CMS-TOP-21-003

CMS-TOP-21-003 ; CERN-EP-2022-172
Search for new physics using effective field theory in 13 TeV pp collision events that contain a top quark pair and a boosted Z or Higgs boson
CMS Collaboration
26 August 2022
Phys. Rev. D 108 (2023) 032008
Abstract: A data sample containing top quark pairs ( $\mathrm{t\bar{t}}$ ) produced in association with a Lorentz-boosted Z or Higgs boson is used to search for signs of new physics using effective field theory. The data correspond to an integrated luminosity of 138 fb $^{-1}$ of proton-proton collisions produced at a center-of-mass energy of 13 TeV at the LHC and collected by the CMS experiment. Selected events contain a single lepton and hadronic jets, including two identified with the decay of bottom quarks, plus an additional large-radius jet with high transverse momentum identified as a Z or Higgs boson decaying to a bottom quark pair. Machine learning techniques are employed to discriminate between $\mathrm{t\bar{t}}$ Z or $\mathrm{t\bar{t}}$ H events and events from background processes, which are dominated by $\mathrm{t\bar{t}}{+}$ jets production. No indications of new physics are observed. The signal strengths of boosted $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H production are measured, and upper limits are placed on the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H differential cross sections as functions of the Z or Higgs boson transverse momentum. The effects of new physics are probed using a framework in which the standard model is considered to be the low-energy effective field theory of a higher energy scale theory. Eight possible dimension-six operators are added to the standard model Lagrangian and their corresponding coefficients are constrained via fits to the data.
Links: e-print arXiv:2208.12837 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Examples of tree-level Feynman diagrams for the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) production processes.
png pdf	Figure 1-a: Examples of tree-level Feynman diagrams for the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) production processes.
png pdf	Figure 1-b: Examples of tree-level Feynman diagrams for the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) production processes.
png pdf	Figure 2: The $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) cross sections in the SM EFT, as ratios to the corresponding SM cross sections, as functions of ${c_{\mathrm{t} \mathrm{Z}}} /{\Lambda}^{2}$ and the Z boson ${p_{\mathrm {T}}}$ (left), and ${c_{\varphi \mathrm{t} \mathrm{b}}} /{\Lambda}^{2}$ and the Higgs boson ${p_{\mathrm {T}}}$ (right), where ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are the WCs for the EFT operators ${O_{\mathrm{u} \mathrm{B}}^\mathrm {(ij)}}$ and ${O_{\varphi \mathrm{u} \mathrm{d}}^\mathrm {(ij)}}$ , respectively [7]. Example Feynman diagrams, in which the vertices affected by ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are marked by a filled dot, are also displayed.
png pdf	Figure 2-a: The $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) cross sections in the SM EFT, as ratios to the corresponding SM cross sections, as functions of ${c_{\mathrm{t} \mathrm{Z}}} /{\Lambda}^{2}$ and the Z boson ${p_{\mathrm {T}}}$ (left), and ${c_{\varphi \mathrm{t} \mathrm{b}}} /{\Lambda}^{2}$ and the Higgs boson ${p_{\mathrm {T}}}$ (right), where ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are the WCs for the EFT operators ${O_{\mathrm{u} \mathrm{B}}^\mathrm {(ij)}}$ and ${O_{\varphi \mathrm{u} \mathrm{d}}^\mathrm {(ij)}}$ , respectively [7]. Example Feynman diagrams, in which the vertices affected by ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are marked by a filled dot, are also displayed.
png pdf	Figure 2-b: The $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) cross sections in the SM EFT, as ratios to the corresponding SM cross sections, as functions of ${c_{\mathrm{t} \mathrm{Z}}} /{\Lambda}^{2}$ and the Z boson ${p_{\mathrm {T}}}$ (left), and ${c_{\varphi \mathrm{t} \mathrm{b}}} /{\Lambda}^{2}$ and the Higgs boson ${p_{\mathrm {T}}}$ (right), where ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are the WCs for the EFT operators ${O_{\mathrm{u} \mathrm{B}}^\mathrm {(ij)}}$ and ${O_{\varphi \mathrm{u} \mathrm{d}}^\mathrm {(ij)}}$ , respectively [7]. Example Feynman diagrams, in which the vertices affected by ${c_{\mathrm{t} \mathrm{Z}}}$ and ${c_{\varphi \mathrm{t} \mathrm{b}}}$ are marked by a filled dot, are also displayed.
png pdf	Figure 3: The simulated DNN score distributions, normalized to unit area, for well-reconstructed $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H signal events in which the reconstructed Z or Higgs boson candidate is matched to both generator-level b quark daughters of the Z or Higgs boson; the remaining $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events; background events from ${\mathrm{t} \mathrm{\bar{t}}}$ + $\mathrm{b} \mathrm{\bar{b}}$ ; and background events from ${\mathrm{t} \mathrm{\bar{t}}}$ + ${\mathrm{c} \mathrm{\bar{c}}}$ and ${\mathrm{t} \mathrm{\bar{t}}}$ + LF. The events satisfy the baseline selection requirements described in Section 5 and contain a Z or Higgs boson candidate with ${p_{\mathrm {T}}} >$ 300 GeV.
png pdf	Figure 4: Soft-drop mass distributions from simulation for background (solid histograms) and signal (dashed histograms) of $\mathrm{Z} /\mathrm{H} \to \mathrm{b} \mathrm{\bar{b}}$ candidate jets in three ${p_{\mathrm {T}}}$ ranges: 200-300 GeV (upper left), 300-450 GeV (upper right), and ${>}450 GeV$ (lower) in simulated samples with DNN score ${>} 0.8$ . The signal distributions represent the SM prediction scaled up by a factor of 10 for easier comparison with the backgrounds. The signal distributions include well-reconstructed $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events as well as $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events that either do not contain Z/H $\to \mathrm{b} \mathrm{\bar{b}}$ or are not well reconstructed. The red hatched bands correspond to the statistical uncertainty in the background.
png pdf	Figure 4-a: Soft-drop mass distributions from simulation for background (solid histograms) and signal (dashed histograms) of $\mathrm{Z} /\mathrm{H} \to \mathrm{b} \mathrm{\bar{b}}$ candidate jets in three ${p_{\mathrm {T}}}$ ranges: 200-300 GeV (upper left), 300-450 GeV (upper right), and ${>}450 GeV$ (lower) in simulated samples with DNN score ${>} 0.8$ . The signal distributions represent the SM prediction scaled up by a factor of 10 for easier comparison with the backgrounds. The signal distributions include well-reconstructed $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events as well as $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events that either do not contain Z/H $\to \mathrm{b} \mathrm{\bar{b}}$ or are not well reconstructed. The red hatched bands correspond to the statistical uncertainty in the background.
png pdf	Figure 4-b: Soft-drop mass distributions from simulation for background (solid histograms) and signal (dashed histograms) of $\mathrm{Z} /\mathrm{H} \to \mathrm{b} \mathrm{\bar{b}}$ candidate jets in three ${p_{\mathrm {T}}}$ ranges: 200-300 GeV (upper left), 300-450 GeV (upper right), and ${>}450 GeV$ (lower) in simulated samples with DNN score ${>} 0.8$ . The signal distributions represent the SM prediction scaled up by a factor of 10 for easier comparison with the backgrounds. The signal distributions include well-reconstructed $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events as well as $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events that either do not contain Z/H $\to \mathrm{b} \mathrm{\bar{b}}$ or are not well reconstructed. The red hatched bands correspond to the statistical uncertainty in the background.
png pdf	Figure 4-c: Soft-drop mass distributions from simulation for background (solid histograms) and signal (dashed histograms) of $\mathrm{Z} /\mathrm{H} \to \mathrm{b} \mathrm{\bar{b}}$ candidate jets in three ${p_{\mathrm {T}}}$ ranges: 200-300 GeV (upper left), 300-450 GeV (upper right), and ${>}450 GeV$ (lower) in simulated samples with DNN score ${>} 0.8$ . The signal distributions represent the SM prediction scaled up by a factor of 10 for easier comparison with the backgrounds. The signal distributions include well-reconstructed $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events as well as $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H events that either do not contain Z/H $\to \mathrm{b} \mathrm{\bar{b}}$ or are not well reconstructed. The red hatched bands correspond to the statistical uncertainty in the background.
png pdf	Figure 5: The percentage of simulated $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) signal events that satisfy the baseline event selection requirements as well as the DNN and mass requirements in bins defined by the reconstructed AK8 jet ${p_{\mathrm {T}}}$ ( $x$ axis) and simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ ( $y$ axis). The rightmost and uppermost bins are unbounded. The value of each bin is the ratio of the event yield in the bin to the total number of simulated signal events with a simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ in the same $y$ -axis bin, including all decay modes of the top quark, Z boson, and Higgs boson. The color scale to the right shows the meaning of the histogram colors.
png pdf	Figure 5-a: The percentage of simulated $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) signal events that satisfy the baseline event selection requirements as well as the DNN and mass requirements in bins defined by the reconstructed AK8 jet ${p_{\mathrm {T}}}$ ( $x$ axis) and simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ ( $y$ axis). The rightmost and uppermost bins are unbounded. The value of each bin is the ratio of the event yield in the bin to the total number of simulated signal events with a simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ in the same $y$ -axis bin, including all decay modes of the top quark, Z boson, and Higgs boson. The color scale to the right shows the meaning of the histogram colors.
png pdf	Figure 5-b: The percentage of simulated $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) signal events that satisfy the baseline event selection requirements as well as the DNN and mass requirements in bins defined by the reconstructed AK8 jet ${p_{\mathrm {T}}}$ ( $x$ axis) and simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ ( $y$ axis). The rightmost and uppermost bins are unbounded. The value of each bin is the ratio of the event yield in the bin to the total number of simulated signal events with a simulated ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ in the same $y$ -axis bin, including all decay modes of the top quark, Z boson, and Higgs boson. The color scale to the right shows the meaning of the histogram colors.
png pdf	Figure 6: Postfit expected (solid histograms) and observed (points) yields for the 2016 (upper), 2017 (middle), and 2018 (lower) data-taking periods in each analysis bin. In the fit, the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H signal cross sections are fixed to the SM predictions. The analysis bins are defined as functions of the DNN score, and the ${p_{\mathrm {T}}}$ and ${m_\text {SD}}$ of the boson candidate AK8 jet. The largest three groupings of bins in each year are defined by the AK8 jet ${p_{\mathrm {T}}}$ . The next six groups are defined by the DNN score, and the smallest groups of three or four bins with the same ${p_{\mathrm {T}}}$ and DNN score correspond to the AK8 jet ${m_\text {SD}}$ . The vertical bars on the points show the statistical uncertainty in the data. The lower panels in each plot give the ratio of the data to the sum of the MC predictions, with the red band representing the total uncertainty in the MC prediction.
png pdf	Figure 6-a: Postfit expected (solid histograms) and observed (points) yields for the 2016 (upper), 2017 (middle), and 2018 (lower) data-taking periods in each analysis bin. In the fit, the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H signal cross sections are fixed to the SM predictions. The analysis bins are defined as functions of the DNN score, and the ${p_{\mathrm {T}}}$ and ${m_\text {SD}}$ of the boson candidate AK8 jet. The largest three groupings of bins in each year are defined by the AK8 jet ${p_{\mathrm {T}}}$ . The next six groups are defined by the DNN score, and the smallest groups of three or four bins with the same ${p_{\mathrm {T}}}$ and DNN score correspond to the AK8 jet ${m_\text {SD}}$ . The vertical bars on the points show the statistical uncertainty in the data. The lower panels in each plot give the ratio of the data to the sum of the MC predictions, with the red band representing the total uncertainty in the MC prediction.
png pdf	Figure 6-b: Postfit expected (solid histograms) and observed (points) yields for the 2016 (upper), 2017 (middle), and 2018 (lower) data-taking periods in each analysis bin. In the fit, the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H signal cross sections are fixed to the SM predictions. The analysis bins are defined as functions of the DNN score, and the ${p_{\mathrm {T}}}$ and ${m_\text {SD}}$ of the boson candidate AK8 jet. The largest three groupings of bins in each year are defined by the AK8 jet ${p_{\mathrm {T}}}$ . The next six groups are defined by the DNN score, and the smallest groups of three or four bins with the same ${p_{\mathrm {T}}}$ and DNN score correspond to the AK8 jet ${m_\text {SD}}$ . The vertical bars on the points show the statistical uncertainty in the data. The lower panels in each plot give the ratio of the data to the sum of the MC predictions, with the red band representing the total uncertainty in the MC prediction.
png pdf	Figure 6-c: Postfit expected (solid histograms) and observed (points) yields for the 2016 (upper), 2017 (middle), and 2018 (lower) data-taking periods in each analysis bin. In the fit, the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H signal cross sections are fixed to the SM predictions. The analysis bins are defined as functions of the DNN score, and the ${p_{\mathrm {T}}}$ and ${m_\text {SD}}$ of the boson candidate AK8 jet. The largest three groupings of bins in each year are defined by the AK8 jet ${p_{\mathrm {T}}}$ . The next six groups are defined by the DNN score, and the smallest groups of three or four bins with the same ${p_{\mathrm {T}}}$ and DNN score correspond to the AK8 jet ${m_\text {SD}}$ . The vertical bars on the points show the statistical uncertainty in the data. The lower panels in each plot give the ratio of the data to the sum of the MC predictions, with the red band representing the total uncertainty in the MC prediction.
png pdf	Figure 7: The observed best fit values (diamond) and SM predictions (star) for the signal strength modifiers $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{H}}}$ versus $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{Z}}}$ for generator-level ${p_{\mathrm {T}}} ^{\mathrm{H}}$ or ${p_{\mathrm {T}}} ^{\mathrm{Z}} >$ 200 GeV. The solid blue and dashed red contours show the 68 and 95% CL regions, respectively.
png pdf	Figure 8: Observed and expected 95% CL upper limits on the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) differential cross sections as a function of the simulated Z and Higgs boson ${p_{\mathrm {T}}}$ . The green and yellow bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits under the SM hypothesis. The black lines represent the observed 95% CL upper limits. The magenta band shows the SM predicted differential cross sections with the PDF + ${\alpha _\mathrm {S}}$ and scale uncertainties. The lower panel shows the ratio of the observed and expected upper limits on the differential cross sections to the SM differential cross sections. The last bin is unbounded.
png pdf	Figure 8-a: Observed and expected 95% CL upper limits on the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) differential cross sections as a function of the simulated Z and Higgs boson ${p_{\mathrm {T}}}$ . The green and yellow bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits under the SM hypothesis. The black lines represent the observed 95% CL upper limits. The magenta band shows the SM predicted differential cross sections with the PDF + ${\alpha _\mathrm {S}}$ and scale uncertainties. The lower panel shows the ratio of the observed and expected upper limits on the differential cross sections to the SM differential cross sections. The last bin is unbounded.
png pdf	Figure 8-b: Observed and expected 95% CL upper limits on the $\mathrm{t\bar{t}}$ Z (left) and $\mathrm{t\bar{t}}$ H (right) differential cross sections as a function of the simulated Z and Higgs boson ${p_{\mathrm {T}}}$ . The green and yellow bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits under the SM hypothesis. The black lines represent the observed 95% CL upper limits. The magenta band shows the SM predicted differential cross sections with the PDF + ${\alpha _\mathrm {S}}$ and scale uncertainties. The lower panel shows the ratio of the observed and expected upper limits on the differential cross sections to the SM differential cross sections. The last bin is unbounded.
png pdf	Figure 9: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-a: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-b: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-c: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-d: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-e: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-f: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-g: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 9-h: Observed (solid black) and expected (dotted red) scans of the negative log-likelihood as a function of each of the eight WCs when the seven other WCs are fixed to their SM values. The 68 and 95% CL intervals are indicated by thin gray lines.
png pdf	Figure 10: The observed 68 and 95% CL intervals for the WCs are shown by the thick and thin bars, respectively. The intervals are found by scanning over a single WC while either profiling the other seven WCs (black) or fixing them to the SM value of zero (red).
png pdf	Figure 11: Observed two-dimensional scans of the negative log-likelihood as a function of two of the eight WCs when all other WCs are fixed to their SM values. The three pairs of WCs scanned have the three largest observed correlation coefficients among all pairs. They are ${c_{\varphi \mathrm{t}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper left), ${c^{3}_{\varphi \mathrm {Q}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper right), and ${c_{\mathrm{t} \mathrm{W}}}$ versus ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The 68, 95, and 99.7% CL intervals are indicated by the solid blue, dashed red, and dotted orange lines, respectively.
png pdf	Figure 11-a: Observed two-dimensional scans of the negative log-likelihood as a function of two of the eight WCs when all other WCs are fixed to their SM values. The three pairs of WCs scanned have the three largest observed correlation coefficients among all pairs. They are ${c_{\varphi \mathrm{t}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper left), ${c^{3}_{\varphi \mathrm {Q}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper right), and ${c_{\mathrm{t} \mathrm{W}}}$ versus ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The 68, 95, and 99.7% CL intervals are indicated by the solid blue, dashed red, and dotted orange lines, respectively.
png pdf	Figure 11-b: Observed two-dimensional scans of the negative log-likelihood as a function of two of the eight WCs when all other WCs are fixed to their SM values. The three pairs of WCs scanned have the three largest observed correlation coefficients among all pairs. They are ${c_{\varphi \mathrm{t}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper left), ${c^{3}_{\varphi \mathrm {Q}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper right), and ${c_{\mathrm{t} \mathrm{W}}}$ versus ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The 68, 95, and 99.7% CL intervals are indicated by the solid blue, dashed red, and dotted orange lines, respectively.
png pdf	Figure 11-c: Observed two-dimensional scans of the negative log-likelihood as a function of two of the eight WCs when all other WCs are fixed to their SM values. The three pairs of WCs scanned have the three largest observed correlation coefficients among all pairs. They are ${c_{\varphi \mathrm{t}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper left), ${c^{3}_{\varphi \mathrm {Q}}}$ versus ${c^{-}_{\varphi \mathrm {Q}}}$ (upper right), and ${c_{\mathrm{t} \mathrm{W}}}$ versus ${c_{\mathrm{t} \mathrm{Z}}}$ (lower). The 68, 95, and 99.7% CL intervals are indicated by the solid blue, dashed red, and dotted orange lines, respectively.
png pdf	Figure 12: Observed 95% CL intervals for the WCs. The intervals are found by scanning over a single WC while fixing the other seven to zero. For comparison, we also show the corresponding 95% CL intervals from Refs. [16,25,27,28], which used events with multiple leptons or photons. The intervals for several of the WCs would be too small to see clearly, and so we have increased their size by the factor given in the label on the left edge of the figure.
png pdf	Figure A1: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-a: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-b: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-c: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-d: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-e: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.
png pdf	Figure A1-f: Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table A.1. These distributions represent the combined 2016-2018 data-taking periods. The hatched bands represent the total statistical and systematic uncertainty in the expected distributions, while the vertical bars on the black points indicate the statistical uncertainty in the observed distributions and the horizontal bars indicate the bin widths. The lower panels show the ratio of the observed yields to the sum of the MC predictions.

Tables
png pdf	Table 1: The set of EFT operators considered in this analysis that affect the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H processes at order $1/\Lambda ^2$ . The couplings are restricted to involve only third-generation quarks. The symbol $\gamma ^\mu$ denotes the Dirac matrices and $\sigma ^{\mu \nu} \equiv i \left (\gamma ^\mu \gamma ^\nu - g^{\mu \nu}\right)$ , where $g^{\mu \nu}$ is the metric tensor and $\tau ^\mathrm {I}$ are the Pauli matrices. The field $\varphi$ is the Higgs boson doublet and $\tilde{\varphi}^\mathrm {j} \equiv \varepsilon _\mathrm {jk} \left (\varphi ^\mathrm {k}\right)^*$ , where $\varepsilon _\mathrm {jk}$ is the Levi-Civita symbol and $\varepsilon _{12} = +$ 1. The quark doublet and the right-handed quark singlets are represented by q, u, and d, respectively. The quantities ${(\varphi^\dagger i\!\overleftrightarrow{D}_{\!\!\mu}\varphi)} \equiv \varphi ^\dagger (iD_\mu \varphi)-(iD_\mu \varphi ^\dagger)\varphi$ and ${(\varphi^\dagger i\!\overleftrightarrow{D}^\mathrm{I}_{\!\!\mu}\varphi)} \equiv \varphi ^{\dagger}\tau ^\mathrm {I}(iD_\mu \varphi)-(iD_\mu \varphi ^\dagger)\tau ^\mathrm {I}\varphi$ , where $D_{\mu}$ is the covariant derivative. The symbols $\mathrm{W} _{\mu \nu}^\mathrm {I}$ and $\mathrm{B} _{\mu \nu}$ are the field strength tensors for the weak isospin and weak hypercharge gauge fields. The abbreviations ${\mathcal {S}_{\mathrm {W}}}$ and ${\mathcal {C}_{\mathrm {W}}}$ denote the sine and cosine of the weak mixing angle in the unitary gauge, respectively. The operators marked with the $\ddagger$ symbol also require their Hermitian conjugate in the Lagrangian.
png pdf	Table 2: Summary of the reconstructed object and event selection requirements.
png pdf	Table 3: The observed and expected best fit ( $\pm$ 1 standard deviation) signal strength modifiers $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{Z}}}$ and $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{H}}}$ for simulated ${p_{\mathrm {T}}} ^{\mathrm{Z}}$ or ${p_{\mathrm {T}}} ^{\mathrm{H}} >$ 200 GeV. The observed uncertainties are broken down into the components arising from the limited size of the data, the limited size of the simulation samples, experimental uncertainties, and theoretical uncertainties.
png pdf	Table 4: The magnitudes of the major sources of systematic uncertainty in the measurement of the signal strength modifiers $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{Z}}}$ and $\mu _{{{\mathrm{t} \mathrm{\bar{t}}} \mathrm{H}}}$ for simulated ${p_{\mathrm {T}}} ^{\mathrm{Z}}$ or ${p_{\mathrm {T}}} ^{\mathrm{H}} >$ 200 GeV.
png pdf	Table 5: Observed and median expected 95% CL upper limits on the $\mathrm{t\bar{t}}$ Z and $\mathrm{t\bar{t}}$ H differential cross sections and on their ratios to the SM predictions for three ${p_{\mathrm {T}}} ^{\mathrm{Z} /\mathrm{H}}$ intervals. The range given with the median expected 95% CL upper limits indicates the range in which 68% of the upper limits are expected to fall, assuming the SM hypothesis.
png pdf	Table 6: Observed 95% CL intervals for the eight WCs in the EFT model. The intervals are determined by scanning over a single WC while either profiling the other seven WCs or fixing them to their SM value of zero.
png pdf	Table A1: Comprehensive list of the input variables of the DNN, which is described in Section 6. The "+'' represents the relativistic four-momentum sum. Some variables are calculated for both the highest ${p_{\mathrm {T}}}$ (leading) and second-highest ${p_{\mathrm {T}}}$ (subleading) jet as indicated.

Summary

Measurements of the signal strengths and 95% confidence level upper limits on the differential cross sections for production of

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H events, where H refers to the Higgs boson, are presented along with constraints on the Wilson coefficients of a leading-order effective field theory. The analysis is performed using the

$\mathrm{b\bar{b}}$ decay mode of the Z or Higgs boson and the lepton plus jets channel of the associated

$\mathrm{t\bar{t}}$ pair. The Z or Higgs boson is required to be Lorentz boosted, with transverse momentum

${p_{\mathrm{T}}} >$ 200 GeV. A deep neural network is employed to discriminate between the

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H signal events and the background, which is dominated by

$\mathrm{t\bar{t}}{+}$ jets production. The data correspond to an integrated luminosity of 138 fb

$^{-1}$ collected with the CMS detector at the CERN LHC from 2016 through 2018. The data are binned as a function of the deep neural network score and the reconstructed

${p_{\mathrm{T}}}$ and mass of the Z or Higgs boson. Binned maximum likelihood fits are employed to extract the observables from the data.

The data are found to be consistent with the expectations from the standard model. The signal strength modifiers for boosted

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H production are measured to be

$\mu_{{\mathrm{t\bar{t}}\mathrm{Z}} } =$ 0.65

$^{+1.04}_{-0.98}$ and

$\mu_{{\mathrm{t\bar{t}}\mathrm{H}} } =$ -0.27

$^{+0.86}_{-0.83}$ , which are both consistent with the expected value, 1. The 95% confidence level upper limits on the differential

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H cross sections range from 2 to 5 times the standard model predicted cross sections for Z or Higgs boson

${p_{\mathrm{T}}} >$ 300 GeV. Results are also presented on eight parameters of a leading-order effective field theory that have a large impact on boosted

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H production. These results represent the most restrictive limits to date on the cross sections for the production of

$\mathrm{t\bar{t}}$ Z and

$\mathrm{t\bar{t}}$ H with Z or Higgs boson

${p_{\mathrm{T}}} >$ 450 GeV. The limits on the Wilson coefficients in the effective field theory are consistent and, in some cases, competitive with the best previous limits.

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