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CMS-TOP-21-011 ; CERN-EP-2022-168
Measurement of the cross section of top quark-antiquark pair production in association with a W boson in proton-proton collisions at $\sqrt{s} =$ 13 TeV
JHEP 07 (2023) 219
Abstract: The production of a top quark-antiquark pair in association with a W boson ($\mathrm{t\bar{t}}$W) is measured in proton-proton collisions at a center-of-mass energy of 13 TeV. The analyzed data was recorded by the CMS experiment at the CERN LHC and corresponds to an integrated luminosity of 138 fb$^{-1}$. Events with two or three leptons (electrons and muons) and additional jets are selected. In events with two leptons, a multiclass neural network is used to distinguish between the signal and background processes. Events with three leptons are categorized based on the number of jets and of jets originating from b quark hadronization, and the lepton charges. The inclusive $\mathrm{t\bar{t}}$W production cross section in the full phase space is measured to be 868 $\pm$ 40 (stat) $\pm$ 51(syst) fb. The $\mathrm{t\bar{t}}$W$^{+}$ and $\mathrm{t\bar{t}}$W$^{-}$ cross sections are also measured as 553 $\pm$ 30 (stat) $\pm$ 30 (syst) fb NU and {343 $\pm$ 26 (stat) $\pm$ 25 (syst) fb, respectively, and the corresponding ratio of the two cross sections is found to be 1.61 $\pm$ 0.15 (stat) $^{+0.07}_{-0.05}$ (syst). The results are consistent with the standard model predictions within two standard deviations, and represent the most precise measurement of these cross sections to date.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
Representative Feynman diagrams of ${\mathrm{t} {}\mathrm{\bar{t}}}$W production at LO (upper row) and NLO (lower row).

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Figure 1-a:
Representative Feynman diagram of ${\mathrm{t} {}\mathrm{\bar{t}}}$W production at LO.

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Figure 1-b:
Representative Feynman diagram of ${\mathrm{t} {}\mathrm{\bar{t}}}$W production at LO.

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Figure 1-c:
Representative Feynman diagram of ${\mathrm{t} {}\mathrm{\bar{t}}}$W production at NLO.

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Figure 1-d:
Representative Feynman diagram of ${\mathrm{t} {}\mathrm{\bar{t}}}$W production at NLO.

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Figure 2:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distributions of the leading (upper left) and subleading (upper right) lepton ${p_{\mathrm {T}}}$, the leading jet ${p_{\mathrm {T}}}$ (middle left), the number of jets (middle right), the number of loose b-tagged jets (lower left), and ${{p_{\mathrm {T}}} ^\text {miss}}$ (lower right) are displayed. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-a:
Distribution of the leading lepton ${p_{\mathrm {T}}}$: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-b:
Distribution of the subleading lepton ${p_{\mathrm {T}}}$: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-c:
Distribution of the leading jet ${p_{\mathrm {T}}}$: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-d:
Distribution of the number of jets: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-e:
Distribution of the number of loose b-tagged jets: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 2-f:
Distribution of ${{p_{\mathrm {T}}} ^\text {miss}}$: comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 3:
Distribution of the number of medium b-tagged jets per event from data (points) and prediction (colored histograms) for events in the trilepton signal region with different numbers of jets (j). Events with total trilepton charge $-$1 and $+$1 are shown in the left and right halves of the plot, respectively. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The lower panel shows the ratio of the event yields in data to the overall sum of the predictions.

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Figure 4:
Comparison of the number of observed (points) and predicted (colored histograms) events in the validation region for nonprompt leptons. The distributions of the number of jets (upper left) and loose b-tagged jets (upper right), and of the ${p_{\mathrm {T}}}$ of the leading jet (lower left) and of the leading lepton (lower right) are displayed. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 4-a:
Distribution of the number of jets: comparison of the number of observed (points) and predicted (colored histograms) events in the validation region for nonprompt leptons. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 4-b:
Distribution of the number of loose b-tagged jets: comparison of the number of observed (points) and predicted (colored histograms) events in the validation region for nonprompt leptons. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 4-c:
Distribution of the ${p_{\mathrm {T}}}$ of the leading jet: comparison of the number of observed (points) and predicted (colored histograms) events in the validation region for nonprompt leptons. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 4-d:
Distribution of the ${p_{\mathrm {T}}}$ of the leading lepton: comparison of the number of observed (points) and predicted (colored histograms) events in the validation region for nonprompt leptons. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 5:
The distributions of the number of jets in events from the control region enriched in WZ and ${\mathrm{t} {}\mathrm{\bar{t}}}$Z production from data (points) and prediction (colored histograms). The events are divided into three groups depending on the number of medium b-tagged jets b in the event. The predictions are shown before the fit to data ("Prefit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 6:
Distribution of the number of jets j and medium b-tagged jets b in events from the control region enriched in ZZ and ${\mathrm{t} {}\mathrm{\bar{t}}}$Z events for data (points) and prediction (colored histograms). Events in the first bin have two Z boson candidates (2Z ) and events in the other bins have exactly one Z boson candidate (1Z). The predictions are shown before the fit to data ("Prefit''). The small contribution from background processes with nonprompt leptons is estimated from simulated event samples. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 7:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distributions of the NN output score are displayed in final states with two leptons of positive (left) and negative (right) charges. The predictions are shown "prefit'' as in Fig.2 (upper row), and with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit'', lower row). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 7-a:
Distribution of the NN output score in final states with two leptons of positive charges. Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown "prefit'' as in Fig.2. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 7-b:
Distribution of the NN output score in final states with two leptons of negative charges. Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown "prefit'' as in Fig.2. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 7-c:
Distribution of the NN output score in final states with two leptons of positive charges. Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 7-d:
Distribution of the NN output score in final states with two leptons of negative charges. Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 8:
Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with positive sum of lepton charges. The distributions of the three-lepton invariant mass are displayed in final states with two (left) and three (right) jets, of which exactly two pass the medium b tagging requirements. The predictions are shown "prefit'' as in Fig. 3 (upper row), and with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit'', lower row). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 8-a:
Distribution of the three-lepton invariant mass in final states with two jets, which exactly pass the medium b tagging requirements: comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with positive sum of lepton charges. The predictions are shown "prefit'' as in Fig. 3. The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 8-b:
Distribution of the three-lepton invariant mass in final states with three jets, of which exactly two pass the medium b tagging requirements: comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with positive sum of lepton charges. The predictions are shown "prefit'' as in Fig. 3. The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 8-c:
Distribution of the three-lepton invariant mass in final states with two jets, which exactly pass the medium b tagging requirements: comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with positive sum of lepton charges. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 8-d:
Distribution of the three-lepton invariant mass in final states with three jets, of which exactly two pass the medium b tagging requirements: comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with positive sum of lepton charges. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 9:
Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with negative sum of lepton charges. The distributions of the three-lepton invariant mass are displayed in final states with two (left) and three (right) jets, of which exactly two pass the medium b tagging requirements. The predictions are shown "prefit'' as in Fig. 3 (upper row), and with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit'', lower row). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panels, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 9-a:
Distribution of the three-lepton invariant mass in final states with two jets, which exactly pass the medium b tagging requirements. Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with negative sum of lepton charges. The predictions are shown "prefit'' as in Fig. 3. The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 9-b:
Distribution of the three-lepton invariant mass in final states with three jets, of which exactly two pass the medium b tagging requirements. Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with negative sum of lepton charges. The predictions are shown "prefit'' as in Fig. 3. The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 9-c:
Distribution of the three-lepton invariant mass in final states with two jets, which exactly pass the medium b tagging requirements. Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with negative sum of lepton charges. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 9-d:
Distribution of the three-lepton invariant mass in final states with three jets, of which exactly two pass the medium b tagging requirements. Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region with negative sum of lepton charges. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied ("postfit''). The vertical bars on the points represent the statistical uncertainties in the data, the horizontal bars the bin widths, and the hatched bands the systematic uncertainty in the predictions. The last bins include the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Figure 10:
The measured ${\mathrm{t} {}\mathrm{\bar{t}}}$W production cross section for the individual dilepton (ee, e$\mu $, $\mu \mu $, and combined) channels and the trilepton channel, as well as their combination. The inner black bars show the statistical uncertainty, and the outer green bars give the total uncertainty. The predictions from two SM calculations from Refs. [16,21] are shown by the black and red vertical lines, with the associated bands corresponding to the total uncertainty.

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Figure 11:
The measurement of the ${\mathrm{t} {}\mathrm{\bar{t}}}$W$^{+}$ vs. ${\mathrm{t} {}\mathrm{\bar{t}}}$W$^{-}$ cross sections (black cross), along with the 68 (green dashed) and 95% (blue solid) CL intervals. The SM prediction provided by the authors of Ref. [21] is shown by the red dot, with the horizontal and vertical bars corresponding to the total uncertainties.

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Figure 12:
The scan of the negative log-likelihood used in the measurement of the cross section ratio ${\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \mathrm{W^{+}}}}/\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \mathrm{W^{-}}}}}$. The best fit value is indicated, with the inner green and outer red bands displaying the 68 and 95% CL intervals, respectively. An SM prediction and its uncertainty, found from the cross section values provided by the authors of Ref. [21], are shown by the vertical blue line and hatched blue band.
Tables

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Table 1:
Number of predicted and observed events in the dilepton and trilepton signal regions before the fit to the data. The uncertainties in the predicted number of events include both the statistical and systematic components. The uncertainties in the total number of predicted background and background plus signal events in each channel are also given. The symbol "--'' indicates that the corresponding background does not apply.

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Table 2:
Sources of systematic uncertainty in the predicted signal and background event yields with their impact on the measured ${\mathrm{t} {}\mathrm{\bar{t}}}$W production cross section, estimated after the fit to the data. Only systematic uncertainty sources with values greater than 0.1% are included in the table. The production cross sections of the ${\mathrm{t} {}\mathrm{\bar{t}}}$W, WZ, ZZ, and ${\mathrm{t} {}\mathrm{\bar{t}}}$Z processes are simultaneously constrained in the fit. The second-to-last row refers to the statistical uncertainty in the simulated event samples.

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Table 3:
Summary of measured and predicted production cross sections of ${\mathrm{t} {}\mathrm{\bar{t}}} $W, ${\mathrm{t} {}\mathrm{\bar{t}}} $W$^{+}$, and ${\mathrm{t} {}\mathrm{\bar{t}}} $W$^{-}$ production, as well as of the ${\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \mathrm{W^{+}}}}/\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \mathrm{W^{-}}}}}$ ratio. The SM predictions quoted at NLO+NNLL accuracy are taken from Refs. [16,15]. The SM predictions quoted at NLO accuracy and including corrections from an improved FxFx merging procedure (NLO+FxFx) have been provided by the authors of Ref. [21]. The theoretical uncertainties include scale variations and PDF uncertainties.
Summary
The cross section of the associated production of a W boson with a top quark-antiquark pair ($\mathrm{t\bar{t}}$W) in proton-proton collisions at $\sqrt{s} =$ 13 TeV is measured using data collected with the CMS detector in 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The measurement is performed in events with two same-sign or three charged leptons (electrons and muons) and additional jets. Events are categorized according to the charges and flavors of the leptons, and the number of jets and jets from the hadronization of b quarks. In the dilepton channel, a multiclass neural network is used to improve the separation of signal from background processes. In the trilepton channel, the invariant mass of the three leptons is used as the discriminating variable. Background contributions with leptons originating from hadron decays, jets or hadrons misidentified as leptons, and with misreconstructed charge are estimated from control samples in data. All other background processes are estimated from simulated event samples, and control samples in data are used to constrain the dominant contributions.

The inclusive $\mathrm{t\bar{t}}$W production cross section in the full phase space is measured to be 868 $\pm$ 40 (stat) $\pm$ 51(syst) fb. The $\mathrm{t\bar{t}}$W$^{+}$ and $\mathrm{t\bar{t}}$W$^{-}$ cross sections are also determined as 553 $\pm$ 30 (stat) $\pm$ 30 (syst) fb NU and 343 $\pm$ 26 (stat) $\pm$ 25 (syst) fb, respectively. The measured ratio between these production cross sections is 1.61 $\pm$ 0.15 (stat) $^{+0.07}_{-0.05}$ (syst). The measured cross sections are larger than but consistent with standard model predictions, while the ${\sigma_{\mathrm{t\bar{t}}\mathrm{W}^{+}}/\sigma_{\mathrm{t\bar{t}}\mathrm{W}^{-}}}$ ratio is smaller than but consistent with the predicted value. These results are all consistent with earlier measurements and are the most precise determinations published to date.
Additional Figures

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Additional Figure 1:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of the leading lepton $ p_{\mathrm{T}} $ is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 2:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of the subleading lepton $ p_{\mathrm{T}} $ is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 3:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of the leading jet $ p_{\mathrm{T}} $ is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 4:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of the number of jets is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 5:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of the number of loose b-tagged jets is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 6:
Comparison of the number of observed (points) and predicted (colored histograms) events in the same-sign dilepton signal region. The distribution of $ p_{\mathrm{T}}^\text{miss} $ is displayed. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. The last bin includes the overflow contributions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 7:
Comparison of the number of observed (points) and predicted (colored histograms) events in the trilepton signal region. The distribution of the number of medium b-tagged jets is displayed. Events with total trilepton charge $-$1 and $ + $1 are shown in the left and right halves of the plot, respectively. The predictions are shown with the values of the normalizations and nuisance parameters obtained in the fit to the data applied (``Postfit''). The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the systematic uncertainty in the predictions. In the lower panel, the ratio of the event yields in data to the overall sum of the predictions is presented.

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Additional Figure 8:
For the nuisance parameters listed in the left column, the pulls $ (\hat{\theta}-\theta_0)/\Delta\theta $ (middle column) and impacts $ \Delta\hat{\mu} $ (right column) are displayed. The 20 nuisance parameters with the largest impacts in the fit used to determine the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ cross section are shown. The impact $ \Delta\hat{\mu} $ is defined as the shift induced in the signal strength $ \mu $ when the nuisance parameter $ \theta $ is varied by $ \pm $1 standard deviation ($ \sigma $). The pull $ (\hat\theta-\theta_0)/\Delta\theta $ is calculated from the values $ \hat{\theta} $ and $ \theta_0 $ after and before the fit of $ \theta $ and from its uncertainty $ \Delta\theta $ before the fit. The label ``correlated'' and the per-year labels indicate nuisance parameters associated with the correlated and uncorrelated parts of a systematic uncertainty.
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