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 ($\mathrm{t\bar{t}}$) 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.


Introduction
The standard model (SM) of particle physics successfully describes a vast range of subatomic phenomena with outstanding precision. However, it cannot explain the existence of dark matter [1][2][3] and faces other difficulties, such as the fine-tuning or hierarchy problem [4,5]. This indicates that the SM is incomplete and may be only a low-energy approximation, which is valid at the energies currently accessible to experiments, to a more fundamental theory. Null results from direct searches for new particles predicted by various models of physics beyond the SM (BSM) suggest that such new particles may be too massive to be produced at the CERN LHC.
The signatures of BSM physics arising from high-mass particles, which may not be directly accessible at the LHC, could appear indirectly in the form of deviations from the SM predictions for production of SM particles. All possible high-energy-scale deviations from the SM can be described at low energy scales by the SM effective field theory (EFT) [6][7][8]. This EFT extends the SM Lagrangian L SM with operators O Because of the 1/Λ d−4 suppression of non-SM terms, the lowest-dimension operators are the most likely to have measurable effects. Dimension-five operators produce lepton-number violation [9,10], which is strongly constrained [11], so this analysis only considers dimension-six operators [12].
The impact of these operators may be detectable in a wide variety of experimental observables. This analysis searches for BSM effects on the production of a pair of top quarks (tt) in association with a Z boson or Higgs boson (H). These processes are particularly interesting, as they provide direct access to the couplings of the top quark to the Z and Higgs bosons. Any deviations of these couplings from their SM values might imply the existence of BSM effects in the electroweak symmetry breaking mechanism, which could be probed in an EFT framework. The ttZ and ttH processes ( Fig. 1) are challenging to measure with high precision because of their low production cross sections. However, with the large amount of data delivered by the LHC, the ATLAS and CMS Collaborations have measured the ttZ [13-16] and ttH [17-24] cross sections with a relative uncertainty of 8 and 20%, respectively. Many of these measurements, especially of ttZ, have been performed in final states containing multiple charged leptons. Additionally, an extensive exploration of EFT effects in collisions producing tt in association with a W, Z, or Higgs boson has been performed by the CMS Collaboration, also in final states containing multiple charged leptons [25]. Other recent analyses have constrained the WCs φud , respectively [7]. Example Feynman diagrams, in which the vertices affected by c tZ and c φtb are marked by a filled dot, are also displayed.
The fraction of ttZ and ttH events whose decay products include a single lepton is much larger than for multiple leptons, but the large background from tt produced in association with multiple jets from quantum chromodynamic (QCD) processes (tt + jets) makes measurements in single-lepton final states extremely challenging. However, at high Z or Higgs boson transverse momentum (p T ), where EFT effects are generally more pronounced, as shown in Fig. 2, we can utilize jet substructure techniques to identify Z/H → bb decays that are reconstructed as a single merged jet, and suppress the tt + jets background. In this analysis, we probe EFT effects in ttZ and ttH events with a single lepton from the decay of one of the top quarks and a high-p T Z or Higgs boson decaying to bb.
We identify high-p T Z or Higgs bosons decaying to bb using a large-radius jet, described below, which is identified using a machine learning technique as being consistent with the decay of a heavy boson to bb. The top quark pair is identified using the combination of a single electron or muon, moderate missing transverse momentum (p miss T , defined below), at least two small-radius jets identified as originating from bottom quarks, which must be well separated from the large-radius Z or Higgs boson jet, and additional small-radius jets to account for the hadronically decaying W boson. A neural network is used to separate signal-like events from the dominant tt + jets background, and the reconstructed mass of the large-radius jet serves to distinguish ttZ and ttH events from each other, as well as from the background. A global fit to the data measures the signal strengths of the ttZ and ttH processes. We also place upper limits on the ttZ and ttH differential cross sections as functions of the p T of the Z boson (p Z T ) and of the Higgs boson (p H T ), and constrain the WCs corresponding to EFT operators that most strongly affect boosted ttZ and ttH topologies.
In this paper, we briefly describe the CMS detector in Section 2 and the Monte Carlo simulation of the signals and backgrounds in Section 3. Sections 4 and 5 discuss the reconstruction of particles and selection of events, respectively, while Section 6 and Appendix A describe the neural network used to separate signal-like events from the backgrounds. In Sections 7 and 8, we detail the sources of systematic uncertainty in our measurements and present the results of those measurements. Lastly, a summary is provided in Section 9. Tabulated results are provided in the HEPData record for this analysis [29].

The CMS detector
The CMS detector is a general-purpose particle detector at the LHC. It is centered on a luminous region where the LHC beams interact and is roughly symmetric under rotations around the beam direction. The inner detector is contained within a 3.8 T magnetic field produced by a 6 m internal diameter solenoid, and is composed of silicon pixel and silicon strip tracking detectors as well as a lead tungstate crystal electromagnetic calorimeter (ECAL) and a brass and scintillator hadron calorimeter. Each component of the inner detector is in turn divided into a cylindrical barrel section and two endcap sections. The magnetic flux from the solenoid is guided through a steel return yoke. Gas-ionization detectors embedded in the flux-return yoke are used to detect muons.
Events are collected using a two-tier trigger system: a hardware-based level-1 trigger [30] and a software-based high-level trigger [31]. The CMS detector is described in more detail along with the coordinate system and basic kinematic variables in Ref. [32].

Data and simulation samples
This analysis is performed using proton-proton (pp) collision data recorded at √ s = 13 TeV at the LHC corresponding to an integrated luminosity of 138 fb −1 , of which 36.3, 41.5, and 59.7 fb −1 were recorded in 2016, 2017, and 2018, respectively [33][34][35]. The data and simulation samples from these three years are treated separately to account for variations in the detector and LHC conditions. The data were recorded using combinations of triggers that require a single electron or muon candidate [31]. The minimum trigger p T thresholds range from 27 to 32 GeV for electrons and from 24 to 27 GeV for muons, depending on the data-taking period.
Monte Carlo (MC) simulation is used to model signal and background events. For the ttZ and ttH signals, and for the subset of tt events containing at least one b hadron that does not originate from a top quark decay (tt + bb), two sets of MC samples are used: one set is generated at next-to-leading order (NLO) in perturbative QCD, and the other set is generated at leading order (LO) in QCD with weights corresponding to a range of WC values, representing various BSM scenarios in the SM EFT. The NLO samples (referred to as "SM samples") are used to model the expected ttZ, ttH, and tt + bb contributions, while the LO samples with EFT weights ("EFT samples") are used to evaluate EFT effects relative to the SM predictions. The MADGRAPH5 aMC@NLO v2.6.0 program [36] is employed to generate the ttZ SM signal samples, while the ttH SM signal samples are generated with the POWHEG v2.0 [37][38][39][40] program. The SM ttZ signal sample is normalized to a production cross section of 0.86 pb, which is computed at NLO with next-to-next-to-leading logarithmic (NNLL) resummation in QCD [41]. Similarly, the SM ttH signal sample is normalized to a production cross section of 0.507 pb, which is computed at NLO in QCD and electroweak corrections [42] when its SM predictions are presented.
The dominant background arises from tt production. Simulated tt events are separated into three flavor categories. These categories are based on the flavor of additional jets at the particle level that do not originate from the top quark decays and that have p T > 20 GeV and pseudorapidity |η| < 2.4: tt + bb consists of events with at least one b hadron that does not originate from a top quark decay; tt + cc consists of events with at least one additional jet that origi- The simulated events are processed through a GEANT4-based [68] simulation of the CMS detector, including the effects of additional pp interactions per bunch crossing, referred to as pileup. The events are reweighted to match the estimated pileup distribution in data, based on the measured instantaneous luminosity.

Simulation of EFT samples
This analysis considers eight dimension-six EFT operators in the Warsaw basis [7] that have a large impact on the ttZ and ttH signal processes and minimal impacts on the background predictions. Table 1 lists the eight operators and corresponding WCs. All couplings are restricted to involve only third-generation quarks because first-and second-generation couplings have been strongly constrained by other analyses and because the ttZ and ttH processes are Table 1: The set of EFT operators considered in this analysis that affect the ttZ and ttH processes at order 1/Λ 2 . The couplings are restricted to involve only third-generation quarks. The symbol γ µ denotes the Dirac matrices and σ µν ≡ i (γ µ γ ν − g µν ), where g µν is the metric tensor and τ I are the Pauli matrices. The field φ is the Higgs boson doublet andφ j ≡ ε jk φ k * , where ε jk is the Levi-Civita symbol and ε 12 = +1. The quark doublet and the right-handed quark singlets are represented by q, u, and d, respectively. The quantities where D µ is the covariant derivative. The symbols W I µν and B µν are the field strength tensors for the weak isospin and weak hypercharge gauge fields. The abbreviations S W and C W denote the sine and cosine of the weak mixing angle in the unitary gauge, respectively. The operators marked with the ‡ symbol also require their Hermitian conjugate in the Lagrangian.
uniquely sensitive to third-generation couplings. The operators that also require their Hermitian conjugate term in the Lagrangian (marked with ‡ in Table 1) can have complex WCs; however, imaginary coefficients lead to charge-conjugation and parity violation, and are generally already constrained [12]. Therefore, following a similar strategy to that used in an earlier CMS analysis [25], only the eight real-component WCs in Table 1 are considered in this analysis.
Samples with EFT effects are generated for the ttZ and ttH signal processes and the tt + bb background using the MADGRAPH5 aMC@NLO v2.6.5 event generator at LO and the NNPDF3.1 NNLO PDF set, following a similar approach to that outlined in Ref. [12]. The EFT effects on the decay of the top quark and the Z and Higgs bosons are expected to be negligible, and are not considered. As is done for the SM samples, the EFT samples are processed through a GEANT4-based [68] simulation of the CMS detector, and event reconstruction is performed in the same manner as for the collision data. Samples of tt + LF and tt + cc background events are also generated with EFT effects, and no observable variations are seen for the eight operators considered. The tt + bb sample shows a nonnegligible EFT effect when varying c bW , which is accounted for in the analysis. The ttZ and ttH signal samples are generated with up to one extra parton in the final state. This improves the precision of the simulation, bringing it closer to NLO in QCD [25,69]. The EFT effects from this approach are found to be compatible with those from the SMEFT@NLO model [70] for the dimension-six operators included in SMEFT@NLO [69].
In the EFT samples, the effects of varying the eight WCs are computed as a weighting factor for each simulated event. The weight w EFT for each event is parameterized as a quadratic function of the eight WCs: where s 0 is the weight arising only from SM processes, subscripts i and j are indices for WCs under consideration, s 1i is the coefficient for the term arising from the interference between one EFT operator and the SM, and s 2ij is the coefficient for the term arising from interference between two EFT operators (for i ̸ = j) or for the term arising solely from one EFT operator (for i = j). In the SM, where all WCs are zero, w EFT is equal to s 0 .

Event reconstruction
Collisions in the CMS detector are reconstructed using the particle-flow (PF) algorithm [71]. This algorithm exploits information from every subsystem of the detector and produces candidate reconstructed objects (PF candidates) in several categories: charged and neutral hadrons, photons, electrons, and muons. The PF candidates are used, in various combinations, to reconstruct higher-level objects such as interaction vertices, hadronic jets, and the ⃗ p miss T . This section describes the reconstruction of the objects that are used in this analysis.
The ⃗ p miss T vector, which is used to estimate the summed ⃗ p T of neutrinos in the event, is defined as the negative vector sum of the ⃗ p T of all PF candidates in the event [72]. Its magnitude is denoted by p miss T . An interaction vertex is a point from which multiple tracks in one event originate. The primary vertex (PV) is taken to be the interaction vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref.
[73]. All selected objects in this analysis must be associated with the PV.
Electron candidates are reconstructed and identified by combining information from the ECAL and the tracking system [74], and they are required to have |η| < 2.5 and p T > 30 (35) GeV for 2016 (2017 and 2018). The variation of the electron candidate p T requirement is related to a change in the electron trigger between 2016 and 2017. Muon candidates are reconstructed as tracks in the silicon tracking system consistent with measurements in the muon system, and associated with calorimeter deposits compatible with the muon hypothesis [75]. Muon candidates are required to have |η| < 2.4 and p T > 30 GeV. Electron and muon candidates are required to be isolated from surrounding hadronic activity and to be consistent with an origin at the PV.
The electron and muon isolation requirement is based on the mini-isolation variable I mini , which is defined as the scalar sum of the p T of all charged hadron, neutral hadron, and photon PF candidates within a variably sized cone around the electron or muon candidate direction [76]. The cone radius ∆R = (∆η) 2 + (∆ϕ) 2 is 10 GeV divided by the lepton p T within the range 50 < p T < 200 GeV. For leptons with p T < 50 GeV (>200 GeV), we use ∆R = 0.2 (0.05). The mini-isolation variable is corrected for contributions from pileup using estimates of the charged and neutral pileup energy inside the cone [74, 75]. Electron and muon candidates are required to have I mini /p T < 0.2 and 0.1, respectively. The overall trigger efficiency, measured in a control region requiring one electron and one muon, is around 86% (87%) for events with an electron (muon) that satisfies these selection criteria.
Two types of jets, small-radius ("AK4") and large-radius ("AK8"), are used in this analysis. Both are reconstructed by clustering charged and neutral PF candidates using the anti-k T jet finding algorithm [77,78], with distance parameters of 0.4 and 0.8, respectively.
The AK4 jets use charged-hadron subtraction [79] for pileup mitigation and are required to have p T > 30 GeV and |η| < 2.4. The AK8 jets use the pileup per particle identification algorithm [79,80] to reduce the effects of pileup and are required to have p T > 200 GeV, |η| < 2.4, and an invariant mass between 50 and 200 GeV. The invariant mass of each AK8 jet, m SD , is calculated using the soft-drop algorithm [81,82] with an angular exponent β = 0 and soft cutoff threshold z cut = 0.1. This algorithm systematically removes soft and collinear radiation from the jet. Its performance in collision data is validated in Ref. [83].
Jet quality criteria [79] are imposed to eliminate jets from spurious sources such as electronics noise. The jet energies are corrected for residual pileup effects [84] and the detector response as a function of p T and η [85]. All jets are required to be separated from the selected electron or muon candidate by ∆R > 0.4 or 0.8 for AK4 and AK8 jets, respectively. Selected AK4 jets may overlap spatially with selected AK8 jets, and may use the same PF candidates.
Jets originating from the hadronization of bottom quarks (b jets) are identified (b tagged) using a secondary-vertex algorithm based on a deep neural network (DEEPCSV) [86]. The "medium" working point of this algorithm is used, which provides a tagging efficiency of 68% for typical b jets from top quark decays [86]. The corresponding misidentification probability for lightflavor jets, which contain only light-flavor hadrons and originate from gluons and up, down, and strange quarks, is 1%, and for charm quark jets (c jets) it is 12% [86].
When a Z or Higgs boson is produced with a large Lorentz boost, its decay products will be collimated and may be reconstructed as a single AK8 jet. We employ a multivariate discriminant to identify AK8 jets containing the decay products from a bb pair. This discriminant is based on a dedicated deep neural network algorithm, the DEEPAK8 bb tagger [83], which is uncorrelated with m SD . By combining the tagger output and m SD , we can identify jets consistent with Z → bb and H → bb decays and use the m SD regions away from the Z and Higgs boson masses as background-enriched control regions. The bb tagger produces a score between 0 and 1. The selected AK8 jet with the largest score in each event is identified as the Z or Higgs boson candidate, provided that the score is greater than 0.8. This bb tagger score requirement together with the m SD requirement produces a bb tagging efficiency of 45-70% for Z → bb decays and 25-60% for H → bb decays, depending on the p T of the AK8 jet. These efficiencies in ttZ and ttH events are affected by contamination from top quark decay products, which is less prominent in ttZ events than in ttH events because the Z boson tends to be better separated from the top quarks. The misidentification rate is roughly 2.5% for jets from QCD multijet events.

Event selection
This analysis targets ttZ or ttH production, where the tt decay products include an electron or muon and a neutrino, plus two b quarks and two other quarks, and the Z or Higgs boson decays to a bb pair. We select events containing exactly one candidate electron or muon, p miss T > 20 GeV, five or more AK4 jets, and a Z or Higgs boson candidate AK8 jet. The electron or muon and the p miss T are expected to arise from the leptonic decay of a W boson. At least one (and sometimes two) of the AK4 jets spatially overlap the AK8 jet because the AK4 and AK8 jet clustering algorithms run independently with no unambiguous way to distinguish AK4 and AK8 jets that share some or all of of their constituent particles. Three or four AK4 jets, corresponding to the hadrons from the tt decay products, are expected to be well separated from the AK8 jet. At least two AK4 jets must be b tagged and separated from the Z or Higgs boson candidate jet by ∆R > 0.8. These requirements are summarized in Table 2.
To remove events with spurious p miss T , we use the event filters described in Ref. [72]. In addition, events in which the lepton candidate and a second lepton of the same flavor but opposite charge have an invariant mass less than 12 GeV are removed from the data set to eliminate leptons from =1 Z or Higgs boson candidate AK8 jet Highest bb tagger score (>0.8) ≥2 b-tagged AK4 jets Satisfy medium DEEPCSV b tag requirements ∆R(b-tagged AK4 jet, Z or Higgs boson candidate) > 0.8 J/ψ or Υ meson decay. This requirement, in combination with the p miss T threshold, is effective at significantly reducing the nonprompt-lepton background. The p T , isolation, and identification requirements are relaxed for the second lepton, because it typically has lower momentum than the primary lepton candidate. Lastly, we remove events that contain an electron PF candidate with p T > 20 GeV, −3 < η < −1.4, and −1.57 < ϕ < −0.87 during the latter part of 2018 because of a malfunction in that part of the hadron calorimeter.

Discrimination of signal against backgrounds
To separate boosted ttZ and ttH signal events from background, we use three discriminating variables: the p T and m SD of the reconstructed Z or Higgs boson candidate AK8 jet, and a global event neural network score. These variables allow us to define regions that are enriched in ttZ, regions that are enriched in ttH, and regions that are dominated by background but kinematically similar to the signal-dominated regions. The use of the boson candidate p T allows us to place upper limits on the ttZ and ttH cross sections differentially as functions of p Z T and p H T , respectively, and provides additional sensitivity to the effects of BSM physics.

Global Event Neural network
We train a deep neural network (DNN) to discriminate between simulated signal events and simulated tt + jets background events. The DNN has 50 input variables, two dense hidden layers, and an output layer consisting of three output nodes. The input variables describe the kinematic properties of reconstructed events and are chosen to provide discrimination power between ttZ or ttH and the tt + jets background, with an emphasis on discrimination against tt + bb events. All of the input variables are listed in Table A.1 in Appendix A, and a subset of the input variable distributions, consisting of variables that rank high in the mutual information feature importance metric [87,88], is shown in Fig. A.1. These distributions are used to verify that the input variables are well modeled. Correlations and nonlinear relationships among the input variables are also well understood, which we verify by comparing the expected and observed distributions of the outputs of the final hidden layer of the DNN.
The variables targeting top quark decays include the b tagger scores and jet p T values, the invariant masses of sets of two or three jets, and the spatial separation between pairs of jets or between jets and leptons. The AK8 jets originating from the decays of boosted Z or Higgs bosons are identified using the bb discriminant score, the number of b-tagged AK4 jets over-lapping the AK8 jet, and the separations between and invariant masses of the candidate AK8 jet and various leptons and jets presumed to come from the tt decay products. Global event variables, including summed p T , sphericity, and aplanarity [89], are calculated using the selected lepton and AK4 jet momenta and the ⃗ p miss T . We combat overtraining of the neural network by employing a batch normalization layer [90] and a dropout layer [91], and by evaluating the training with an independent validation data set, which is 60% of the size of the training data set.
This neural network is a multiclass classifier with three output nodes, each trained to identify a single class of events: ttZ and ttH signal, tt + bb background, and tt + LF and tt + cc background. Only well-reconstructed ttZ and ttH signal events are used in the training, i.e., the reconstructed Z or Higgs boson candidate is matched to both generator-level b quark daughters of the Z or Higgs boson with ∆R(AK8 jet, b) < 0.6. The three outputs for each event are scaled so that their sum is one. The focal loss function [92] is employed to balance the relative importance of the three classes of events during training despite an imbalance in the number of simulated events in each class.
Although multiple classes are used during training, only the signal-oriented output node is used in the analysis for the purpose of distinguishing background from signal. Even though they are not directly used, the two background-oriented nodes do affect the signal-oriented output via the scaling, and their presence improves the discrimination power compared to a binary-classification neural network. Figure 3 shows the DNN output score for well-reconstructed ttZ and ttH signal events, for ttZ and ttH events that either do not contain a Z or Higgs boson decaying to bb or are not well reconstructed, for tt + bb background events, and for tt + cc and tt + LF background events. The distributions of well-reconstructed signal events show strong separation from those of background events, especially tt + cc and tt + LF. All ttZ and ttH events, even those that either do not contain Z/H → bb or are not well reconstructed, are included as signal events in the analysis, even though they are separated in Fig. 3. Because our sensitivity to BSM effects is dominated by high-p T events, Fig. 3 only includes events with p Z/H T > 300 GeV.

Analysis bins
Data collected in 2016, 2017, and 2018 are treated separately, and are divided among bins based on the p T and m SD of the reconstructed Z or Higgs boson candidate and the DNN score. The DNN score provides signal-rich and background-rich regions, enhancing the sensitivity of the analysis. The m SD provides a region enriched in ttZ in the vicinity of the Z boson mass, a region enriched in ttH in the vicinity of the Higgs boson mass, and two sidebands with higher and lower m SD that are kinematically similar but depleted in ttZ and ttH signal. The sensitivity to BSM effects is enhanced at high p T , as shown in Fig. 2, so binning based on the reconstructed p T of the boson candidate improves the resulting constraints on the WCs.
Events from each year are divided among three bins based on the p T of the reconstructed Z or Higgs boson candidate: 200-300, 300-450, and >450 GeV, motivated by the simplified template cross section binning definition for ttH [42]. Within each p T range, events are assigned to one of six bins based on the DNN score. The DNN score binning is unique to each p T bin in each year, and is chosen so that the ttZ and ttH signal events are divided among six intervals bounded by 0, 5, 25, 35, 50, 70, and 100% of the total expected yield of well-reconstructed signal events, ordered from low to high DNN score.  The simulated DNN score distributions, normalized to unit area, for well-reconstructed ttZ and ttH 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 ttZ and ttH events; background events from tt + bb; and background events from tt + cc and tt + LF. The events satisfy the baseline selection requirements described in Section 5 and contain a Z or Higgs boson candidate with p T > 300 GeV. 105 < m SD < 200 GeV because of low signal and background yields. Figure 4 shows the m SD distributions of reconstructed Z or Higgs boson candidates in three p T ranges for simulated signal and background events. The 75 < m SD < 105 GeV bin provides a ttZ enriched region for all candidate AK8 jet p T values, while the 105 < m SD < 145 GeV bin is enriched in ttH for p T > 300 GeV. The ttH events with p T < 300 GeV do not show a clear peak in m SD around the Higgs boson mass, because its decay products are less likely to be fully contained in the AK8 jet. Binning using the boson candidate p T and m SD and the DNN score results in a total of 66 bins for each data-taking year.
When setting upper limits on the differential cross sections as functions of p Z T and p H T , the ttZ and ttH simulated signal samples are each divided into four subsamples according to the p T of the simulated Z or Higgs boson, respectively. The p Z T and p H T bins are 0-200, 200-300, 300-450, and >450 GeV. The three highest p T bins match the candidate AK8 jet p T bins, and are used to obtain the differential cross section results. In events that fall into the generator-level p Z/H T < 200 GeV bin, the Z or Higgs boson does not have sufficient boost to be reconstructed as a single AK8 jet. Therefore, the rate of those events is not treated as an unconstrained parameter, but rather is fixed to the SM expectation. For the measurement of the signal strengths of the ttZ and ttH processes with generator-level p Z/H T > 200 GeV, the subsample with generatorlevel p Z/H T < 200 GeV is fixed to the SM expectation, but it is unconstrained for the measurement of the WCs. Figure 5 shows the expected distribution of the candidate AK8 jet p T in each of the three highest p T subsamples of SM ttZ and ttH production for the subset of events that fall into the two or three highest DNN bins and have an AK8 jet mass consistent with Z or Higgs boson decay. These two-dimensional distributions serve as the folding matrices M ij , which describe the relationship between the simulated and reconstructed distributions, when    setting upper limits on the differential cross sections.

Systematic uncertainties
The systematic uncertainties in the measurements arise from theoretical and experimental sources and may affect both the overall rates of the signals and backgrounds, as well as the shapes of the templates used in the fit to the data. The systematic uncertainties are treated as nuisance parameters in the final fit to the data. Except where otherwise noted, the nuisance parameters are given Gaussian constraints in the fit. The theoretical uncertainties are all treated as fully correlated across the entire data-taking period, while some of the experimental uncertainties are treated independently in each data-taking year and others are fully correlated.
We account for the statistical uncertainty in the simulation caused by the finite size of the simulated data sets using the approach described in Refs. [93,94].

Theoretical uncertainties
The signal and background processes are scaled according to their expected cross sections, which are calculated at NLO or higher order as described in Section 3. The uncertainties in these cross sections arise from the choice of the renormalization (µ R ) and factorization scales (µ F ) as well as from uncertainty in the PDFs, including uncertainty in the value of the strong coupling constant α S used in the PDFs. The scales µ R and µ F are varied up and down by a factor of two, and the PDFs and α S are varied following the PDF4LHC prescription [95]. The resulting variation in the cross sections is treated as a set of nuisance parameters with lognormal constraints depending on the process and the initial state. These nuisance parameters only affect the overall yield of each process.
The choice of µ R and µ F scales, as well as the PDF, may also affect the simulation of the kinematic distributions of the particles in the final state. In the simulation of the matrix elements, the scales are varied up and down by a factor of two, and the PDF is varied within its uncertainties [95]. Similarly, the scales that control the amount of initial-and final-state radiation are varied up and down independently by a factor of two. Although the parton shower scale variations affect all processes, special handling is required for the tt + bb background. Variations in the parton shower scales affect the fraction of tt + bb events within the tt + jets background. The effect on the tt + bb yield is calculated within the tt + jets (5FS) MC sample and then propagated to the tt + bb (4FS) MC sample. Because the effect of these uncertainties on the overall yields has already been accounted for, these variations only affect the acceptance or the shape of the distributions in the inclusive phase space. This is treated as a set of nuisance parameters, depending again on the process and the initial state.
For the POWHEG samples, the matching between the matrix element and parton shower simulation of the tt + jets backgrounds is governed by the h damp parameter. The tt + jets backgrounds are simulated with h damp = 1.379m t , where m t is the mass of the top quark, and smaller simulated samples are produced with h damp = 0.874m t and h damp = 2.305m t to evaluate the effects of varying this parameter [64]. We treat this uncertainty as a nuisance parameter with a lognormal constraint that affects the overall yields of the tt + jets backgrounds.
Any remnants of the pp collision that do not participate in the hard-scattering process are referred to as the "underlying event". The simulation is tuned to reproduce the kinematic distributions of the underlying event [64]. The effects of the residual uncertainty in the tune are evaluated in separate simulations of the tt + jets backgrounds. The uncertainty in the underlyingevent tune is treated as a nuisance parameter with a log-normal constraint affecting the overall yields of the tt + jets backgrounds.
The cross section of the tt + bb background is treated as an unconstrained nuisance parameter. Moreover, the rate of the tt + 2b subset of the tt + bb background is varied by up to 50% because of the uncertainty in modeling the gluon fragmentation process [43].
The tt + cc production cross section has been measured with an uncertainty of approximately 20% [96]. However, we assume a larger uncertainty of 50% because of the differences between the phase space studied in Ref. [96] and the phase space relevant for this study.

Experimental uncertainties
The templates in the fit are scaled to their expected yields using the integrated luminosity represented by our data set. The integrated luminosities recorded in 2016, 2017, and 2018 are measured with uncertainties of 1.2, 2.3, and 2.5%, respectively [33][34][35]. These measurements are mostly uncorrelated from year to year, and we treat the uncertainty in the integrated luminosity with a set of nuisance parameters with log-normal constraints representing the correlated and uncorrelated components. This does not affect the shapes of the templates, while all of the other experimental uncertainties do affect the template shapes.
The distribution of the number of pileup interactions in simulated events is reweighted to match the observed pileup distribution in data, assuming a total inelastic pp cross section of 69.2 mb [97]. This cross section is varied up and down by 4.6%, and the resulting effects on the simulation are treated as independent nuisance parameters for each year. This accounts for year-to-year variations in the differences between the interaction vertex multiplicity distribution in data and simulation.
The simulation is corrected, using p T -and η-dependent scale factors, for residual differences between data and simulation in the reconstruction, identification, and isolation of the lepton, and in the trigger efficiency. The uncertainties in these scale factors are treated as independent nuisance parameters for each year. The trigger efficiency scale factor includes a correction and accompanying uncertainty component caused by a gradual drift in the timing of the inputs to the ECAL level-1 trigger in the forward region during 2016 and 2017 [30].
The jet energy scales for AK4 and AK8 jets in simulation are corrected to match data, and these corrections are varied within their uncertainties [85]. These effects are split among 11 independent subsources of uncertainty, some of which are correlated among the years. The uncertainty subsources affecting both AK4 and AK8 jets are treated as correlated. Similarly, the energy resolutions of AK4 and AK8 jets are known to be worse in data than in simulation, so the simulated jet energies are smeared to improve their agreement with data [85]. The amount of smearing is varied within the uncertainty in the required amount of smearing, and the effects of this variation are handled independently for each year. Additionally, the smearing procedure is performed independently for AK4 and for AK8 jets, so the corresponding uncertainties are uncorrelated. Corrections are also applied to the scale and resolution of m SD for AK8 jets, and these corrections are varied within their uncertainties. Corrections to the m SD values from simulation are derived from a comparison of simulated and measured samples of events in a region enriched with merged W → qq ′ decays from tt events [98]. The m SD corrections remove a residual dependence on the jet p T , and match the simulated jet mass scale and resolution to those observed in data. These corrections are varied within their uncertainties. The effects of these variations are treated as independent nuisance parameters for each year.
The performance of the DEEPCSV b tagger is slightly different in simulation than in data. We correct the simulation separately for the tagging of b jets, the tagging of c jets, and the misidentification of light-flavor jets using efficiency scale factors [86]. Uncertainties in these scale factors arise from a variety of effects, including variations in the jet energy scales, the finite size of the samples used to measure the scale factors, and background contamination in the data regions used to measure the scale factors. The uncertainties in the scale factors for each effect are treated as nuisance parameters, some of which are correlated from year to year and some of which are independent for each year. Similarly, the efficiency of the DEEPAK8 bb tagger is also corrected in simulation to better match the data. The scale factors are obtained using a collection of AK8 jets enriched in gluon splitting to a bb pair based on the presence of secondary vertices [83,86]. The uncertainty in this correction is treated independently for each year.

Results
Using the discriminating variables described in Section 6, namely the boson candidate AK8 jet p T , its m SD , and the full event neural network score, we measure the signal strengths of boosted ttZ and ttH production, determine 95% confidence level (CL) upper limits on ttZ and ttH cross sections, and constrain the effects of BSM physics arising from dimension-six operators in an EFT framework.
To perform these measurements, we use binned maximum likelihood fits, in which the signal and background model is compared to the data in each bin. The likelihood function used to fit the data is the Poisson likelihood with a rate described by the signal and background model, where λ i (θ POI , θ nuis ) = S i (θ POI , θ nuis ) + B i (θ nuis ) and where i is a bin index, which runs over all the bins, D i is the number of observed events, S i is the number of events predicted by the signal model, B i is the number of predicted back-ground events, θ POI is the set of parameters of interest (POIs), and θ nuis is the set of nuisance parameters. The background model depends only on the nuisance parameters, while the signal model depends on both the nuisance parameters and the POIs. The overall likelihood function is the product of L data and the constraint factors for each of the nuisance parameters, which introduce a likelihood penalty when the nuisance parameters shift from their nominal values. The constraint factors are Gaussian with a few exceptions, which are detailed in Section 7. The tt + bb rate is only constrained to be positive and otherwise is unconstrained in the fit. The factors representing the statistical uncertainties in the simulation use the approach described in Ref. [93].
For each fit, the likelihood function is maximized in terms of both the POIs and the nuisance parameters in order to obtain the best fit values of the POIs. Confidence intervals for the POIs are obtained by profiling the likelihood ratio [99], where the denominator is the maximized likelihood and the numerator is the maximized likelihood given a fixed value for one or more POIs. We perform one-dimensional and two-dimensional scans of the likelihood ratio in which one or two POIs are repeatedly fixed to specific values while the likelihood is maximized as a function of all the remaining parameters. The 95% CL upper limits are set with the asymptotic approximation [100] of the modified frequentist CL s criterion [101,102], in which the profile likelihood ratio is modified for upper limits [99] and used as the test statistic.
We validate the results by comparing them to the results we would obtain by considering each data-taking year independently. The results from each year are in agreement with each other and with the full results.
The observed yields in the 198 analysis bins are shown in Fig. 6, together with the expected yields from signal and background processes as predicted by the SM simulation, after fitting to the data (postfit).

Signal strengths and upper limits on differential cross sections
To facilitate comparisons with theoretical predictions, we isolate and remove the effects of limited detector acceptance and response to ttZ and ttH production using a maximum likelihood unfolding technique as described in Section 5 of Ref. [103]. Using this technique, we perform a measurement of the signal strengths of boosted ttZ and ttH production, i.e., the ratios of the measured ttZ and ttH production cross sections to the cross sections predicted by the SM as defined in Section 3. The measurement is performed in the region of generator-level phase space defined by the rapidity requirement |y Z/H | < 2.5 and p Z/H T > 200 GeV. The POIs that affect the signal model are the ttZ and ttH production signal strengths, µ tt Z and µ tt H , respectively. The results are shown in Fig. 7 and Table 3, and the impacts ∆µ on µ tt Z versus µ tt H from the major sources of systematic uncertainty are listed in Table 4. The ∆µ for ttZ and ttH are obtained by freezing one group of nuisance parameters at a time, and subtracting, in quadrature, the resulting 68% interval from the full fit interval. The observed correlation between µ tt Z and µ tt H is −10%. The observed yield for the tt + bb background is higher than the nominal SM prediction from the MC simulation, but it is consistent with the findings of other CMS measurements [96,104,105].
Because the uncertainties in the boosted ttZ and ttH cross sections are large, we are not able to provide two-sided confidence intervals in individual bins of p       Jet mass scale and resolution ±0.10 ±0.08  , which, along with the cross section corresponding to each subsample, form the signal model and its POIs. When setting the upper limit on one differential cross section, the other differential cross sections are profiled. The 95% CL upper limits on the differential cross sections are given in Fig. 8 and Table 5.

Effective field theory constraints
We constrain eight WCs from the LO dimension-six EFT model described in Section 3.1. Again, we impose a generator-level requirement on the rapidity of the Z or Higgs boson, |y Z/H | < 2.5. The effects of varying the WCs are computed as a weight w EFT for each simulated event in the   We maximize the likelihood function in terms of the WCs and the various nuisance parameters representing the systematic uncertainties.
We perform a likelihood scan for each WC while fixing the seven other WCs to their SM value of zero. With the WCs fixed, we find the maximum likelihood as a function of the nuisance parameters. We extract 68 and 95% CL intervals from the resulting profiled likelihood as shown in Fig. 9. We also perform a second scan for each WC in which the seven other WCs are not fixed, so that the likelihood is maximized as a function of the nuisance parameters and seven of the eight WCs. Both sets of intervals are summarized in Fig. 10, and the 95% CL intervals are summarized in Table 6. Because of partial degeneracies in the effects of the WCs, the constraints on the WCs from the two different likelihood scans tend to differ for c − φQ , c 3 φQ , c φt , c tW , and c tZ . To further explore this, two-dimensional likelihood scans are performed for pairs of WCs while the remaining six WCs are fixed to zero. Figure 11 shows the 68, 95, and 99.7% CL regions extracted from the scans for the three pairs of WCs that exhibit the largest postfit correlations. As shown in Table 1, two of these WC pairs (c 3 φQ , c − φQ ) and (c tW , c tZ ) apply to the same operators O

CMS
138 fb -1 (13 TeV) 68% CL interval Others fixed to SM Others profiled 95% CL interval Others fixed to SM Others profiled 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).  The likelihood scans for the WCs are sometimes bimodal, as can be seen in Fig. 9 for c t φ and c bW . This arises because the predicted yields in each analysis bin are quadratic as functions of the WCs, so the observed or expected yields may be most consistent with the predictions at two distinct WC values. The observed WC constraints are tighter than expected because the observed yields of tt + bb and ttH are higher and lower, respectively, than the SM expectations. All of the WC constraints are in close agreement with the SM with the exception of c t φ , which shows a weak tension with the SM. This tension is dominated by the yield of ttH, which is smaller than expected, as seen in Figs. 7 and 8. Figure 12 compares the 95% CL intervals from this analysis with previous CMS measurements, which used events with multiple leptons or photons [16,25,27,28]. There is good agreement among the various results, and in some cases the limits from this analysis are comparable to the best previously published limits.

Summary
Measurements of the signal strengths and 95% confidence level upper limits on the differential cross sections for production of ttZ and ttH 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 bb decay mode of the Z or Higgs boson and the lepton plus jets channel of the associated tt pair. The Z or Higgs boson is required to be Lorentz boosted, with transverse momentum p T > 200 GeV. A deep neural network is employed to discriminate between the ttZ and ttH signal events and the background, which is dominated by tt + 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 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 ttZ and ttH production are measured to be µ tt Z = 0.65 +1.04 −0.98 and µ tt 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 ttZ and ttH cross sections range from 2 to 5 times the standard model predicted cross sections for Z or Higgs boson p T > 300 GeV. Results are also presented on eight parameters of a leading-order effective field theory that have a large impact on boosted ttZ and ttH production. These results represent the most restrictive limits to date on the cross sections for the production of ttZ and ttH with Z or Higgs boson p 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.
[105] CMS Collaboration, "Measurement of the ttbb production cross section in the all-jet final state in pp collisions at √ s = 13 TeV", Phys. Lett. B 803 (2020) 135285, doi:10.1016/j.physletb.2020.135285, arXiv:1909.05306.  Fig. A.1. Table A.1: 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 T (leading) and second-highest p T (subleading) jet as indicated. Name Description tt system b p T p T of the leading (subleading) b jet b score DEEPCSV score of the leading (subleading) b jet q p T p T of the leading (subleading) non-b jet q score DEEPCSV score of the leading (subleading) non-b jet ∆R(b, q) minimum ∆R between the leading (subleading) b jet and any non-b jet ∆R(q, q)

A Neural network input variables
∆R between the two non-b jets closest to the leading (subleading) b jet m(q + q) invariant mass of the two non-b jets closest to the leading (subleading) b jet ∆R(b, q + q) ∆R between the leading (subleading) b jet and the sum of the nearest two non-b jets m(b + q + q) invariant mass of the leading (subleading) b jet and the nearest two non-b jets ∆R(Z/H, b + q + q) ∆R between the Z or Higgs boson candidate and the sum of the leading (subleading) b jet and the two non-b jets nearest to the leading (subleading) b jet ∆R(Z/H, b + b + q + q + ℓ) ∆R between the Z or Higgs boson candidate and the sum of the leading and subleading b jets, the two non-b jets nearest to the leading (subleading) b jet, and the lepton m T (b + ℓ, ⃗ p miss ∆R between the leading and subleading b jets ∆R(Z/H, q) ∆R between the Z or Higgs boson candidate and the leading non-b jet ∆R(Z/H, b) ∆R between the Z or Higgs boson candidate and the leading b jet ∆R(Z/H, ℓ) ∆R between the Z or Higgs boson candidate and the lepton m(Z/H + ℓ) invariant mass of the Z or Higgs boson candidate and the lepton ∆R(b, ℓ) ∆R between the leading (subleading) b jet and the lepton m(b + ℓ) invariant mass of the leading (subleading) b jet and the lepton N(b out ) number of b jets outside the Z or Higgs boson candidate cone (∆R > 0.8) N(q out ) number of non-b jets outside the Z or Higgs boson candidate cone (∆R > 0.8) Event topology N(AK8 jets) number of AK8 jets, including the Z or Higgs boson candidate N(AK4 jets) number of AK4 jets N(Z/H) number of AK8 jets with a minimum AK8 bb tagger score of 0.8 AK8 m SD maximum m SD of AK8 jets, excluding the Z or Higgs boson candidate H T (b out ) H T of the b jets outside the Z or Higgs boson candidate cone (∆R > 0.8) H T (b out , q out , ℓ) H T of all AK4 jets outside the Z or Higgs boson candidate cone (∆R > 0.8) and the lepton sphericity sphericity calculated from the AK4 jets and the lepton [89] aplanarity aplanarity calculated from the AK4 jets and the lepton [89] Z or Higgs boson candidate substructure b in score maximum (minimum) DEEPCSV score of AK4 jets within the Z or Higgs boson candidate cone (∆R < 0.8) ∆R(b in , b out ) ∆R between one b jet within the Z or Higgs boson candidate cone (∆R < 0.8) and the leading b jet outside of the Z or Higgs boson candidate cone N(b in ) number of b jets within the Z or Higgs boson candidate cone (∆R < 0.8) N(q in ) number of non-b jets within the Z or Higgs boson candidate cone (∆R < 0.8) Z/H bb score AK8 bb tagger score of the Z or Higgs boson candidate