Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$ and photon isolation cone radius $R=0.4$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$ and photon isolation cone radius $R=0.4$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$ and photon isolation cone radius $R=0.4$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $|\eta^{\gamma}|<0.6$ and photon isolation cone radius $R=0.2$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.6<|\eta^{\gamma}|<0.8$ and photon isolation cone radius $R=0.2$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.8<|\eta^{\gamma}|<1.37$ and photon isolation cone radius $R=0.2$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$ and photon isolation cone radius $R=0.2$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$ and photon isolation cone radius $R=0.2$.

Measured cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$ and photon isolation cone radius $R=0.2$.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $|\eta^{\gamma}|<0.6$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.6<|\eta^{\gamma}|<0.8$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.8<|\eta^{\gamma}|<1.37$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$ and isolation cone radius $0.4$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $|\eta^{\gamma}|<0.6$ and isolation cone radius $0.2$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.6<|\eta^{\gamma}|<0.8$ and isolation cone radius $0.2$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $0.8<|\eta^{\gamma}|<1.37$ and isolation cone radius $0.2$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$ and isolation cone radius $0.2$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$ and isolation cone radius $0.2$ at NNLO QCD.

Predicted cross sections for inclusive isolated-photon production as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$ and isolation cone radius $0.2$ at NNLO QCD.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $|\eta^{\gamma}|<0.6$.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $0.6<|\eta^{\gamma}|<0.8$.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $0.8<|\eta^{\gamma}|<1.37$.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$.

Measured ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $|\eta^{\gamma}|<0.6$ at NNLO QCD.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $0.6<|\eta^{\gamma}|<0.8$ at NNLO QCD.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $0.8<|\eta^{\gamma}|<1.37$ at NNLO QCD.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $1.56<|\eta^{\gamma}|<1.81$ at NNLO QCD.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $1.81<|\eta^{\gamma}|<2.01$ at NNLO QCD.

Predicted ratio of the differential cross sections for inclusive isolated-photon production for $R=0.2$ and $R=0.4$ as a function of $E_{\rm T}^{\gamma}$ for $2.01<|\eta^{\gamma}|<2.37$ at NNLO QCD.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $|\eta^{\gamma}|<0.6$.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $0.6<|\eta^{\gamma}|<0.8$.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $0.8<|\eta^{\gamma}|<1.37$.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $1.56<|\eta^{\gamma}|<1.81$.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $1.81<|\eta^{\gamma}|<2.01$.

Measured fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $2.01<|\eta^{\gamma}|<2.37$.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $|\eta^{\gamma}|<0.6$ at NNLO QCD.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $0.6<|\eta^{\gamma}|<0.8$ at NNLO QCD.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $0.8<|\eta^{\gamma}|<1.37$ at NNLO QCD.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $1.56<|\eta^{\gamma}|<1.81$ at NNLO QCD.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $1.81<|\eta^{\gamma}|<2.01$ at NNLO QCD.

Predicted fiducial integrated cross section for inclusive isolated-photon production as a function of $R$ for $2.01<|\eta^{\gamma}|<2.37$ at NNLO QCD.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the signal region, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $W$+jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Expected distributions of the MEM discriminant $P(S|X)$ in the SR, for the s-channel single-top signal, and for the $t\bar{t}$ and $W$+jets backgrounds, for MEM discriminant values larger than $2.0\times10^{-4}$. Each distribution is normalised to unity. The binning is the same as the optimised binning used in the signal extraction fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $W$+jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 3-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 4-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty bands indicate the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR before the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore not included. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$, after subtraction of all backgrounds. The fitted distribution for the simulation of the signal is shown together with the post-fit uncertainty in the backgrounds. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Pre-fit and post-fit event yields in the SR, for MEM discriminant values larger than $2.0\times10^{-4}$. The central value of the event yield for each process is calculated by summing the values of the discriminant bin contents, using the nominal expected yield for the pre-fit value, and the best-fit estimate for the post-fit value. The error includes statistical and systematic uncertainties summed in quadrature. All sources of systematic uncertainties are included, taking into account correlations and anti-correlations in the post-fit case. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore only included in the post-fit uncertainties.

Observed impact of the different sources of uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. The 'Systematic uncertainties' category combines all sources of systematic uncertainties. The statistical uncertainty is obtained by repeating the fit after having fixed all nuisance parameters, including the $t\bar{t}$ and $W$+jets normalisation factors. 'Total' gives the total uncertainty on the measurement.

Observed impact of the different sources of $t\bar{t}$ modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and 'ME/PS matching' to the matching of the ME to the parton shower.

Observed impact of the different sources of s-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of t-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of $tW$ modelling uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and '$t\bar{t}$ overlap' to the algorithm removing the overlap between $tW$ and $t\bar{t}$ production at NLO, as described in Section 7 in the paper.

Observed impact of the different sources of PDF uncertainties on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the ${E}_{T}^{miss}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the $m_{T}^{W}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Nuisance parameters ranked according to their post-fit impacts on the best-fit value of the ratio $\mu$ of the measured cross-section to the predicted cross-section. In the figure, only the 20 nuisance parameters with the largest post-fit impacts are shown. The empty (solid) blue rectangles illustrate the pre-fit (post-fit) impact on $\mu$, corresponding to the upper axis. The pre-fit (post-fit) impact of each nuisance parameter, $\Delta\mu$, is calculated as the difference in the fitted value of $\mu$ between the nominal fit and the fit when fixing the corresponding nuisance parameter to $\hat{\theta}\pm\Delta\theta$ ($\hat{\theta}\pm\Delta\hat{\theta}$), where $\hat{\theta}$ is the best-fit value of the nuisance parameter and $\Delta\theta$ ($\Delta\hat{\theta}$) is its pre-fit (post-fit) uncertainty. Several systematic uncertainties are split into different nuisance parameters, which are indicated by NP. JES (JER) indicates jet energy scale (resolution), and $\gamma$ indicates a nuisance parameter associated to the MC statistics in one of the 18 bins numbered from 0 to 17. The black points show the best-fit values of the nuisance parameters, with the error bars representing the post-fit uncertainties. Each nuisance parameter is shown wrt. its nominal value, $\theta_0$, and in units of its pre-fit uncertainty, except the free-floating normalisation factors of the $t\bar{t}$ and $W$+jets backgrounds, and the parameters associated to the MC statistics in each bin, for which the post-fit values and uncertainties are shown.

Correlation matrix of the nuisance parameters and of the ratio $\mu$ of the measured cross-section to the predicted cross-section. The correlations are given after the fit to data. In the figure, only the parameters which have a correlation of at least 0.2 with any other parameter are shown.

Distribution of the MEM discriminant $P(S|X)$ in the SR for MEM discriminant values larger than $2.0\times10^{-4}$, for the collision data used for the measurement, and for 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.

Measured values of the signal cross-section and of the $t\bar{t}$ and $W$+jets normalisation factors, obtained by statistical-only fits to the collision data used for the measurement, and to 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The central values and their statistical uncertainties are obtained by repeating the fit after having fixed all nuisance parameters, except the $t\bar{t}$ and $W$+jets normalisation factors, which are let free-floating (unlike for the statistical uncertainty on the cross-section quoted in the paper). The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.

Distribution of the NN output in the $\geq$1fj$\,$SR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the NN output in the $t\bar{t}\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Total event yield in the $W\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the scalar sum of the jet transverse momenta in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark+photon system in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the scalar sum of the jet transverse momenta in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the invariant mass of the $b$-tagged jet and the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of $p_{\mathrm{T}}$ of the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the difference in $\eta$ between the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the energy of the system formed by the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark and photon system in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the parton-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the particle-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

This table lists the kinematic requirements on parton-level objects used to define of the fiducial phase space for the parton-level measurement. Frixione isolation ($\href{https://arxiv.org/abs/hep-ph/9801442}{\text{hep-ph/9801442}}$) with a chosen radius of $\Delta R = 0.2$ is applied to photons ($\gamma$). The measured fiducial parton-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b) = 688\pm 23(\text{stat.})^{+75}_{-71}(\text{syst.})\,$fb.

This table lists the kinematic requirements on particle-level objects used to define of the fiducial phase space for the particle-level measurement. The particle level objects are photons ($\gamma$) not from a hadron decay, neutrinos not from a hadron decay ($\nu$), prompt electrons and muons ($\ell$) "dressed" by adding close-by ($\Delta R < 0.1$) photons, and anti-$k_t$ $R = 0.4$ jets built from stable particles ($\tau > 30\,$ps) and tau leptons excluding neutrinos and prompt dressed muons. Jets are $b$-tagged ($b$-jet) using ghost-matched $b$-hadrons with $p_{\text{T}} > 5\,$GeV. Apart from the kinematic requirements, isolation and overlap removal criteria are applied. Jets within $\Delta R = 0.4$ of a photon are removed if the $p_{\text{T}}$ of charged particles within $\Delta R = 0.3$ of the photon is smaller than $10\,\%$ of its $p_{\text{T}}$. Jets within $\Delta R = 0.4$ of a lepton are removed. Events are removed where a photon is close ($\Delta R < 0.4$) to a lepton or a surviving jet. The measured fiducial particle-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b)+\sigma_{t(\rightarrow l\nu b\gamma)q} = 303\pm 9(\text{stat.})^{+33}_{-32}(\text{syst.})\,$fb.

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.

Acceptance * reconstruction efficiency for the P P --> bbA --> Zh --> llbb signals in the 2-lepton channel.

Acceptance * reconstruction efficiency for the P P --> Wprime --> Zh --> lvbb/cc signals in the 0-lepton channel.

Acceptance * reconstruction efficiency for the P P --> Wprime --> Zh --> lvbb/cc signals in the 1-lepton channel.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the resolved 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the resolved 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the merged 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the merged 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the resolved 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the resolved 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the merged 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the merged 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 3+ b-tag signal region. The background prediction is shown after a background-only maximum-likelihood bbA fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the resolved 3+ b-tag signal region. The background prediction is shown after a background-only maximum-likelihood bbA fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 2 b-tag signal region with additional b-tagged track jets not associated with the large-R jet. The background prediction is shown after a background-only maximum-likelihood bbA fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the merged 1+2 b-tag signal region with additional b-tagged track jets not associated with the large-R jet. The background prediction is shown after a background-only maximum-likelihood bbA fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the resolved 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the resolved 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the merged 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 1-lepton channel in the merged 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{Vh}$ for the 2-lepton channel in the resolved top control region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 1 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 2 b-tag sideband control region. The background prediction is shown after a background-only maximum-likelihood Z' fit to the data. In the plot, the last bin contains the overflow.

Upper limits on Zprime to Z h production cross section times branching fraction in pb.

Upper limits on Wprime to W h production cross section times branching fraction in pb.

Upper limits on ggA to Z h production cross section times branching fraction in pb.

Upper limits on bbA to Z h production cross section times branching fraction in pb.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 220 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 260 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 300 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 340 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 380 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 400 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 420 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 440 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 460 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 500 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 600 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 700 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 800 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 900 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 1000 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 1200 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 1400 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 1600 GeV.

Expected and observed two-dimensional likelihood scans of the b-associated production cross section times branching fraction vs the gluon-fusion production cross section times branching fraction at $m_{A}$ = 2000 GeV.

Acceptance * reconstruction efficiency for the P P --> A --> Zh --> vvbb signal in the 0-lepton channel.

Acceptance * reconstruction efficiency for the P P --> A --> Zh --> llbb signal in the 2-lepton channel.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the resolved 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 1 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Event distributions of $m_{T,Vh}$ for the 0-lepton channel in the merged 2 b-tag signal region. The background prediction is shown after a background-only maximum-likelihood W' fit to the data. In the plot, the last bin contains the overflow.

Distributions of expected upper limits at 95% confidence level on the cross section of P P --> A --> Zh as a function of bbA fraction an signal mass.

Distributions of observed upper limits at 95% confidence level on the cross section of P P --> A --> Zh as a function of bbA fraction an signal mass.

Signal selection efficiency ($\epsilon$) times acceptance ($A$) as a function of $H^{\pm}$. The estimated $\epsilon\times A$ arises from the lepton selection and triggering (∼30%) as well as jet selection and flavour tagging (∼10% or lower). The decrease of $\epsilon\times A$ for $m_{H^{\pm}}$ = 120 GeV and higher is expected from the kinematic constraint on the $H^{\pm}$ decay products due to the top-quark mass.

Observed and expected multivariate discriminant distribution in the $\ell\ell\ell\ell jj$ SR.

Observed and expected multivariate discriminant distribution in the $\ell\ell\nu\nu jj$ SR.

Distribution of $m(e^{\pm},\mu^{\pm})_{\mathrm{lead}}$ in the electron-muon signal region after the background-only fit.

Distribution of $m(\mu^{\pm},\mu^{\pm})_{\mathrm{lead}}$ in the muon-muon signal region after the background-only fit.

Distribution of $m(\ell^{\pm},\ell^{\prime \pm})_{\mathrm{lead}}$ in the three-lepton signal region after the background-only fit.

Event yield in the four-lepton signal region after the background-only fit.

Two-lepton signal region weighted cutflows for electron-electron channel. Data and a few representative signal samples are presented alongside the main background contributions. Yield stands for the observed yield in data and the expected yields based on $\sigma \cdot \mathcal{L}$ for the signal and background samples. Top quark and multiboson process backgrounds are merged under the 'other' category.

Two-lepton signal region weighted cutflows for electron-muon channel. Data and a few representative signal samples are presented alongside the main background contributions. Yield stands for the observed yield in data and the expected yields based on $\sigma \cdot \mathcal{L}$ for the signal and background samples. Top quark and multiboson process backgrounds are merged under the 'other' category.

Two-lepton signal region weighted cutflows for muon-muon channel. Data and a few representative signal samples are presented alongside the main background contributions. Yield stands for the observed yield in data and the expected yields based on $\sigma \cdot \mathcal{L}$ for the signal and background samples. Top quark and multiboson process backgrounds are merged under the 'other' category.

Three-lepton signal region weighted cutflow for $\ell \ell \ell$ channel. Data and a few representative signal samples are presented alongside the main background contributions. Yield stands for the observed yield in data and the expected yields based on $\sigma \cdot \mathcal{L}$ for the signal and background samples. Top quark and multiboson process backgrounds are merged under the 'other' category.

Four-lepton signal region weighted cutflow for $\ell \ell \ell \ell$ channel. Data and a few representative signal samples are presented alongside the main background contributions. Yield stands for the observed yield in data and the expected yields based on $\sigma \cdot \mathcal{L}$ for the signal and background samples. Top quark, Drell-Yan, and multiboson process backgrounds are merged under the 'other' category.

Correlation matrix for the unfolded cross section.

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial Born-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Measured fiducial dressed-level cross section for a single leptonic decay channel $\ell'^\pm \nu \ell^+ \ell'^-$ of the $W$ and $Z$ bosons, where $\ell, \ell' = e, \mu$. The relative uncertainties are reported as percentages. The systematic uncertainties are in order of appearance: total uncorrelated systematic and correlated systematics related respectively to unfolding, electrons, muons, jets, reducible and irreducible backgrounds and pileup. The last bin is a cross section for all events above the lower end of the bin.

Correlation matrix for the unfolded cross section.

Summary of the impact of different categories of systematic uncertainties on the background estimate in BDT bins, after the background-only fit. The individual uncertainties can be correlated and do not necessarily add in quadrature to equal the total background uncertainty.

Observed and expected exclusion limits at 95% CL on BR(H$\to\gamma\gamma_d$) as function of the $\gamma_d$ mass.

Background, data and signal yields in bins of BDT, in the SR and in the VV$\gamma$ CR, before the background-only fit. The expectations for the signal are shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties are statistical for data, while for backgrounds include statistical and systematic sources.

Number of events after each cut in SR for 139fb$^{-1}$ for ZH, H$\to\gamma\gamma_d$ considering BR=5% and massless dark photon. Generator-level filters are applied on the total events. Only the statistical uncertainty is shown.

Distribution of the BDT classifier response in data and for the expected SM background after the background-only fit, in the ee channel. The expectations for signal are also shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties shown are statistical for data, while for backgrounds include statistical and systematic sources.

Distribution of the BDT classifier response for data and for the expected SM background after the background-only fit, in the $\mu\mu$ channel. The expectations for signal are also shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties shown are statistical for data, while for backgrounds include statistical and systematic sources.