Combination of the Searches for Pair-Produced Vectorlike Partners of the Third-Generation Quarks at s p = 13 TeV with the ATLAS Detector

A combination of the searches for pair-produced vectorlike partners of the top and bottom quarks in various decay channels ( T → Zt=Wb=Ht , B → Zb=Wt=Hb ) is performed using 36 . 1 fb − 1 of pp collision data at ﬃﬃﬃ s p ¼ 13 TeV with the ATLAS detector at the Large Hadron Collider. The observed data are found to be in good agreement with the standard model background prediction in all individual searches. Therefore, combined 95% confidence-level upper limits are set on the production cross section for a range of vectorlike quark scenarios, significantly improving upon the reach of the individual searches. Model-independent limits are set assuming the vectorlike quarks decay to standard model particles. A singlet T is excluded for masses below 1.31 TeV and a singlet B is excluded for masses below 1.22 TeV. Assuming a weak isospin ð T; B Þ doublet and j V Tb j ≪ j V tB j , T and B masses below 1.37 TeV are excluded.

M. Aaboud et al. * (ATLAS Collaboration) (Received 9 August 2018;published 20 November 2018) A combination of the searches for pair-produced vectorlike partners of the top and bottom quarks in various decay channels (T → Zt=Wb=Ht, B → Zb=Wt=Hb) is performed using 36.1 fb −1 of pp collision data at ffiffi ffi s p ¼ 13 TeV with the ATLAS detector at the Large Hadron Collider. The observed data are found to be in good agreement with the standard model background prediction in all individual searches. Therefore, combined 95% confidence-level upper limits are set on the production cross section for a range of vectorlike quark scenarios, significantly improving upon the reach of the individual searches. Modelindependent limits are set assuming the vectorlike quarks decay to standard model particles. A singlet T is excluded for masses below 1.31 TeV and a singlet B is excluded for masses below 1.22 TeV. Assuming a weak isospin ðT; BÞ doublet and jV Tb j ≪ jV tB j, T and B masses below 1.37 TeV are excluded. DOI: 10.1103/PhysRevLett.121.211801 Introduction.-Naturalness arguments [1] suggest there should be a mechanism that cancels out the quadratically divergent contributions to the Higgs boson mass caused by radiative corrections from standard model (SM) particles. Several explanations are proposed in theories beyond the SM. Little Higgs [2,3] and composite Higgs [4,5] models introduce a spontaneously broken global symmetry, with the Higgs boson emerging as a pseudo Nambu-Goldstone boson [6]. Such models predict the existence of vectorlike quarks (VLQs), color-triplet spin-1=2 fermions whose leftand right-handed chiralities transform in the same way under weak isospin [7,8]. In these models, VLQs are expected to couple preferentially to third-generation quarks [7,9] and can have flavor-changing neutral-current decays in addition to charged-current decays. An up-type VLQ T with charge þ2=3 can decay into Wb, Zt, or Ht. Similarly, a down-type quark B with charge −1=3 can decay into Wt, Zb, or Hb. In order to be consistent with results from precision electroweak measurements, the mass-splitting between VLQs belonging to the same SU(2) multiplet is required to be small [10], forbidding cascade decays such as T → WB. Couplings between the VLQs and the firstand second-generation quarks, although not favored, are not excluded [11,12].
At the Large Hadron Collider (LHC), VLQs with masses below approximately 1 TeV would mainly be pair produced, a process dominated by the strong interaction. The corresponding predicted cross section ranges from 195 to 2.0 fb for quark masses from 800 to 1500 GeV [13] and depends only on the quark mass. Production of single VLQs via the electroweak interaction is also possible, but depends on the strength of the interaction between the new quarks and the weak gauge bosons. Representative Feynman diagrams for BB and TT production and decay are shown in Fig. 1.
The branching ratio (B) for each decay mode (T → Wb; Zt; Ht and B → Wt; Zb; Hb) depends on the VLQ mass and weak-isospin quantum numbers, as calculated in Ref. [8]. For a singlet T, all three decay modes have sizable branching ratios, while the charged-current decay mode T → Wb is absent if T is either in a ðX; TÞ doublet, where X is a VLQ with a charge of þ5=3, or in a ðT; BÞ doublet with jV Tb j ≪ jV tB j, where V ij are the elements of a generalized Cabibbo-Kobayashi-Maskawa matrix [8,14,15]. Since the T quark branching ratios are identical in both doublets, no distinction is made between them when referring to the doublet T results. A singlet B will have a sizable branching ratio to all three decay channels, while the branching ratios in the doublet case depend on whether it is in a ðT; BÞ doublet or ðB; YÞ doublet, where Y is a VLQ with a charge of −4=3. For a ðB; YÞ doublet, only neutral current couplings to SM quarks are allowed at leading order (LO), so the B → Wt decay is forbidden. Conversely, for a ðT; BÞ doublet with jV Tb j ≪ jV tB j, B → Wt is the only allowed decay. Therefore, the specific B doublet scenario will be stated when interpreting the results.
Contributing analyses.-Searches for pair-produced VLQ partners of the third-generation quarks have been performed by ATLAS [16][17][18][19][20][21][22] and CMS [23][24][25] [31,32] as well as dedicated top and Higgs jet tagging to classify the events into 22 and 12 search regions for the zero-lepton and one-lepton selections, respectively. The final discriminant is the scalar sum (S T ) of the transverse momenta of the selected jets, lepton, and missing transverse momentum. The dominant background is the associated production of a tt pair with b-and c-quark jets, which is modeled via Monte Carlo (MC) simulation and assigned dedicated modeling uncertainties.
WðlνÞb þ X [17]: This analysis primarily targets TT → WbWb events with one W decaying leptonically and the other hadronically. Event selection requires one lepton, ≥ 3 jets, at least one of them being b-tagged, and a hadronically decaying W boson identified using jet substructure techniques [33]. The final discriminant is the reconstructed mass of the T → Wb → lνb candidate. The dominant background is from tt pair production, which is modeled using MC simulation with dedicated modeling uncertainties.
WðlνÞt þ X [18]: Very similar to the WðlνÞb þ X analysis, this analysis is optimized to target BB signals, especially in the case where B → Wt. This analysis discriminates between the signal and the dominant tt background in the signal regions using either a boosted decision tree discriminant or the reconstructed mass of the B candidate.
ZðννÞt þ X [19]: This analysis targets TT → ZtZt events with an invisible Z decay. Events must have E miss T > 300 GeV, one charged lepton from the decay of a top quark, and ≥ 4 small-radius jets, which are reclustered [34] into large-radius jets. The analysis defines a singlebin signal region that capitalizes on various E miss T -based variables and requires at least two high-mass large-radius jets due to hadronically decaying top quarks and/or heavy bosons from the VLQ decays. The dominant backgrounds are tt þ jets, W þ jets, and single-top events, which are estimated from MC simulation and normalized using dedicated control regions.
ZðllÞt=b þ X [20]: This analysis searches for TT and BB events containing a leptonically decaying Z boson (Z → l þ l − ) and at least two b-jets. The analysis has one trilepton signal region and three dilepton signal regions, depending on the number of large-radius jets (0, 1, or ≥ 2). The final discriminant depends on the signal region. The dominant backgrounds for the dilepton channels are Z þ jets and/or tt and diboson, while the trilepton channels are dominated by diboson (WZ) and ttZ events, each modeled by MC simulation and validated with dedicated control regions.
Trilepton or same-sign dilepton [21]: This analysis targets TT and BB decays with multilepton final states, with particular emphasis on events containing a pair of charged leptons with the same electric charge ("same sign"). Eight single-bin signal regions are defined in accord with the number of leptons and b-tagged jets. The background composition for this analysis varies between signal regions. Contributions from instrumental backgrounds (fake or nonprompt leptons and electrons with incorrectly measured charge) are estimated using data-driven techniques, while background processes with prompt leptons, originating mostly from tt þ W and diboson events, are modeled with MC simulations.
Fully hadronic [22]: This analysis focuses on final states with zero leptons, low E miss T , at least four (small-radius) high-p T jets, and at least two b-tagged jets. This is the only analysis with significant sensitivity to BB → HbHb. Small-radius jets are reclustered into large-radius jets, which may be identified as top quarks, W=Z, or H bosons using a multiclass deep neural network [35]. The final discriminant is the distribution of the signal likelihood calculated using the matrix-element method [36]. The dominant background is from multijet production, which is estimated using a data-driven technique. Most of the analyses were designed to be complementary. While each analysis provides sensitivity to various decay configurations, the most sensitive is shown in Table I. All analyses use consistent definitions for the reconstructed physics objects, so only a few additional selection requirements were needed to suppress overlap. Compared to the standalone analyses, the WðlνÞb þ X and ZðννÞt þ X analyses removed events with ≥6 jets and ≥3 b-jets to avoid overlap with the HðbbÞt þ X selection. The ZðννÞt þ X analysis also requires S T < 1.8 TeV in a control region to mitigate the overlap with a signal region in the WðlνÞb þ X analysis. To reduce overlap with the ZðllÞt=b þ X analysis, the trilepton or same-sign dilepton analysis removed events with more than three leptons or events with a lepton pair having an invariant mass compatible with a Z boson (Z veto). This Z veto is the only added selection requirement with significant impact on the individual analysis sensitivity; however, that sensitivity is recovered by the ZðllÞt=b þ X analysis. After applying these additional selection requirements, the fraction of events falling into more than one analysis region was evaluated to be less than 1% between any two signal regions and less than 3% between any pair of signal or control regions and has negligible impact on the results.
The VLQ signal samples used by the analyses were generated with the LO generator PROTOS v2.2 [37] using the NNPDF2.3 LO [38] set of parton distribution functions (PDF) and passed to PYTHIA 8.186 [39] for parton showering and fragmentation. The samples are normalized using cross sections computed with TOP++ v2.0 [13] at next-to-next-to-leading order (NNLO) in QCD, including resummation of next-to-next-to-leading logarithmic soft gluon terms [40][41][42][43][44], and using the MSTW 2008 NNLO [45,46] PDF. Further information about simulated events and details of the background estimations for each analysis can be found in the respective publications.
Statistical analysis.-The statistical analysis is the same as in the individual analyses and is based on a binned likelihood function constructed as the product of the Poisson probabilities of all bins entering the combination. This function depends on the signal-strength parameter μ, a factor multiplying the theoretical signal cross section (μ ≡ σ=σ theory ), and a set of nuisance parameters that encode the effect of the systematic uncertainties on the signal and background expectations. These parameters are included with Gaussian or log-normal constraints. Additional unconstrained nuisance parameters are included to control the normalization of the main backgrounds, following the settings used in the standalone searches. The combination is achieved by performing a fit with all bins from all the regions considered from each analysis.
The analysis is limited by statistical uncertainties, and the precise correlation model for the systematic TABLE I. The most sensitive decay channel for each analysis entering the combination. A "Á Á Á" indicates that the analysis was not used for that signal process.

Analysis
TT decay BB decay HtHt W t W t Fully hadronic [22] HtHt HbHb uncertainties was found to not significantly affect the results. The detector-related uncertainties are treated as fully correlated across analyses, with the following exceptions. The central values and uncertainties of the b-tagging and the luminosity measurement were updated after the publication of the ZðννÞt þ X and WðlνÞb þ X analyses. Therefore, to avoid propagating constraints caused by the change in the method, these uncertainties are correlated between the ZðννÞt þ X and WðlνÞb þ X analyses, but uncorrelated with the other searches, which are correlated among themselves. The modeling uncertainties and background normalization parameters are treated as uncorrelated between analyses. Although some background processes are common to multiple analyses, the phase space and the techniques used to estimate those backgrounds can be quite different. Residual correlations are therefore expected to be negligible.
Results.-The behavior of the combination is consistent with the fits from the individual analyses. The postfit values of all nuisance parameters are compatible with the standalone analyses, with the constraints generally determined by the analysis most sensitive to the given nuisance parameter. Similarly, the background predictions in each analysis after the combined fit are very close to the results from the standalone analyses. After the combination, no significant excess is observed in the data, so 95% confidence level (C.L.) limits are set on the cross section of a VLQ signal. To increase the applicability and usefulness of this combination, limits are evaluated both for benchmark scenarios with specific branching ratios and for general combinations of branching ratios.
For an assumed set of branching ratios, upper limits are set on the production cross sections for TT and BB as a function of the VLQ mass using the CL s method [47,48] with the asymptotic approximation [49]. Observed and expected upper limits on the TT cross sections as a function of mass are shown in Fig. 2 for the benchmark scenarios of an isospin singlet or doublet T. Analogous limits on the BB cross section are shown in Fig. 3. The observed limits from the individual analyses, after the additional selections defined in this Letter, are also shown. For a singlet T, masses below 1.31 TeV are excluded, while a T in an isospin doublet is excluded for masses below 1.37 TeV. A singlet B is excluded for masses below 1.22 TeV, a B in a ðT; BÞ doublet is excluded for masses below 1.37 TeV, and a B in a ðB; YÞ doublet is excluded for masses below 1.14 TeV.
The combination is significantly more sensitive than any one analysis. For example, in the case of the SU(2) singlet, the observed limit on the TT cross section is improved by up to a factor of ∼1.7, which translates to an increase of 110 GeV in the observed mass limit.
In addition, model-independent lower limits are set on the VLQ mass for all combinations of branching ratios, assuming BðT → HtÞ þ BðT → ZtÞ þ BðT → WbÞ ¼ 1 and BðB → HbÞ þ BðB → ZbÞ þ BðB → WtÞ ¼ 1. The resulting lower limits on the VLQ mass as a function of branching ratio are presented in Fig. 4. Limits corresponding to BðT → WbÞ ¼ 1 and BðB → WtÞ ¼ 1 are found to also be applicable to YȲ → WbWb and XX → WtWt, respectively. The high degree of complementarity between the analyses is clearly demonstrated in Fig. 4. For any combination of branching ratios, the combined analysis leads to observed (expected) lower mass limits of 1.31 (1.22) TeV for T and 1.03 (0.98) TeV for B. Limits on the signal strength, which can be used to interpret the results in scenarios with additional VLQ decays that escape detection [50], are available in the HEPData repository [51,52].
Conclusion.-The ATLAS Collaboration has performed a combination of seven analyses searching for pair-produced VLQs. Upper limits on the cross section are determined and used to set lower limits on the VLQ mass for various benchmark scenarios and for general combinations of branching ratios. This combination results in the most stringent limits to date on VLQ pair production. Because of the high degree of complementarity between the analyses, the combination has significantly better sensitivity than the standalone analyses, for the first time excluding T (B) masses below 1.31 (1.03) TeV for any combination of decays into SM particles.  [53].
[30] ATLAS Collaboration, Performance of missing transverse momentum reconstruction with the ATLAS detector using proton-proton collisions at ffiffi ffi s p ¼ 13 TeV, arXiv: