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| CMS-PAS-TOP-23-004 | ||
| 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} $). The data were recorded in pp collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-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. | ||
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Links:
CDS record (PDF) ;
Physics Briefing ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| 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 1-a:
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 1-b:
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 1-c:
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 2-a:
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 2-b:
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 2-c:
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 2-d:
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 2-e:
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 3-a:
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 3-b:
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 3-c:
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 3-d:
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 3-e:
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 4-a:
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 4-b:
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 4-c:
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 4-d:
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 5-a:
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 5-b:
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 5-c:
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 5-d:
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 5-e:
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 5-f:
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 b-jet multiplicity in the four lepton region (left) and the jet multiplicity in the zero b-jet control region (right). These distributions are added to the fit for the inclusive measurements. |
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Figure 6-a:
Distributions of the b-jet multiplicity in the four lepton region (left) and the jet multiplicity in the zero b-jet control region (right). These distributions are added to the fit for the inclusive measurements. |
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Figure 6-b:
Distributions of the b-jet multiplicity in the four lepton region (left) and the jet multiplicity in the zero b-jet 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 b-jet 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 8-a:
Postfit distributions of the b-jet 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 8-b:
Postfit distributions of the b-jet 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 8-c:
Postfit distributions of the b-jet 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 8-d:
Postfit distributions of the b-jet 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 8-e:
Postfit distributions of the b-jet 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 generator-level 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 9-a:
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 generator-level 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 9-b:
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 generator-level 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 9-c:
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 generator-level 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 9-d:
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 generator-level 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 10-a:
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 10-b:
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 10-c:
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 10-d:
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 10-e:
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 10-f:
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 11-a:
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 11-b:
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 11-c:
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 11-d:
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 12-a:
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 12-b:
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 12-c:
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 12-d:
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 12-e:
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 12-f:
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 13-a:
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 13-b:
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 13-c:
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 13-d:
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 14-a:
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 14-b:
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 14-c:
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 14-d:
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 14-e:
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 proton-proton collisions at a center-of-mass 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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