CMSPASTOP18009  
Measurement of top quark pair production in association with a Z boson in protonproton collisions at $\sqrt{s} = $ 13 TeV  
CMS Collaboration  
March 2019  
Abstract: A measurement of the cross section of top quark pair production in association with a Z boson using protonproton collisions at a centerofmass energy of 13 TeV at the LHC is performed. The data sample corresponds to an integrated luminosity of 77.5 fb$^{1}$, collected by the CMS experiment during 2016 and 2017. The measurement is performed in the three and fourlepton final states. The production cross section is measured to be $\sigma(\mathrm{t}\overline{\mathrm{t}}\mathrm{Z})= $ 1.00$ ^{+0.06}_{0.05}$ (stat)$^{+0.07}_{0.06}$ (syst) pb. Differential cross sections are measured as a function of the transverse momentum of the Z boson and the angular distribution of the decay lepton. New stringent limits on the anomalous couplings of the top quark to the Z boson are obtained, including estimates of Wilson coefficients of standard model effective field theory.  
Links:
CDS record (PDF) ;
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These preliminary results are superseded in this paper, JHEP 03 (2020) 056. The superseded preliminary plots can be found here. 
Figures  
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Figure 1:
Distributions of the predicted and observed yields versus lepton flavor (upper left), and the reconstructed transverse momentum of the Z boson candidates (upper right) in the WZenriched data control region, and versus lepton flavor (lower left) and number of b jets (lower right) in the ZZenriched control region. The shaded band represents the total uncertainty in the prediction of the signal and background. The lower panels show the ratio of the data to the theoretical predictions. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. 
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Figure 1a:
Distribution of the predicted and observed yields versus lepton flavor in the WZenriched data control region.The shaded band represents the total uncertainty in the prediction of the signal and background. The lower panel shows the ratio of the data to the theoretical predictions. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. 
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Figure 1b:
Distribution of the reconstructed transverse momentum of the Z boson candidates in the WZenriched data control region. The shaded band represents the total uncertainty in the prediction of the signal and background. The lower panel shows the ratio of the data to the theoretical predictions. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. 
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Figure 1c:
Distribution of the predicted and observed yields versus lepton flavor in the ZZenriched control region. The shaded band represents the total uncertainty in the prediction of the signal and background. The lower panel shows the ratio of the data to the theoretical predictions. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. 
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Figure 1d:
Distribution of the number of b jets in the ZZenriched control region. The shaded band represents the total uncertainty in the prediction of the signal and background. The lower panel shows the ratio of the data to the theoretical predictions. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. 
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Figure 2:
Distributions of the predicted and observed yields in regions enriched with nonprompt lepton backgrounds in $ {{\mathrm {t}\overline {\mathrm {t}}}} $like processes as a function of the lepton flavors (left), the $ {p_{\mathrm {T}}} $ of the lowest$ {p_{\mathrm {T}}} $ lepton (middle), and $ {N_{{\mathrm {b}}}} $ (right). The shaded band represents the total uncertainty in the prediction of the background and the signal processes. The lower panels show the ratio of the data to the predictions from simulation. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. See Section 4 for the definition of each background category. 
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Figure 2a:
Distribution of the predicted and observed yields in regions enriched with nonprompt lepton backgrounds in $ {{\mathrm {t}\overline {\mathrm {t}}}} $like processes as a function of the lepton flavors. The shaded band represents the total uncertainty in the prediction of the background and the signal processes. The lower panels show the ratio of the data to the predictions from simulation. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. See Section 4 for the definition of each background category. 
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Figure 2b:
Distribution of the predicted and observed yields in regions enriched with nonprompt lepton backgrounds in $ {{\mathrm {t}\overline {\mathrm {t}}}} $like processes as a function of the $ {p_{\mathrm {T}}} $ of the lowest$ {p_{\mathrm {T}}} $ lepton. The shaded band represents the total uncertainty in the prediction of the background and the signal processes. The lower panels show the ratio of the data to the predictions from simulation. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. See Section 4 for the definition of each background category. 
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Figure 2c:
Distribution of the predicted and observed yields in regions enriched with nonprompt lepton backgrounds in $ {{\mathrm {t}\overline {\mathrm {t}}}} $like processes as a function of $ {N_{{\mathrm {b}}}} $. The shaded band represents the total uncertainty in the prediction of the background and the signal processes. The lower panels show the ratio of the data to the predictions from simulation. The inner band gives the statistical uncertainty in the ratio, and the outer band the total uncertainty. See Section 4 for the definition of each background category. 
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Figure 3:
Observed data as a function of $ {N_\text {j}} $ and $ {N_{{\mathrm {b}}}} $ for events with 3 and 4 leptons, compared to the simulated signal and background yields, as obtained from the fit. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Event distributions are shown as a function of the lepton flavor (upper left), $ {N_{{\mathrm {b}}}} $ (upper middle), $ {N_\text {j}} $ (upper right), dilepton invariant mass ${m(\ell \ell)}$ (lower left), ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$ (lower middle), and ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$ (lower right). The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4a:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of the lepton flavor. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4b:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of $ {N_{{\mathrm {b}}}} $. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4c:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of $ {N_\text {j}} $. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4d:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of the dilepton invariant massThe hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4e:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 4f:
Observed data in a ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ dominated region, compared to signal and background yields, as obtained from the fit. Shown is the event distribution as a function of ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$. The hatched band shows the total uncertainty associated with the signal and background predictions, as obtained from the fit. 
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Figure 5:
Measured differential ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ production cross sections in the full phase space as a function of the transverse momentum ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$ of the Z boson (top row), and ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$, as defined in the text (bottom row). Shown are the absolute (left) and normalized (right) cross sections. The data are represented by the points. The inner (outer) vertical bars indicate the statistical (total) uncertainties, respectively. The histogram shows the prediction from the MadGraph 5_aMC@NLO Monte Carlo simulation, and the hatched band indicates the theory uncertainties in the prediction. The lower planels display the ratio between prediction and measurement. 
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Figure 5a:
Measured differential ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ production cross section in the full phase space as a function of the transverse momentum ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$ of the Z boson. Shown is the absolute cross section. The data are represented by the points. The inner (outer) vertical bars indicate the statistical (total) uncertainties, respectively. The histogram shows the prediction from the MadGraph 5_aMC@NLO Monte Carlo simulation, and the hatched band indicates the theory uncertainties in the prediction. The lower planels display the ratio between prediction and measurement. 
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Figure 5b:
Measured differential ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ production cross section in the full phase space as a function of the transverse momentum ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$ of the Z boson. Shown is the normalized cross section. The data are represented by the points. The inner (outer) vertical bars indicate the statistical (total) uncertainties, respectively. The histogram shows the prediction from the MadGraph 5_aMC@NLO Monte Carlo simulation, and the hatched band indicates the theory uncertainties in the prediction. The lower planels display the ratio between prediction and measurement. 
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Figure 5c:
Measured differential ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ production cross section in the full phase space as a function of ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$, as defined in the text. Shown is the absolute cross section. The data are represented by the points. The inner (outer) vertical bars indicate the statistical (total) uncertainties, respectively. The histogram shows the prediction from the MadGraph 5_aMC@NLO Monte Carlo simulation, and the hatched band indicates the theory uncertainties in the prediction. The lower planels display the ratio between prediction and measurement. 
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Figure 5d:
Measured differential ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ production cross section in the full phase space as a function of ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$, as defined in the text. Shown is the normalized cross section. The data are represented by the points. The inner (outer) vertical bars indicate the statistical (total) uncertainties, respectively. The histogram shows the prediction from the MadGraph 5_aMC@NLO Monte Carlo simulation, and the hatched band indicates the theory uncertainties in the prediction. The lower planels display the ratio between prediction and measurement. 
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Figure 6:
Predicted and observed yields (postfit) for the combined 2016 and 2017 data sets in the control and signal regions. In the $N_{\ell}=$ 3 control and signal regions (bins 112), each of the 4 ${{p_{\mathrm {T}}} ({\mathrm {Z}})}$ categories is further split into 3 ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$ bins. Due to the lower expected event count in the $N_{\ell}=4$ signal regions (bins 1315) no categorization in terms of ${\cos {\theta ^\ast _{{\mathrm {Z}}}}}$ is applied. The red dashed line shows the bestfit point to the observed result in one of the EFT planes. 
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Figure 7:
Results of scans in two 2D planes in the EFT interpretation. The color map reflects the negative loglikelihood ratio $q$ w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. 
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Figure 7a :
Results of scans in the $c_{\mathrm{tZ}}^{I}$$c_{\mathrm{tZ}}$ plane in the EFT interpretation. The color map reflects the negative loglikelihood ratio $q$ w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. 
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Figure 7b :
Results of scans in the $c_{\phi\mathrm{t}}$$c_{\phi Q}^{}$ plane in the EFT interpretation. The color map reflects the negative loglikelihood ratio $q$ w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. 
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Figure 8:
Results of scans in the electroweak dipole moment plane (left) and axialvector and vector current coupling plane (right). The color map reflects the negative loglikelihood ratio w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. The area between the gray ellipses in the axialvector and vector current coupling plane corresponds to the observed 68% C.L. area from a previous CMS result [76]. 
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Figure 8a:
Result of a scan in the electroweak dipole moment plane. The color map reflects the negative loglikelihood ratio w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. The area between the gray ellipses in the axialvector and vector current coupling plane corresponds to the observed 68% C.L. area from a previous CMS result [76]. 
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Figure 8b:
Result of a scan in the axialvector and vector current coupling plane. The color map reflects the negative loglikelihood ratio w.r.t the bestfit value. The yellow and red dashed lines indicate one and two standard deviations from the bestfit value. The area between the gray ellipses in the axialvector and vector current coupling plane corresponds to the observed 68% C.L. area from a previous CMS result [76]. 
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Figure 9:
Loglikelihood ratios for 1D scans of Wilson coefficients. Wilson coefficients that are not shown on the respective plot are set to 0. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangle indicates the SM value. Previously excluded regions at 95% CL [4] (if available) are indicated by the gray hatched band. Indirect constraints from [77] are shown as light red hatched band. 
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Figure 9a:
Loglikelihood ratio for a scan of the $c_{\phi Q}^{}$ Wilson coefficient. Other Wilson coefficients that are not shown on the respective plot are set to 0. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangle indicates the SM value. Previously excluded regions at 95% CL [4] (if available) are indicated by the gray hatched band. Indirect constraints from [77] are shown as light red hatched band. 
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Figure 9b:
Loglikelihood ratio for a scan of the $c_{\phi\mathrm{t}}$ Wilson coefficient. Other Wilson coefficients that are not shown on the respective plot are set to 0. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangle indicates the SM value. Previously excluded regions at 95% CL [4] (if available) are indicated by the gray hatched band. Indirect constraints from [77] are shown as light red hatched band. 
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Figure 9c:
Loglikelihood ratio for a scan of the $c_{\mathrm{tZ}}$ Wilson coefficient. Other Wilson coefficients that are not shown on the respective plot are set to 0. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangle indicates the SM value. Previously excluded regions at 95% CL [4] (if available) are indicated by the gray hatched band. Indirect constraints from [77] are shown as light red hatched band. 
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Figure 9d:
Loglikelihood ratio for a scan of the $c_{\mathrm{tZ}}^{I}$ Wilson coefficient. Other Wilson coefficients that are not shown on the respective plot are set to 0. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangle indicates the SM value. Previously excluded regions at 95% CL [4] (if available) are indicated by the gray hatched band. Indirect constraints from [77] are shown as light red hatched band. 
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Figure 10:
Loglikelihood ratios for 1D scans of anomalous couplings. $C_{1,V}=0.24$ (SM value) for the scan of $C_{1,A}$ (top left) and $C_{1,A}=0.60$ (SM value) for the scan of $C_{1,V}$ (top right). The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangles indicate the SM values. 
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Figure 10a:
Loglikelihood ratios for a scan of the $C_{1,A}$ anomalous coupling. $C_{1,V}=0.24$ (SM value) for the scan. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangles indicate the SM values. 
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Figure 10b:
Loglikelihood ratios for a scan of the $C_{1,V}$ anomalous coupling. $C_{1,A}=0.60$ (SM value) for the scan. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangles indicate the SM values. 
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Figure 10c:
Loglikelihood ratios for a scan of the $C_{2,A}$ anomalous coupling. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangles indicate the SM values. 
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Figure 10d:
Loglikelihood ratios for a scan of the $C_{2,V}$ anomalous coupling. The cyan and orange colored areas correspond to the 68% and 95% confidence level intervals around the bestfit value, respectively. The red triangles indicate the SM values. 
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Figure 11:
Comparison of the observed 95% confidence level intervals (solid black) with the previous CMS result based on the inclusive cross section measurement [4] (red), the most recent ATLAS result [5] (blue), direct limits from the SMEFiT framework [78] (orange) and the TopFitter collaboration [79] (green), as well as indirect limits from electroweak data [77] (dashed black) on the Wilson coefficients. 
Tables  
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Table 1:
Event generators used to simulate events for the various processes. The version of the NNPDF set used for the hard process is shown for samples corresponding to the 2016 (2017) data sets. 
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Table 2:
Summary of the sources, magnitudes, treatments, and effects of the systematic uncertainties in the final ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ cross section measurement. The first column indicates the source of the uncertainties, the second column shows the corresponding input uncertainty range on each background source and the signal. The third column indicates how correlations are treated between uncertainties in the 2016 and the 2017 data, and the fourth column shows the resulting uncertainty in the ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ cross section. 
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Table 3:
Measured ${{{\mathrm {t}\overline {\mathrm {t}}}} {\mathrm {Z}}}$ signal strengths for events with 3 and 4 leptons, and the value from the combined fit. 
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Table 4:
Predicted and observed yields, and total uncertainties in the signalenriched sample of events. 
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Table 5:
Definition of the signal and control regions. 
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Table 6:
Expected and observed 68% and 95% CL intervals from this measurement for the listed Wilson coefficients. Constraints from a previous CMS measurement [4] and indirect constraints from precision electroweak data [77] are shown for comparison. 
Summary 
A measurement has been presented of top quark pair production in association with a Z boson using a data sample of protonproton collisions at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 77.5 fb$^{1}$, collected by the CMS detector. The analysis is performed in the three and fourlepton final states using analysis categories defined with jet and b jet multiplicities. Data samples enriched in background processes are used to validate predictions, as well as to constrain their uncertainties. Thanks to the larger data set used and reduced systematic uncertainties such as those associated with the lepton identification, the precision on the measured cross section is substantially improved with respect to previous measurements reported in Refs. [4,5]. The measured inclusive cross section is $\sigma({\mathrm{t\bar{t}}\mathrm{Z}} )=$ 1.00$ ^{+0.06}_{0.05}$ (stat)$^{+0.07}_{0.06}$ (syst) pb, in agreement with the standard model prediction. This is not only the most precise measurement today, but also the first measurement with better precision compared to the theoretical prediction at NLO in QCD. Furthermore, absolute and normalized differential cross sections for the transverse momentum of the Z boson as well as ${\cos{\theta^\ast_{\mathrm{Z}}} }$ are presented for the first time. The SM predictions at NLO are found to be in good agreement with the measured inclusive and differential cross sections. The measurement is also interpreted in terms of anomalous interactions of the t quark with the Z boson. Confidence intervals for anomalous vector and axialvector current couplings and dipole moment interactions are presented. Wilson coefficients in the top quark effective field theory are similarly constrained. 
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