CMSPASTOP23007  
Measurements of polarization, spin correlations, and entanglement in top quark pairs using lepton+jets events from pp collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
13 June 2024  
Abstract: Measurements of the polarization and spin correlations in top quark pairs ($ \mathrm{t\bar t} $) are presented using events with a single electron or muon and jets in the final state. The measurements are based on protonproton collision data from the LHC at $ \sqrt{s}= $ 13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb$ ^{1} $. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed in bins of additional observables such as the mass of the $ \mathrm{t\bar t} $ system and the top quark scattering angle. Inclusive coefficients are obtained by combining the results of all fitted bins. From the measured spin correlations, conclusions on the $ \mathrm{t\bar t} $ spin entanglement are drawn. The standard model predicts entangled spin $ \mathrm{t\bar t} $ states at the production threshold and at high masses of the $ \mathrm{t\bar t} $ system. Entanglement is observed for the first time in events with high $ \mathrm{t\bar t} $ mass, with an observed (expected) significance of 6.7 (5.6) standard deviations. The observed level of entanglement cannot be explained by classical exchange of information between the two particles alone. The observed (expected) significance for entanglement attributable to spacelike separated $ \mathrm{t\bar t} $ pairs is 5.4 (4.1) standard deviations.  
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Distribution of $ S_\mathrm{NN} $ in the 2b (left) and 1b (right) categories for $ \mu $+jets events. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction, while the vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 1a:
Distribution of $ S_\mathrm{NN} $ in the 2b (left) and 1b (right) categories for $ \mu $+jets events. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction, while the vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 1b:
Distribution of $ S_\mathrm{NN} $ in the 2b (left) and 1b (right) categories for $ \mu $+jets events. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction, while the vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 2:
Reconstruction efficiency of the NN (left) and fraction of correctly reconstructed events (right) as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ estimated from the simulation. The values are shown separately for the 1b and 2b categories with the $ S_\mathrm{low} $ and $ S_\mathrm{high} $ selection. The event counts $ N_\mathrm{correct} $ and $ N_\mathrm{reco} $ refer to the number of correctly reconstructed and ``reconstructable'' $ \mathrm{t \bar{t}} $ events, respectively. All reconstructed events regardless of the process are labeled $ N_\mathrm{all} $. 
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Figure 2a:
Reconstruction efficiency of the NN (left) and fraction of correctly reconstructed events (right) as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ estimated from the simulation. The values are shown separately for the 1b and 2b categories with the $ S_\mathrm{low} $ and $ S_\mathrm{high} $ selection. The event counts $ N_\mathrm{correct} $ and $ N_\mathrm{reco} $ refer to the number of correctly reconstructed and ``reconstructable'' $ \mathrm{t \bar{t}} $ events, respectively. All reconstructed events regardless of the process are labeled $ N_\mathrm{all} $. 
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Figure 2b:
Reconstruction efficiency of the NN (left) and fraction of correctly reconstructed events (right) as a function of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ estimated from the simulation. The values are shown separately for the 1b and 2b categories with the $ S_\mathrm{low} $ and $ S_\mathrm{high} $ selection. The event counts $ N_\mathrm{correct} $ and $ N_\mathrm{reco} $ refer to the number of correctly reconstructed and ``reconstructable'' $ \mathrm{t \bar{t}} $ events, respectively. All reconstructed events regardless of the process are labeled $ N_\mathrm{all} $. 
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Figure 3:
Comparison of the $ \cos(\chi) $ (left) and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (right) distributions of the simulated background in the control region (red line) and in the 1b signal category (stacked histograms). The data points show the distribution in the control region after subtracting the predicted $ \mathrm{t \bar{t}} $ and single top contributions. Data to MC agreement in the control region can be seen by comparing the data points to the red line. The dashed orange lines show the distribution after requiring the $ S_\mathrm{NN} $ selections in the control region. The dashed light blue distribution is obtained by taking into account the mismatch of the normalization in the control region when subtracting the $ \mathrm{t \bar{t}} $ and single top contributions. All distributions are normalized to the event yields of the stacked histogram. The gray uncertainty band shows the statistical uncertainties in the prediction. The lower panels show the ratios of the various distributions with respect to the simulated background in the 1b signal category. 
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Figure 3a:
Comparison of the $ \cos(\chi) $ (left) and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (right) distributions of the simulated background in the control region (red line) and in the 1b signal category (stacked histograms). The data points show the distribution in the control region after subtracting the predicted $ \mathrm{t \bar{t}} $ and single top contributions. Data to MC agreement in the control region can be seen by comparing the data points to the red line. The dashed orange lines show the distribution after requiring the $ S_\mathrm{NN} $ selections in the control region. The dashed light blue distribution is obtained by taking into account the mismatch of the normalization in the control region when subtracting the $ \mathrm{t \bar{t}} $ and single top contributions. All distributions are normalized to the event yields of the stacked histogram. The gray uncertainty band shows the statistical uncertainties in the prediction. The lower panels show the ratios of the various distributions with respect to the simulated background in the 1b signal category. 
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Figure 3b:
Comparison of the $ \cos(\chi) $ (left) and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ (right) distributions of the simulated background in the control region (red line) and in the 1b signal category (stacked histograms). The data points show the distribution in the control region after subtracting the predicted $ \mathrm{t \bar{t}} $ and single top contributions. Data to MC agreement in the control region can be seen by comparing the data points to the red line. The dashed orange lines show the distribution after requiring the $ S_\mathrm{NN} $ selections in the control region. The dashed light blue distribution is obtained by taking into account the mismatch of the normalization in the control region when subtracting the $ \mathrm{t \bar{t}} $ and single top contributions. All distributions are normalized to the event yields of the stacked histogram. The gray uncertainty band shows the statistical uncertainties in the prediction. The lower panels show the ratios of the various distributions with respect to the simulated background in the 1b signal category. 
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Figure 4:
Distribution in $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 4a:
Distribution in $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 4b:
Distribution in $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 4c:
Distribution in $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 4d:
Distribution in $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 5:
Distribution in $ \cos(\theta_\mathrm{p}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 5a:
Distribution in $ \cos(\theta_\mathrm{p}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 5b:
Distribution in $ \cos(\theta_\mathrm{p}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 5c:
Distribution in $ \cos(\theta_\mathrm{p}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 5d:
Distribution in $ \cos(\theta_\mathrm{p}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 6:
Distribution in $ \phi_\mathrm{p} $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 6a:
Distribution in $ \phi_\mathrm{p} $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 6b:
Distribution in $ \phi_\mathrm{p} $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 6c:
Distribution in $ \phi_\mathrm{p} $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 6d:
Distribution in $ \phi_\mathrm{p} $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 7:
Distribution of $ \cos(\chi) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 7a:
Distribution of $ \cos(\chi) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 7b:
Distribution of $ \cos(\chi) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 7c:
Distribution of $ \cos(\chi) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 7d:
Distribution of $ \cos(\chi) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 8:
Distribution of $ \cos(\tilde{\chi}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 8a:
Distribution of $ \cos(\tilde{\chi}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 8b:
Distribution of $ \cos(\tilde{\chi}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 8c:
Distribution of $ \cos(\tilde{\chi}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 8d:
Distribution of $ \cos(\tilde{\chi}) $ in all four categories. The data (points) are compared to the prediction (stacked histograms). The $ \mathrm{t \bar{t}} $ and single top components are taken from the prediction, while the multijet/EW background is obtained from a control region. The $ \mathrm{t \bar{t}} $ contribution is split into the correctly and wrongly reconstructed, ``nonreconstructable'', and non $ \mathrm{e}/\mu $+jets events. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty on the data. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 9:
Examples of unrolled 4dimensional distributions $ L\Sigma_m $ and $ T_m $ as functions of $ \phi_{p(\bar{p})} $ and $ \theta_{p(\bar{p})} $ for the individual coefficients of the polarization vectors and the spin correlation matrix for events with 400 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 600 GeV and $ \cos(\theta) < $ 0.4. The $ L\Sigma_m $ (red lines) are the distributions at the generator level in the full phase space, and the $ T_m $ (blue lines) are the distributions in the 2b $ S_\mathrm{high} $ category for the 2018 luminosity. The events are required to be reconstructed and generated in the same $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bin. The detector level distributions are enhanced by a factor of 40 to improve their visibility. 
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Figure 9a:
Examples of unrolled 4dimensional distributions $ L\Sigma_m $ and $ T_m $ as functions of $ \phi_{p(\bar{p})} $ and $ \theta_{p(\bar{p})} $ for the individual coefficients of the polarization vectors and the spin correlation matrix for events with 400 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 600 GeV and $ \cos(\theta) < $ 0.4. The $ L\Sigma_m $ (red lines) are the distributions at the generator level in the full phase space, and the $ T_m $ (blue lines) are the distributions in the 2b $ S_\mathrm{high} $ category for the 2018 luminosity. The events are required to be reconstructed and generated in the same $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bin. The detector level distributions are enhanced by a factor of 40 to improve their visibility. 
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Figure 9b:
Examples of unrolled 4dimensional distributions $ L\Sigma_m $ and $ T_m $ as functions of $ \phi_{p(\bar{p})} $ and $ \theta_{p(\bar{p})} $ for the individual coefficients of the polarization vectors and the spin correlation matrix for events with 400 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 600 GeV and $ \cos(\theta) < $ 0.4. The $ L\Sigma_m $ (red lines) are the distributions at the generator level in the full phase space, and the $ T_m $ (blue lines) are the distributions in the 2b $ S_\mathrm{high} $ category for the 2018 luminosity. The events are required to be reconstructed and generated in the same $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bin. The detector level distributions are enhanced by a factor of 40 to improve their visibility. 
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Figure 9c:
Examples of unrolled 4dimensional distributions $ L\Sigma_m $ and $ T_m $ as functions of $ \phi_{p(\bar{p})} $ and $ \theta_{p(\bar{p})} $ for the individual coefficients of the polarization vectors and the spin correlation matrix for events with 400 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 600 GeV and $ \cos(\theta) < $ 0.4. The $ L\Sigma_m $ (red lines) are the distributions at the generator level in the full phase space, and the $ T_m $ (blue lines) are the distributions in the 2b $ S_\mathrm{high} $ category for the 2018 luminosity. The events are required to be reconstructed and generated in the same $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bin. The detector level distributions are enhanced by a factor of 40 to improve their visibility. 
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Figure 9d:
Examples of unrolled 4dimensional distributions $ L\Sigma_m $ and $ T_m $ as functions of $ \phi_{p(\bar{p})} $ and $ \theta_{p(\bar{p})} $ for the individual coefficients of the polarization vectors and the spin correlation matrix for events with 400 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 600 GeV and $ \cos(\theta) < $ 0.4. The $ L\Sigma_m $ (red lines) are the distributions at the generator level in the full phase space, and the $ T_m $ (blue lines) are the distributions in the 2b $ S_\mathrm{high} $ category for the 2018 luminosity. The events are required to be reconstructed and generated in the same $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bin. The detector level distributions are enhanced by a factor of 40 to improve their visibility. 
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Figure 10:
Prefit (upper) and postfit (lower) distributions comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). The $ x $axis shows the bin number of the unrolled 4dimensional distribution of $ \theta_{p} $, $ \phi_{p} $, $ \theta_{\bar{p}} $, and $ \phi_{\bar{p}} $, listed from the inner to the outer most variable in each of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins. For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 10a:
Prefit (upper) and postfit (lower) distributions comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). The $ x $axis shows the bin number of the unrolled 4dimensional distribution of $ \theta_{p} $, $ \phi_{p} $, $ \theta_{\bar{p}} $, and $ \phi_{\bar{p}} $, listed from the inner to the outer most variable in each of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins. For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
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Figure 10b:
Prefit (upper) and postfit (lower) distributions comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). The $ x $axis shows the bin number of the unrolled 4dimensional distribution of $ \theta_{p} $, $ \phi_{p} $, $ \theta_{\bar{p}} $, and $ \phi_{\bar{p}} $, listed from the inner to the outer most variable in each of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins. For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 11:
Prefit (upper) and postfit (lower) distributions of $ \cos(\chi) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ D $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 11a:
Prefit (upper) and postfit (lower) distributions of $ \cos(\chi) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ D $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 11b:
Prefit (upper) and postfit (lower) distributions of $ \cos(\chi) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ D $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 12:
Prefit (upper) and postfit (lower) distributions of $ \cos(\tilde{\chi}) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ \tilde{D} $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 12a:
Prefit (upper) and postfit (lower) distributions of $ \cos(\tilde{\chi}) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ \tilde{D} $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 12b:
Prefit (upper) and postfit (lower) distributions of $ \cos(\tilde{\chi}) $ comparing the data (points) to the POWHEG +PYTHIA simulation (stacked histograms) for the $ \tilde{D} $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ in the 2b $ S_\mathrm{high} $ category (2018). For the illustration of resolution effects, $ \mathrm{t \bar{t}} $ events generated in two selected $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ bins are shown in different shades of red. All other $ \mathrm{t \bar{t}} $ contributions are shown in light red. A model without any spin polarization and correlations is shown as a blue line. The gray uncertainty band indicates the combined statistical and systematic uncertainties in the prediction. The vertical bars on the points show the statistical uncertainty. The ratios of data to the predicted yields are provided in the lower panels. 
png pdf 
Figure 13:
Results of the inclusive full matrix measurement obtained by combining the bins of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ \cos(\theta) $ (right) measurements. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 13a:
Results of the inclusive full matrix measurement obtained by combining the bins of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ \cos(\theta) $ (right) measurements. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 13b:
Results of the inclusive full matrix measurement obtained by combining the bins of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ (left) and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ \cos(\theta) $ (right) measurements. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 14:
Results of the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 14a:
Results of the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 14b:
Results of the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 14c:
Results of the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 14d:
Results of the full matrix measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 15:
Results of the full matrix measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 15a:
Results of the full matrix measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 15b:
Results of the full matrix measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 15c:
Results of the full matrix measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
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Figure 15d:
Results of the full matrix measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 16:
Results of the full matrix measurement in bins of $ \cos(\theta) < $ 0.4 and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 16a:
Results of the full matrix measurement in bins of $ \cos(\theta) < $ 0.4 and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 16b:
Results of the full matrix measurement in bins of $ \cos(\theta) < $ 0.4 and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 16c:
Results of the full matrix measurement in bins of $ \cos(\theta) < $ 0.4 and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
png pdf 
Figure 16d:
Results of the full matrix measurement in bins of $ \cos(\theta) < $ 0.4 and $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measurements (markers) are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA and MINNLO+PYTHIA. 
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Figure 17:
Entanglement results for the $ D $ measurement in the threshold region (upper left), $ \tilde{D} $ measurement in the high $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ region (upper right), and the full matrix measurement in different $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ regions (lower). The measurements (points) are shown with their uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. The observed (expected) significance to deviate from the boundary of separable states (green region) is quoted in standard deviations. 
png pdf 
Figure 17a:
Entanglement results for the $ D $ measurement in the threshold region (upper left), $ \tilde{D} $ measurement in the high $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ region (upper right), and the full matrix measurement in different $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ regions (lower). The measurements (points) are shown with their uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. The observed (expected) significance to deviate from the boundary of separable states (green region) is quoted in standard deviations. 
png pdf 
Figure 17b:
Entanglement results for the $ D $ measurement in the threshold region (upper left), $ \tilde{D} $ measurement in the high $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ region (upper right), and the full matrix measurement in different $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ regions (lower). The measurements (points) are shown with their uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. The observed (expected) significance to deviate from the boundary of separable states (green region) is quoted in standard deviations. 
png pdf 
Figure 17c:
Entanglement results for the $ D $ measurement in the threshold region (upper left), $ \tilde{D} $ measurement in the high $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ region (upper right), and the full matrix measurement in different $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ regions (lower). The measurements (points) are shown with their uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. The observed (expected) significance to deviate from the boundary of separable states (green region) is quoted in standard deviations. 
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Figure 18:
The observed levels of entanglement characterized by $ \Delta_\mathrm{E} $ are shown in the threshold region using the $ D $ measurement (first bin), and in the high $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ region using the full matrix measurement (second bin). The measurements (points) are shown with their uncertainties and compared to the predictions of POWHEG +PYTHIA. The horizontal blue lines correspond to the maximum level of entanglement $ \Delta_\mathrm{E\,crit} $ that can be explained by the exchange of information between t and $ \bar{\mathrm{t}} $ at the speed of light. The significance in standard deviations by which the measurement exceeds $ \Delta_\mathrm{E\,crit} $ (unity) is quoted in blue (gray) and indicated by corresponding arrows. 
Tables  
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Table 1:
Results of the inclusive $ D $ and $ \tilde{D} $ measurements from the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ vs. $ \cos(\theta) $ and $ p_{\mathrm{T}}(\mathrm{t}) $ vs. $ \cos(\theta) $ binning. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
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Table 2:
Results of the $ D $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
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Table 3:
Results of the $ D $ measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
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Table 4:
Results of the $ \tilde{D} $ measurement in bins of $ m({\mathrm{t}\bar{\mathrm{t}}} ) $. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
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Table 5:
Results of the $ \tilde{D} $ measurement in bins of $ p_{\mathrm{T}}(\mathrm{t}) $. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
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Table 6:
Results of the $ m({\mathrm{t}\bar{\mathrm{t}}} ) $ for $ \cos(\theta) < $ 0.4 $ \tilde{D} $ measurement. The measured values are shown with the combined statistical and systematic uncertainties and compared to the predictions of POWHEG +PYTHIA, POWHEG + HERWIG, MadGraph5_aMC@NLO+PYTHIA, and MINNLO+PYTHIA. 
Summary 
The polarization and spin correlations in top quark pair ($ \mathrm{t \bar{t}} $) production are measured in the $ \mathrm{e}/\mu $+jets channels. The entanglement between the spins of the top quark and antiquark is determined from the measured spin correlations. The measurements are based on protonproton collision data at $ \sqrt{s} = $ 13 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$ ^{1} $. The decay products of the top quarks are identified using an artificial neural network. The coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously from the angular distributions of $ \mathrm{t \bar{t}} $ decay products using a binned likelihood fit. This is done both inclusively and in various regions of the phase space. The standard model predicts entangled $ \mathrm{t \bar{t}} $ states at the production threshold and at high masses of the $ \mathrm{t \bar{t}} $ system. Entanglement is observed in events with high $ \mathrm{t \bar{t}} $ mass, with an observed (expected) significance of 6.7 (5.6) standard deviations, while in events with low transverse momentum of the top quark a significance of 3.5 (4.4) standard deviations is observed (expected). This is the first observation of entanglement at high $ \mathrm{t \bar{t}} $ mass and cannot be explained by classical exchange of information between the two particles alone. The observed (expected) significance for entanglement attributable to spacelike separated $ \mathrm{t \bar{t}} $ pairs is 5.4 (4.1) standard deviations. 
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