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CMS-TOP-24-003 ; CERN-EP-2025-170

Measurements of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ differential cross sections and the leptonic charge asymmetry at $ \sqrt{s}= $ 13 TeV

CMS Collaboration

16 September 2025

Submitted to J. High Energy Phys.

Abstract: Measurements of properties of top quark-antiquark pair production in association with a W boson in proton-proton collisions at a center-of-mass energy of 13 TeV are presented, using a data sample corresponding to an integrated luminosity of 138 fb$ ^{-1} $, recorded by the CMS experiment at the CERN LHC. Events are selected based on the presence of either two leptons with the same electric charge or three leptons, and multiple jets and b-tagged jets. We present measurements of differential production cross sections as a function of kinematic variables sensitive to different aspects of the process modeling, using a multivariate discriminator in the two-lepton selection region and a simple selection-based method in the three-lepton region. The normalized cross section measurements are generally consistent with the standard model expectations, while we observe larger values compared to the expectations in the absolute cross section measurements, consistent with previous inclusive cross section measurements. In addition, we measure the leptonic charge asymmetry of this process, obtaining an observed value of $ A_\text{c}^{\ell}= -0.19 ^{+0.16}_{-0.18} $, consistent with the expectation of $-0.085 \pm 0.006$ predicted by next-to-leading order simulations.

Links: e-print arXiv:2509.13512 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Examples of Feynman diagrams for $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ production: at LO (left) and one of the NLO diagrams introducing sizeable electroweak corrections (right).
png pdf	Figure 1-a: Examples of Feynman diagrams for $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ production: at LO (left) and one of the NLO diagrams introducing sizeable electroweak corrections (right).
png pdf	Figure 1-b: Examples of Feynman diagrams for $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ production: at LO (left) and one of the NLO diagrams introducing sizeable electroweak corrections (right).
png pdf	Figure 2: An overview of all control regions (CR) and signal regions (SR) used in the analysis.
png pdf	Figure 3: $ p_{\mathrm{T}} $ of the sub-leading lepton (left) and $ |\eta| $ of the subleading lepton (right), in a VR enriched with nonprompt leptons by applying requirements on the number of (b-tagged) jets orthogonal to the SR, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 3-a: $ p_{\mathrm{T}} $ of the sub-leading lepton (left) and $ |\eta| $ of the subleading lepton (right), in a VR enriched with nonprompt leptons by applying requirements on the number of (b-tagged) jets orthogonal to the SR, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 3-b: $ p_{\mathrm{T}} $ of the sub-leading lepton (left) and $ |\eta| $ of the subleading lepton (right), in a VR enriched with nonprompt leptons by applying requirements on the number of (b-tagged) jets orthogonal to the SR, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 4: Number of selected b-tagged jets in the event (upper left), number of selected jets in the event (upper right), $ p_{\mathrm{T}} $ of the sub-leading lepton (lower left), and $ |\eta| $ of the sub-leading lepton (lower right), in a CR enriched with nonprompt leptons by inverting the $ p_{\mathrm{T}}^\text{miss} $ requirement, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 4-a: Number of selected b-tagged jets in the event (upper left), number of selected jets in the event (upper right), $ p_{\mathrm{T}} $ of the sub-leading lepton (lower left), and $ |\eta| $ of the sub-leading lepton (lower right), in a CR enriched with nonprompt leptons by inverting the $ p_{\mathrm{T}}^\text{miss} $ requirement, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 4-b: Number of selected b-tagged jets in the event (upper left), number of selected jets in the event (upper right), $ p_{\mathrm{T}} $ of the sub-leading lepton (lower left), and $ |\eta| $ of the sub-leading lepton (lower right), in a CR enriched with nonprompt leptons by inverting the $ p_{\mathrm{T}}^\text{miss} $ requirement, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 4-c: Number of selected b-tagged jets in the event (upper left), number of selected jets in the event (upper right), $ p_{\mathrm{T}} $ of the sub-leading lepton (lower left), and $ |\eta| $ of the sub-leading lepton (lower right), in a CR enriched with nonprompt leptons by inverting the $ p_{\mathrm{T}}^\text{miss} $ requirement, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 4-d: Number of selected b-tagged jets in the event (upper left), number of selected jets in the event (upper right), $ p_{\mathrm{T}} $ of the sub-leading lepton (lower left), and $ |\eta| $ of the sub-leading lepton (lower right), in a CR enriched with nonprompt leptons by inverting the $ p_{\mathrm{T}}^\text{miss} $ requirement, for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 5: $ p_{\mathrm{T}} $ of the leading lepton (left), $ |\eta| $ of the leading lepton (right), in a CR enriched with charge-misidentified leptons and additional jets for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 5-a: $ p_{\mathrm{T}} $ of the leading lepton (left), $ |\eta| $ of the leading lepton (right), in a CR enriched with charge-misidentified leptons and additional jets for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 5-b: $ p_{\mathrm{T}} $ of the leading lepton (left), $ |\eta| $ of the leading lepton (right), in a CR enriched with charge-misidentified leptons and additional jets for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR as described in Section 7 for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 6: Number of selected (b-tagged) jets in the event for events with three leptons passing the loose (left) and tight (right) selection after the fit to the data in the SR and CR as described in Section 7. Events with no b-tagged jets are classified in bins 1 to 4, events with one b-tagged jet are classified in bins 5 to 9 (8) and events with more than one b tag are classified in bins 10 (9) to 13 (12) for the loose (tight) lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 6-a: Number of selected (b-tagged) jets in the event for events with three leptons passing the loose (left) and tight (right) selection after the fit to the data in the SR and CR as described in Section 7. Events with no b-tagged jets are classified in bins 1 to 4, events with one b-tagged jet are classified in bins 5 to 9 (8) and events with more than one b tag are classified in bins 10 (9) to 13 (12) for the loose (tight) lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 6-b: Number of selected (b-tagged) jets in the event for events with three leptons passing the loose (left) and tight (right) selection after the fit to the data in the SR and CR as described in Section 7. Events with no b-tagged jets are classified in bins 1 to 4, events with one b-tagged jet are classified in bins 5 to 9 (8) and events with more than one b tag are classified in bins 10 (9) to 13 (12) for the loose (tight) lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 7: $ p_{\mathrm{T}} $ of the leading lepton (upper left), $ p_{\mathrm{T}} $ of the subleading jet (upper right), scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (lower left), and the number of selected jets in the event (lower right), in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 7-a: $ p_{\mathrm{T}} $ of the leading lepton (upper left), $ p_{\mathrm{T}} $ of the subleading jet (upper right), scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (lower left), and the number of selected jets in the event (lower right), in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 7-b: $ p_{\mathrm{T}} $ of the leading lepton (upper left), $ p_{\mathrm{T}} $ of the subleading jet (upper right), scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (lower left), and the number of selected jets in the event (lower right), in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 7-c: $ p_{\mathrm{T}} $ of the leading lepton (upper left), $ p_{\mathrm{T}} $ of the subleading jet (upper right), scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (lower left), and the number of selected jets in the event (lower right), in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 7-d: $ p_{\mathrm{T}} $ of the leading lepton (upper left), $ p_{\mathrm{T}} $ of the subleading jet (upper right), scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (lower left), and the number of selected jets in the event (lower right), in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin.
png pdf	Figure 8: Distribution of the BDT output node in the two-lepton signal selection for the loose lepton selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 9: Distributions defined in a two-dimensional grid between the MVA score and the variable of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 9-a: Distributions defined in a two-dimensional grid between the MVA score and the variable of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 9-b: Distributions defined in a two-dimensional grid between the MVA score and the variable of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 9-c: Distributions defined in a two-dimensional grid between the MVA score and the variable of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 9-d: Distributions defined in a two-dimensional grid between the MVA score and the variable of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data in the SR and CR for the loose lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction.
png pdf	Figure 10: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 10-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 10-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 10-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 10-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 11: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 11-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 11-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 11-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 11-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 12: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 12-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 12-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 12-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 12-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 13: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 13-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 13-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 13-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 13-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 14: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 14-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 14-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 14-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 14-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 15: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 15-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 15-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 15-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 15-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 16: Absolute (upper row) and normalized (lower row) differential cross section differential cross section measured as a function of the $ \Delta R(\ell_1,\ell_2) $ and the $ \Delta R(\ell_1,\text{jet})_{\text{min}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 16-a: Absolute (upper row) and normalized (lower row) differential cross section differential cross section measured as a function of the $ \Delta R(\ell_1,\ell_2) $ and the $ \Delta R(\ell_1,\text{jet})_{\text{min}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 16-b: Absolute (upper row) and normalized (lower row) differential cross section differential cross section measured as a function of the $ \Delta R(\ell_1,\ell_2) $ and the $ \Delta R(\ell_1,\text{jet})_{\text{min}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 16-c: Absolute (upper row) and normalized (lower row) differential cross section differential cross section measured as a function of the $ \Delta R(\ell_1,\ell_2) $ and the $ \Delta R(\ell_1,\text{jet})_{\text{min}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 16-d: Absolute (upper row) and normalized (lower row) differential cross section differential cross section measured as a function of the $ \Delta R(\ell_1,\ell_2) $ and the $ \Delta R(\ell_1,\text{jet})_{\text{min}} $, using the MVA-based method. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 17: Scalar $ p_{\mathrm{T}} $ sum of the jets in the event (left) and scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (right); in the trilepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 17-a: Scalar $ p_{\mathrm{T}} $ sum of the jets in the event (left) and scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (right); in the trilepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 17-b: Scalar $ p_{\mathrm{T}} $ sum of the jets in the event (left) and scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (right); in the trilepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents are divided by bin width.
png pdf	Figure 18: Absolute differential cross section measured as a function of the $ H_{\mathrm{T}} $ (left) and the scalar sum of the lepton $ p_{\mathrm{T}} $'s, using the counting method in the 3 $ \ell $ SR. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 18-a: Absolute differential cross section measured as a function of the $ H_{\mathrm{T}} $ (left) and the scalar sum of the lepton $ p_{\mathrm{T}} $'s, using the counting method in the 3 $ \ell $ SR. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 18-b: Absolute differential cross section measured as a function of the $ H_{\mathrm{T}} $ (left) and the scalar sum of the lepton $ p_{\mathrm{T}} $'s, using the counting method in the 3 $ \ell $ SR. The upper panels show the results of the measurement together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. The lower panels show the ratio between the predictions and the measurement. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure 19: Categorization of three-lepton events for the measurement of the leptonic charge asymmetry.
png pdf	Figure 20: Left: Observed yields in the 32 bins used in the analysis for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Right: the observed (black) and expected (red) likelihood scan as a function of $ A_\text{c}^{\ell} $. The shaded areas correspond to the 68 and 95% confidence level intervals around the best-fit value, respectively.
png pdf	Figure 20-a: Left: Observed yields in the 32 bins used in the analysis for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Right: the observed (black) and expected (red) likelihood scan as a function of $ A_\text{c}^{\ell} $. The shaded areas correspond to the 68 and 95% confidence level intervals around the best-fit value, respectively.
png pdf	Figure 20-b: Left: Observed yields in the 32 bins used in the analysis for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Right: the observed (black) and expected (red) likelihood scan as a function of $ A_\text{c}^{\ell} $. The shaded areas correspond to the 68 and 95% confidence level intervals around the best-fit value, respectively.
png pdf	Figure A1: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-a: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-b: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-c: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-d: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-e: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A1-f: Distributions of some variables of interest in the two-lepton signal selection for data (points) and predictions (filled histograms) after the fit to the data for the tight lepton selection. Left: number of selected jets in the event (negative, positive signed leptons SR). Middle: scalar $ p_{\mathrm{T}} $ sum of selected jets in the event (negative, positive signed leptons SR). Right: scalar $ p_{\mathrm{T}} $ sum of the leptons in the event (negative, positive signed leptons SR). The lower panels show the ratio of the data to the sum of the postfit predictions (points) and the ratio of the data to the prefit predictions (red line). The vertical lines on the data points represent the statistical uncertainty in the data and the hatched (filled) band corresponds to the total uncertainty in the postfit (prefit) prediction. Events that exceed the range of the plot are included in the last bin. The bin contents of the middle and right side plots are divided by the width of the bin.
png pdf	Figure A2: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A2-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A2-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A2-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A2-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the jet multiplicity (left) and $ H_{\mathrm{T}} $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A3: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A3-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A3-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A3-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A3-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading jet $ p_{\mathrm{T}} $ (left) and leading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A4: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A4-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A4-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A4-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A4-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the subleading jet $ p_{\mathrm{T}} $ (left), and subleading jet $ |\eta| $ (right), using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A5: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A5-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A5-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A5-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A5-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the leading (left) and subleading (right) lepton $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A6: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A6-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A6-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A6-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A6-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the maximum $ |\eta| $ of the selected leptons (left) and the sum of their $ p_{\mathrm{T}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A7: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A7-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A7-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A7-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A7-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the invariant mass of the leptons (left) and the $ |\Delta\eta(\ell_1,\ell_2)| $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A8: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the $ \Delta R(\ell_1, \ell_2) $ and the $ \Delta R(\ell_1, jet)_{\text{min}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A8-a: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the $ \Delta R(\ell_1, \ell_2) $ and the $ \Delta R(\ell_1, jet)_{\text{min}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A8-b: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the $ \Delta R(\ell_1, \ell_2) $ and the $ \Delta R(\ell_1, jet)_{\text{min}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A8-c: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the $ \Delta R(\ell_1, \ell_2) $ and the $ \Delta R(\ell_1, jet)_{\text{min}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.
png pdf	Figure A8-d: Absolute (upper row) and normalized (lower row) differential cross section measured as a function of the $ \Delta R(\ell_1, \ell_2) $ and the $ \Delta R(\ell_1, jet)_{\text{min}} $, using the MVA-based and the counting method. The upper panels show the results of the two measurements together with the theoretical predictions. The blue band shows the uncertainty of the prediction from Ref. [17]. Each two lower panels shows the ratio between the predictions and each of the measurements. The vertical lines on the unfolded data points represent the total experimental uncertainty of the unfolded cross section, while the horizontal bars show the statistical component of the uncertainty.

Tables
png pdf	Table 1: Variables as a function of which the signal cross section is measured.
png pdf	Table 2: Overview of input variables to the BDT and their prefit $ p $-values, obtained in a $ \chi^2 $ goodness-of-fit test.
png pdf	Table 3: The $ p $-values from the $ \chi^2 $ goodness-of-fit tests comparing the absolute (column 1 and 2) and normalized (column 3 and 4) differential cross sections predicted by the new FxFx model [17] with the two measurements in the 2 $ \ell\mkern1mu\text{SS} $ region.

Summary

Measurements of properties of top quark-antiquark pair production in association with a W boson ($ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $) in proton-proton collisions at a center-of-mass energy of 13 TeV are performed using a data sample corresponding to an integrated luminosity of 138 fb$ ^{-1} $, recorded by the CMS experiment. Events with either two leptons with the same electric charge or three leptons, and multiple jets and b-tagged jets are used. The differential cross sections as a function of kinematic variables sensitive to the modeling of the $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ process are measured, using a multivariate discriminator for events in the two-lepton region and a counting method for events in the three-lepton region. Overall, the normalized differential cross section measurements are generally consistent with the standard model expectations, while the absolute cross sections are above the theoretical predictions by approximately one standard deviation, consistent with previous inclusive cross section measurements. In addition to the differential cross sections, the leptonic charge asymmetry of this process is measured to be $ A_\text{c}^{\ell}=-0.19 ^{+0.16}_{-0.18} $, consistent with the expectation of $-0.085 \pm 0.006$ predicted by next-to-leading order simulations.

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