Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{1})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}^{\mathrm{add.}}_{2})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{2})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{add.}})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\Delta\mathrm{R}_{\mathrm{b}\mathrm{b}}^{\mathrm{avg}}$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}_{3})|$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}_{3})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}_{3})$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}_{3})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}_{4})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}_{4})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $H^{\mathrm{b}}_{\mathrm{T}}$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Normalized differential cross section of $H^{\mathrm{b}}_{\mathrm{T}}$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $|\eta(\mathrm{b}^{\mathrm{extra}}_{1})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{1})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}^{\mathrm{extra}}_{2})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{2})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{extra}})|$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $H^{\mathrm{j}}_{\mathrm{T}}$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Normalized differential cross section of $H^{\mathrm{j}}_{\mathrm{T}}$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $\mathrm{m}_{\mathrm{b}\mathrm{b}}^{\mathrm{max}}$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $H^{\mathrm{light}}_{\mathrm{T}}$ in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $H^{\mathrm{light}}_{\mathrm{T}}$ in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space.

Normalized differential cross section of $N_{\mathrm{jets}}$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Normalized differential cross section of $N_{\mathrm{jets}}$ in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space.

Normalized differential cross section of $N_{\mathrm{b}}$ in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space.

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}^{\mathrm{add.}}_{1})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{1})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}^{\mathrm{add.}}_{2})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{2})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{add.}})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\Delta\mathrm{R}_{\mathrm{b}\mathrm{b}}^{\mathrm{avg}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}_{3})|$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}_{3})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}_{3})$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}_{3})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}_{4})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}_{4})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $H^{\mathrm{b}}_{\mathrm{T}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $H^{\mathrm{b}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}^{\mathrm{extra}}_{1})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{1})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}^{\mathrm{extra}}_{2})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{2})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{extra}})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $H^{\mathrm{j}}_{\mathrm{T}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $H^{\mathrm{j}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $\mathrm{m}_{\mathrm{b}\mathrm{b}}^{\mathrm{max}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $H^{\mathrm{light}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $H^{\mathrm{light}}_{\mathrm{T}}$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Correlation of parameters of interest in fit of $N_{\mathrm{jets}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $N_{\mathrm{jets}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Correlation of parameters of interest in fit of $N_{\mathrm{b}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}^{\mathrm{add.}}_{1})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{1})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}^{\mathrm{add.}}_{2})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{add.}}_{2})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{add.}})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{add.}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\Delta\mathrm{R}_{\mathrm{b}\mathrm{b}}^{\mathrm{avg}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}_{3})|$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}_{3})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}_{3})$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}_{3})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}_{4})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}_{4})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{b}}_{\mathrm{T}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{b}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $|\Delta\phi(\mathrm{lj}^{\mathrm{extra}}_{1},\mathrm{b}_{\mathrm{soft}})|$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}^{\mathrm{extra}}_{1})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{1})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}^{\mathrm{extra}}_{2})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}^{\mathrm{extra}}_{2})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $|\eta(\mathrm{b}\mathrm{b}^{\mathrm{extra}})|$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\Delta\mathrm{R}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\mathrm{m}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{b}\mathrm{b}^{\mathrm{extra}})$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $p_{\mathrm{T}}(\mathrm{lj}^{\mathrm{extra}}_{1})$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{j}}_{\mathrm{T}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{j}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $\mathrm{m}_{\mathrm{b}\mathrm{b}}^{\mathrm{max}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{light}}_{\mathrm{T}}$ observable in $\geq 6$ jets: $\geq 3 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $H^{\mathrm{light}}_{\mathrm{T}}$ observable in $\geq 7$ jets: $\geq 4 \mathrm{b}$, $\geq 3$ light phase space

Covariances of all nuisance parameters and POIs in fit of $N_{\mathrm{jets}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $N_{\mathrm{jets}}$ observable in $\geq 6$ jets: $\geq 4 \mathrm{b}$ phase space

Covariances of all nuisance parameters and POIs in fit of $N_{\mathrm{b}}$ observable in $\geq 5$ jets: $\geq 3 \mathrm{b}$ phase space

Fiducial cross sections from the measurements of all observables, compared to predictions from different ttbb simulation approaches. For each of the normalized differential measurements the fiducial cross section in the respective phase space is also determined. In the paper only one representative observable is quoted for each fiducial phase space, while here the measured cross section with the uncertainties from the fit to the respective observable is summarized.

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.

The covariance matrix containing the experimental uncertainties of the particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section as a function of the XCone-jet mass.

The covariance matrix containing the model uncertainties of the particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section 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.

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

The covariance matrix containing the statistical uncertainties of the normalized particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section as a function of the XCone-jet mass.

The covariance matrix containing the experimental uncertainties of the normalized particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section as a function of the XCone-jet mass.

The covariance matrix containing the model uncertainties of the normalized particle-level $\mathrm{t}\overline{\mathrm{t}}$ differential cross section as a function of the XCone-jet mass.

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

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

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

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

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.

Correlation matrix for the individual sources of systematic uncertainty considered in the analysis, for the combined opposite sign (OS) and same sign (SS) binned-template profile likelihood fit to data. The OS or SS refers to the charge signs of the primary lepton and the soft muon. The gamma parameters are NPs used to describe the effect of the limited statistics of the samples.

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$ region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-1j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region,Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{uH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{cH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

Observed upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Observed upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Predicted and observed yields in each of the analysis regions considered in leptonic channel.

Predicted and observed yields in each of the analysis regions considered in hadronic channel.

Absolute uncertainties on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$ obtained from the combined fit to the data.

Summary of 95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$, significance and best-fit branching ratio in the signal regions. The values in the tables are in the form of observed(expected).

Comparison between data and MC simulation for kinematic distributions based on events in the signal candidate sample for \Delta|y|. The vertical bars on the points show the statistical uncertainty in the data. The shaded bands represent the total uncertainty in the MC predictions. The lower panels give the ratio of the data to the sum of the MC

Comparison between data and MC simulation for \Delta|y| for each of the 12 analysis channels for the low mass region prior to maximum likelihood fit. The vertical bars on the points show the statistical uncertainty in the data. The shaded bands represent the total uncertainty in the MC predictions. The lower panels give the ratio of the data to the sum of the MC

Comparison between data and MC simulation for \Delta|y| for each of the 12 analysis channels for the low mass region after the maximum likelihood fit. The vertical bars on the points show the statistical uncertainty in the data. The shaded bands represent the total uncertainty in the MC predictions. The lower panels give the ratio of the data to the sum of the MC

Comparison between data and MC simulation for \Delta|y| for each of the 12 analysis channels for the high mass region prior to the maximum likelihood fit. The vertical bars on the points show the statistical uncertainty in the data. The shaded bands represent the total uncertainty in the MC predictions. The lower panels give the ratio of the data to the sum of the MC

Comparison between data and MC simulation for \Delta|y| for each of the 12 analysis channels for the high mass region after the maximum likelihood fit. The vertical bars on the points show the statistical uncertainty in the data. The shaded bands represent the total uncertainty in the MC predictions. The lower panels give the ratio of the data to the sum of the MC

Measured A_{C}^{fid} in different mass regions after combining the two lepton channels. The vertical bars on the points show the statistical uncertainty in the data

Measured A_{C} in the full phase space in different mass regions after combining the two lepton channels. The vertical bars on the points show the statistical uncertainty in the data

The +/- standard deviation (\sigma) impacts of the nuisance parameters corresponding to the systematic uncertainties in the full phase space A_{C} measurement for mttbar > 750GeV. The red and blue bars show the effect on the unfolded AC values for up and down variations of the systematic uncertainty. The MC statistical uncertainties are omitted here.

Covariance matrix for the extrapolation uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the total uncertainty (i.e. fit including stat., not extrapolation) for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Correlation matrix for all nuisance parameters and parameters of interest of the Likelihood fit.

This table is a numerical representation of Fig. 8 for all nuisance parameters.