $\frac{\Delta\phi}{\pi}(b_{l},t_{h})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $\frac{\Delta\phi}{\pi}(b_{l},t_{h})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $p_T^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $p_T^{t\bar{t}}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $\frac{\Delta\phi}{\pi}(t_{h},t_{l})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $\frac{\Delta\phi}{\pi}(t_{h},t_{l})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $H_T^{t\bar{t}+jets}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $H_T^{t\bar{t}+jets}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $N^j$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $N^j$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $p_T^{j,1}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $p_T^{j,1}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $m(j_1, t_h)$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $m(j_1, t_h)$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_{2}, t_{h})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_{2}, t_{h})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_{1}, j_{2})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_{1}, j_{2})$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute differential cross-section as a function of $p_T^{j,2}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative differential cross-section as a function of $p_T^{j,2}$ at particle level in the boosted topology. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 1. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 2. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ $\geq$ 3. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 1. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 2. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $N^j$ at particle level in the boosted topology in $N^j$ $\geq$ 3. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 355.0 GeV < $p_T^{t,h}$ < 398.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 398.0 GeV < $p_T^{t,h}$ < 496.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 496.0 GeV < $p_T^{t,h}$ < 2000.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 355.0 GeV < $p_T^{t,h}$ < 398.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 398.0 GeV < $p_T^{t,h}$ < 496.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $p_T^{j,1}$ vs $p_T^{t,h}$ at particle level in the boosted topology in 496.0 GeV < $p_T^{t,h}$ < 2000.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 355.0 GeV < $p_T^{t,h}$ < 398.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 398.0 GeV < $p_T^{t,h}$ < 496.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 496.0 GeV < $p_T^{t,h}$ < 2000.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 355.0 GeV < $p_T^{t,h}$ < 398.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 398.0 GeV < $p_T^{t,h}$ < 496.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $p_T^{t,h}$ at particle level in the boosted topology in 496.0 GeV < $p_T^{t,h}$ < 2000.0 GeV. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 1. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 2. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Relative double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ $\geq$ 3. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 1. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ = 2. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Absolute double-differential cross-section as a function of $\frac{\Delta\phi}{\pi}(j_1, t_h)$ vs $N^j$ at particle level in the boosted topology in $N^j$ $\geq$ 3. The measured differential cross-section is compared with the prediction obtained with the Powheg+Pythia8 Monte Carlo generator.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x&ndash;y plane (L_xy) for LLPs decaying in the barrel (|&eta;|&lt;1.4) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

Trigger efficiency for simulated signal events as a function of the LLP decay position in the x&ndash;y plane (L_xy) for LLPs decaying in the barrel (|&eta;|&lt;1.4) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the high-E_T L1 triggers with E_T thresholds of 60 GeV and 100 GeV and by the two versions of the low-E_T L1 triggers. Only statistical uncertainties are shown.

The NN output scores in the dijet control region for the low-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the low-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with no adversary network. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

The NN output scores in the dijet control region for the high-E_T training with an adversary network included. Statistical uncertainties are shown in all plots. In cases where training with adversary networks is considered, the systematic uncertainty related to modelling discrepancies is included as well.

Distribution of the low-E_T per-event BDT in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Distribution of the high-E_T per-event BDT outputs in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown.

Sequential impact of each requirement on the number of events passing the selection for the high-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Sequential impact of each requirement on the number of events passing the selection for the low-E_T selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events.

Application of the modified ABCD method to the final high-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B&middot; N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

Application of the modified ABCD method to the final low-E_T selections. The a priori estimate refers to the "pre-unblinding" case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple N^bkg_A=(N^bkg_B&middot; N^bkg_C)/N^bkg_D relation. The a posteriori estimate refers to the "post-unblinding" case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signal-plus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources.

95% CL expected and observed limits on the BR of SM Higgs bosons to pairs of neutral LLPs (B_{H&rarr; ss}), showing the &plusmn; 1 &sigma; (green) and &plusmn; 2 &sigma; (yellow) expected limit bands, as well as a comparison with the results from previous ATLAS searches [36,78]. The cross-section for SM Higgs boson gluon--gluon fusion production is assumed to be 48.6 pb.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 &le; |&eta;| &lt; 2.5) for one of the low-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

Trigger efficiency of simulated signal events as a function of the LLP decay position in the z direction for LLPs decaying in the calorimeter endcaps (1.4 &le; |&eta;| &lt; 2.5) for one of the high-E_T signal samples for HLT CalRatio triggers seeded by the 60 GeV-high-E_T trigger and by the two versions of the low-E_T triggers.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The simulated efficiencies as a function of c times the mean proper lifetime (c&tau;) of s for several different MC samples. A weight-based extrapolation procedure is used to determine the efficiency at a given mean proper lifetime.

The event BDT in the dijet control region for the low-E_T training training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The event BDT in the dijet control region for the high-E_T training. The uncertainties are combined statistical and ML modelling systematic uncertainty.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 60 GeV compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 125 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available. The 125 GeV mediator is assumed to be the SM Higgs boson.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 200 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 400 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; mass of 600 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

The 95% CL observed limits, expected limits and &plusmn; 1 &sigma; and 2 &sigma; bands for the &Phi; masses of of 1000 GeV, compared to the results from the 2016-data analysis and subsequent combinations, where available.

Efficiency for an event to enter Region A of the high-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in decay position in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, &infin;] m for LLPs with |&eta;| &lt; 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, &infin; ] m for LLPs with |&eta;|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or &tau; in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) &times; (number of p_T bins &times; number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the high-E_T selections, for overall efficiencies above 0.5%, the results are typically accurate to around 25%, but below this the efficiency can be overestimated and therefore should not be used for re-interpration.

Efficiency for an event to enter Region A of the low-E_T selection, as a function of the two LLP kinematics, decay type and decay position. LLP p_T is binned in the ranges of [0, 50 , 100, 200 , 400, 1600] GeV (5 bins), the LLP decay position is binned in L_xy in [0, 1.5, 2, 2.5, 3, 3.5, 3.9, &infin;] m for LLPs with |&eta;| &lt; 1.5 and L_z in [0, 3.6, 4.2, 4.8, 5.5, 6, &infin; ] m for LLPs with |&eta;|geq1.5, 13 bins in all. Finally, four decay types are considered: LLPs decaying to pairs of c, b, t, or &tau; in bins 0, 1, 2, 3 respectively. The efficiency is presented as a function of "Bin Index", which is calculated as follows: Bin Index = (decay position bin index ) &times; (number of p_T bins &times; number of decay type bins) + p_T bin index * (number of decay type bin) + decay type bin index. The efficiency for a given pair-produced LLP sample can be obtained by summing the efficiency values for each event as extracted from this map, and dividing it by the total number of events in the sample. The efficiency map is symmetric between the LLPs, so the choice of LLP1 and LLP2 is arbitrary. For the low-E_T selections, for overall efficiencies above 0.15%, the results are typically accurate to around 33%, and below this the efficiency is typically accurate up to a factor of 3.