CMSPASTOP23004  
Inclusive and differential measurement of top quark cross sections in association with a Z boson  
CMS Collaboration  
27 March 2024  
Abstract: A measurement is presented of the inclusive and differential cross sections for top quark production in association with a Z boson, in pairs ($ \mathrm{t\bar{t}Z} $) or with a single top quark ($ \mathrm{tZq} $ and $ \mathrm{tWZ} $). The data were recorded in pp collisions at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{1} $. Events with exactly three leptons, electrons or muons, are selected. A deep neural network is trained to separate the signal processes and the backgrounds. The $ \mathrm{t\bar{t}Z} $ and $ \mathrm{tWZ} $ processes are measured together due to their similar experimental signature and significant interference beyond leading order. A combined profile likelihood approach is used to unfold the differential cross sections, to account for systematic uncertainties, and to determine the correlations between the two signal categories in one global fit. The inclusive cross sections for a dilepton invariant mass within 70 and 110 GeV are measured to be 1.14 $ \pm $ 0.07 pb for the sum of $ \mathrm{t\bar{t}Z} $ and $ \mathrm{tWZ} $, and 0.81 $ \pm $ 0.10 pb for $ \mathrm{tZq} $. While good agreement of the data with the standard model prediction is found for the $ \mathrm{tZq} $ process, the measured inclusive cross section for $ \mathrm{t\bar{t}Z}+\mathrm{tWZ} $ has a ratio to the central value of the prediction of 1.17 $ \pm $ 0.07.  
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Leading order diagrams for the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ (left), $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (middle), and $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (right) processes. 
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Figure 1a:
Leading order diagrams for the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ (left), $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (middle), and $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (right) processes. 
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Figure 1b:
Leading order diagrams for the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ (left), $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (middle), and $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (right) processes. 
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Figure 1c:
Leading order diagrams for the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ (left), $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (middle), and $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (right) processes. 
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Figure 2:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 2a:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 2b:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 2c:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 2d:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 2e:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (middle left), the number of b jets (middle right), and the $ \eta $ of the jet with the highest pseudorapidity. The data and their statistical uncertainties are indicated by bullets and error bars. The hatched area indicates the systematic uncertainty in the expectation, including the statistical uncertainty of the MC samples. In the legend, "$ {\mathrm{t}\overline{\mathrm{t}}} $X" refers to backgrounds involving the associated production of top quarks with bosons (e.g., $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $), and "X$ \gamma $" denotes the associated production of bosons and photons. 
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Figure 3:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 3a:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 3b:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 3c:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 3d:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 3e:
Distributions after final event selection for: the $ p_{\mathrm{T}} $ of the reconstructed Z boson (upper left), the $ p_{\mathrm{T}} $ of the lepton arising from the W boson $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R(\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+}, \ell^{}) $ (middle right), and the cosine of the polar angle between the Z boson and its negatively charged decay lepton, boosted into the Z boson rest frame (lower). Further details are described in the caption of Fig. 2. 
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Figure 4:
Distributions for events selected in the region with $ m(\ell^{+}\ell^{})  m(\mathrm{Z}) > $ 20 GeV for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (lower left), and the number of b jets (lower right). Further details are described in the caption of Fig. 2. 
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Figure 4a:
Distributions for events selected in the region with $ m(\ell^{+}\ell^{})  m(\mathrm{Z}) > $ 20 GeV for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (lower left), and the number of b jets (lower right). Further details are described in the caption of Fig. 2. 
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Figure 4b:
Distributions for events selected in the region with $ m(\ell^{+}\ell^{})  m(\mathrm{Z}) > $ 20 GeV for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (lower left), and the number of b jets (lower right). Further details are described in the caption of Fig. 2. 
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Figure 4c:
Distributions for events selected in the region with $ m(\ell^{+}\ell^{})  m(\mathrm{Z}) > $ 20 GeV for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (lower left), and the number of b jets (lower right). Further details are described in the caption of Fig. 2. 
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Figure 4d:
Distributions for events selected in the region with $ m(\ell^{+}\ell^{})  m(\mathrm{Z}) > $ 20 GeV for: the $ p_{\mathrm{T}} $ of the lepton with the highest (upper left) and second highest (upper right) transverse momentum, the number of jets (lower left), and the number of b jets (lower right). Further details are described in the caption of Fig. 2. 
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Figure 5:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5a:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5b:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5c:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5d:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5e:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 5f:
Distributions of output values in the three DNN output nodes for the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (upper), $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle), and background (lower). In the left column, the inclusive distributions are shown, i.e.,, each selected event enters each of the output nodes. In the right column, each event enters exactly one of the three distributions, namely the one for which the output score is largest. These distributions, which by construction can not have entries below 1/3, are the templates that will be used for the signal extraction. Further details are described in the caption of Fig. 2. 
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Figure 6:
Distributions of the bjet multiplicity in the four lepton region (left) and the jet multiplicity in the zero bjet control region (right). These distributions are added to the fit for the inclusive measurements. 
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Figure 6a:
Distributions of the bjet multiplicity in the four lepton region (left) and the jet multiplicity in the zero bjet control region (right). These distributions are added to the fit for the inclusive measurements. 
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Figure 6b:
Distributions of the bjet multiplicity in the four lepton region (left) and the jet multiplicity in the zero bjet control region (right). These distributions are added to the fit for the inclusive measurements. 
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Figure 7:
Likelihood scan of the two measured inclusive cross sections normalized to the SM predictions $ \mu_{{\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z}} $ and $ \mu_{\mathrm{t}\mathrm{Z}\mathrm{q}} $. 
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Figure 8:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 8a:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 8b:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 8c:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 8d:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 8e:
Postfit distributions of the bjet multiplicity in events with four leptons (upper left) and the jet multiplicity distribution in events with zero b jets (upper right). The corresponding prefit distributions are presented in Fig. 6. Postfit distributions in the output nodes for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (middle left), $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ (middle right), and the background (lower). The corresponding prefit distributions are presented in the right column of Fig. 5. 
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Figure 9:
Prefit (upper) and postfit (lower) output node distributions for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right). Separate templates are shown for each bin of reconstructed $ p_{\mathrm{T}}(\mathrm{Z}) $. The signal samples are further split into four components each, according to the generatorlevel bins of $ p_{\mathrm{T}}(\mathrm{Z}) $. In the legend, the numerical suffixes (0, 1, 2, 3) represent bin indices. 
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Figure 9a:
Prefit (upper) and postfit (lower) output node distributions for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right). Separate templates are shown for each bin of reconstructed $ p_{\mathrm{T}}(\mathrm{Z}) $. The signal samples are further split into four components each, according to the generatorlevel bins of $ p_{\mathrm{T}}(\mathrm{Z}) $. In the legend, the numerical suffixes (0, 1, 2, 3) represent bin indices. 
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Figure 9b:
Prefit (upper) and postfit (lower) output node distributions for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right). Separate templates are shown for each bin of reconstructed $ p_{\mathrm{T}}(\mathrm{Z}) $. The signal samples are further split into four components each, according to the generatorlevel bins of $ p_{\mathrm{T}}(\mathrm{Z}) $. In the legend, the numerical suffixes (0, 1, 2, 3) represent bin indices. 
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Figure 9c:
Prefit (upper) and postfit (lower) output node distributions for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right). Separate templates are shown for each bin of reconstructed $ p_{\mathrm{T}}(\mathrm{Z}) $. The signal samples are further split into four components each, according to the generatorlevel bins of $ p_{\mathrm{T}}(\mathrm{Z}) $. In the legend, the numerical suffixes (0, 1, 2, 3) represent bin indices. 
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Figure 9d:
Prefit (upper) and postfit (lower) output node distributions for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right). Separate templates are shown for each bin of reconstructed $ p_{\mathrm{T}}(\mathrm{Z}) $. The signal samples are further split into four components each, according to the generatorlevel bins of $ p_{\mathrm{T}}(\mathrm{Z}) $. In the legend, the numerical suffixes (0, 1, 2, 3) represent bin indices. 
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Figure 10:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10a:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10b:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10c:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10d:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10e:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 10f:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 11:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 11a:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 11b:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
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Figure 11c:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 11d:
Differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12a:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12b:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12c:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12d:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12e:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 12f:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $ (upper), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (middle), and $ \Delta \phi(\ell^{+},\,\ell^{}) $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 13:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 13a:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 13b:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 13c:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 13d:
Normalized differential cross sections for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ (left column) and the sum of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ (right column) differential cross sections as a function of $ \Delta R $ (Z,t) (upper), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). The inner (outer) error bars indicate the statistical (total) uncertainty, while the blue area refers to the uncertainty on the theory prediction. 
png pdf 
Figure 14:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
png pdf 
Figure 14a:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
png pdf 
Figure 14b:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
png pdf 
Figure 14c:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
png pdf 
Figure 14d:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
png pdf 
Figure 14e:
Covariance matrices for the simultaneous fit. The plot refers to the case where the measurement is performed as a function of $ p_{\mathrm{T}}(\mathrm{Z}) $, (upper left), $ p_{\mathrm{T}}(\ell_\mathrm{W}) $ (upper right), $ \Delta R (\mathrm{Z}, \ell_\mathrm{W}) $ (middle left), $ \Delta \phi(\ell^{+},\,\ell^{}) $ (middle right), and $ \cos\theta^\ast_{\mathrm{Z}} $ (lower). 
Tables  
png pdf 
Table 1:
Systematic uncertainty sources and their relative impact on the inclusive $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z} $ and $ \mathrm{t}\mathrm{Z}\mathrm{q} $ cross section measurement. 
Summary 
The first simultaneous measurement of single and pair production of top quarks in association with a Z boson is performed. The data were recorded by the CMS experiment at the CERN LHC in protonproton collisions at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{1} $. Events with three leptons are selected. The separation between the signals is achieved using a deep neural network classifier with three output nodes for the combined $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $ and $ \mathrm{t}\mathrm{W}\mathrm{Z} $ processes, the $ \mathrm{t}\mathrm{Z}\mathrm{q} $ process, and backgrounds. The inclusive cross sections are measured to be $ \sigma({\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z}+\mathrm{t}\mathrm{W}\mathrm{Z}) = $ 1.14 $ \pm $ 0.07 pb for the sum of $ \mathrm{t}\mathrm{W}\mathrm{Z} $ and $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $, and $ \sigma(\mathrm{t}\mathrm{Z}\mathrm{q})= $ 0.81 $ \pm $ 0.10 pb for $ \mathrm{t}\mathrm{Z}\mathrm{q} $ production. Both results are evaluated for a dilepton invariant mass within 70 and 110 GeV. The cross sections are measured differentially as functions of several observables. Generally good agreement is found for the $ \mathrm{t}\mathrm{Z}\mathrm{q} $ process, while for $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{Z} $+$ \mathrm{t}\mathrm{W}\mathrm{Z} $, a clear trend is observed as a function of the transverse momentum $ p_{\mathrm{T}} $ of the lepton originating from the top quark, leading to a significant excess of the data over expectation at low values of $ p_{\mathrm{T}} $. 
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