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| CMS-TOP-21-010 ; CERN-EP-2022-158 | ||
| Measurement of inclusive and differential cross sections for single top quark production in association with a W boson in proton-proton collisions at $ \sqrt{s} =$ 13 TeV | ||
| CMS Collaboration | ||
| 1 August 2022 | ||
| JHEP 07 (2023) 046 | ||
| Abstract: Measurements of the inclusive and normalised differential cross sections are presented for the production of single top quarks in association with a W boson in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data used were recorded with the CMS detector at the LHC during 2016-2018, and correspond to an integrated luminosity of 138 fb$^{-1}$. Events containing one electron and one muon in the final state are analysed. For the inclusive measurement, a multivariate discriminant, exploiting the kinematic properties of the events is used to separate the signal from the dominant $\mathrm{t\bar{t}}$ background. A cross section of 79.2 $\pm$ 0.9 (stat) $^{+7.7}_{-8.0}$ (syst) $\pm$ 1.2 (lumi) pb is obtained, consistent with the predictions of the standard model. For the differential measurements, a fiducial region is defined according to the detector acceptance, and the requirement of exactly one jet coming from the fragmentation of a bottom quark. The resulting distributions are unfolded to particle level and agree with the predictions at next-to-leading order in perturbative quantum chromodynamics. | ||
| Links: e-print arXiv:2208.00924 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Leading-order Feynman diagrams for single top quark production in the tW mode. The charge-conjugate modes are implicitly included. |
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Figure 1-a:
Leading-order Feynman diagram for single top quark production in the tW mode. The charge-conjugate mode is implicitly included. |
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Figure 1-b:
Leading-order Feynman diagram for single top quark production in the tW mode. The charge-conjugate mode is implicitly included. |
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Figure 2:
Feynman diagrams for tW single top quark production at NLO that are removed from the signal definition in the DR scheme. The charge-conjugate modes are implicitly included. |
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Figure 2-a:
Feynman diagram for tW single top quark production at NLO that are removed from the signal definition in the DR scheme. The charge-conjugate mode is implicitly included. |
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Figure 2-b:
Feynman diagram for tW single top quark production at NLO that are removed from the signal definition in the DR scheme. The charge-conjugate mode is implicitly included. |
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Figure 2-c:
Feynman diagram for tW single top quark production at NLO that are removed from the signal definition in the DR scheme. The charge-conjugate mode is implicitly included. |
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Figure 3:
Left: the number of events from data (points) and predicted from simulation (coloured histograms) before the fit in the ${\mathrm{e^{\pm}} {\mu ^\mp}}$ sample as a function of the number of jets and b-tagged jets. Right: the number of loose jets per event in the ${\mathrm{e^{\pm}} {\mu ^\mp}}$ sample from the 1j1b region. The vertical bar on the points shows the statistical uncertainty in the data. The hatched band represents the sum of the statistical and systematic uncertainties before the fit. The lower panels show the ratio of data to the sum of the expected yields. |
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Figure 3-a:
The number of events from data (points) and predicted from simulation (coloured histograms) before the fit in the ${\mathrm{e^{\pm}} {\mu ^\mp}}$ sample as a function of the number of jets and b-tagged jets. The vertical bar on the points shows the statistical uncertainty in the data. The hatched band represents the sum of the statistical and systematic uncertainties before the fit. The lower panel shows the ratio of data to the sum of the expected yields. |
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Figure 3-b:
The number of loose jets per event in the ${\mathrm{e^{\pm}} {\mu ^\mp}}$ sample from the 1j1b region. The vertical bar on the points shows the statistical uncertainty in the data. The hatched band represents the sum of the statistical and systematic uncertainties before the fit. The lower panel shows the ratio of data to the sum of the expected yields. |
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Figure 4:
Distributions from data (points) and MC simulations (coloured histograms) of the four most discriminating variables used for the BDT training of the 1j1b region: (upper left) the magnitude of the transverse momentum of the dilepton + jet system; (upper right) the centrality, defined in the text, of the dilepton + jet system; (lower left) the invariant mass of the dilepton + jet + ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ system; and (lower right) the ${p_{\mathrm {T}}}$ of the leading loose jet. The last bin of each distribution includes the overflow events. The first bin in the lower right plot contains events with 0 loose jets. The vertical bars on the points give the statistical uncertainty in the data, and the grey bands represent the sum of the statistical and systematic uncertainties in the MC predictions. The lower panels show the ratio of the data to the sum of the MC predictions. |
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Figure 4-a:
Distribution of the magnitude of the transverse momentum of the dilepton + jet system, used for the BDT training of the 1j1b region, from data (points) and MC simulations (coloured histograms). The last bin includes the overflow events. The vertical bars on the points give the statistical uncertainty in the data, and the grey bands represent the sum of the statistical and systematic uncertainties in the MC predictions. The lower panel shows the ratio of the data to the sum of the MC predictions. |
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Figure 4-b:
Distribution of the centrality, defined in the text, of the dilepton + jet system, used for the BDT training of the 1j1b region, from data (points) and MC simulations (coloured histograms). The last bin includes the overflow events. The vertical bars on the points give the statistical uncertainty in the data, and the grey bands represent the sum of the statistical and systematic uncertainties in the MC predictions. The lower panel shows the ratio of the data to the sum of the MC predictions. |
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Figure 4-c:
Distribution of the invariant mass of the dilepton + jet + ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ system, used for the BDT training of the 1j1b region, from data (points) and MC simulations (coloured histograms). The last bin includes the overflow events. The vertical bars on the points give the statistical uncertainty in the data, and the grey bands represent the sum of the statistical and systematic uncertainties in the MC predictions. The lower panel shows the ratio of the data to the sum of the MC predictions. |
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Figure 4-d:
Distribution of the ${p_{\mathrm {T}}}$ of the leading loose jet, used for the BDT training of the 1j1b region, from data (points) and MC simulations (coloured histograms). The last bin includes the overflow events. The first bin contains events with 0 loose jets. The vertical bars on the points give the statistical uncertainty in the data, and the grey bands represent the sum of the statistical and systematic uncertainties in the MC predictions. The lower panel shows the ratio of the data to the sum of the MC predictions. |
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Figure 5:
The measured distributions from data (points) and MC simulations (coloured histograms) of the six observables used to measure the tW differential cross sections. Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin of each distribution contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panels show the ratio of the data to the sum of the MC expectations. |
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Figure 5-a:
The measured distribution of the ${p_{\mathrm {T}}}$ of the leading lepton, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 5-b:
The measured distribution of the ${p_{\mathrm {T}}}$ of the jet, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 5-c:
The measured distribution of ${\Delta \varphi (\mathrm{e^{\pm}}, {\mu ^\mp})}$, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 5-d:
The measured distribution of ${|{p_z}| (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 5-e:
The measured distribution of ${m(\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 5-f:
The measured distribution of ${{m_{\mathrm {T}}} (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}}, {\vec{p}_{\mathrm {T}}^{\,\text {miss}}})}$, for data (points) and MC simulations (coloured histograms). Signal events in the 1j1b region with 0 loose jets (0j$ _{l}$) are selected. The last bin contains the overflow events. The vertical bars on the data show the statistical uncertainty. The hatched band displays the sum of the statistical and systematic uncertainties in the MC predictions before the fit. The lower panel shows the ratio of the data to the sum of the MC expectations. |
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Figure 6:
The distributions of the BDT outputs for events in the 1j1b (upper left) and 2j1b (upper right) regions, and the subleading jet ${p_{\mathrm {T}}}$ for the 2j2b region (lower). The data (points) and the MC predictions (coloured histograms) after the fit are shown. The vertical bars on the points represent the statistical uncertainty in the data, and the hatched band the total uncertainty in the MC prediction. The lower panels display the ratio of the data to the sum of the MC (points) predictions after the fit, with the bands giving the corresponding uncertainties. |
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Figure 6-a:
The distribution of the BDT outputs for events in the 1j1b region. The data (points) and the MC predictions (coloured histograms) after the fit are shown. The vertical bars on the points represent the statistical uncertainty in the data, and the hatched band the total uncertainty in the MC prediction. The lower panel displays the ratio of the data to the sum of the MC (points) predictions after the fit, with the bands giving the corresponding uncertainties. |
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Figure 6-b:
The distribution of the BDT outputs for events in the 2j1b region. The data (points) and the MC predictions (coloured histograms) after the fit are shown. The vertical bars on the points represent the statistical uncertainty in the data, and the hatched band the total uncertainty in the MC prediction. The lower panel displays the ratio of the data to the sum of the MC (points) predictions after the fit, with the bands giving the corresponding uncertainties. |
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Figure 6-c:
The distribution of the subleading jet ${p_{\mathrm {T}}}$ for the 2j2b region. The data (points) and the MC predictions (coloured histograms) after the fit are shown. The vertical bars on the points represent the statistical uncertainty in the data, and the hatched band the total uncertainty in the MC prediction. The lower panel displays the ratio of the data to the sum of the MC (points) predictions after the fit, with the bands giving the corresponding uncertainties. |
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Figure 7:
The 20 largest impacts ${\Delta \hat{\mu}}$ (right column) and pulls ${({\hat{\theta}} - {\theta _0})/ {\Delta \theta}}$ (middle column) of the nuisance parameters listed in the left column from the ML fit used to determine the inclusive tW cross section. The horizontal bars on the pulls show the ratio of the uncertainties of the fit result to the previous ones, effectively giving the constraint on the nuisance parameter. The label "corr.'' refers to the correlated component of the uncertainty over the three years and "uncorr.'' the uncorrelated component for each year. The JES uncertainties are divided into several sources, where "JES-Absolute'' groups contributions from scale corrections in the barrel, pileup corrections, and initial- and final-state radiation corrections; "JES-Relative sample'' encodes the uncertainty in the $\eta $-dependent calibration of the jets; "JES-BBEC1'' refers to pileup removal in the barrel (BB) and the first part of the endcaps (1.3 $ < {{| \eta |}} < $ 2.5; EC1) and also a contribution from scale corrections in the barrel; and "JES-Flavour QCD'' comes from the corrections applied to correct the different detector response to gluon and quark jets. |
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Figure 8:
Normalised fiducial differential tW production cross section as functions of the ${p_{\mathrm {T}}}$ of the leading lepton (upper left), ${{p_z} (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$ (upper right), ${p_{\mathrm {T}}}$ of the jet (middle left), ${m(\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$ (middle right), ${\Delta \varphi (\mathrm{e^{\pm}}, {\mu ^\mp})}$ (lower left), and ${{m_{\mathrm {T}}} (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}}, {\vec{p}_{\mathrm {T}}^{\,\text {miss}}})}$ (lower right). The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panels, the ratio of the predictions to the data is shown. |
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Figure 8-a:
Normalised fiducial differential tW production cross section as functions of the ${p_{\mathrm {T}}}$ of the leading lepton. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
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Figure 8-b:
Normalised fiducial differential tW production cross section as functions of ${{p_z} (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
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Figure 8-c:
Normalised fiducial differential tW production cross section as functions of the ${p_{\mathrm {T}}}$ of the jet. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
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Figure 8-d:
Normalised fiducial differential tW production cross section as functions of ${m(\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}})}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
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Figure 8-e:
Normalised fiducial differential tW production cross section as functions of ${\Delta \varphi (\mathrm{e^{\pm}}, {\mu ^\mp})}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
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Figure 8-f:
Normalised fiducial differential tW production cross section as functions of ${{m_{\mathrm {T}}} (\mathrm{e^{\pm}}, {\mu ^\mp}, {\mathrm {j}}, {\vec{p}_{\mathrm {T}}^{\,\text {miss}}})}$. The vertical bars on the points give the statistical uncertainty in the data, the horizontal bars show the bin width. Predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS, POWHEG + HERWIG 7 (H7) DR, MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor are also shown. The grey band represents the statistical uncertainty and the orange band the total uncertainty. In the lower panel, the ratio of the predictions to the data is shown. |
| Tables | |
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Table 1:
Selection requirements for particle-level objects. |
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Table 2:
Definition of the fiducial region. |
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Table 3:
The number of observed and MC predicted events after the fit in the 1j1b, 2j1b, and 2j2b regions. The statistical uncertainties in the data and the total uncertainties in the predictions are given. |
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Table 4:
The $p$-values from the goodness-of-fit tests comparing the six differential cross section measurements with the predictions from POWHEG (PH) + PYTHIA 8 (P8) DR and DS and POWHEG + HERWIG 7 (H7) DR. The complete covariance matrix from the results and the statistical uncertainties in the predictions are taken into account. |
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Table 5:
The $p$-values from the goodness-of-fit tests comparing the six differential cross section measurements with the predictions from MadGraph 5_aMC@NLO (aMC) + PYTHIA 8 DR, DR2, DS, and DS with a dynamic factor. The complete covariance matrix from the results and the statistical uncertainties in the predictions are taken into account. |
| Summary |
|
The measurements of the inclusive and normalised differential cross sections for the production of a top quark in association with a W boson using proton-proton collision data at $ \sqrt{s} =$ 13 TeV. The data, corresponding to an integrated luminosity of 138 fb$^{-1}$, were recorded by the CMS detector, contain events with an electron and a muon of opposite charge. For the inclusive measurement, the events have been categorised depending on the number of jets and jets originating from the fragmentation of bottom quarks. The signal is measured using a maximum likelihood fit to the distribution of boosted decision tree discriminants in two of the categories, and to the transverse momentum (${p_{\mathrm{T}}}$) distribution of the second-highest-${p_{\mathrm{T}}}$ jet in a third category. The measured inclusive cross section is 79.2 $\pm$ 0.9 (stat) $^{+7.7}_{-8.0}$ (syst) $\pm$ 1.2 (lumi) pb, with a total relative uncertainty of about 10%. This is the most precise measurement of this quantity yet published. The leading uncertainty sources are the jet energy scale corrections, the normalisation in the non-W/Z background, the matrix element scales of the tW process, and the modelling of the final-state radiation in the $\mathrm{t\bar{t}}$ and tW processes. The differential cross section measurements are performed as a function of six kinematical observable of the events in the fiducial phase space corresponding to the selection criteria. The results have relative uncertainties in the range of 10-50%, depending on the measured observable, with larger values in the tails of the distributions. There is overall good agreement between the measurements and the predictions from the different event generators. The different approaches used to simulate the tW events give similar values in all the distributions, which points to small effects of tW/$\mathrm{t\bar{t}}$ interference on these distributions in the defined fiducial region. |
| Additional Figures | |
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Additional Figure 1:
Response matrix between detector and particle level for the $ p_{\mathrm{T}} $ of the leading lepton. |
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Additional Figure 2:
Response matrix between detector and particle level for the $ p_\text{Z}(\mathrm{e}^\pm, \mu^\mp, j) $. |
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Additional Figure 3:
Response matrix between detector and particle level for the $ p_{\mathrm{T}} $ of the jet. |
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Additional Figure 4:
Response matrix between detector and particle level for the $ m(\mathrm{e}^\pm, \mu^\mp,j) $. |
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Additional Figure 5:
Response matricx between detector and particle level for the $ \Delta\varphi(\mathrm{e}^\pm, \mu^\mp) $. |
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Additional Figure 6:
Response matrix between detector and particle level for the $ m_{\text{T}}(\mathrm{e}^\pm, \mu^\mp, j, p_{\mathrm{T}}^\text{miss}) $. |
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Additional Figure 7:
Covariance matrix including all uncertainties of the differential result for the $ p_{\mathrm{T}} $ of the leading lepton. |
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Additional Figure 8:
Covariance matrix including all uncertainties of the differential result for the $ p_\text{Z}(\mathrm{e}^\pm, \mu^\mp, j) $. |
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Additional Figure 9:
Covariance matrix including all uncertainties of the differential result for the $ p_{\mathrm{T}} $ of the jet. |
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Additional Figure 10:
Covariance matrix including all uncertainties of the differential result for the $ m(\mathrm{e}^\pm, \mu^\mp, j) $. |
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Additional Figure 11:
Covariance matrix including all uncertainties of the differential result for the $ \Delta\varphi(\mathrm{e}^\pm, \mu^\mp) $. |
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Additional Figure 12:
Covariance matrix including all uncertainties of the differential result for the $ m_{\text{T}}(\mathrm{e}^\pm, \mu^\mp, j, p_{\mathrm{T}}^\text{miss}) $. |
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