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| CMS-PAS-TOP-18-006 | ||
| Measurement of the top quark polarization and $\mathrm{t \bar t}$ spin correlations in dilepton final states at $\sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| December 2018 | ||
| Abstract: Measurements of the top quark polarization and top quark pair ($\mathrm{t \bar t}$) spin correlations are presented using events containing two leptons produced in proton-proton collisions at a center-of-mass energy of $\sqrt{s}= $ 13 TeV. The data were recorded by the CMS experiment at the CERN LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A set of parton-level normalized differential cross sections, sensitive to each of the independent coefficients of the spin-dependent parts of the $\mathrm{t \bar t}$ production density matrix, is measured for the first time at $\sqrt{s}= $ 13 TeV. The measured distributions and extracted coefficients are compared with standard model predictions from Monte Carlo simulations with next-to-leading-order (NLO) accuracy in quantum chromodynamics (QCD) and from NLO QCD calculations including weak and mixed QCD-weak corrections. All measurements are found to be consistent with the expectations of the standard model, and are used in a simultaneous fit to constrain the anomalous chromomagnetic dipole moment of the top quark to $-0.07 < C_\text{tG}/\Lambda^{2} < 0.16 $ TeV$^{-2}$ at 95% confidence level. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, PRD 100 (2019) 072002. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows. From left to right the top quark polarization is measured with respect to the $\hat{k}$, $\hat{r}$, and $\hat{n}$ (upper rows), and $\hat{k^*}$ and $\hat{r^*}$ reference axes (lower rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 1-a:
Reconstructed distribution of $\cos\theta ^i$ for top quarks. The top quark polarization is measured with respect to the $\hat{k}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-b:
Reconstructed distribution of $\cos\theta ^i$ for top quarks. The top quark polarization is measured with respect to the $\hat{r}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-c:
Reconstructed distribution of $\cos\theta ^i$ for top quarks. The top quark polarization is measured with respect to the $\hat{n}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-d:
Reconstructed distribution of $\cos\theta ^i$ for top antiquarks. The top quark polarization is measured with respect to the $\hat{k}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-e:
Reconstructed distribution of $\cos\theta ^i$ for top antiquarks. The top quark polarization is measured with respect to the $\hat{r}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-f:
Reconstructed distribution of $\cos\theta ^i$ for top antiquarks. The top quark polarization is measured with respect to the $\hat{n}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-g:
Reconstructed distribution of $\cos\theta ^i$ for top quarks. The top quark polarization is measured with respect to the $\hat{k^*}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-h:
Reconstructed distribution of $\cos\theta ^i$ for top quarks. The top quark polarization is measured with respect to the $\hat{r^*}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-i:
Reconstructed distribution of $\cos\theta ^i$ for top antiquarks. The top quark polarization is measured with respect to the $\hat{k^*}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 1-j:
Reconstructed distribution of $\cos\theta ^i$ for top antiquarks. The top quark polarization is measured with respect to the $\hat{r^*}$ reference axis. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panel. |
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Figure 2:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-a:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-b:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-c:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-d:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-e:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-f:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-g:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-h:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-i:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-j:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-k:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 2-l:
Reconstructed distributions for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The vertical bars on the data points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms (considered in Section 6) are indicated by hatched bands. The ratio of the prediction to the data is shown in the lower panels. |
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Figure 3:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From left to right the top quark polarization is measured with respect to the $\hat{k}$, $\hat{r}$, and $\hat{n}$ (upper rows), and $\hat{k^*}$ and $\hat{r^*}$ reference axes (lower rows). The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 3-a:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top quark polarization is measured with respect to the $\hat{k}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-b:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top quark polarization is measured with respect to the $\hat{k}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-c:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top quark polarization is measured with respect to the $\hat{n}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-d:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top antiquarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top antiquark polarization is measured with respect to the $\hat{k}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-e:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top antiquarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top antiquark polarization is measured with respect to the $\hat{r}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-f:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top antiquarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top antiquark polarization is measured with respect to the $\hat{n}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-g:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top quark polarization is measured with respect to the $\hat{k^*}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
png pdf |
Figure 3-h:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top quark polarization is measured with respect to the $\hat{r^*}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 3-i:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top antiquarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top antiquark polarization is measured with respect to the $\hat{k^*}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
png pdf |
Figure 3-j:
Unfolded normalized differential cross sections with respect to $\cos\theta ^i$ for top antiquarks, corresponding to the polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. The top antiquark polarization is measured with respect to the $\hat{r^*}$ reference axis. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panel. |
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Figure 4:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-a:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-b:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-c:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-d:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-e:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-f:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-g:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-h:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-i:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
png pdf |
Figure 4-j:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-k:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-l:
Unfolded normalized differential cross sections for the $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation observables. The vertical bars on the data points represent the total uncertainties, with the statistical component indicated by a horizontal bar. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5:
Total statistical correlation matrix for all measured bins of the normalized differential cross sections (6 bins for each variable). |
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Figure 6:
Total systematic correlation matrix for all measured bins of the normalized differential cross sections (6 bins for each variable). |
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Figure 7:
Measured polarization coefficients and their total uncertainties. Coefficients from the POWHEG.V2 simulation are quoted with a combination of statistical and scale uncertainties, while the uncertainties for the MadGraph.5\_aMC@NLO simulation are statistical only. The calculated coefficients are quoted with scale uncertainties [3]. |
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Figure 8:
Measured spin correlation coefficients and asymmetries and their total uncertainties. Coefficients from the POWHEG.V2 simulation are quoted with a combination of statistical and scale uncertainties, while the uncertainties for the MadGraph.5\_aMC@NLO simulation are statistical only. The calculated coefficients are quoted with scale uncertainties [3]. |
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Figure 9:
Measured cross spin correlation coefficients and their total uncertainties. Coefficients from the POWHEG.V2 simulation are quoted with a combination of statistical and scale uncertainties, while the uncertainties for the MadGraph.5\_aMC@NLO simulation are statistical only. The calculated coefficients are quoted with scale uncertainties [3]. |
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Figure 10:
Total statistical correlation matrix for all measured coefficients and the laboratory frame asymmetries. |
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Figure 11:
Total systematic correlation matrix for all measured coefficients and the laboratory frame asymmetries. |
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Figure 12:
Measured values of $f_{\mathrm {SM}}$, the strength of the measured spin correlations relative to the SM prediction. The uncertainties shown are a combination of those from experimental (statistical and systematic) and theoretical sources. |
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Figure 13:
Left: $\Delta \chi ^{2}$ values from the fit to the data are shown in the left plot as a function of ${C_\text {tG}/\Lambda ^{2}}$. The green area indicates 1$\sigma $ CL, the orange the 2$\sigma $ CL. Right: Decrease in total uncertainty on ${C_\text {tG}/\Lambda ^{2}}$ for the case of adding one distribution at a time to the $\chi ^{2}$ minimization. |
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Figure 13-a:
$\Delta \chi ^{2}$ values from the fit to the data are shown in the left plot as a function of ${C_\text {tG}/\Lambda ^{2}}$. The green area indicates 1$\sigma $ CL, the orange the 2$\sigma $ CL. |
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Figure 13-b:
Decrease in total uncertainty on ${C_\text {tG}/\Lambda ^{2}}$ for the case of adding one distribution at a time to the $\chi ^{2}$ minimization. |
| Tables | |
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Table 1:
Observables and corresponding measured coefficients and production spin density matrix coefficient functions. For the laboratory-frame observables, there is no direct correspondence with the coefficient functions. |
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Table 2:
Measured coefficients and their total uncertainties. Coefficients from the POWHEG.V2 simulation are quoted with a combination of statistical and scale uncertainties, while the uncertainties for the MadGraph.5\_aMC@NLO simulation are statistical only. The calculated coefficients are quoted with scale uncertainties [3]. |
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Table 3:
Summary of the systematic uncertainties in the extracted top quark polarization coefficients. |
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Table 4:
Summary of the systematic uncertainties in the extracted $ {{\mathrm {t}\overline {\mathrm {t}}}} $ spin correlation coefficients. |
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Table 5:
Measured sums and differences of the $B$ coefficients and their statistical and systematic uncertainties. The calculated coefficients are quoted with scale uncertainties. |
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Table 6:
Values of $f_{\mathrm {SM}}$, the strength of the measured spin correlations relative to the SM prediction for the given observable, derived from the numbers in Table 2. The uncertainties shown are statistical, systematic, and theoretical, respectively. The total uncertainty in each result, found by adding the individual uncertainties in quadrature, is shown in the last column. |
| Summary |
| We present measurements of the top quark polarization and $ \mathrm{t\bar{t}} $ spin correlations, probing all the independent coefficients of the top quark spin-dependent parts of the $ \mathrm{t\bar{t}} $ production density matrix for the first time at $\sqrt{s}=$ 13 TeV. Each coefficient is extracted from a normalized differential cross section, unfolded to the parton level and extrapolated to the full phase space. The measurements are made using a data sample of pp collision events containing two leptons, recorded by the CMS experiment in 2016 and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The measured distributions and extracted coefficients are compared with standard model predictions from Monte Carlo simulations with NLO accuracy in QCD and from NLO QCD calculations including weak and mixed QCD-weak corrections. All measurements are found to be consistent with the expectations of the standard model. Statistical and systematic covariance matrices are provided for the set of all measured bins, and are used in a simultaneous fit to constrain the anomalous chromomagnetic dipole moment of the top quark. A constraint of $-0.07 < {C_\text{tG}/\Lambda^{2}}\ < 0.16 $ TeV$^{-2}$ at 95% CL is obtained, with the impact from neglecting contributions quadratic in ${C_\text{tG}/\Lambda^{2}}$ found to be small. |
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