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.

Product of efficiency and acceptance of the event selection for T signal events as a function of the particle mass $m_\mathrm{T}$ and width $\Gamma$ for the different hypotheses considered.

Product of efficiency and acceptance of the event selection for T signal events as a function of the particle mass $m_\mathrm{T}$ and width $\Gamma$ for the different hypotheses considered.

Product of efficiency and acceptance of the event selection for T signal events as a function of the particle mass $m_\mathrm{T}$ and width $\Gamma$ for the different hypotheses considered.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with 0 forward jets. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved validation region with at least 1 forward jet. Data are compared to backgrounds are after the data-driven extraction is performed.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the partially merged region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with 0 forward jets. Data are compared to backgrounds obtained post-fit.

Distribution of the transverse mass $M_T$ reconstructed from the top quark and the missing transverse energy in the resolved region with at least 1 forward jet. Data are compared to backgrounds obtained post-fit.

Observed and expected 95% CL upper limits on the product of the cross section and branching fraction of a T decaying to a hadronic top quark and a Z boson to neutrinos as a function of the T mass, for a T with a width of 0.01 $ imes$ its mass.

Observed and expected 95% CL upper limits on the product of the cross section and branching fraction of a T decaying to a hadronic top quark and a Z boson to neutrinos as a function of the T mass, for a T with a width of 0.1 $ imes$ its mass.

Observed and expected 95% CL upper limits on the product of the cross section and branching fraction of a T decaying to a hadronic top quark and a Z boson to neutrinos as a function of the T mass, for a T with a width of 0.2 $ imes$ its mass.

Observed and expected 95% CL upper limits on the product of the cross section and branching fraction of a T decaying to a hadronic top quark and a Z boson to neutrinos as a function of the T mass, for a T with a width of 0.3 $ imes$ its mass.

Model independent observed 95% CL upper limits on the product of the cross section and branching fraction of a T decaying to a top quark and a Z boson as a function of the T mass and width.

Singlet model 95% CL excluded values of the product of the cross section and branching fraction for a T decaying to a top quark and a Z boson.

Distribution of $m_{T}(W)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

Summary of the one-dimensional intervals at 68 and 95% CL.

Summary of the one-dimensional intervals at 68 and 95% CL.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

The distribution of Top jet $ au_{3}/ au_{2}$ for the simulation of backgrounds and a 2400 GeV (left-handed) b* signal. The area of the total background contribution and area of the signal component are separately normalized to unity. All analysis selections are applied with the exception of the variable being plotted.

The distribution of W jet $ au_{2}/ au_{1}$ for the simulation of backgrounds and a 2400 GeV (left-handed) b* signal. The area of the total background contribution and area of the signal component are separately normalized to unity. All analysis selections are applied with the exception of the variable being plotted.

The distribution of m_{W} for the simulation of backgrounds and a 2400 GeV (left-handed) b* signal. The area of the total background contribution and area of the signal component are separately normalized to unity. All analysis selections are applied with the exception of the variable being plotted.

The distribution of Top jet DeepCSV score for the simulation of backgrounds and a 2400 GeV (left-handed) b* signal. The area of the total background contribution and area of the signal component are separately normalized to unity. All analysis selections are applied with the exception of the variable being plotted.

The distribution of m_{t} for the simulation of backgrounds and a 2400 GeV (left-handed) b* signal. The area of the total background contribution and area of the signal component are separately normalized to unity. All analysis selections are applied with the exception of the variable being plotted.

Distributions of $m_{tW}$ in the signal region for an interval of $m_{t}$ (65-105 GeV).

Distributions of $m_{tW}$ in the signal region for an interval of $m_{t}$ (105-225 GeV).

Distributions of $m_{tW}$ in the signal region for an interval of $m_{t}$ (225-285 GeV).

Distributions of $m_{tW}$ in themultijet control region of the signal region for an interval of $m_{t}$ (65-105 GeV).

Distributions of $m_{tW}$ in themultijet control region of the signal region for an interval of $m_{t}$ (105-225 GeV).

Distributions of $m_{tW}$ in themultijet control region of the signal region for an interval of $m_{t}$ (225-285 GeV).

Distributions of $m_{t}$ in the ttbar measurement region for an interval of $m_{tar{t}}$ (1200-1300 GeV).

Distributions of $m_{t}$ in the ttbar measurement region for an interval of $m_{tar{t}}$ (1300-1800 GeV).

Distributions of $m_{t}$ in the ttbar measurement region for an interval of $m_{tar{t}}$ (1800-3000 GeV).

Distributions of $m_{t}$ in themultijet control region of the ttbar measurement region for an interval of $m_{tar{t}}$ (1200-1300 GeV).

Distributions of $m_{t}$ in themultijet control region of the ttbar measurement region for an interval of $m_{tar{t}}$ (1300-1800 GeV).

Distributions of $m_{t}$ in themultijet control region of the ttbar measurement region for an interval of $m_{tar{t}}$ (1800-3000 GeV).

Detailed list of the contribution of each source of uncertainty to the total uncertainty on the measured values of $\sigma(tq)$, $\sigma(\bar{t}q)$, $R_t$, and $\sigma(tq+\bar{t}q)$. The evaluation of the systematic uncertainties has a statistical uncertainty of $0.3\,\%$. Uncertainties contributing less than $1.0\,\%$ are marked with "$<1$" in the paper. To provide numerical values for this table in HEPdata, these uncertainties are approximated with $\pm 0.5\,\%$. This approximation is applied to all measurements for the following uncertainties$:$ JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by-jets, JES pileup, $b$-JES, jet vertex fraction, mistag efficiency and $W+\;$jets shape variation. For the measurement of $\sigma(tq)$ the approximation is applied in addition to the following uncertainties$:$ JES flavor response, $c$-tagging efficiency, $t\bar{t}$ generator + parton shower and $t\bar{t}$ ISR/FSR. For the measurement of $\sigma(\bar{t}q)$ the approximation is applied in addition to these uncertainties$:$ JES flavor response, $b/\bar{b}$ acceptance, and $t\bar{t}$ ISR/FSR. For the measurement of $R_t$ the approximation is applied in addition to these uncertainties$:$ JES detector, $b$-tagging efficiency, $c$-tagging efficiency, $b/\bar{b}$ acceptance and $tq$ scale variations. For the measurement of $\sigma(tq+\bar{t}q)$ the approximation is applied in addition to these uncertainties$:$ JES flavor response, $c$-tagging efficiency, $b/\bar{b}$ acceptance, $t\bar{t}$ generator + parton shower and $t\bar{t}$ ISR/FSR.

Differential t-channel top-quark production cross sections and normalized differential t-channel top-quark production cross sections as functions of ABS(YRAP(T)).

The cross sections for top-quark and top-antiquark production in the t-channel, together with the cross-section ratio.

Differential t-channel top-quark production cross sections and normalized differential t-channel top-quark production cross sections as functions of ABS(YRAP(TBAR)).

Parametrization factors for the $m_{t}$ dependence [see Eq. (4) in the paper] of $\sigma(tq)$, $\sigma(\bar tq)$, and $\sigma(t q+\bar t q)$.

The cross sections for top-quark and top-antiquark production in the t-channel, together with the cross-section ratio.

The value of $|V_{tb}|^{2}$ is extracted by dividing the measured value of $\sigma(t q+\bar t q)$ by the prediction of the approximate NNLO calculation. The experimental and theoretical uncertainties are added in quadrature.

Event yields for the 2-jet-$\ell^{+}$ and 2-jet-$\ell^{-}$ HPR channels. The expectation for the signal and background yields correspond to the result of the binned maximum-likelihood fit described in Sec. $\mathrm{VI~D}$ in the paper. The uncertainty of the expectations is the normalization uncertainty of each process after the fit, as described in Sec. $\mathrm{VII~F}$ in the paper.

Migration matrix relating the parton level $p_{\mathrm{T}}(t)$ shown on the $y$ axis and the reconstruction level $p_{\mathrm{T}}(\ell \nu b)$ shown on the $x$ axis for the top-quark $p_{\mathrm{T}}$ distribution.

Migration matrix relating the parton level $p_{\mathrm{T}}(\bar t)$ shown on the $y$ axis and the reconstruction level $p_{\mathrm{T}}(\ell \nu b)$ shown on the $x$ axis for the top-antiquark $p_{\mathrm{T}}$ distribution.

Migration matrix relating the parton level $|y(t)|$ shown on the $y$ axis and the reconstruction level $|y(\ell \nu b)|$ shown on the $x$ axis for the top-quark $|y|$ distribution.

Migration matrix relating the parton level $|y(\bar t)|$ shown on the $y$ axis and the reconstruction level $|y(\ell \nu b)|$ shown on the $x$ axis for the top-antiquark $|y|$ distribution.

Differential t-channel top-quark production cross section as a function of $p_{\mathrm{T}}(t)$ with the uncertainties for each bin given in percent.

Differential t-channel top-quark production cross section as a function of $p_{\mathrm{T}}(\bar t)$ with the uncertainties for each bin given in percent.

Differential t-channel top-quark production cross section as a function of $|y(t)|$ with the uncertainties for each bin given in percent.

Differential t-channel top-quark production cross section as a function of $|y(\bar t)|$ with the uncertainties for each bin given in percent.

Normalized differential t-channel top-quark production cross section as a function of $p_{\mathrm{T}}(t)$ with the uncertainties for each bin given in percent.

Normalized differential t-channel top-quark production cross section as a function of $p_{\mathrm{T}}(\bar t)$ with the uncertainties for each bin given in percent.

Normalized differential t-channel top-quark production cross section as a function of $|y(t)|$ with the uncertainties for each bin given in percent.

Normalized differential t-channel top-quark production cross section as a function of $|y(\bar t)|$ with the uncertainties for each bin given in percent.

Comparison between the measured differential cross sections and the predictions from the NLO calculation using the MSTW2008 PDF set. For each variable and prediction a $\chi^{2}$ value is calculated with HERAfitter using the covariance matrix of each measured spectrum. The theory uncertainties of the predictions are treated as uncorrelated. The number of degrees of freedom (NDF) is equal to the number of bins in the measured spectrum.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{\mathrm{d}\sigma}{\mathrm{d}p_{\mathrm{T}}(t)}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, jet-vertex fraction, $b/\bar{b}$ acceptance, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, $W+$ jets shape variation, and $t \bar{t}$ generator. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{\mathrm{d}\sigma}{\mathrm{d}p_{\mathrm{T}}(\bar t)}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, $b-$JES, jet-vertex fraction, mistag efficiency, $b/\bar{b}$ acceptance, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, $W+$ jets shape variation, and $t \bar{t}$ generator. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{\mathrm{d}\sigma}{\mathrm{d}|y(t)|}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, jet-vertex fraction, $b/\bar{b}$ acceptance, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, $W+$ jets shape variation, $t \bar{t}$ generator, $t \bar{t}$ ISR/FSR, and unfolding. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{\mathrm{d}\sigma}{\mathrm{d}|y(\bar t)|}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, $b-$JES, jet-vertex fraction, $b/\bar{b}$ acceptance, mistag efficiency, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, $W+$ jets shape variation, $t \bar{t}$ generator, $t \bar{t}$ ISR/FSR, and unfolding. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{1}{\sigma}\dfrac{\mathrm{d}\sigma}{\mathrm{d}p_{\mathrm{T}}(t)}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. The JES $\eta$ intercalibration uncertainty has a sign switch from the first to the second bin. For the $tq$ generator $+$ parton shower uncertainty a sign switch is denoted with $\mp$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, $b-$JES, jet-vertex fraction, $b/\bar{b}$ acceptance, $c-$tagging efficiency, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, lepton uncertainties, $W+$ jets shape variation, and $t \bar{t}$ generator. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{1}{\sigma}\dfrac{\mathrm{d}\sigma}{\mathrm{d}p_{\mathrm{T}}(\bar t)}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. Sign switches within one uncertainty are denoted with $\mp$ and $\pm$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, $b-$JES, jet-vertex fraction, $b/\bar{b}$ acceptance, mistag efficiency, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, lepton uncertainties, $W+$ jets shape variation, and $t \bar{t}$ generator. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{1}{\sigma}\dfrac{\mathrm{d}\sigma}{\mathrm{d}|y(t)|}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. Sign switches within one uncertainty are denoted with $\mp$ and $\pm$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content$:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, b-JES, jet-vertex fraction, $b/\bar{b}$ acceptance, $b-$tagging efficiency, $c-$tagging efficiency, mistag efficiency, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, lepton uncertainties, $W+$jets shape variation, $t \bar{t}$ generator, $t \bar{t}$ISR/FSR, and unfolding. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Detailed list of the contribution of each source of uncertainty to the total relative uncertainty on the measured $\dfrac{1}{\sigma}\dfrac{\mathrm{d}\sigma}{\mathrm{d}|y(\bar t)|}$ distribution given in percent for each bin. The list includes only those uncertainties that contribute with more than $1\%$. Sign switches within one uncertainty are denoted with $\mp$ and $\pm$. The following uncertainties contribute to the total uncertainty with less than $1\%$ to each bin content $:$ JES detector, JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by jets, JES pileup, JES flavor composition, JES flavor response, b-JES, jet energy resolution, jet-vertex fraction, $b/\bar{b}$ acceptance, $b-$tagging efficiency, $c-$ tagging efficiency, mistag efficiency, $E_{\mathrm{T}}^{\mathrm{miss}}$ modeling, lepton uncertainties, $W+$ jets shape variation, $t \bar{t}$ generator, $t \bar{t}$ ISR/FSR, and unfolding. In cases when the uncertainty is report to be "$<1\%$" in the table of the paper the uncertainty is approximated by a value of $0.5\%$.

Statistical correlation matrices for the differential cross section as a function of $p_{\mathrm{T}}(t)$.

Statistical correlation matrices for the differential cross section as a function of $p_{\mathrm{T}}(\bar t)$.

Statistical correlation matrices for the differential cross section as a function of $|y(t)|$.

Statistical correlation matrices for the differential cross section as a function of $|y(\bar t)|$.

Statistical correlation matrices for the normalized differential cross section as a function of $p_{\mathrm{T}}(t)$.

Statistical correlation matrices for the normalized differential cross section as a function of $p_{\mathrm{T}}(\bar t)$.

Statistical correlation matrices for the normalized differential cross section as a function of $|y(t)|$.

Statistical correlation matrices for the normalized differential cross section as a function of $|y(\bar t)|$.

The normalized particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section in the fiducial region as a function of the XCone-jet mass.

The normalized particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section in the fiducial region as a function of the XCone-jet mass.

The covariance matrix containing the statistical uncertainties of Figure 2a is shown.

The covariance matrix containing the statistical uncertainties of Figure 2a is shown.

The covariance matrix containing the experimental uncertainties of Figure 2a is shown.

The covariance matrix containing the experimental uncertainties of Figure 2a is shown.

The covariance matrix containing the model uncertainties of Figure 2a is shown.

The covariance matrix containing the model uncertainties of Figure 2a is shown.

The covariance matrix containing the statistical uncertainties of Figure 2b is shown.

The covariance matrix containing the statistical uncertainties of Figure 2b is shown.

The covariance matrix containing the experimental uncertainties of Figure 2b is shown.

The covariance matrix containing the experimental uncertainties of Figure 2b is shown.

The covariance matrix containing the model uncertainties of Figure 2b is shown.

The covariance matrix containing the model uncertainties of Figure 2b is shown.

Lower mass exclusion limits for scalar and vector LQs.

Observed upper limits on the production cross section for pair production of LQs decaying into a top quark and a muon or bottom quark and a neutrino at 95% CL in the $M_{LQ} - B(LQ \rightarrow t\mu)$ plane.

Lower mass exclusion limits for scalar and vector LQs.

Comparison of data with estimated backgrounds in the $\tilde{E}_\text{T}^\text{miss}$ distribution with the TZCR1 event selection except for the requirement on $\tilde{E}_\text{T}^\text{miss}$. The variables $\tilde{E}_\text{T}^\text{miss}$ and $\tilde{m}_\text{T}$ are constructed in the same way as $E_\text{T}^\text{miss}$ and $m_\text{T}$ but treating the leading photon transverse momentum as invisible. The predicted backgrounds are scaled with normalization factors. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflow.

Comparison of data with estimated backgrounds in the $\tilde{m}_\text{T}$ distribution with the TZCR1 event selection except for the requirement on $\tilde{m}_\text{T}$. The variables $\tilde{E}_\text{T}^\text{miss}$ and $\tilde{m}_\text{T}$ are constructed in the same way as $E_\text{T}^\text{miss}$ and $m_\text{T}$ but treating the leading photon transverse momentum as invisible. The predicted backgrounds are scaled with normalization factors. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflow.

Comparison of the observed data ($n_\text{obs}$) with the predicted background ($n_\text{exp}$) in the validation and signal regions. The background predictions are obtained using the background-only fit configuration. The bottom panel shows the significance of the difference between data and predicted background, where the significance is based on the total uncertainty ($\sigma_\text{tot}$).

Jet multiplicity distributions for events where exactly two signal leptons are selected. No correction factors are included in the background normalizations. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflow.

Jet multiplicity distributions for events where exactly one lepton plus one $\tau$ candidate are selected. No correction factors are included in the background normalizations. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin includes overflow.

The $E_\text{T}^\text{miss}$ distribution in SR1. In the plot, the full event selection in the corresponding signal region is applied, except for the requirement on $E_\text{T}^\text{miss}$. The predicted backgrounds are scaled with normalization factors. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin contains the overflow. Benchmark signal models are overlaid for comparison. The benchmark models are specified by the gluino and stop masses, given in TeV in the table.

The $m_\text{T}$ distribution in SR1. In the plot, the full event selection in the corresponding signal region is applied, except for the requirement on $m_\text{T}$. The predicted backgrounds are scaled with normalization factors. The uncertainty band includes statistical and all experimental systematic uncertainties. The last bin contains the overflow. Benchmark signal models are overlaid for comparison. The benchmark models are specified by the gluino and stop masses, given in TeV in the table.

Expected (black dashed) 95% excluded regions in the plane of $m_{\tilde{g}}$ versus $m_{\tilde{t}_1}$ for gluino-mediated stop production.

Observed (red solid) 95% excluded regions in the plane of $m_{\tilde{g}}$ versus $m_{\tilde{t}_1}$ for gluino-mediated stop production.

Expected (black dashed) 95% excluded regions in the plane of $m_{\tilde{t}_1}$ versus $m_{\tilde{\chi}_1^0}$ for direct stop production.

Observed (red solid) 95% excluded regions in the plane of $m_{\tilde{t}_1}$ versus $m_{\tilde{\chi}_1^0}$ for direct stop production.

The expected upper limits on $T$ quark pair production times the squared branching ratio for $T \rightarrow tZ$ as a function of the $T$ quark mass.

The observed upper limits on $T$ quark pair production times the squared branching ratio for $T \rightarrow tZ$ as a function of the $T$ quark mass.

The expected limits on $T$ quarks as a function of the branching ratios $B\left(T \rightarrow bW\right)$ and $B\left(T \rightarrow tH\right)$ for a $T$ quark with a mass of 800 GeV. The $T$ is assumed to decay in three possible ways: $T \to tZ$, $T \to tH$, and $T \to bW$.

The observed limits on $T$ quarks as a function of the branching ratios $B\left(T \rightarrow bW\right)$ and $B\left(T \rightarrow tH\right)$ for a $T$ quark with a mass of 800 GeV. The $T$ is assumed to decay in three possible ways: $T \to tZ$, $T \to tH$, and $T \to bW$.

The $m_\text{T}$ distribution in the WVR2-tail validation region which has the same preselection and jet $p_\text{T}$ requirements as SR2.

The $am_\text{T2}$ distribution in the WVR2-tail validation region which has the same preselection and jet $p_\text{T}$ requirements as SR2.

Large-radius jet mass ($R=1.2$), decomposed into the number of small-radius jet constituents. The lower panel shows the ratio of the total data to the total prediction (summed over all jet multiplicities). Events are required to have one lepton, four jets with $p_\text{T}>80,50,40,40$ GeV, at least one $b$-tagged jet, $E_\text{T}^\text{miss}>200$ GeV, and $m_\text{T}>30$ GeV.

Distribution of $m_\text{T2}^\tau$ in data for a selection enriched in $t\bar{t}$ events with one hadronically decaying $\tau$. Events that have no hadronic $\tau$ candidate (that passes the Loose identification criteria, as well as other requirements) are not shown in the plot.

Upper limits on the model cross-section in units of pb for the gluino-mediated stop models.

Upper limits on the model cross-section in units of pb for the models with direct stop pair production.

Illustration of the best expected signal region per signal grid point for the gluino-mediated stop models. This mapping is used for the final combined exclusion limits.

Illustration of the best expected signal region per signal grid point for models with direct stop pair production. This mapping is used for the final combined exclusion limits.

Expected $CL_s$ values for the gluino-mediated stop models.

Observed $CL_s$ values for the gluino-mediated stop models.

Expected $CL_s$ values for the direct stop pair production models.

Observed $CL_s$ values for the direct stop pair production models.

Expected limit using SR1 for models with direct stop pair production and an unpolarized stop (and bino LSP).

Expected limit using SR1 for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Expected limit using SR1 for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Observed limit using SR1 for models with direct stop pair production and an unpolarized stop (and bino LSP).

Observed limit using SR1 for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Observed limit using SR1 for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Expected limit using SR2 for models with direct stop pair production and an unpolarized stop (and bino LSP).

Expected limit using SR2 for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Expected limit using SR2 for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Observed limit using SR2 for models with direct stop pair production and an unpolarized stop (and bino LSP).

Observed limit using SR2 for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Observed limit using SR2 for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Expected limit using SR1+SR2 (best expected) for models with direct stop pair production and an unpolarized stop (and bino LSP).

Expected limit using SR1+SR2 (best expected) for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Expected limit using SR1+SR2 (best expected) for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Observed limit using SR1+SR2 (best expected) for models with direct stop pair production and an unpolarized stop (and bino LSP).

Observed limit using SR1+SR2 (best expected) for models with direct stop pair production with $\tilde{t}_1=\tilde{t}_L$ (and bino LSP).

Observed limit using SR1+SR2 (best expected) for models with direct stop pair production with $\tilde{t}_1\sim\tilde{t}_R$ (and bino LSP).

Acceptance for SR1 in the gluino-mediated stop models. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Acceptance for SR1 in the direct stop pair production. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Acceptance for SR2 in the gluino-mediated stop models. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Acceptance for SR2 in the direct stop pair production. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Acceptance for SR3 in the gluino-mediated stop models. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Acceptance for SR3 in the direct stop pair production. The acceptance is defined as the fraction of signal events that pass the analysis selection performed on generator-level objects, therefore emulating an ideal detector with perfect particle identification and no measurement resolution effects.

Efficiency for SR1 in the gluino-mediated stop models. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Efficiency for SR1 in the direct stop pair production. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Efficiency for SR2 in the gluino-mediated stop models. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Efficiency for SR2 in the direct stop pair production. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Efficiency for SR3 in the gluino-mediated stop models. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Efficiency for SR3 in the direct stop pair production. The efficiency is the ratio between the expected signal rate calculated with simulated data passing all the reconstruction level cuts applied to reconstructed objects, and the signal rate for an ideal detector (with perfect particle identification and no measurement resolution effects).

Distribution of $m_{{\rm T}2}(\ell, \tau_{\mathrm{had}})$ for events passing all the lepton-hadron HM signal region requirements, except that on the variable itself. The SM background process have been normalised using a fit to the data observed in CRs.

Expected exclusion contour at 95% CL in the (scalar top, scalar tau) mass plane from the combination of all selections.

Observed exclusion contour at 95% CL in the (scalar top, scalar tau) mass plane from the combination of all selections.

The region / analysis with the best expected upper limit on the signal cross-section (95% CL) as a function of the stop and stau masses. 1: SRLM, 2: SRHH, 3: two-lepton channel analysis, 5: SRHM.

The 95% CL excluded cross section times branching ratio, using the best expected SR / analysis for each mass point.

The cut flow on the raw generated events for the signal point (scalar top mass, scalar tau mass) = (337,148) GeV for the hadron-hadron SR. The production cross section for this signal point is $1.00 \pm 0.14$ pb. Quality Cuts indicate a set of cuts applied to ensure good quality events in data. A full description of the cuts used is given in the text. The original input file has a filter applied to it that ensures that all the events have $E_T^{miss}>60$ GeV or one electron or muon with $p_\mathrm{T} > 20$ GeV at truth level. After the filter is applied (efficiency = 0.883) there are 100000 events remaining.

The cut flow on the raw generated events for the signal point (scalar top mass, scalar tau mass) = (195,87) GeV for the lepton-hadron LM SR. The production cross section for this signal point is $21 \pm 3$ pb. Quality Cuts indicate a set of cuts applied to ensure good quality events in data. A full description of the cuts used is given in the text. The original input file has a filter applied to it that ensures that all the events have $E_T^{miss}<60$ GeV and one electron or muon with $p_\mathrm{T} > 20$ GeV at truth level. After the filter is applied (efficiency = 0.117) there are 50000 events remaining before applying the event weights.

The cut flow on the raw generated events for the signal point (scalar top mass, scalar tau mass) = (391,337) GeV for the lepton-hadron HM SR. The production cross section for this signal point is $0.41 \pm 0.06$ pb. Quality Cuts indicate a set of cuts applied to ensure good quality events in data. A full description of the cuts used is given in the text. The original input file has a filter applied to it that ensures that all the events have either $E_T^{miss}>150$ GeV or at least one electron or muon with $p_\mathrm{T} > 20$ GeV at truth level. After the filter is applied (efficiency = 0.925) there are 50000 events remaining before applying the event weights.