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| CMS-PAS-TOP-21-001 | ||
| Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| June 2021 | ||
| Abstract: A search for new top quark interactions is performed within the framework of an effective field theory using the associated production of either one ($\mathrm{t}\mathrm{Z}$) or two ($\mathrm{t}\bar{\mathrm{t}}\mathrm{Z}$) top quarks with a Z boson in multilepton final states. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = $ 13 TeV, collected by the CMS experiment at the CERN LHC. Five dimension-six operators modifying the electroweak interactions of the top quark are considered. Novel machine-learning techniques are used to enhance the sensitivity to effects arising from these operators. Distributions used for the signal extraction are parameterized in terms of Wilson coefficients (WCs) describing the interaction strengths of the operators. All five WCs are fit to the data and confidence intervals at 95% confidence level are computed. All intervals contain the standard model expectations for the WC values. | ||
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, JHEP 12 (2021) 083. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Representative Feynman diagrams at tree level for ${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$ (upper left), ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ (upper right), and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ (lower) production. The diagrams for ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ production are shown for the five-flavor scheme. |
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Figure 1-a:
Representative Feynman diagrams at tree level for ${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$ (upper left), ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ (upper right), and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ (lower) production. The diagrams for ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ production are shown for the five-flavor scheme. |
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Figure 1-b:
Representative Feynman diagrams at tree level for ${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$ (upper left), ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ (upper right), and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ (lower) production. The diagrams for ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ production are shown for the five-flavor scheme. |
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Figure 1-c:
Representative Feynman diagrams at tree level for ${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$ (upper left), ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ (upper right), and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ (lower) production. The diagrams for ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ and ${\mathrm{t}}{\mathrm{W}}{\mathrm{Z}}$ production are shown for the five-flavor scheme. |
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Figure 2:
Pre-fit data-to-simulation comparisons for several observables in the SR-3$\ell$. From left to right and top to bottom, the distributions correspond to: the relative azimuthal angle $\Delta \phi $ between the two leptons from the Z boson decay; the maximum DeepJet discriminant among all selected jets; the absolute pseudorapidity of the recoiling jet; the b jet multiplicity; the lepton asymmetry; and ${{p_{\mathrm {T}}} ^\text {miss}}$, respectively. The lower panels display the ratios of the observed event yields to their predicted values. The NPL background is modeled with the data-based procedure described in Section 5. Underflows and overflows are shown in the first and last bins, respectively. |
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Figure 3:
Pre-fit data-to-simulation comparisons for the distributions of the ${\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}$ (left), ${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$ (middle), and Others (right) output nodes. The lower panels display the ratios of the observed event yields to their predicted values. For each distribution, only the events that have their maximal value in the corresponding output node are included. |
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Figure 4:
Post-fit data-to-simulation comparisons for the distributions that are common to all fits, corresponding to counting experiments in the CRs and SR-${{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}$-4$\ell$ (left), and to the ${m_\text {T}^\mathrm{W}}$ observable in the {\text {SR-Others}} (right), after the 5D fit. The lower panels display the ratios of the observed event yields to their predicted values. |
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Figure 5:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 5D fit (upper) and for the 1D fit to ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). |
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Figure 5-a:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 5D fit (upper) and for the 1D fit to ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). |
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Figure 5-b:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 5D fit (upper) and for the 1D fit to ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). |
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Figure 6:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 1D fits to ${c_{\mathrm{t} \mathrm{W}}}$ (upper) and to ${c^{3}_{\varphi \mathrm {Q}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). Open-headed arrows indicate points that are outside the vertical range of the figure. |
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Figure 6-a:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 1D fits to ${c_{\mathrm{t} \mathrm{W}}}$ (upper) and to ${c^{3}_{\varphi \mathrm {Q}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). Open-headed arrows indicate points that are outside the vertical range of the figure. |
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Figure 6-b:
Post-fit data-to-simulation comparisons for the distributions used in the SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$ (left) and SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ (right), for the 1D fits to ${c_{\mathrm{t} \mathrm{W}}}$ (upper) and to ${c^{3}_{\varphi \mathrm {Q}}}$ (lower). The middle panels display the ratios of the observed event yields to their predicted values. For each region, the lower panel shows the change of the event yield in each bin with respect to the SM prediction for two arbitrary EFT scenarios, both for the main signal process in the region (thick lines) and for the total prediction (dashed lines). Open-headed arrows indicate points that are outside the vertical range of the figure. |
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Figure 7:
Two-dimensional scans of the negative log-likelihood as a function of ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\mathrm{t} \mathrm{W}}}$ (left), or as a function of ${c^{-}_{\varphi \mathrm {Q}}}$ and ${c_{\varphi \mathrm{t}}}$ (right). The SM and best fit points are indicated by diamond- and cross-shaped markers, respectively. The thin blue line and thick red line represent the 68% and 95% CL contours, respectively. |
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Figure 7-a:
Two-dimensional scans of the negative log-likelihood as a function of ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\mathrm{t} \mathrm{W}}}$ (left), or as a function of ${c^{-}_{\varphi \mathrm {Q}}}$ and ${c_{\varphi \mathrm{t}}}$ (right). The SM and best fit points are indicated by diamond- and cross-shaped markers, respectively. The thin blue line and thick red line represent the 68% and 95% CL contours, respectively. |
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Figure 7-b:
Two-dimensional scans of the negative log-likelihood as a function of ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\mathrm{t} \mathrm{W}}}$ (left), or as a function of ${c^{-}_{\varphi \mathrm {Q}}}$ and ${c_{\varphi \mathrm{t}}}$ (right). The SM and best fit points are indicated by diamond- and cross-shaped markers, respectively. The thin blue line and thick red line represent the 68% and 95% CL contours, respectively. |
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Figure 8:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
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Figure 8-a:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
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Figure 8-b:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
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Figure 8-c:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
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Figure 8-d:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
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Figure 8-e:
Observed (thick black lines) and expected (thin gray lines) one-dimensional scans of the negative log-likelihood as a function of each of the five WCs, while fixing the other WCs to their SM values of zero. The 68% and 95% CL confidence intervals are indicated by the colored areas. |
| Tables | |
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Table 1:
List of dimension-six EFT operators considered in this analysis and their corresponding WCs. The linear combinations of WCs to which they correspond in the Warsaw basis are indicated. The abbreviations $ {s_{\mathrm {W}}} $ and $ {c_{\mathrm {W}}} $ denote the sine and cosine of the weak mixing angle (in the unitary gauge), respectively. The definitions of the relevant Warsaw-basis operators can be found in Ref. [19]. |
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Table 2:
Summary of the main selection requirements applied in each signal and control region. A dash indicates that the selection requirement is not applied. |
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Table 3:
Input variables to the {NN-SM} and to the eight {NN-EFTs}. A hyphen indicates that the variable is not used. The three-momentum of an object includes the ${p_{\mathrm {T}}}$, $\eta $, and $\phi $ components of its momentum. The symbol $\ell _{\mathrm{t}}$ denotes the lepton produced in the decay of the top quark t; $j'$ denotes the recoiling jet; $b$ denotes the b jet associated with the leptonic top quark decay; $(\ell ^{\mathrm{Z}}_{1},\ell ^{\mathrm{Z}}_{2})$ denote the leptons produced in the Z boson decay; ${\cos\theta ^{\star}_{\mathrm{Z}}}$ is defined as the cosine of the angle between the direction of the Z boson in the detector reference frame, and the direction of the negatively-charged lepton from the Z boson decay in the rest frame of the Z boson. Other observables were defined in Section 3. |
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Table 4:
Summary of the different sources of systematic uncertainty included in the measurements. The first column indicates the source of the uncertainty. The second column indicates whether the source affects the event yields, the shapes of the observables, or both. In the third column, the symbols "sss'' and "--'' indicate 100% and 0% correlations between the data-taking periods, respectively. |
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Table 5:
Observables used in each region for the different fits. The {NN-SM} is trained to separate different SM processes, while the other NNs are trained to identify new effects arising from one or more EFT operators, as described in Section 6. |
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Table 6:
Expected and observed 95% CL confidence intervals for all WCs. The intervals in the first and second columns are obtained by scanning over a single WC, while fixing the other WCs to their SM values of zero. The intervals in the third and fourth columns are obtained by performing a 5D fit in which all five WCs are treated as free parameters. As explained in Section 8, the 1D intervals are obtained from separate fits to different observables in the SR-${{\mathrm{t}}{\mathrm{Z}}{\mathrm{q}}}$ and SR-${{{\mathrm{t} {}\mathrm{\bar{t}}}}{\mathrm{Z}}}$, while the 5D intervals are obtained from one single fit. |
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Table 7:
Impacts from different groups of sources of systematic uncertainty on each individual WC. To estimate the impact of a given group, the corresponding sources of systematic uncertainty are excluded, the 1D fits to the data are repeated, and the reduction in the width of the confidence interval is quoted for each WC in %. |
| Summary |
|
A search for new top quark interactions has been performed within the framework of an effective field theory (EFT) using the associated production of either one ($\mathrm{t}\mathrm{Z}$) or two ($\mathrm{t}\bar{\mathrm{t}}\mathrm{Z}$) top quarks with a Z boson in multilepton final states. The data sample corresponds to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = $ 13 TeV, and was collected in 2016-2018 by the CMS experiment. Five dimension-six operators modifying the electroweak interactions of the top quark were considered. The event yields and kinematic properties of the signal processes were parameterized with Wilson coefficients (WCs) describing the interaction strengths of these operators. A multivariate analysis relying upon machine-learning techniques was designed in order to enhance the sensitivity to effects arising from the considered EFT operators. A multiclass neural network was trained to distinguish between standard model (SM) processes and was used to define three subregions enriched in $\mathrm{t}\mathrm{Z}\mathrm{q}$, $\mathrm{t}\bar{\mathrm{t}}\mathrm{Z}$, and background events, respectively. Additional neural networks were trained to separate events generated either at the SM point or for nonzero values of the WCs, and were used to construct optimal observables. This is the first time that machine-learning techniques accounting for interference between EFT operators and the SM amplitude are used in a full-fledged LHC analysis. Results were extracted from a simultaneous fit to the data in six event categories for all three years. Confidence intervals were determined for each WC, while either keeping the other WCs fixed to zero or treating all five WCs as free parameters. Two-dimensional contours were produced for pairs of WCs to illustrate their correlations. All results are consistent with the SM at 95% confidence level. |
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