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

A data sample containing top quark pairs ($t\overline{t}$) 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 $138{\mathrm{fb}}^{-1}$ 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 $t\overline{t}Z$ or $t\overline{t}H$ events and events from background processes, which are dominated by $t\overline{t}+\text{jets}$ production. No indications of new physics are observed. The signal strengths of boosted $t\overline{t}Z$ and $t\overline{t}H$ production are measured, and upper limits are placed on the $t\overline{t}Z$ and $t\overline{t}H$ 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.

Figure 1

Examples of tree-level Feynman diagrams for the $t\overline{t}Z$ (left) and $t\overline{t}H$ (right) production processes.

Figure 2

The $t\overline{t}Z$ (upper) and $t\overline{t}H$ (lower) cross sections in the SM EFT, as ratios to the corresponding SM cross sections, as functions of $c_{tZ}/{\mathrm{\Lambda }}^2$ and the $Z$ boson $p_{\mathrm{T}}$ (upper), and $c_{\phi tb}/{\mathrm{\Lambda }}^2$ and the Higgs boson $p_{\mathrm{T}}$ (lower), where $c_{tZ}$ and $c_{\phi tb}$ are the WCs for the EFT operators $O_{uB}^{(\mathrm{ij})}$ and $O_{\phi ud}^{(\mathrm{ij})}$, respectively [7]. Example Feynman diagrams, in which the vertices affected by $c_{tZ}$ and $c_{\phi tb}$ are marked by a filled dot, are also displayed.

Figure 3

The simulated DNN score distributions, normalized to unit area, for well-reconstructed $t\overline{t}Z$ and $t\overline{t}H$ 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 $t\overline{t}Z$ and $t\overline{t}H$ events, background events from $t\overline{t}+b\overline{b}$, and background events from $t\overline{t}+c\overline{c}$ and $t\overline{t}+\mathrm{LF}$. The events satisfy the baseline selection requirements described in Sec. 5 and contain a $Z$ or Higgs boson candidate with $p_{\mathrm{T}}>300\mathrm{GeV}$.

Figure 4

Soft-drop mass distributions from simulation for background (solid histograms) and signal (dashed histograms) of $Z/H\to b\overline{b}$ candidate jets in three $p_{\mathrm{T}}$ ranges: 200–300 GeV (upper), 300–450 GeV (middle), and $>450\mathrm{GeV}$ (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 $t\overline{t}Z$ and $t\overline{t}H$ events as well as $t\overline{t}Z$ and $t\overline{t}H$ events that either do not contain $Z/H\to b\overline{b}$ or are not well reconstructed. The red hatched bands correspond to the statistical uncertainty in the background.

Figure 5

The percentage of simulated $t\overline{t}Z$ (upper) and $t\overline{t}H$ (lower) 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 $p_{\mathrm{T}}^{Z/H}$ ($y$ 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 $p_{\mathrm{T}}^{Z/H}$ 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.

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 $t\overline{t}Z$ and $t\overline{t}H$ 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 $m_{\mathrm{SD}}$ 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 $m_{\mathrm{SD}}$. 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.

Figure 7

The observed best fit values (diamond) and SM predictions (star) for the signal strength modifiers ${\mu }_{t\overline{t}H}$ versus ${\mu }_{t\overline{t}Z}$ for generator-level $p_{\mathrm{T}}^H$ or $p_{\mathrm{T}}^Z>200\mathrm{GeV}$. The solid blue and dashed red contours show the 68% and 95% CL regions, respectively.

Figure 8

Observed and expected 95% CL upper limits on the $t\overline{t}Z$ (left) and $t\overline{t}H$ (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 $\mathrm{PDF}+{\alpha }_{\mathrm{S}}$ 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.

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.

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).

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 $c_{\phi t}$ versus $c_{\phi Q}^{-}$ (upper left), $c_{\phi Q}^3$ versus $c_{\phi Q}^{-}$ (upper right), and $c_{tW}$ versus $c_{tZ}$ (lower). The 68%, 95%, and 99.7% CL intervals are indicated by the solid blue, dashed red, and dotted orange lines, respectively.

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.

Figure 13

Prefit expected (colored histograms) and observed (point) distributions of selected DNN input variables, each of which is described in detail in Table 7. 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.