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Measurements of both the inclusive and differential production cross sections of a top-quark-antiquark pair in association with a $Z$ boson ($t\bar{t}Z$) are presented. The measurements are performed by targeting final states with three or four isolated leptons (electrons or muons) and are based on $\sqrt{s} = 13$ TeV proton-proton collision data with an integrated luminosity of 139 fb$^{-1}$, recorded from 2015 to 2018 with the ATLAS detector at the CERN Large Hadron Collider. The inclusive cross section is measured to be $\sigma_{t\bar{t}Z} = 0.99 \pm 0.05$ (stat.) $\pm 0.08$ (syst.) pb, in agreement with the most precise theoretical predictions. The differential measurements are presented as a function of a number of kinematic variables which probe the kinematics of the $t\bar{t}Z$ system. Both absolute and normalised differential cross-section measurements are performed at particle and parton levels for specific fiducial volumes and are compared with theoretical predictions at different levels of precision, based on a $\chi^{2}/$ndf and $p$-value computation. Overall, good agreement is observed between the unfolded data and the predictions.
The measured $t\bar{t}\text{Z}$ cross-section value and its uncertainty based on the fit results from the combined trilepton and tetralepton channels. The value corresponds to the phase-space region where the difermion mass from the Z boson decay lies in the range $70 < m_{f\bar{f}} < 110$ GeV.
The measured $t\bar{t}\text{Z}$ cross-section value and its uncertainty based on the fit results from the combined trilepton and tetralepton channels. The value corresponds to the phase-space region where the difermion mass from the Z boson decay lies in the range $70 < m_{f\bar{f}} < 110$ GeV.
List of relative uncertainties of the measured inclusive $t\bar{t}\text{Z}$ cross section from the combined fit. The uncertainties are symmetrised for presentation and grouped into the categories described in the text. The quadratic sum of the individual uncertainties is not equal to the total uncertainty due to correlations introduced by the fit.
List of relative uncertainties of the measured inclusive $t\bar{t}\text{Z}$ cross section from the combined fit. The uncertainties are symmetrised for presentation and grouped into the categories described in the text. The quadratic sum of the individual uncertainties is not equal to the total uncertainty due to correlations introduced by the fit.
The definitions of the trilepton signal regions: for the inclusive measurement, a combination of the regions with pseudo-continuous $b$-tagging 3$\ell$-Z-1$b$4$j$-PCBT and 3$\ell$-Z-2$b$3$j$-PCBT is used, whereas for the differential measurement, only the region 3$\ell$-Z-2$b$3$j$, with a fixed $b$-tagging WP is employed.
The definitions of the trilepton signal regions: for the inclusive measurement, a combination of the regions with pseudo-continuous $b$-tagging 3$\ell$-Z-1$b$4$j$-PCBT and 3$\ell$-Z-2$b$3$j$-PCBT is used, whereas for the differential measurement, only the region 3$\ell$-Z-2$b$3$j$, with a fixed $b$-tagging WP is employed.
The definitions of the four tetralepton signal regions. The regions are defined to target different $b$-jet multiplicities and flavour combinations of the non-Z leptons.
The definitions of the four tetralepton signal regions. The regions are defined to target different $b$-jet multiplicities and flavour combinations of the non-Z leptons.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|$ in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the absolute parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the normalised parton-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel.
The total correlation matrix of the absolute particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}$ of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the absolute value of rapidity of the $Z$ boson in the 3$\ell$+4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{l \textrm{non-}Z}$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta y (Z, t_{\textrm{lep}})|/\pi$ in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 3$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (l_{t}^{+}, l_{\bar{t}}^{-})|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $|\Delta \phi (t\bar{t}, Z)|/\pi$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the $p_{\textrm{T}}^{t\bar{t}}$ in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel.
The total correlation matrix of the normalised particle-level differential cross-section measured in the fiducial phase-space as a function of the number of jets in the 4$\ell$ channel.
Inclusive and differential cross-sections for the production of top quarks in association with a photon are measured with proton$-$proton collision data corresponding to an integrated luminosity of 139 fb$^{-1}$. The data were collected by the ATLAS detector at the LHC during Run 2 between 2015 and 2018 at a centre-of-mass energy of 13 TeV. The measurements are performed in a fiducial volume defined at parton level. Events with exactly one photon, one electron and one muon of opposite sign, and at least two jets, of which at least one is $b$-tagged, are selected. The fiducial cross-section is measured to be $39.6\,^{+2.7}_{-2.3}\,\textrm{fb}$. Differential cross-sections as functions of several observables are compared with state-of-the-art Monte Carlo simulations and next-to-leading-order theoretical calculations. These include cross-sections as functions of photon kinematic variables, angular variables related to the photon and the leptons, and angular separations between the two leptons in the event. All measurements are in agreement with the predictions from the Standard Model.
The measured fiducial cross-section in the electron-muon channel. The first uncertainty is the statistical uncertainty and the second one is the systematic uncertainty.
The absolute differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The absolute differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The normalised differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The uncertainty is decomposed into four components which are the signal modelling uncertainty, the background modelling uncertainty, the experimental uncertainty, and the data statistical uncertainty.
The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the absolute differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the photon pT in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the photon $|\eta|$ in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the minimum $\Delta R$ between the photon and the leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the $\Delta\phi$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The total correlation matrix of the normalised differential cross-section measured in the fiducial phase-space as a function of the $|\Delta\eta|$ between the two leptons in the electron-muon channel. The individual systematic uncertainties are symmetrized before deriving the correlation matrix.
The statistical correlation matrix of all the absolute differential cross-sections measured in the fiducial phase-space in the electron-muon channel.
The statistical correlation matrix of all the normalised differential cross-sections measured in the fiducial phase-space in the electron-muon channel.
Fiducial region definition.
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