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| CMS-TOP-18-006 ; CERN-EP-2019-073 | ||
| Measurement of the top quark polarization and $\mathrm{t\bar{t}}$ spin correlations using dilepton final states in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 8 July 2019 | ||
| Phys. Rev. D 100 (2019) 072002 | ||
| Abstract: Measurements of the top quark polarization and top quark pair ($\mathrm{t\bar{t}}$) spin correlations are presented using events containing two oppositely charged leptons ($\mathrm{e^{+}}\mathrm{e^{-}}$ , $\mathrm{e}^{\pm}\mu^{\mp}$ , or $\mu\mu$) produced in proton-proton collisions at a center-of-mass energy of 13 TeV. The data were recorded by the CMS experiment at the 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 13 TeV. The measured distributions and extracted coefficients are compared with standard model predictions from simulations at next-to-leading-order (NLO) accuracy in quantum chromodynamics (QCD), and from NLO QCD calculations including electroweak corrections. All measurements are found to be consistent with the expectations of the standard model. The normalized differential cross sections are used in fits to constrain the anomalous chromomagnetic and chromoelectric dipole moments of the top quark to $-0.24 < {C_\text{tG}/\Lambda^{2}} < 0.07 $ TeV$^{-2}$ and $-0.33 < {C^{I}_\text{tG}/\Lambda^{2}} < 0.20 $ TeV$^{-2}$, respectively, at 95% confidence level. | ||
| Links: e-print arXiv:1907.03729 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} \mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles $\text {p}$ represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 1-a:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} \mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles $\text {p}$ represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 1-b:
Coordinate system used for the spin measurements, illustrated in the scattering plane for $\Theta < \pi /2$ (left) and $\Theta > \pi /2$ (right), where the signs of $\hat{r}$ and $\hat{n}$ are flipped at $\Theta =\pi /2$ as shown in Eq. (4). The $\hat{k}$ axis is defined by the top quark direction, measured in the ${\mathrm{t} \mathrm{\bar{t}}}$ CM frame. For the basis used to define the coefficient functions in Eq. (3), the incoming particles $\text {p}$ represent the incoming partons, while for the basis used to measure the coefficients in Eqs. (8)-(10) they represent the incoming protons. |
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Figure 2:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-a:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-b:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-c:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-d:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-e:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-f:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-g:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-h:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-i:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 2-j:
Reconstructed distributions of $\cos\theta ^i$ for top quarks (antiquarks) in the first and third (second and fourth) rows, where $i$ refers to the reference axis with which the angle $\theta ^i$ is measured. From left to right, $i=\hat{k}$, $\hat{r}$, $\hat{n}$ (upper two rows), and $i=\hat{k}^*$, $\hat{r}^*$ (lower two rows). The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-a:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-b:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-c:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-d:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-e:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-f:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-g:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-h:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-i:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-j:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-k:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 3-l:
Reconstructed angular distributions used in the measurement of the ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation observables. The data (points) are compared to the simulated predictions (histograms). The vertical bars on the points represent statistical uncertainties, and the estimated systematic uncertainties in the simulated histograms are indicated by hatched bands. The ratio of the data to the sum of the predicted signal and background is shown in the lower panels. |
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Figure 4:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-a:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-b:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-c:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-d:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-e:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 4-f:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^i$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{i}$ ($B_{2}^{i})$. From top to bottom, the reference axis $i=\hat{k}$, $\hat{r}$, $\hat{n}$. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^{i*}$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{{i*}}$ ($B_{2}^{{i*}})$. The reference axis $i^*=\hat{k}^*$ (top row) and $\hat{r}^*$ (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5-a:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^{i*}$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{{i*}}$ ($B_{2}^{{i*}})$. The reference axis $i^*=\hat{k}^*$ (top row) and $\hat{r}^*$ (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5-b:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^{i*}$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{{i*}}$ ($B_{2}^{{i*}})$. The reference axis $i^*=\hat{k}^*$ (top row) and $\hat{r}^*$ (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5-c:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^{i*}$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{{i*}}$ ($B_{2}^{{i*}})$. The reference axis $i^*=\hat{k}^*$ (top row) and $\hat{r}^*$ (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 5-d:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections with respect to $\cos\theta ^{i*}$ for top quarks (antiquarks) in the first (second) column, probing polarization coefficients $B_{1}^{{i*}}$ ($B_{2}^{{i*}})$. The reference axis $i^*=\hat{k}^*$ (top row) and $\hat{r}^*$ (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-a:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-b:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-c:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-d:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-e:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 6-f:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the diagonal spin correlation observables (first two rows) and the laboratory-frame observables (bottom row). The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-a:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-b:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-c:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-d:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-e:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 7-f:
Unfolded data (points) and predicted (horizontal lines) normalized differential cross sections for the cross spin correlation observables. The vertical lines on the points represent the total uncertainties, with the statistical components indicated by horizontal bars. The ratios of various predictions to the data are shown in the lower panels. |
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Figure 8:
Values of the total statistical correlation matrix using the gray scale on the right for all measured bins of the normalized differential cross sections. Each group of six bins along each axis corresponds to a measured distribution, and for conciseness is labeled by the name of the associated coefficient (as defined in Table 1). |
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Figure 9:
Values of the total systematic correlation matrix using the gray scale on the right for all measured bins of the normalized differential cross sections. Each group of six bins along each axis corresponds to a measured distribution, and for conciseness is labeled by the name of the associated coefficient (as defined in Table 1). |
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Figure 10:
Measured values of the polarization coefficients (circles) and the predictions from POWHEGv2 (triangles), MadGraph 5\_aMC@NLO (inverted triangles), and the NLO calculation [4] (squares). The inner vertical bars on the circles give the statistical uncertainty in the data and the outer bars the total uncertainty. The numerical measured values with their statistical and systematic uncertainties are given on the right. The vertical bars on the values from simulation represent a combination of the statistical and scale uncertainties, while for the calculated values they represent the scale uncertainties. |
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Figure 11:
Measured values of the spin correlation coefficients and asymmetries (circles) and the predictions from POWHEGv2 (triangles), MadGraph 5\_aMC@NLO (inverted triangles), the NLO calculation [3,4] (squares), and the NNLO calculation [69] (cross). The inner vertical bars on the circles give the statistical uncertainty in the data and the outer bars the total uncertainty. The numerical measured values with their statistical and systematic uncertainties are given on the right. The vertical bars on the values from simulation represent a combination of the statistical and scale uncertainties, while for the calculated values they represent the scale uncertainties. |
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Figure 12:
Measured values of the cross spin correlation coefficients (circles) and the predictions from POWHEGv2 (triangles), MadGraph 5\_aMC@NLO (inverted triangles), and the NLO calculation [4] (squares). The inner vertical bars on the circles give the statistical uncertainty in the data and the outer bars the total uncertainty. The numerical measured values with their statistical and systematic uncertainties are given on the right. The vertical bars on the values from simulation represent a combination of the statistical and scale uncertainties, while for the calculated values they represent the scale uncertainties. |
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Figure 13:
Values of the total statistical correlation matrix using the gray scale on the right for all measured coefficients and the laboratory-frame asymmetries. |
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Figure 14:
Values of the total systematic correlation matrix using the gray scale on the right for all measured coefficients and the laboratory-frame asymmetries. |
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Figure 15:
Measured values of $f_{\mathrm {SM}}$, the strength of the measured spin correlations relative to the SM prediction. The inner vertical bars give the statistical uncertainty, the middle bars the total experimental uncertainty (statistical and systematic), and the outer bars the total uncertainty. The numerical measured values with their uncertainties are given on the right. |
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Figure 16:
The $\Delta \chi ^{2}$ values from the fit to the data as a function of ${C_\text {tG}/\Lambda ^{2}}$. The solid line is the result of the nominal fit, and the dotted and dashed lines show the most-positive and most-negative shifts in best fit ${C_\text {tG}/\Lambda ^{2}}$, respectively, when the theoretical inputs are allowed to vary within their uncertainties. The vertical line denotes the best fit value from the nominal fit, and the inner and outer areas indicate the 68 and 95% CL, respectively. |
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Figure 17:
Measured values of and uncertainties in the fitted anomalous couplings, assuming other anomalous couplings to be zero. The first and second quoted uncertainties are from experimental (statistical and systematic, at 68% CL) and theoretical sources, respectively, and are shown by the inner and outer vertical bars on the points. The expected SM value is shown by the vertical line. |
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Figure 18:
The two-dimensional 68% (solid curve) and 95% (dotted curve) CL limits on (upper left) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{\text {VV}}}$, (upper right) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{1}}$, and (lower) $ {\hat{d}_{\mathrm{t}}}$ vs. $ {\hat{c}_{-\,-}}$. The central value from the nominal fit is shown by the cross and the SM prediction by the diamond. "Theory unc. up'' refers to the fit value when $\mu _\mathrm {R}$ and $\mu _\mathrm {F}$ are simultaneously increased by a factor of 2, and "theory unc. down'' when they are decreased by the same factor. |
png pdf |
Figure 18-a:
The two-dimensional 68% (solid curve) and 95% (dotted curve) CL limits on (upper left) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{\text {VV}}}$, (upper right) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{1}}$, and (lower) $ {\hat{d}_{\mathrm{t}}}$ vs. $ {\hat{c}_{-\,-}}$. The central value from the nominal fit is shown by the cross and the SM prediction by the diamond. "Theory unc. up'' refers to the fit value when $\mu _\mathrm {R}$ and $\mu _\mathrm {F}$ are simultaneously increased by a factor of 2, and "theory unc. down'' when they are decreased by the same factor. |
png pdf |
Figure 18-b:
The two-dimensional 68% (solid curve) and 95% (dotted curve) CL limits on (upper left) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{\text {VV}}}$, (upper right) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{1}}$, and (lower) $ {\hat{d}_{\mathrm{t}}}$ vs. $ {\hat{c}_{-\,-}}$. The central value from the nominal fit is shown by the cross and the SM prediction by the diamond. "Theory unc. up'' refers to the fit value when $\mu _\mathrm {R}$ and $\mu _\mathrm {F}$ are simultaneously increased by a factor of 2, and "theory unc. down'' when they are decreased by the same factor. |
png pdf |
Figure 18-c:
The two-dimensional 68% (solid curve) and 95% (dotted curve) CL limits on (upper left) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{\text {VV}}}$, (upper right) $ {\hat{\mu}_{\mathrm{t}}}$ vs. $ {\hat{c}_{1}}$, and (lower) $ {\hat{d}_{\mathrm{t}}}$ vs. $ {\hat{c}_{-\,-}}$. The central value from the nominal fit is shown by the cross and the SM prediction by the diamond. "Theory unc. up'' refers to the fit value when $\mu _\mathrm {R}$ and $\mu _\mathrm {F}$ are simultaneously increased by a factor of 2, and "theory unc. down'' when they are decreased by the same factor. |
| Tables | |
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Table 1:
Observables and their corresponding measured coefficients, production spin density matrix coefficient functions, and P and CP symmetry properties. For the laboratory-frame asymmetries shown in the last two rows, there is no direct correspondence with the coefficient functions. |
png pdf |
Table 2:
The $\chi ^2$ between the data and the predictions for all measured normalized differential cross sections (Figs. 4-7). The last column refers to the prediction in the case of no spin correlation (SC) or polarization (pol). The $\chi ^2$ values are evaluated using the sum of the measured statistical and systematic covariance matrices. The number of degrees of freedom (dof) is 5 for all observables. In the last row, the $\chi ^2$ values are given for the set of all measured bins. |
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Table 3:
Measured coefficients and asymmetries and their total uncertainties. Predicted values from simulation are quoted with a combination of statistical and scale uncertainties, while the NLO calculated values are quoted with their scale uncertainties [3,4]. The NNLO QCD prediction for $ {A_{{{| \Delta \phi _{\ell \ell} |}}}}$, with scale uncertainties, is 0.115$^{+0.005}_{-0.001}$ [69]. |
png pdf |
Table 4:
Summary of the systematic, statistical, and total uncertainties in the extracted top quark polarization coefficients. A dash (--) is shown where the values are ${<}$0.0005. |
png pdf |
Table 5:
Summary of the systematic, statistical, and total uncertainties in the extracted ${\mathrm{t} \mathrm{\bar{t}}}$ spin correlation coefficients and asymmetries. A dash (--) is shown where the values are ${<}$0.0005. |
png pdf |
Table 6:
Measured sums and differences of the $B$ coefficients and their statistical and systematic uncertainties. The NLO calculated coefficients are quoted with their scale uncertainties [4]. |
png pdf |
Table 7:
Values of $f_{\mathrm {SM}}$, the strength of the measured spin correlations relative to the SM prediction, derived from the measurements in Table 3. The uncertainties shown are statistical, systematic, and theoretical, respectively. Their sum in quadrature is shown in the last column. |
png pdf |
Table 8:
Anomalous couplings associated with the dimension-six operators relevant for hadronic ${\mathrm{t} \mathrm{\bar{t}}}$ production, the operator type of the effective interaction vertex they represent, and their P and CP symmetry properties. It is not possible to combine the isospin-1 operators such that they have definite properties with respect to C and P [4]. |
png pdf |
Table 9:
The 95% CL limits on the anomalous couplings listed in Table 8, derived from fitting the distributions measured in Section 8.1 and setting other anomalous couplings to zero. The confidence intervals include only the experimental uncertainties as in Section 9.1. The theoretical uncertainties, the $\chi ^2$ values (dof = 19), and the distributions used in each fit are given in the last three columns. For conciseness, the distributions are labeled by their associated coefficients (as defined in Table 1). A dash (--) is shown where the values are ${<}$0.0005. |
| Summary |
|
Measurements of the top quark polarization and $\mathrm{t\bar{t}}$ spin correlations are presented, probing all of the independent coefficients of the top quark spin-dependent parts of the $\mathrm{t\bar{t}}$ production density matrix for the first time in proton-proton collisions 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 events containing two oppositely charged leptons ($\mathrm{e^{+}}\mathrm{e^{-}}$ , $\mathrm{e}^{\pm}\mu^{\mp}$ , or $\mu\mu$) and two or more jets, of which at least one is identified as coming from the hadronization of a bottom quark. The data were recorded by the CMS experiment in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. The measured normalized differential cross sections and coefficients are compared with standard model predictions from simulations with next-to-leading order (NLO) accuracy in quantum chromodynamics (QCD) and from NLO QCD calculations including electroweak corrections. The measured distribution of the absolute value of the difference in azimuthal angle between the two leptons in the laboratory frame is additionally compared with a next-to-next-to-leading-order QCD prediction. All of the 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 simultaneous fits to constrain the contributions from ten dimension-six effective operators. Two of these operators represent the anomalous chromomagnetic and chromoelectric dipole moments of the top quark, and constraints on their Wilson coefficients of $-0.24 < {C_\text{tG}/\Lambda^{2}} < 0.07$ TeV$^{-2}$ and $-0.33 < {C^{I}_\text{tG}/\Lambda^{2}} < 0.20 $ TeV$^{-2}$, respectively, are obtained at 95% confidence level. This constitutes a substantial improvement over previous direct constraints. |
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