Search for production of vector-like quark pairs and of four top quarks in the lepton-plus-jets final state in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

A search for pair production of vector-like quarks, both up-type ($T$) and down-type ($B$), as well as for four-top-quark production, is presented. The search is based on $pp$ collisions at $\sqrt{s}=8$ TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and corresponding to an integrated luminosity of 20.3 fb$^{-1}$. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon with high transverse momentum, large missing transverse momentum and multiple jets. Dedicated analyses are performed targeting three cases: a $T$ quark with significant branching ratio to a $W$ boson and a $b$-quark ($T\bar{T} \to Wb$+X), and both a $T$ quark and a $B$ quark with significant branching ratio to a Higgs boson and a third-generation quark ($T\bar{T} \to Ht$+X and $B\bar{B} \to Hb$+X respectively). No significant excess of events above the Standard Model expectation is observed, and 95% CL lower limits are derived on the masses of the vector-like $T$ and $B$ quarks under several branching ratio hypotheses assuming contributions from $T \to Wb$, $Zt$, $Ht$ and $B \to Wt$, $Zb$, $Hb$ decays. The 95% CL observed lower limits on the $T$ quark mass range between 715 GeV and 950 GeV for all possible values of the branching ratios into the three decay modes, and are the most stringent constraints to date. Additionally, the most restrictive upper bounds on four-top-quark production are set in a number of new physics scenarios.


Introduction
The discovery of a new particle consistent with the Standard Model (SM) Higgs boson by the ATLAS [1] and CMS [2] collaborations is a major milestone in high-energy physics. However, the underlying nature of electroweak symmetry breaking remains unknown. Naturalness arguments [3] require that quadratic divergences that arise from radiative corrections to the Higgs boson mass must be cancelled by some new mechanism in order to avoid fine-tuning. To that effect, several explanations have been proposed in theories beyond the SM (BSM). In supersymmetry, the cancellation comes from assigning superpartners to the SM bosons and fermions. Alternatively, Little Higgs [4,5] and Composite Higgs [6,7] models introduce a spontaneously broken global symmetry, with the Higgs boson emerging as a pseudo-Nambu-Goldstone boson [8]. Such models predict the existence of vector-like quarks, defined as colour-triplet spin-1/2 fermions whose left-and right-handed chiral components have the same transformation properties under the weak-isospin SU(2) gauge group [9,10]. In these models vector-like quarks are expected to couple preferentially to third-generation quarks [9,11] and they can have flavour-changing neutral current decays, in addition to the charged-current decays characteristic of chiral quarks. As a result, an up-type quark T with charge +2/3 can decay not only to a W boson and a b-quark, but also to a Higgs or Z boson and a top quark (T → Wb, Zt, and Ht). Similarly, a down-type quark B with charge −1/3 can decay to a Higgs or Z boson and a b-quark, in addition to decaying to a W boson and a top quark (B → Wt, Zb, and Hb). In order to be consistent with the results from the precision electroweak measurements, a small mass splitting between vector-like quarks belonging to the same SU(2) multiplet is required [12], which forbids cascade decays such as T → W B and leaves direct decays into SM particles as the only possibility. Couplings between the vector-like quarks and the first and second quark generations, although not favoured, are not excluded [13,14]. This leads to a rich phenomenology at the LHC, which the experiments are investigating.
Early searches for the pair production of exotic heavy quarks published by the ATLAS and CMS collaborations focused on exclusive decay modes assuming a 100% branching ratio. These include searches for TT → W + bW −b [15][16][17][18], BB → ZbZb [19][20][21], and BB → W + tW −t [20,22,23]. The limits derived from these searches cannot easily be applied to other branching ratio values, due to the potentially large expected signal contamination from mixed decay modes. A more general search strategy should consider simultaneously all three decay modes, providing a more extensive coverage of possible signal contributions. In absence of an excess, quasi-model-independent limits would be set in the plane defined by the branching ratios to two of the decay modes 1 as a function of the heavy-quark mass. The first search that considered all three decay modes in the interpretation of results, performed by the ATLAS Collaboration using pp collisions at √ s = 7 TeV, primarily targeted the TT → W + bW −b process [24]. Using the full dataset collected at √ s = 8 TeV, the ATLAS Collaboration has recently published searches for heavy quarks decaying to a Z boson and a third-generation quark [25], and searches for heavy quarks decaying predominantly to Wt in events with one lepton and jets [26] and in events with two leptons of the same charge or three leptons [27]. In the context of vector-like quarks, these searches are used to probe TT and BB production, and the three decay modes are considered in the interpretation of the results. The CMS Collaboration has published an inclusive search for TT production [28] resulting from the combination of several analyses in lepton-plus-jets and multilepton final states at √ s = 8 TeV. This search set 95% confidence level (CL) lower limits on the T quark mass ranging between 690 GeV and 780 GeV for all possible values of the branching ratios into the three decay modes.
The results presented in this paper complete the program of searches for pair production of vector-like quarks decaying into third-generation quarks by the ATLAS Collaboration using the pp dataset collected at √ s = 8 TeV. Three separate searches are presented, all of them focused on the pair production of vector-like quarks in final states involving one isolated electron or muon, high missing transverse momentum from the undetected neutrino and multiple jets. The first search, referred to as TT → Wb+X, is optimised for TT production with at least one T → Wb decay, where the resulting W boson acquires a high momentum from the large T quark mass. The second search, referred to as TT → Ht+X, targets TT production with at least one T → Ht decay, with H → bb, resulting in events with high jet multiplicity and a large number of jets tagged as originating from b-quarks. The third search, referred to as BB → Hb+X, is instead focused on BB production with at least one B → Hb decay and H → bb, in events with the same final-state signature probed by the TT → Ht+X search. In all three searches the isolated lepton and the high missing transverse momentum are provided by the leptonic decay of a W boson originating in the decay of a vector-like quark, a top quark, or a Higgs boson.
The large mass of the top quark makes it a prime candidate to help uncover the dynamics behind electroweak symmetry breaking and/or new physics at the electroweak scale. In many new physics models the top quark plays a prominent role, often participating in new interactions related to electroweak symmetry breaking, or preferentially coupling to new degrees of freedom. Such BSM scenarios usually predict an enhanced rate of events containing four top quarks (tttt) in the final state, compared to the SM production via the strong interaction. Examples include top quark compositeness [29][30][31], Randall-Sundrum extra dimensions [32], models with coloured scalars [33][34][35][36][37][38], or universal extra dimensions [39][40][41]. The CMS Collaboration has performed a search for SM tttt production at √ s = 8 TeV in the lepton-plus-jets final state [42], setting an observed (expected) 95% CL upper limit on the production cross section of 32 fb (32 fb). Using multilepton final states, the ATLAS Collaboration has also searched for SM tttt production at √ s = 8 TeV, setting an observed (expected) 95% CL upper limit of 70 fb (27 fb) [27]. The observed limit is higher than the expected one owing to an excess of data above the background expectation with a significance of 2.5 standard deviations. In addition, the ATLAS multilepton search sensitively probes several of the above BSM scenarios giving rise to large enhancements in tttt production. Given its sensitivity to a wide range of models, the TT → Ht+X search presented in this paper is also used to search for a tttt signal, within the SM as well as in the same BSM scenarios as the ATLAS multilepton search, with comparable sensitivity.

ATLAS detector
The ATLAS detector [43] consists of the following main subsystems: an inner tracking system, electromagnetic and hadronic calorimeters, and a muon spectrometer. The inner detector provides tracking information from silicon pixel and microstrip detectors in the pseudorapidity 2 range |η| < 2.5 and from a straw-tube transition radiation tracker covering |η| < 2.0, all immersed in a 2 T axial magnetic field provided by a superconducting solenoid. The electromagnetic (EM) sampling calorimeter uses lead as the absorber material and liquid-argon (LAr) as the active medium, and is divided into barrel (|η| < 1.475) and end-cap (1.375 < |η| < 3.2) regions. Hadron calorimetry is also based on the sampling technique, with either scintillator tiles or LAr as the active medium, and with steel, copper, or tungsten as the absorber material. The calorimeters cover |η| < 4.9. The muon spectrometer measures the deflection of muons with |η| < 2.7 using multiple layers of high-precision tracking chambers located in a toroidal field of approximately 0.5 T and 1 T in the central and end-cap regions of ATLAS, respectively. The muon spectrometer is also instrumented with separate trigger chambers covering |η| < 2.4. A three-level trigger system [44] is used to select interesting events. The first-level trigger is implemented in custom electronics and uses a subset of detector information to reduce the event rate to at most 75 kHz. This is followed by two software-based trigger levels exploiting the full detector information and yielding a typical recorded event rate of 400 Hz during 2012.

Object reconstruction
The main reconstructed objects considered in this search are electrons, muons, jets, b-jets and missing transverse momentum.
Electron candidates [45] are reconstructed from energy deposits (clusters) in the EM calorimeter that are matched to reconstructed tracks in the inner detector. The candidates are required to have a transverse energy 3 E T greater than 25 GeV and |η cluster | < 2.47, where |η cluster | is the pseudorapidity of the cluster associated with the electron candidate. Candidates in the EM calorimeter transition region 1.37 < |η cluster | < 1.52 are excluded. Electrons are required to satisfy "tight" quality requirements [45], which include stringent selection requirements on calorimeter, tracking and combined variables that provide good separation between prompt electrons and jets. The longitudinal impact parameter of the electron track with respect to the event's primary vertex (see section 4), z 0 , is required to be less than 2 mm. To reduce the background from non-prompt electrons resulting from semileptonic decays of b-or c-hadrons, and from jets with a high fraction of their energy deposited in the EM calorimeter, electron candidates must also satisfy calorimeter-and track-based isolation requirements. The calorimeter isolation variable is based on the energy sum of cells within a cone of radius ∆R = (∆φ) 2 + (∆η) 2 = 0.2 around the direction of each electron candidate, and an η-dependent requirement is made, giving an average efficiency of 90% for prompt electrons from Z boson decays. This energy sum excludes cells associated with the electron cluster and is corrected for leakage from the electron cluster itself and for energy deposits from additional pp interactions within the same bunch crossing ("pileup"). A further 90%-efficient isolation requirement is made on the track transverse momentum (p T ) sum around the electron in a cone of radius ∆R = 0.3.
Muon candidates [46,47] are reconstructed from track segments in the various layers of the muon spectrometer and matched with tracks found in the inner detector. The final candidates are refitted using the complete track information from both detector systems and are required to satisfy p T > 25 GeV y-axis points upward. Cylindrical coordinates (r,φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). For the purpose of the fiducial selection, this is calculated relative to the geometric centre of the detector; otherwise, it is relative to the reconstructed primary vertex of each event. 3 The electron transverse energy is defined as E T = E cluster / cosh η track , where E cluster is the energy of the cluster in the calorimeter and η track is the pseudorapidity of its associated track. and |η| < 2.5. Muons are required to have a hit pattern in the inner detector consistent with a wellreconstructed track to ensure good p T resolution. The longitudinal impact parameter of the muon track with respect to the primary vertex, z 0 , is required to be less than 2 mm. Muons are required to satisfy a p T -dependent track-based isolation requirement: the scalar sum of the p T of the tracks within a cone of variable radius ∆R = 10 GeV/p µ T around the muon (excluding the muon track itself) must be less than 5% of the muon p T (p µ T ). This requirement has good signal efficiency and background rejection even under high-pileup conditions, as well as in boosted configurations where the muon is close to a jet. For muons from W decays in simulated tt events the average efficiency of the isolation requirement is about 95%.
Jets are reconstructed with the anti-k t algorithm [48][49][50] with a radius parameter R = 0.4 from calibrated topological clusters [51,52] built from energy deposits in the calorimeters. Prior to jet finding, a local cluster calibration scheme [53] is applied to correct the topological cluster energies for the effects of non-compensating response of the calorimeter, dead material and out-of-cluster leakage. The corrections are obtained from simulations of charged and neutral particles. After energy calibration [54], jets are required to have p T > 25 GeV and |η| < 2.5. To reduce the contamination due to jets originating from pileup interactions, a requirement that the so-called "jet vertex fraction" (JVF) be above 0.5 is applied to jets with p T < 50 GeV and |η| < 2.4. This requirement ensures that at least 50% of the scalar sum of the p T of the tracks matched to the jet comes from tracks originating from the primary vertex. During jet reconstruction, no distinction is made between identified electrons and jet energy deposits. Therefore, if any of the jets lie within ∆R = 0.2 of a selected electron, the closest jet is discarded in order to avoid double-counting of electrons as jets. Finally, any electron or muon within ∆R = 0.4 of a selected jet is discarded.
Jets are identified as originating from the hadronisation of a b-quark (b-tagged) via an algorithm [55] that uses multivariate techniques to combine information from the impact parameters of displaced tracks as well as topological properties of secondary and tertiary decay vertices reconstructed within the jet. For each jet, a value for the multivariate b-tagging discriminant is calculated, and is considered b-tagged if this value is above a given threshold. The threshold used in this search corresponds to 70% efficiency to tag a b-quark jet, with a light-jet rejection factor 4 of ∼130 and a charm-jet rejection factor of 5, as determined for jets with p T > 20 GeV and |η| < 2.5 in simulated tt events.
The missing transverse momentum (E miss T ) is constructed [56] from the vector sum of all calorimeter energy deposits 5 contained in topological clusters. All topological cluster energies are corrected using the local cluster calibration scheme discussed above. Those topological clusters associated with a highp T object (e.g. jet or electron) are further calibrated using their respective energy corrections. In addition, contributions from the p T of selected muons are included in the calculation of E miss T .

Data sample and event preselection
This search is based on pp collision data at √ s = 8 TeV collected by the ATLAS experiment between April and December 2012. Only events recorded with a single-electron or single-muon trigger under stable beam conditions and for which all detector subsystems were operational are considered. The corresponding integrated luminosity is 20.3±0.6 fb −1 [57]. Single-lepton triggers with different p T thresholds are combined in a logical OR in order to increase the overall efficiency. The p T thresholds are 24 or 60 GeV for the electron triggers and 24 or 36 GeV for the muon triggers. The triggers with the lower p T threshold include isolation requirements on the candidate lepton, resulting in inefficiencies at high p T that are recovered by the triggers with higher p T threshold. Events satisfying the trigger selection are required to have at least one reconstructed vertex with at least five associated tracks with p T > 400 MeV, consistent with originating from the beam collision region in the x-y plane. The average number of pp interactions per bunch crossing is approximately 20, resulting in several vertices reconstructed per event. If more than one vertex is found, the hard-scatter primary vertex is taken to be the one which has the largest sum of the squared transverse momenta of its associated tracks. For the event topologies considered in this paper, this requirement leads to a probability to reconstruct and select the correct hard-scatter primary vertex larger than 99%.
Events are required to have exactly one reconstructed electron or muon and at least four jets satisfying the quality and kinematic criteria discussed in section 3. The selected lepton is required to match, with ∆R < 0.15, the lepton reconstructed by the trigger. The background from multijet production is suppressed by a requirement on E miss T as well as on the transverse mass of the lepton and E miss T (m W T ). 6 For both lepton selections the requirements are E miss T > 20 GeV and E miss T + m W T > 60 GeV. Further suppression of the background not including b-quark jets is achieved by requiring at least one b-tagged jet in the TT → Wb+X search, and at least two b-tagged jets in the TT → Ht+X and BB → Hb+X searches. In the following, events satisfying either the electron or muon selections are combined and treated as a single analysis channel.

Signal modelling
This section describes the different signal scenarios considered in the interpretation of the results, together with details of how they are modelled in the analysis.

Vector-like quark pair production
Vector-like quarks with mass below approximately 1 TeV are mostly produced in pairs via the strong interaction in pp collisions at √ s = 8 TeV. For higher masses, single production mediated by the electroweak interaction can potentially dominate, depending on the strength of the interaction between the new quarks and the weak gauge bosons. The predicted pair-production cross section ranges from 5.3 pb for a quark mass of 350 GeV to 3.3 fb for a quark mass of 1000 GeV, with an uncertainty that increases from 8% to 14% over this mass range. This cross section is independent of the electroweak quantum numbers of the new heavy quark and just depends on its mass. It was computed using Top++ v2.0 [58] at next-to-next-toleading order (NNLO) in QCD, including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms [59][60][61][62][63], and using the MSTW 2008 NNLO [64,65] set of parton distribution functions (PDF). Theoretical uncertainties result from variations on the factorisation and renormalisation scales, as well as from uncertainties on the PDF and α S . The latter two represent the largest contribution to the overall theoretical uncertainty on the cross section and were calculated using the PDF4LHC prescription [66] with the MSTW 2008 68% CL NNLO, CT10 NNLO [67,68] and NNPDF2.3 5f FFN [69] PDF sets.
where p T is the transverse momentum (energy) of the muon (electron) and ∆φ is the azimuthal angle separation between the lepton and the direction of the missing transverse momentum.
As discussed in section 1, vector-like quarks can couple preferentially to third-generation quarks, as the mixing between weak eigenstates of the same electric charge is proportional to the mass of the SM quark [9,11], and thus present a rich phenomenology. In particular, a vector-like quark has neutralcurrent tree-level decays to a Z or H boson plus a SM quark, in addition to the charged-current decay mode to a W boson and a SM quark, which is the only decay mode chiral quarks can have. Figure 1 depicts representative Feynman diagrams for the signals probed by the searches discussed in this paper. The branching ratios to each of these decay modes vary as a function of the heavy-quark mass and depend on its weak-isospin (SU(2)) quantum numbers [10]. Figure 2(a) shows the branching ratios as a function of T quark mass in the SU(2) singlet and doublet hypotheses. 7 In the case of a singlet, all three decay modes have sizeable branching ratios, while the charged-current decay mode T → Wb is absent in the doublet cases. The doublet prediction is valid for an (X, T ) doublet, where the charge of the X quark is +5/3, as well as a (T, B) doublet when a mixing assumption of |V T b | |V tB | is made, where V i j are the elements of a generalised Cabibbo-Kobayashi-Maskawa matrix [10]. Since the T quark branching ratios are identical in both doublets, in the following no distinction between them is made when referring to the T quark doublet hypothesis. Similarly, figure 2(b) shows the branching ratios as a function of B quark mass in the singlet and doublet hypotheses. In the case of a (T, B) doublet with the mixing assumption |V T b | |V tB |, BR(B → Wt) = 1, while such a decay mode is absent for the (B, Y) doublet case, where the charge of the Y quark is −4/3. The Y quark is equivalent to a chiral quark since it only has charged-current decays, Y → W − b.
Simulated samples of TT and BB are generated with the leading-order (LO) generator Protos v2.2 [70] using the MSTW 2008 LO PDF set and passed to Pythia 6.426 [71] for parton showering and fragmentation. The AUET2B [72] set of optimised parameters for the underlying event (UE) description, referred to as the "UE tune", is used. The vector-like quarks are forced to decay with a branching ratio of 1/3 to each of the three modes (W, Z, H). Arbitrary sets of branching ratios consistent with the three decay modes summing to unity are obtained by reweighting the samples using particle-level information. Samples are generated assuming singlet couplings and for heavy-quark masses between 350 GeV and 1100 GeV in steps of 50 GeV. Additional samples are produced at two mass points (350 GeV and 600 GeV) assuming doublet couplings in order to confirm that kinematic differences arising from the different chirality of singlet and doublet couplings are negligible in this analysis. In all simulated samples (both signal and background) used in this search, the top quark and SM Higgs boson masses are set to 172.5 GeV and 125 GeV respectively. The samples are normalised using the Top++ cross section predictions discussed above.

Four-top-quark production
The production cross section for four-top-quark events in the SM is very small (σ tttt 1 fb at √ s = 8 TeV) [73,74], but it can be significantly enhanced in several BSM scenarios. Figure 3 depicts representative LO Feynman diagrams for four-top-quark production within the SM and the different BSM scenarios considered in this paper. A class of models involving new heavy vector particles strongly coupled to the right-handed top quark, such as top quark compositeness [29][30][31] or Randall-Sundrum extra dimensions [32], can be described via an effective field theory (EFT) involving a four-fermion contact   Figure 2: Branching ratios for the different decay modes as a function of heavy-quark mass in the case of (a) a vector-like T quark and (b) a vector-like B quark, as computed with Protos. In both cases the branching ratios are provided for an SU(2) singlet and two different SU(2) doublet scenarios. interaction [75] ( figure 3(b)). The Lagrangian assumed is where t R is the right-handed top quark spinor, γ µ are the Dirac matrices, C 4t is the coupling constant, and Λ is the energy scale of new physics. Only the contact interaction operator with right-handed top quarks is considered, since left-handed operators are already strongly constrained by the precision electroweak measurements [76].
In addition, two specific models are considered involving new heavy particles: scalar gluon (sgluon) pair production and a Universal Extra Dimensions (UED) model. Sgluons are colour-adjoint scalars, denoted by σ, that appear in several extensions of the SM, both supersymmetric [33, 34] and nonsupersymmetric [35][36][37][38]. The dominant production mode at the LHC is in pairs via the strong interaction, gg → σσ. For sgluon masses above twice the top quark mass, the dominant decay mode is into tt, giving rise to a four-top-quark final state ( figure 3(c)). The UED model considered has two extra dimensions that are compactified using the geometry of the real projective plane (2UED/RPP) [39], leading to a discretisation of the momenta along their directions. A tier of Kaluza-Klein towers is labelled by two integers, k and , referred to as "tier (k, )". Within a given tier, the squared masses of the particles are given at leading order by m 2 = k 2 /R 2 4 + 2 /R 2 5 , where πR 4 and πR 5 are the size of the two extra dimensions. The model is parameterised by R 4 and R 5 or, alternatively, by m KK = 1/R 4 and ξ = R 4 /R 5 . Four-top-quark production can arise from tier (1,1), where particles from this tier have to be pair produced because of symmetries of the model. Then they chain-decay to the lightest particle of this tier, the heavy photon A (1,1) , by emitting SM particles ( figure 3(d)). The branching ratios of A (1,1) into SM particles are not predicted by the model, although the decay into tt is expected to be dominant [40]. Four-top-quark events can also arise from tiers (2,0) and (0,2) via a similar mechanism. In this case the expected cross section for four-top-quark production is reduced compared to that from tier (1,1) since each state in tiers (2,0) and (0,2) can decay directly into a pair of SM particles or into a pair of states in tiers (1,0) or (0,1) via bulk interactions, resulting in smaller branching ratios for decay into tt [40]. In the following, when considering four-top-quark production from a given tier, it is assumed that the A photon in that tier decays with 100% branching ratio into tt while A photons from other tiers cannot decay into tt. Within this model, observations of dark-matter relic abundance prefer values of m KK between 600 GeV and 1200 GeV [41].
Simulated samples of four-top-quark production within the SM, within an EFT model, and within the 2UED/RPP model, are generated with the Madgraph5 1.3.33 [77] LO generator and the MSTW 2008 PDF set, interfaced to Pythia 8.1 [78] and the AU2 UE tune [79]. In the case of the 2UED/RPP model, samples are generated for four different values of m KK (600, 800, 1000 and 1200 GeV) and the Bridge [80] generator is used to decay the pair-produced excitations from tier (1,1) generated by Madgraph5. Constraints for tiers (2,0) and (0,2) can be derived from those for tier (1,1) together with the theoretical cross sections. Samples of four-top-quark production via sgluon pairs are generated with Pythia 6.426 with the CTEQ6L1 [81] PDF set and the AUET2B UE tune, for seven different values of the sgluon mass between 350 GeV and 1250 GeV, and normalised to the NLO theoretical cross section [82].
Events from minimum-bias interactions are simulated with the Pythia 8.1 generator with the MSTW 2008 LO PDF set and the A2 tune [79]. They are overlaid on the simulated signal events according to the luminosity profile of the recorded data. The contributions from these pileup interactions are modelled both within the same bunch crossing as the hard-scattering process and in neighbouring bunch crossings. Finally, the generated samples are processed through a simulation [83] of the detector geometry and response using Geant4 [84] with a fast simulation of the calorimeter response [83]. All samples are processed through the same reconstruction software as the data. Simulated events are corrected so that the object identification efficiencies, energy scales and energy resolutions match those determined from data control samples.

Background modelling
After event preselection, the main background is tt+jets production, with the production of a W boson in association with jets (W+jets) and multijet events contributing to a lesser extent. Small contributions arise from single top quark, Z+jets and diboson (WW, WZ, ZZ) production, as well as from the associated production of a vector boson V (V = W, Z) or a Higgs boson and a tt pair (ttV and ttH). Multijet events contribute to the selected sample via the misidentification of a jet or a photon as an electron or via the presence of a non-prompt lepton, e.g. from a semileptonic b-or c-hadron decay; the corresponding yield is estimated via data-driven methods. The rest of the background contributions are estimated from simulation and normalised to their theoretical cross sections. In the case of the tt+jets and W/Z+jets background predictions, further corrections are applied to improve agreement between the data and simulation, as discussed in sections 6.1 and 6.2 respectively.
All simulated background samples utilise Photos 2.15 [85] to simulate photon radiation and Tauola 1.20 [86] to simulate τ decays. Similarly to the signal samples, they also include a simulation of pileup interactions, and are processed through a full Geant4 detector simulation and the same reconstruction software as the data. Further details about the modelling of each of the backgrounds are provided below.

tt+jets background
Simulated samples of tt+jets events are generated with the next-to-leading-order (NLO) generator Powheg-Box 2.0 [87][88][89][90] using the CT10 PDF set [67]. The nominal sample is interfaced to Pythia 6.425 [71] with the CTEQ6L1 PDF set and the Perugia2011C UE tune [91]. An alternative sample, used to study the uncertainty related to the fragmentation model, is interfaced to Herwig v6.520 [92] with the CTEQ6L1 PDF set and Jimmy v4.31 [93] to simulate the UE. The tt+jets samples are normalised to the theoretical cross section obtained with Top++, performed at NNLO in QCD and including resummation of NNLL soft gluon terms.
The tt+jets samples are generated inclusively, but events are categorised depending on the flavour content of additional particle jets in the event (i.e. jets not originating from the decay of the tt system). Particle jets are reconstructed with the anti-k t algorithm with a radius parameter R = 0.4 and are required to have p T > 15 GeV and |η| < 2.5. Events where at least one such particle jet is matched within ∆R < 0.4 to a b-hadron with p T > 5 GeV not originating from a top quark decay are labelled as tt + bb events. Similarly, events where at least one such particle jet is matched within ∆R < 0.4 to a c-hadron with p T > 5 GeV not originating from a W boson decay, that are not labelled already as tt + bb, are labelled as tt + cc events. Events labelled as either tt + bb or tt + cc are generically referred to below as tt+HF events, where HF stands for "heavy flavour". The remaining events are labelled as tt+light-jet events, including those with no additional jets. In Powheg+Pythia the modelling of tt+HF is via the parton-shower evolution. To study uncertainties related to this simplified description, an alternative tt+jets sample is generated with Madgraph5 1.5.11 using the CT10 PDF set. It includes tree-level diagrams with up to three additional partons (including b-and c-quarks) and is interfaced to Pythia 6.425.
Since the best possible modelling of the tt+jets background is a key aspect of these searches, a correction is applied to simulated tt events in Powheg+Pythia based on the ratio of the differential cross sections measured in data and simulation at √ s = 7 TeV as a function of top quark p T and tt system p T [94]. The stability of the ratio between √ s = 7 TeV and √ s = 8 TeV was studied to support the usage of √ s = 7 TeV data to correct the simulation at √ s = 8 TeV. This correction significantly improves agreement between simulation and data in distributions such as the jet multiplicity and the p T of decay products of the tt system. This correction is applied only to tt+light-jets and tt + cc events. The modelling of the tt + bb background, particularly important for the Ht/Hb+X searches, is improved by reweighting the Powheg+Pythia prediction to an NLO prediction of tt + bb including parton showering [95], based on Sherpa+OpenLoops [96,97] using the CT10 PDF set. This reweighting is performed for different topologies of tt + bb in such a way that the inter-normalisation of each of the categories and the relevant kinematic distributions are at NLO accuracy. More details about the modelling of the tt+jets background can be found in ref. [98].

W/Z+jets background
Samples of W/Z+jets events are generated with up to five additional partons using the Alpgen v2.14 [99] LO generator and the CTEQ6L1 PDF set, interfaced to Pythia v6.426 for parton showering and fragmentation. To avoid double-counting of partonic configurations generated by both the matrix-element calculation and the parton shower, a parton-jet matching scheme ("MLM matching") [100] is employed. The W+jets samples are generated separately for W+light-jets, Wbb+jets, Wcc+jets, and Wc+jets. The Z+jets samples are generated separately for Z+light-jets, Zbb+jets, and Zcc+jets. Overlap between V QQ+jets (V = W, Z and Q = b, c) events generated from the matrix-element calculation and those generated from parton-shower evolution in the W/Z+light-jets samples is avoided via an algorithm based on the angular separation between the extra heavy quarks: if ∆R(Q,Q) > 0.4, the matrix-element prediction is used, otherwise the parton-shower prediction is used. Both the W+jets and Z+jets background contributions are normalised to their inclusive NNLO theoretical cross sections [101]. Further corrections are applied to W/Z+jets events in order to better describe data in the preselected sample. Scale factors for each of the W+jets categories (Wbb+jets, Wcc+jets, Wc+jets and W+light-jets) are derived for events with one lepton and at least four jets by simultaneously analysing six different event categories, defined by the b-tag multiplicity (0, 1 and ≥2) and the sign of the lepton charge. The b-tag multiplicity provides information about the heavy-flavour composition of the W+jets background, while the lepton charge is used to determine the normalisation of each component, exploiting the expected charge asymmetry for W+jets production in pp collisions as predicted by Alpgen. In the case of Z+jets events, a correction to the heavy-flavour fraction was derived to reproduce the relative rates of Z+2-jets events with zero and one b-tagged jets observed in data. In addition, the Z boson p T spectrum was compared between data and the simulation in Z+2-jets events, and a reweighting function was derived in order to improve the modelling.

Other simulated background
Samples of single-top-quark backgrounds corresponding to the t-channel, s-channel and Wt production mechanisms are generated with Powheg-Box 2.0 [102,103] using the CT10 PDF set and interfaced to Pythia 6.425 with the CTEQ6L1 PDF set and the Perugia2011C UE tune. Overlaps between the tt and Wt final states are removed using the "diagram removal" scheme [104]. The single-top-quark samples are normalised to the approximate NNLO theoretical cross sections [105][106][107] calculated using the MSTW 2008 NNLO PDF set.
The WW/WZ/ZZ+jets samples are generated with up to three additional partons using Alpgen v2.13 and the CTEQ6L1 PDF set, interfaced to Herwig v6.520 and Jimmy v4.31 for parton showering, fragmentation and UE modelling. The MLM parton-jet matching scheme is used. The WW+jets samples require at least one of the W bosons to decay leptonically, while the WZ/ZZ+jets samples require one Z boson to decay leptonically, with the other boson decaying inclusively. Additionally, WZ+jets samples requiring the W and Z bosons to decay leptonically and hadronically respectively, are generated with up to three additional partons (including massive b-and c-quarks) using Sherpa v1.4.1 and the CT10 PDF set. All diboson samples are normalised to their NLO theoretical cross sections [108] Samples of ttV events, including ttWW, are generated with up to two additional partons using Madgraph5 1.3.28 with the CTEQ6L1 PDF set, and interfaced to Pythia 6.425 with the AUET2B UE tune. A sample of ttH events is generated with the PowHel framework [109], which combines the Powheg-Box generator and NLO matrix elements obtained from the HELAC-Oneloop package [110]. The sample is generated using the CT10nlo PDF set [67]. Showering is performed with Pythia 8.1 using the CTEQ6L1 PDF set and the AU2 UE tune [72,111]. Inclusive decays of the Higgs boson are assumed in the generation of the ttH sample. The ttV samples are normalised to the NLO cross section predictions [112]. The ttH sample is normalised using the NLO cross section [113][114][115] and the Higgs decay branching ratios [116][117][118][119] collected in ref. [120].

Multijet background
Multijet events can enter the selected data sample through several production and misreconstruction mechanisms. In the electron channel, the multijet background consists of non-prompt electrons as well as misidentified photons (e.g. with a conversion into an e + e − pair) or jets with a high fraction of their energy deposited in the EM calorimeter. In the muon channel, the background contributed by multijet events is predominantly due to final states with non-prompt muons, such as those from semileptonic b-or c-hadron decays.
The multijet background normalisation and shape are estimated directly from data by using the "matrix method" technique [121]. The matrix method exploits differences in lepton-identification-related properties between prompt, isolated leptons from W and Z boson decays (referred to as "real leptons" below) and those where the leptons are either non-isolated or result from the misidentification of photons or jets (referred to as "fake leptons" below). For this purpose, two samples are defined after imposing the final kinematic selection criteria, differing only in the lepton identification criteria: a "tight" sample and a "loose" sample, the former being a subset of the latter. The tight selection employs the complete set of lepton identification criteria used in the analysis. For the loose selection the lepton isolation requirements are omitted. The method assumes that the number of selected events in each sample (N loose and N tight ) can be expressed as a linear combination of the numbers of events with real and fake leptons, so that the number of multijet events in the tight sample is given by where real ( fake ) represents the probability for a real (fake) lepton that satisfies the loose criteria to also satisfy the tight ones. Both probabilities are measured in data control samples. To measure real , samples enriched in real leptons from W bosons decays are selected by requiring high E miss T or m W T . The average real is ∼0.75 (∼0.98) in the electron (muon) channel. To measure fake , samples enriched in multijet background are selected by requiring either low E miss T (electron channel) or high impact parameter significance for the lepton track (muon channel). The average fake value is ∼0.35 (∼0.20) in the electron (muon) channel. Dependencies of real and fake on quantities such as lepton p T and η, ∆R between the lepton and the closest jet, or number of b-tagged jets, are parameterised in order to obtain a more accurate estimate.

Search for TT → W b+X production
This search is sensitive to TT production where at least one of the T quarks decays into a W boson and a b-quark, although it is particularly optimised for TT → W + bW −b events. One of the W bosons present in the final state is then required to decay leptonically. After the preselection described in section 4, further background suppression is achieved by applying requirements aimed at exploiting the distinct kinematic features of the signal. The large T quark mass results in energetic W bosons and b-quarks in the final state with large angular separation between them, while the decay products from the boosted W bosons have small angular separation. The combination of these properties is very effective in distinguishing the dominant tt background since tt events with boosted W boson configurations are rare and are typically characterised by a small angular separation between the W boson and the b-quark from the top quark decay.
To take advantage of these properties, it is necessary to identify the hadronically decaying W boson (W had ) as well as the b-jets in the event. The candidate b-jets are defined as the two jets with the highest b-tag discriminant value, although only one of them is explicitly required to be b-tagged in the event selection. candidates are characterised by two reconstructed jets. In the construction of both types of W had candidates, the two candidate b-jets are not considered.
A W type I had candidate is defined as a single jet with p T > 400 GeV, which is the typical p T above which the decay products from a W boson would have an angular separation ∆R ≤ R cone = 0.4. A W type II had candidate is defined as a dijet system with p T > 250 GeV, angular separation ∆R( j, j) < 0.8 and mass within the range of 60-120 GeV. The asymmetric window about the W-boson mass value is chosen in order to increase the acceptance for hadronically decaying Z bosons from TT → WbZt events. Any jets satisfying the W type I had requirements are excluded from consideration when forming W type II had candidates. The leptonically decaying W boson (W lep ) is reconstructed using the lepton and E miss T , which is taken as a measurement of the neutrino p T . Requiring that the invariant mass of the lepton-neutrino system equals the nominal W boson mass allows reconstruction of the longitudinal momentum of the neutrino up to a two-fold ambiguity. If two solutions exist, they are both considered. If no real solution exists, the pseudorapidity of the neutrino is set equal to that of the lepton, since in the kinematic regime of interest the decay products of the W boson tend to be collinear. Table 1 summarises the event selection requirements. Two selections, "loose" and "tight", are defined, with the latter being more restrictive than the former and representing the final selection. As discussed below, the loose selection is used to validate the background modelling in a kinematic regime close to the final selection. The loose selection considers preselected events with at least one W type I had or W type II had candidate. If multiple W had candidates are found in a given event, the one with the highest p T is chosen. Figure 4(a) shows the distribution of the number of W had candidates after preselection. The events must satisfy H T > 800 GeV, where H T is the scalar sum of the lepton p T , E miss T and the p T of the selected jets. The H T distribution peaks at ∼2m T for signal events, which makes the H T > 800 GeV requirement particularly efficient for signal with m T 400 GeV, while rejecting a large fraction of the background. Figure 4(b) shows the distribution of H T after the requirement of ≥1 W had candidate and prior to the H T > 800 GeV requirement. In addition, the highest-p T b-jet candidate (b 1 ) and the next-to-highest-p T b-jet candidate (b 2 ) are required to have p T (b 1 ) > 160 GeV and p T (b 2 ) > 110 (80)   The tight selection adds further requirements that are particularly effective at suppressing tt background.

Requirements Preselection
Exactly one electron or muon E miss First, a large angular separation between the W bosons and the b-jets from the top quark decay is required: min(∆R( , b 1,2 )) > 1.4 and min(∆R(W had , b 1,2 )) > 1.4. Figure 5(b) shows the distributions of min(∆R( , b 1,2 )) after loose selection and prior to the min(∆R( , b 1,2 )) > 1.4 requirement. Finally, additional requirements are made on is the smallest absolute difference between the reconstructed heavy-quark masses obtained by pairing the W lep and W had candidates with the two b-jet candidates as described in the following. The reconstruction of the W lep candidate usually yields two solutions, and there are two possible ways to pair the b-jet candidates with the W boson candidates to form the heavy quarks. Among all possible combinations, the one yielding the smallest ∆m is chosen. The main discriminating variable used in this search is the reconstructed heavyquark mass (m reco ), built from the W had candidate and one of the two b-jet candidates. The resulting m reco distributions for the loose and tight selections are shown in figure 6 for the sum of W type I had and W type II had events. The tight selection has the better expected sensitivity, and only this selection is chosen to derive the final result of the search. The loose selection, displaying a significant tt background at low m reco which is in good agreement with the expectation, provides further confidence in the background modelling prior to the application of b-jet isolation requirements in the tight selection. Table 2 presents a summary of the background estimates for the loose and tight selections, as well as a comparison of the total predicted and observed yields. The quoted uncertainties include both the statistical and systematic contributions. The latter are discussed in section 10. The predicted and observed yields are in agreement within these uncertainties.  Figure 4: TT → Wb+X search: distribution of (a) the number of hadronically decaying W boson (W had ) candidates after preselection requirements, and (b) the scalar sum (H T ) of the transverse momenta of the lepton, the selected jets and the missing transverse momentum after preselection and ≥1 W had candidate requirements. The data (solid black points) are compared to the SM prediction (stacked histograms). The contributions from backgrounds other than tt are combined into a single background source referred to as "Non-tt". The total uncertainty on the background estimation is shown as a black hashed band. The expected contribution from a vector-like T quark with mass m T = 600 GeV under the assumption BR(T → Wb) = 1, multiplied by a factor of 50, is also shown (red dashed histogram). The lower panel shows the ratio of data to the SM prediction. The last bin contains the overflow.

Search for TT → Ht+X and tt tt production
This search is focused on TT production where at least one of the T quarks decays into a Higgs boson and a top quark resulting from the following processes: TT → HtHt, ZtHt and WbHt. 8 For the dominant H → bb decay mode, the final-state signature is characterised by high jet and b-tag multiplicities, which provide a powerful experimental handle to suppress the background. Similarly, this search is also sensitive to TT → ZtZt and WbZt, with Z → bb. High jet and b-tag multiplicities are also characteristic of tttt events (both within the SM and in BSM extensions), which makes this search also sensitive to this process. Figure 7(a) compares the jet multiplicity distribution after preselection (described in section 4) between the total background and several signal scenarios. Signal events have, on average, higher jet multiplicity than the background. The higher b-quark content of signal events results in a higher b-tag multiplicity than for the background, as illustrated in figure 7(b) for events with ≥6 jets. Therefore, after preselection, the final selection requirements are ≥5 jets of which ≥2 jets are b-tagged, leaving a sample completely dominated by tt+jets background. In order to ensure a non-overlapping analysis sample and to facilitate the combination of results, events accepted by the Wb+X search are rejected. This veto only removes about 2% of the events with ≥6 jets and ≥4 b-tagged jets in data.
In order to optimise the sensitivity of the search, the selected events are categorised into different channels depending on the number of jets (5 and ≥6) and on the number of b-tagged jets (2, 3 and ≥4). The channel with ≥6 jets and ≥4 b-tagged jets has the largest signal-to-background ratio and therefore drives the sensitivity of the search. The channels with two and three b-tagged jets have significantly lower signal-to-background ratio. These are particularly useful to calibrate the tt+jets background prediction and constrain the related systematic uncertainties. In the case of the channel with ≥6 jets and ≥4 b-tagged jets the background uncertainty is dominated by uncertainties on the b-tagging, jet energy calibration and physics modelling, including the tt+HF content. A detailed discussion of the systematic uncertainties considered is given in section 10. In addition, events with ≥6 jets and 3 or ≥4 b-tagged jets are split into two channels each depending on the value of the invariant mass of the two b-tagged jets with lowest ∆R separation: M min∆R For high values of m T , the Higgs boson from the T → Ht decay has high p T , and the bb pair from the Higgs boson decay has smaller angular separation than other pairs resulting from combinatorial background. As shown in figure 8(a), the M min∆R bb variable provides a good approximation to the reconstructed H → bb invariant mass and allows the separation of these channels into channels depleted or enriched in T → Ht, H → bb decays, the latter having a higher signal-to-background ratio. Therefore, the total number of   Figure 7: TT → Ht+X search (simulated events): comparison of (a) the jet multiplicity distribution after preselection, and (b) the b-tag multiplicity distribution after the requirement of ≥6 jets, between the total background (shaded histogram) and several signal scenarios considered in this search: TT production in the T quark singlet (red solid histogram) and doublet (red dashed histogram) cases, and sgluon pair production giving a four-top-quark final state (red dotted histogram). A mass of 600 GeV is assumed for the T quark and the sgluon.   analysis channels considered in this search is eight: To further improve the separation between signal and background, the distinct kinematic features of the signal are exploited. In particular, the large T quark mass results in energetic leptons and jets in the final state, and H T provides a suitable discriminating variable between signal and background. Figure 8(b) compares the H T distribution between signal and background for events with ≥6 jets and ≥4 b-tagged jets. The H T distribution is quite similar for different signal scenarios corresponding to pair production of exotic particles with the same mass (600 GeV in this case), and significantly different from that of the background. The discrimination between signal and background increases with mass. Figures 9 and 10 show the comparison of data and prediction for the H T distributions in each of the analysis channels considered. The corresponding predicted and observed yields per channel can be found in table 3. Following the statistical procedure outlined in section 11, a fit to the observed H T distributions in data in the eight analysis channels is performed. This provides an improved background prediction with smaller uncertainties, and hence improved sensitivity to a signal. The results are presented in section 12.

Search for BB → Hb+X production
This search is focused on BB production where at least one of the B quarks decays into a Higgs boson and a b quark, a decay mode that was omitted from previous searches [25][26][27]. In particular, the BB → HbHb   Table 3: TT → Ht+X search: predicted and observed yields in each of the analysis channels considered. The background prediction is shown before the fit to data. Also shown are the signal predictions for different benchmark scenarios considered. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties on the yields. Consequently, this search considers the same discriminating variable, H T , and the same eight analysis channels as the TT → Ht+X search. Figure 11(a) illustrates the good separation between signal and background in the H T distribution for events passing the preselection requirements and with ≥ 6 jets and ≥ 4 b-tagged jets. A peculiarity of the B → Hb decay mode is that the b-jet originating (directly) from the B-quark decay can have very high transverse momentum in the case of a heavy B quark. To exploit this feature, the event selection is tightened relative to that used in the TT → Ht+X search by raising the minimum p T requirement on the two highest-p T (leading) b-tagged jets to p T > 150 GeV. Figure 11(b) shows the distribution of the subleading b-jet p T for events passing the preselection requirements and with ≥ 6 jets and ≥ 4 b-tagged jets. The tighter requirement on the subleading b-jet p T rejects about 90% of the tt background while retaining a large acceptance for the BB → Hb+X signal. This search is also sensitive to other BB final states, such as BB → HbWt, that typically do not involve multilepton final states in the topologies usually searched for (opposite-sign dileptons with a Z → + − candidate, same-sign dileptons, and trileptons), and is thus complementary to previous searches [25-27].    Table 4: BB → Hb+X search: predicted and observed yields in each of the analysis channels considered. The background prediction is shown before the fit to data. Also shown are the signal predictions for different benchmark scenarios considered. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties on the yields.

Systematic uncertainties
Several sources of systematic uncertainty are considered that can affect the normalisation of signal and background and/or the shape of their corresponding final discriminant distributions. Individual sources of systematic uncertainty are considered uncorrelated. Correlations of a given systematic uncertainty are maintained across processes and channels. Table 5 presents a list of all systematic uncertainties considered in the analyses and indicates whether they are taken to be normalisation-only, or to affect both shape and normalisation. Table 6 presents a summary of the systematic uncertainties for the TT → Wb+X search and their impact on the normalisation of signal and backgrounds. A similar summary is presented for the TT → Ht+X and BB → Hb+X searches in tables 7 and 8 respectively, restricted to the highest-sensitivity channel and displaying only the signal and the tt+jets background categories. Tables 7 and 8 also show the impact of the systematic uncertainties before and after the fit to data.
In the case of the TT → Wb+X search, the total systematic uncertainty in the background normalisation is approximately 29%, with the dominant contributions originating from the normalisation of the W+jets background (20%), jet energy scale (+17%/−12%) and the tt+HF normalisation (11%). The total systematic uncertainty in the signal normalisation is +8%/−10%, with comparable contributions from jet energy scale and b-tagging uncertainties.
The leading sources of systematic uncertainty in the TT → Ht+X and BB → Hb+X searches vary depending on the analysis channel considered, but they typically originate from tt+jets modelling (including tt+HF), jet energy scale and b-tagging. For example, the total systematic uncertainty in the background normalisation in the highest-sensitivity channel (≥6 j, ≥4 b, high M min∆R bb ) of the TT → Ht+X search is approximately 37%, with the largest contributions originating from tt+HF normalisation (23%), jet energy scale (10%) and b-tagging (9%). However, as discussed previously, the fit to data in the eight analysis channels in these searches allows the overall background uncertainty to be reduced significantly, to approximately 5% in the case of the TT → Ht+X search. More details about the fit to data can be found in section 12.1. The total systematic uncertainty on the signal normalisation is approximately 15%, almost all due to b-tagging uncertainties.
The following sections describe each of the systematic uncertainties considered in the analyses.

Luminosity
The uncertainty on the integrated luminosity is 2.8%, affecting the overall normalisation of all processes estimated from the simulation. It is derived following the same methodology as that detailed in ref. [57].

Leptons
Uncertainties associated with leptons arise from the reconstruction, identification and trigger, as well as the lepton momentum scale and resolution. The reconstruction and identification efficiency of electrons and muons, as well as the efficiency of the trigger used to record the events, differ slightly between data and simulation. Scale factors are derived using tag-and-probe techniques on Z → + − ( = e, µ) data  Table 5: List of systematic uncertainties considered. An "N" means that the uncertainty is taken as normalisationonly for all processes and channels affected, whereas "SN" means that the uncertainty is taken on both shape and normalisation. Some of the systematic uncertainties are split into several components for a more accurate treatment. and simulated samples, and are applied to the simulation to correct for differences. Additional sources of uncertainty originate from the corrections applied to adjust the lepton momentum scale and resolution in the simulation to match those in data, measured using reconstructed distributions of the Z → + − and J/ψ → + − masses, as well as the measured E/p in W → eν events, where E and p are the electron energy and momentum, as measured by the calorimeter and the tracker respectively. The combined effect of all these uncertainties results in an overall normalisation uncertainty on the signal and background of

Jets and missing transverse momentum
Uncertainties associated with jets arise from the efficiency of jet reconstruction and identification based on the JVF variable, as well as the jet energy scale and resolution. The uncertainty associated with the jet reconstruction efficiency is assessed by randomly removing 0.2% of the jets with p T below 30 GeV, which is the level of disagreement between data and the simulation, and has a negligible impact in the analysis. The per-jet efficiency to satisfy the JVF requirement is measured in Z(→ + − )+1-jet events in data and simulation, selecting separately events enriched in hard-scatter jets and events enriched in jets from pileup, and good agreement is found. The associated uncertainty is estimated by changing the nominal JVF cut value by ±0.1 and repeating the analysis using the modified cut value, resulting in normalisation uncertainties in the range of 1-5%, depending on the jet multiplicity under consideration and the p T spectra of the jets. The jet energy scale and its uncertainty were derived by combining information from test-beam data, LHC collision data and simulation [54]. The jet energy scale uncertainty is split into 22 uncorrelated sources with their respective jet p T and η dependences and are treated independently in this analysis. It represents one of the leading sources of uncertainty associated with reconstructed objects, affecting the normalisations of signal and backgrounds by approximately 5% and 15% respectively, in the most signal-rich channels considered. The jet energy resolution was measured in data and simulation  ) channel and their impact (in %) on the normalisation of signal and backgrounds, before and after the fit to data. Only sources of systematic uncertainty resulting in a normalisation change of at least 0.5% are displayed. The signal shown corresponds to a singlet vector-like T quark with mass m T = 600 GeV. The total post-fit uncertainty can be different from the sum in quadrature of individual sources due to the anti-correlations between them resulting from the fit to the data. as a function of jet p T and rapidity using dijet events. They are found to agree within 10%, and the corresponding uncertainty is assessed by smearing the jet p T in the simulation.
The E miss T reconstruction is affected by uncertainties associated with leptons and jet energy scales and resolutions, which are propagated to E miss T and thus are included under the corresponding uncertainty categories in tables 6-8. Additional small uncertainties associated with the modelling of the underlying event, in particular its impact on the p T scale and resolution of unclustered energy, are also taken into account and are displayed in tables 6-8 under the category of "Missing transverse momentum".

Heavy-and light-flavour tagging
Efficiencies to tag jets from b-and c-quarks in the simulation are corrected to match the efficiencies in data by p T -dependent factors in the approximate ranges 0.9-1.0 and 0.9-1.1 respectively, whereas the light-jet efficiency is scaled by p T -and η-dependent scale factors in the range 1.2-1.5 [55,122]. Uncertainties on these scale factors include a total of six independent sources affecting b-jets and four independent sources affecting c-jets. Each of these uncertainties has different jet p T dependence. Twelve uncertainties are considered for the light-jets tagging, which depend on the jet p T and η regions. These systematic uncertainties are taken as uncorrelated between b-jets, c-jets, and light-jets. An additional uncertainty is included due to the extrapolation of the b-, c-, and light-jet-tagging scale factors for jets   with p T beyond the kinematic reach of the data calibration samples used: p T > 300 GeV for b-and c-jets, and p T > 750 GeV for light-jets. This uncertainty is evaluated in the simulation by comparing the tagging efficiencies while varying e.g. the fraction of tracks with shared hits in the silicon detectors or the fraction of fake tracks resulting from random combinations of hits, both of which typically increase at high p T due to growing track multiplicity and density of hits within the jet. These uncertainties are taken to be correlated among the three jet flavours. As an example, the uncertainties on the tagging efficiencies for b-jets and c-jets with 300 GeV ≤ p T < 500 GeV are 14% and 23% respectively.

tt+jets
A number of systematic uncertainties affecting the modelling of tt+jets are considered. These include the uncertainty on the theoretical prediction for the inclusive cross section, uncertainties associated with the reweighting procedure applied to tt+light-jets and tt + cc processes, uncertainties affecting the modelling of tt+HF-jets production, and uncertainties associated with the choice of parton shower and hadronisation model. A summary of these uncertainties can be found below. Additional details can be found in ref. [98].
An uncertainty of +5%/−6% is assumed for the inclusive tt production cross section [58], including contributions from varying the factorisation and renormalisation scales and uncertainties arising from the PDF, α S and the top quark mass. The PDF and α S uncertainties were calculated using the PDF4LHC prescription.
Uncertainties associated with the reweighting procedure applied to tt+light-jets and tt + cc processes include the nine leading sources of uncertainty in the differential cross section measurement at √ s = 7 TeV [94], dominated by the modelling of initial-and final-state radiation and the choice of event generator for tt production.
Uncertainties affecting the modelling of tt + bb production include those associated with the NLO prediction from Sherpa+OpenLoops, which is used for reweighting of the default Powheg tt + bb prediction. These include three different scale variations, including changing the functional form of the renormalisation scale, changing the functional form of the factorisation and resummation scales, and varying the renormalisation scale by a factor of two up and down. In addition, a different shower recoil model scheme and two alternative PDF sets (MSTW and NNPDF) are considered. A fraction of the tt + bb background predicted by Powheg+Pythia originates from multiple parton interactions or final-state radiation from top decay products. Such backgrounds are not part of the NLO prediction, and these two categories are kept separate and subject to additional normalisation uncertainties. The NLO corrections and associated systematic uncertainties are adjusted so that the overall normalisation of the tt + bb background at the particle level is fixed, i.e. effectively only migrations across categories and distortions to the shape of the kinematic distributions are considered. Detailed comparisons of tt + bb between Powheg+Pythia and Sherpa+OpenLoops show that the cross sections agree to better than 50%, which is taken as a normalisation uncertainty for tt + bb.
Beyond the uncertainties associated with the reweighting procedure, additional uncertainties are assigned to the modelling of the tt + cc component of the background, which again is not part of the NLO prediction used for tt + bb. These include two uncertainties taken as the full difference between applying and not applying the reweightings of the top quark and tt p T spectra. In addition, four uncertainties are considered associated with the choice of LO generator: the full difference between Powheg+Pythia and Madgraph5+Pythia simulations, as well as variations in generator parameters (factorisation and renormalisation scales, matching threshold and c-quark mass), which are derived using Madgraph5+Pythia simulations and applied to the Powheg+Pythia simulation. Analogously to the procedure used in the tt + bb background estimate, these uncertainties are adjusted so that the overall normalisation of the tt + cc background at the particle level is fixed. Finally, an overall normalisation uncertainty of 50% is also assigned to the tt + cc component, taken as uncorrelated with the same normalisation uncertainty applied to tt + bb, since only the tt + bb process is normalised to a NLO prediction.
An uncertainty due to the choice of parton shower and hadronisation model is derived by comparing events produced by Powheg interfaced to Pythia or Herwig. In the case of tt+light-jets and tt + cc, a reweighting of the top quark and tt p T spectra is also applied to the Powheg+Herwig samples to ensure reliable modelling of the top quark kinematics. The corresponding correction factors were recalculated for Powheg+Herwig in order to match the differential cross section measurements at √ s = 7 TeV. In the case of tt + bb, the various HF categories and the corresponding partonic kinematics in Powheg+Herwig are reweighted to match the NLO prediction of Sherpa+OpenLoops, so that only the effect of changing the hadronisation model is propagated. Given the different effect of this uncertainty on the tt+light-jets, tt + cc and tt + bb, it is treated as uncorrelated between the three processes. This treatment prevents an undue reduction of this systematic uncertainty on tt + cc and tt + bb by constraining it for tt+light-jets via the fit to data in the highly populated channels with two b-tagged jets.

W/Z+jets
Uncertainties affecting the modelling of the W/Z+jets background include 5% from their respective normalisations to the theoretical NNLO cross sections [101], as well as an additional 24% normalisation uncertainty added in quadrature for each additional inclusive parton multiplicity bin, based on a comparison among different algorithms for merging LO matrix elements and parton showers [123]. The above uncertainties are taken as uncorrelated between W+jets and Z+jets.

Other simulated background
Uncertainties affecting the modelling of the single-top-quark background include a +5%/−4% uncertainty on the total cross section estimated as a weighted average of the theoretical uncertainties on t-, Wt-and schannel production [105][106][107], as well as a systematic uncertainty on Wt-channel production concerning the separation between tt and Wt at NLO [124]. The latter is estimated by comparing the nominal sample, which uses the so-called "diagram subtraction" scheme, with an alternative sample using the "diagram removal" scheme.
Uncertainties on the diboson background normalisation include 5% from the NLO theoretical cross sections [108] added in quadrature to an uncertainty of 24% due to the extrapolation to the high jet multiplicity channels, following the procedure discussed in section 10.3.2.
Uncertainties on the ttV and ttH normalisations are 30% and +9%/−12% respectively, from the uncertainties on their respective NLO theoretical cross sections [112,120,125]. Additional small uncertainties arising from scale variations, which change the amount of initial-state radiation and thus the event kinematics, are also included.

Multijet
Uncertainties on the data-driven multijet background estimate receive contributions from the limited sample size in data, particularly at high jet and b-tag multiplicities, as well as from the uncertainty on the rate of fake leptons, estimated in different control regions (e.g. selected with either an upper E miss T or m W T requirement). A combined normalisation uncertainty of 50% due to all these effects is assigned, which is taken as correlated across jet and b-tag multiplicity bins, but uncorrelated between electron and muon channels. No explicit shape uncertainty is assigned since the large statistical uncertainties associated with the multijet background prediction, which are uncorrelated bin-to-bin in the final discriminating variable, effectively cover all possible shape uncertainties.

Statistical analysis
For a given search, the distributions of the final discriminating variables in each of the analysis channels considered are combined to test for the presence of a signal. The statistical analysis is based on a binned likelihood function L(µ, θ) constructed as a product of Poisson probability terms over all bins considered in the analysis. This function depends on the signal-strength parameter µ, a multiplicative factor to the theoretical signal production cross section, and θ, a set of nuisance parameters that encode the effect of systematic uncertainties on the signal and background expectations and are implemented in the likelihood function as Gaussian or log-normal priors. Therefore, the total number of expected events in a given bin depends on µ and θ. The nuisance parameters θ allow variations of the expectations for signal and background according to the corresponding systematic uncertainties, and their fitted values correspond to the deviations from the nominal expectations that globally provide the best fit to the data. This procedure allows a reduction of the impact of systematic uncertainties on the search sensitivity by taking advantage of the highly populated background-dominated channels included in the likelihood fit. It requires a good understanding of the systematic effects affecting the shapes of the discriminant distributions. Detailed validation studies of the fitting procedure have been performed using the simulation. To verify the improved background prediction, fits are performed under the background-only hypothesis. Differences between the data and the background prediction are checked relative to the smaller post-fit uncertainties in kinematic variables other than the ones used in the fit.
The test statistic q µ is defined as the profile likelihood ratio: q µ = −2 ln(L(µ,θ µ )/L(μ,θ)), whereμ and θ are the values of the parameters that maximise the likelihood function (with the constraint 0 ≤μ ≤ µ), andθ µ are the values of the nuisance parameters that maximise the likelihood function for a given value of µ. Statistical uncertainties in each bin of the discriminant distributions are also taken into account via dedicated parameters in the fit. The test statistic q µ is implemented in the RooFit package [126,127] and is used to measure the compatibility of the observed data with the background-only hypothesis (i.e. the discovery test) setting µ = 0 in the profile likelihood ratio: q 0 = −2 ln(L(0,θ 0 )/L(μ,θ)). The p-value (referred to as p 0 ) representing the compatibility of the data with the background-only hypothesis is estimated by integrating the distribution of q 0 from background-only pseudo-experiments, approximated using the asymptotic formulae given in ref. [128,129], above the observed value of q 0 . Some model dependence exists in the estimation of the p 0 -value, as a given signal scenario needs to be assumed in the calculation of the denominator of q µ , even if the overall signal normalisation is left floating and fitted to data. The observed p 0 -value is checked for each explored signal scenario. In the absence of any significant excess above the background expectation, upper limits on the signal production cross section for each of the signal scenarios considered are derived by using q µ in the CL s method [130,131]. For a given signal scenario, values of the production cross section (parameterised by µ) yielding CL s <0.05, where CL s is computed using the asymptotic approximation [128,129], are excluded at ≥95% CL.

Results
This section presents the results obtained from the searches discussed in sections 7-9, following the statistical analysis discussed in section 11.

Likelihood fits to data
The consideration of high-statistics background-dominated channels in the analysis allows an improved background prediction with significantly reduced systematic uncertainties to be obtained during the statistical analysis, as discussed in section 11. This is the strategy adopted in the TT → Ht+X and BB → Hb+X searches. In contrast, the small number of data events in the TT → Wb+X search results in virtually the same background prediction and uncertainties both pre-fit and post-fit. Figures 14  and 15 show the comparison of data and the post-fit background prediction for the H T distributions in each of the analysis channels considered in the TT → Ht+X search. The corresponding comparisons for the BB → Hb+X search can be found in figures 16 and 17. The fit to the data is performed under the background-only hypothesis. Tables with the corresponding predicted and observed yields per channel can be found in appendix A.
Compared to the pre-fit distributions shown in sections 8 and 9, the total background uncertainty is significantly reduced after the fit, not only in the background-dominated channels, but also in the signal-rich channels. The reduced uncertainty results from the significant constraints provided by the data on some systematic uncertainties, as well as the anti-correlations among sources of systematic uncertainty resulting from the fit to the data. For example, the uncertainty in the tt+bb background in the highest-sensitivity channel (≥6 j, ≥4 b, high M min∆R bb ) is reduced from about 60% prior to the fit to about 15% and 30% in the TT → Ht+X and the BB → Hb+X searches, respectively. The larger post-fit uncertainty in the case of the BB → Hb+X search is partly caused by the smaller number of data events due to the selection requirements being tighter than in the TT → Ht+X search.

Limits on TT production
The compatibility of the data with the background prediction is assessed by computing the p 0 -value for each signal scenario considered, defined by the assumed values for the heavy quark mass (see Sect. 5.1) and the three decay branching ratios, which are varied in steps of 0.05 requiring that they add up to unity. In the case of the TT → Wb+X search alone, the smallest p 0 -value found, 0.023, is obtained for m T = 600 GeV, BR(T → Wb) = 0.30 and BR(T → Ht) = 0.65 [BR(T → Zt) = 1 − BR(T → Wb) − BR(T → Ht) = 0.05], and corresponds to a local significance of 2.0 standard deviations above the background-only prediction. In the case of the TT → Ht+X search, the smallest p 0 -value found, 0.44, is obtained for m T = 600 GeV, BR(T → Wb) = 0.0, BR(T → Ht) = 0.0, and BR(T → Zt) = 1.0, and corresponds to a local significance of 0.2 standard deviations above the background-only prediction. Thus, no significant excess above the background expectation is found in either of the two searches.
Since the two searches have complementary sensitivity to different decay modes of a vector-like T quark, they are combined in a single likelihood function taking into account the correlation of systematic uncertainties. Upper limits at 95% CL on the TT production cross section are set in several benchmark scenarios as a function of the T quark mass m T and are compared to the theoretical prediction from Top++, as shown in figure 18. The resulting lower limits on m T correspond to the central value of the theoretical cross section. The scenarios considered involve different assumptions on the decay branching ratios: BR(T → Wb) = 1, singlet and doublet. Only the TT → Wb+X search is sensitive to a T quark with BR(T → Wb) = 1, yielding an observed (expected) 95% CL lower limit of m T > 770 (795) GeV. This represents the most stringent limit to date, and is also applicable to a Y vector-like quark with electric charge of −4/3 and decaying into a W − boson and a b quark. Both searches are sensitive to a vector-like singlet T quark. The TT → Wb+X and TT → Ht+X searches yield observed (expected) 95% CL limits of m T > 660 (670) GeV and m T > 765 (720) GeV respectively. The combination of both analyses results in a slight improvement over the TT → Ht+X search alone, yielding m T > 800 (755) GeV. Finally, only the TT → Ht+X search is sensitive to a vector-like doublet T quark, yielding an observed (expected) 95% CL lower limit of m T > 855 (820) GeV.
The same searches are used to derive exclusion limits on vector-like T quark production for different values of m T and as a function of BR(T → Wb) and BR(T → Ht). To probe this branching ratio plane, the signal samples are reweighted by the ratio of the desired branching ratio to the original branching ratio in Protos, and the complete analysis is repeated. The resulting 95% CL exclusion limits are shown in figure 19 for the combination of the TT → Wb+X and TT → Ht+X searches, for different values  The combined results set observed lower limits on the T quark mass ranging between 715 GeV and 950 GeV for all possible values of the branching ratios into the three decay modes. This implies that any branching ratio scenario is excluded at 95% CL for a T quark with mass below 715 GeV. The corresponding range of expected lower limits is between 675 GeV and 885 GeV. The exclusion limits for the individual searches can be found in appendix B. These figures illustrate the complementarity of these searches and how their combination improves over simply taking the most sensitive search for each assumed branching ratio scenario, leading to large regions in the branching ratio plane being excluded.
In addition to the combined TT → Wb+X and TT → Ht+X result discussed in this paper, the ATLAS Collaboration has performed searches for TT production in several multilepton final states: same-sign dileptons and trileptons [27] and opposite-sign dileptons and trileptons with a Z boson candidate [25] (referred to as the Zb/t+X search). These searches have overlapping selections and have not been combined. Figure 21 summarises the most restrictive observed and expected T quark mass limits in the plane of BR(T → Ht) versus BR(T → Wb), set by any of these searches. The observed lower limits on the T quark mass range between 730 GeV and 950 GeV for all possible values of the branching ratios into the three decay modes, representing an improvement over previous results [28]. The corresponding range of expected lower limits is between 715 GeV and 885 GeV.

Limits on tt tt production
The Ht+X analysis is also used to set limits on four-top-quark production considering different signal benchmark scenarios: SM-like tttt, tttt via an EFT model with a four-top-quark contact interaction, sgluon pair production with decay into tt, and tttt+X via the 2UED/RPP model. Except for the case of SM-like tttt production, for which the ATLAS multilepton search [27] achieves the best expected sensitivity, in all other benchmark scenarios this analysis achieves the most restrictive expected bounds.
In the case of tttt production with the SM kinematics, the observed (expected) 95% CL upper limit on the production cross section is 23 fb (32 fb), or 34 (47) times the SM prediction. In this scenario the expected sensitivity of this analysis is comparable to that of previous searches [27,42]. In the case of tttt production via an EFT model, the observed (expected) 95% CL upper limit on the production cross section is 12 fb (16 fb). The improved sensitivity in the case of the EFT model results from the harder H T spectrum compared to that of SM tttt production. The upper limit on the production cross section can be translated into an observed (expected) limit on the free parameter of the model, |C 4t |/Λ 2 < 6.6 TeV −2 (7.7 TeV −2 ).
The resulting observed and expected upper limits on the sgluon pair production cross section times branching ratio are shown in figure 26 as a function of the sgluon mass and are compared to the theoretical prediction. The observed (expected) 95% CL limit on the sgluon mass is 1.06 TeV (1.02 TeV).
Finally, in the context of the 2UED/RPP model, the observed and expected upper limits on the production cross section times branching ratio are shown in figure 27 as a function of m KK for the symmetric case (ξ = R 4 /R 5 = 1), assuming production by tier (1,1) alone. The comparison to the LO theoretical cross section translates into an observed (expected) 95% CL limit on m KK of 1.12 TeV (1.10 TeV). Four-topquark events can also arise from tiers (2,0) and (0,2). In those tiers the theoretical production cross sections can be calculated, leading to more robust results (i.e. there is no need to assume a particular       branching ratio). The dependence of the tier kinematics on the tier mass also allows the extrapolation of constraints on tier (1,1) to tiers (2,0) and (0,2). Excluding a given production cross section for tier (1,1) at a given m KK is equivalent to excluding this production cross section for tier (2,0) alone at m KK / √ 2 and for tier (0,2) at m KK / √ 2ξ. The contribution of tier (0,2) vanishes as ξ increases (highly asymmetric case). Figure 28 presents the observed and expected upper limits on the production cross section times branching ratio as function of m KK for two scenarios: tiers (2,0)+(0,2) alone in the symmetric case, and tier (2,0) alone in the highly asymmetric case. In both cases a branching ratio of A (1,1) → tt of 0% is assumed. The corresponding observed (expected) 95% CL limits on m KK are 0.61 TeV (0.60 TeV) and 0.57 TeV (0.55 TeV) respectively.   95% CL observed limit 95% CL expected limit σ 1 ± 95% CL expected limit σ 2 ± 95% CL expected limit (b) Figure 28: Observed (solid line) and expected (dashed line) 95% CL upper limits on the production cross section times branching ratio of four-top-quark events as a function of the Kaluza-Klein mass (m KK ) from (a) tiers (2,0)+(0,2) alone in the symmetric case and (b) tier (2,0) alone in the highly asymmetric case. The surrounding shaded bands correspond to ±1 and ±2 standard deviations around the expected limit. The thin red line shows the theoretical prediction for the production cross section of four-top-quark events.

Conclusion
A search for pair production of vector-like quarks, both up-type (T ) and down-type (B), as well as fourtop-quark production has been performed using pp collision data at √ s = 8 TeV corresponding to an integrated luminosity of 20.3 fb −1 recorded with the ATLAS detector at the CERN Large Hadron Collider. The final states considered have an isolated electron or muon with high transverse momentum, large missing transverse momentum and at least four jets. Three different analyses are optimised to reach the best sensitivity to the decay channels TT → Wb+X, TT → Ht+X and BB → Hb+X.
No significant deviation from the Standard Model expectation is observed and lower limits on the masses of the vector-like T (B) quark are derived as a function of the branching ratios BR(T → Wb), BR(T → Zt), and BR(T → Ht) (respectively BR(B → Wt), BR(B → Zb), and BR(B → Hb)). The combination of the TT → Wb+X, TT → Ht+X analyses yields observed lower limits on the T quark mass ranging between 715 GeV and 950 GeV for all possible values of the branching ratios into three decay modes, and are the most stringent constraints to date. The BB → Hb+X analysis is the first search to target specifically this decay mode and leads to an observed lower limit on the B quark mass of 580 GeV for BR(B → Hb) = 1. Finally, a summary of all ATLAS vector-like quark pair production searches is given. For BB production, the observed lower limits on the B quark mass range between 575 GeV and 813 GeV for all possible values of the branching ratios into the three decay modes.
The TT → Ht+X analysis is also used to set limits on four-top-quark production, both in the Standard Model and in several new physics scenarios, including a four-fermion contact interaction, sgluon pair production and a universal extra dimensions model. In the case of Standard Model production, a cross section larger than 23 fb is excluded at the 95% CL. The most restrictive limits to date are obtained for four-top-quark production in the various new physics scenarios considered. tt+light-jets 32200 ± 1500 2940 ± 220 49.  Table 9: TT → Ht+X search: predicted and observed yields in each of the analysis channels considered. The background prediction is shown after the fit to data under the background-only hypothesis. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties on the yields, computed taking into account correlations among nuisance parameters and among processes.  Table 10: BB → Hb+X search: predicted and observed yields in each of the analysis channels considered. The background prediction is shown after the fit to data under the background-only hypothesis. The quoted uncertainties are the sum in quadrature of statistical and systematic uncertainties on the yields, computed taking into account correlations among nuisance parameters and among processes.
B. Limits on TT production from individual searches Figure 29 shows 95% CL upper limits on the TT production cross section as a function of the T quark mass obtained by the individual TT → Wb+X and TT → Ht+X searches for the singlet scenario. The TT → Wb+X and TT → Ht+X searches yield observed (expected) 95% CL limits of m T > 660 (665) GeV and m T > 765 (720) GeV respectively. Figure 30 shows the 95% CL exclusion limits on vector-like T quark production, for different values of m T and as a function of the two branching ratios BR(T → Wb) and BR(T → Ht), obtained by the TT → Wb+X search. Figure 31(a,b) present the corresponding expected and observed T quark mass limits respectively, in the plane of BR(T → Ht) versus BR(T → Wb).           [28] CMS Collaboration, Inclusive search for a vector-like T quark with charge 2 3 in pp collisions at √ s =