Search for vectorlike charge 2 = 3 T quarks in proton-proton collisions at

A search for fermionic top quark partners T of charge 2 = 3 is presented. The search is carried out in proton-proton collisions corresponding to an integrated luminosity of 19 . 7 fb − 1 collected at a center-of-mass energy of ﬃﬃﬃ s p ¼ 8 TeV with the CMS detector at the LHC. The T quarks are assumed to be produced strongly in pairs and can decay into tH , tZ , and bW . The search is performed in five exclusive channels: a single-lepton channel, a multilepton channel, two all-hadronic channels optimized either for the bW or the tH decay, and one channel in which the Higgs boson decays into two photons. The results are found to be compatible with the standard model expectations in all the investigated final states. A statistical combination of these results is performed and lower limits on the T quark mass are set. Depending on the branching fractions, lower mass limits between 720 and 920 GeV at 95% confidence level are found. These are among the strongest limits on vectorlike T quarks obtained to date.


I. INTRODUCTION
The discovery of a Higgs boson with a mass of 125 GeV by the ATLAS [1] and CMS [2,3] collaborations motivates the search for exotic states involving the newly discovered particle. The nature of electroweak symmetry breaking and the mechanism that stabilizes the mass of the Higgs particle are not entirely clear. These questions could be explained by physics beyond the standard model (SM), such as supersymmetry. Nonsupersymmetric explanations are given by little Higgs models [4,5], models with extra dimensions [6,7], and composite Higgs models [6][7][8] in which the Higgs boson appears as a pseudo-Nambu-Goldstone boson [9]. These theories predict the existence of heavy vectorlike quarks. The left-handed and righthanded components of vectorlike quarks transform in the same way under the electroweak symmetry group, in contrast to the SM fermions, which transform as chiral particles under the SM symmetry group SUð3Þ c × SUð2Þ L × Uð1Þ Y . This property of the vectorlike quarks allows direct mass terms in the Lagrangian of the form mψψ that do not violate gauge invariance. As a consequence, and in contrast to the other quark families, vectorlike quarks do not acquire their mass via Yukawa couplings. In many of the models mentioned above the vectorlike quarks couple predominantly to the third generation quarks only. This means that they may have the following three decay modes: tH, tZ, and bW [10]. A model of vectorlike T quarks with charge 2=3e, which are produced in pairs via strong interaction, is used as a benchmark for this analysis.
A fourth generation of chiral fermions, replicating one of the three generations of the SM with identical quantum numbers, is disfavored by electroweak fits within the framework of the SM [11]. This is mostly because of large modifications of the Higgs production cross sections and branching fractions (B), if a single SM-like Higgs doublet is assumed. Heavy vectorlike quarks decouple from low energy loop-level electroweak corrections and are not similarly constrained by the measurements of the Higgs boson properties [10].
Early T quark searches by the CMS Collaboration [12][13][14] have assumed 100% branching fractions to various final states. More recent searches [15] do not make specific assumptions for the branching fractions. Searches for T quarks have been performed also by the ATLAS Collaboration, setting lower limits on the T quark mass ranging from 715 to 950 GeV, for different T quark branching fractions [16][17][18].
In this paper, results of searches for T quark production in proton-proton collisions, using the CMS detector at the CERN LHC, are presented for five different decay modes. One of the searches [15] is inclusive and sets limits for all possible branching fractions. This analysis is based on leptonic final states and is described in Sec. VA. The other four analyses have a good sensitivity in optimized regions, but they do not cover the full range of branching fractions. The analysis described in Sec. V B is specifically optimized to find T → bW decays. The searches presented in Sec. V C and Sec. V D are optimized for all-hadronic final states in the decays T → bW and T → tH. The search discussed in Sec. V E is sensitive to T → tH decays, where the Higgs boson decays to a pair of photons. The two analyses presented in Secs. VA and V C are discussed in detail in separate publications [15,19]. The remaining three analysis are published here for the first time.
The CMS detector is briefly described in Sec. II. Section III describes the data and the simulated samples. Section IV gives details about the reconstruction techniques used by the analyses. Section VI describes the combination and the treatment of systematic uncertainties. Section VII presents the results of the combination.

II. THE CMS DETECTOR
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors.
In the region of pseudorapidity jηj < 1. 74 [20], the HCAL cells have widths of 0.087 in η and 0.087 radians in azimuth (ϕ). In the η-ϕ plane, and for jηj < 1. 48, the HCAL cells map on to 5 × 5 ECAL crystals arrays to form calorimeter towers projecting radially outwards from close to the nominal interaction point. At larger values of jηj, the size of the towers increases and the matching ECAL arrays contain fewer crystals. Within each tower, the energy deposits in ECAL and HCAL cells are summed to define the calorimeter tower energies, subsequently used to provide the energies and directions of hadronic jets.
The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with transverse momentum p T ≈ 45 GeV from Z → ee decays ranges from 1.7% for nonshowering electrons in the barrel region to 4.5% for showering electrons in the endcaps [21]. The energy resolution for photons with transverse energy E T ≈ 60 GeV varies between 1.1% and 2.6% in the ECAL barrel, and from 2.2% to 5% in the endcaps [22].
The silicon tracker measures charged particles within the pseudorapidity range jηj < 2.5. It consists of 1440 silicon pixel and 15 148 silicon strip detector modules. For nonisolated particles of 1 < p T < 10 GeV and jηj < 1.4, the track resolutions are typically 1.5% in p T and 25-90 ð45-150Þ μm in the transverse (longitudinal) impact parameter [23].
A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [20].

III. EVENT SAMPLES
This analysis makes use of data recorded with the CMS detector in proton-proton collisions at a center-of-mass energy of ffiffi ffi s p ¼ 8 TeV corresponding to an integrated luminosity of 19.5 fb −1 for the analysis described in Sec. VA, and 19.7 fb −1 for the other analyses. Events are selected by a multistage trigger system. The single-lepton channels are based on single-muon and single-electron triggers. The single-muon sample is obtained by the requirement of an isolated muon candidate, with highlevel trigger thresholds of p T > 24 GeV (inclusive search, Sec. VA) or p T > 40 GeV (single-lepton search, Sec. V B). In the electron sample, a single isolated electron trigger with p T > 27 GeV is required. Multilepton events are selected by requiring at least two lepton candidates, one with p T > 17 GeV and the other with p T > 8 GeV in the high-level trigger. The all-hadronic final states require large hadronic activity in the detector, namely that the scalar p T sum of reconstructed jets is larger than 750 GeV. This quantity is evaluated in the high-level trigger from jets with p T > 40 GeV using calorimeter information only. For searches in the diphoton final state, two photons are required.
The photon E T thresholds in the high-level trigger are 26 (18) GeV and 36 (22) GeV on the leading (subleading) photon, depending on the running period.
The contributions from SM processes are generally predicted using simulated event samples. For some backgrounds, however, the simulations are not fully reliable, and control samples of data are used to determine their contribution. The background estimation for the individual channels is discussed in Sec. V.
For W þ jets and Z þ jets production, samples with up to four partons are generated and merged using the MLM scheme with k T jets [29,30]. The CTEQ6M parton distribution functions (PDF) are used for POWHEG, while for the other generators the CTEQ6L1 [31] PDFs are used. In all cases, PYTHIA 6.426 [28] is used to simulate the hadronization and the parton showering.
The TT signal process is simulated using MADGRAPH 5.1, allowing up to two additional hard partons. A series of mass hypotheses between 500 and 1000 GeV are generated in steps of 100 GeV. The inclusive cross sections for the signal samples and the tt samples are calculated at next-to-next-to-leading order (NNLO) for gg → tt þ X. The fixed-order calculations are supplemented with soft-gluon resummations having next-to-next-to-leading logarithmic accuracy [32]. The tt cross sections are computed based on the TOP++ v2.0 implementation using the MSTW2008nnlo68cl PDFs and the 5.9.0 version of LHAPDF [32,33]. The tt cross section is computed to be 252.9 pb, assuming a top quark mass of 172.5 GeV. The model-independent cross sections calculated for the signal samples are listed in Table I.
Minimum bias interactions are generated using PYTHIA and are superimposed on the simulated events to mimic the effect of additional proton-proton collisions within a single bunch crossing (pileup). The pileup distributions of the simulated signal and background events match that observed in data, with an average of 21 reconstructed collisions per beam crossing.

IV. EVENT RECONSTRUCTION
Tracks are reconstructed using an iterative tracking procedure [23]. The primary vertices are reconstructed with a deterministic annealing method [34] from all tracks in the event that are compatible with the location of the proton-proton interaction region. The vertex with the highest P ðp track T Þ 2 is defined as the primary interaction vertex (PV), whose position is determined from an adaptive vertex fit [35].
The particle-flow event reconstruction algorithm [36,37] reconstructs and identifies each individual particle, using an optimized combination of information from the various elements of the CMS detector. The energy of muons is obtained from the curvature of the corresponding track. The energy of electrons is determined from a combination of the electron momentum at the PV as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero suppression effects and for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.
Muon (electron) candidates are required to originate from the PV and to be isolated within ΔR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔηÞ 2 þ ðΔϕÞ 2 p < 0.4ð0.3Þ around the lepton direction, where Δη (Δϕ) indicates the difference in pseudorapidity η (ϕ) from the lepton direction. The degree of isolation is quantified by the ratio of the p T sum of all additional particles reconstructed in the isolation cone to the p T of the lepton candidate. This ratio for a muon (electron) is required to be less than 0.12 (0.10). Together with the lepton identification requirements, the isolation conditions strongly suppress backgrounds from jets containing leptons.
Photons are identified as ECAL energy clusters not linked to the extrapolation of any charged particle trajectory to the ECAL. The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects. In the ECAL barrel section, an energy resolution of about 1% is achieved for unconverted or late-converting photons in the tens of GeV energy range. The remaining barrel photons are measured with an energy resolution of about 1.3% up to jηj ¼ 1, rising to about 2.5% at jηj ¼ 1.4. In the endcaps, the resolution of unconverted or late-converting photons is about 2.5%, while all other photons have a resolution between 3 and 4% [38].
For each event, hadronic jets are reconstructed by applying the anti-k T (AK) algorithm [39,40] and/or the Cambridge-Aachen (CA) [41] jet clustering algorithms to the reconstructed particles. The AK algorithm is used with a jet size parameter of 0.5 (AK5 jets). In some analyses both algorithms are used. The algorithms are applied independently of each other to the full set of reconstructed particles. Charged particles that do not originate from the PV are removed from the jets. The momentum of each jet is defined as the vector sum of all particle momenta in the jet cluster, and is found in the simulation to be within 5% to 10% of the true particle-level momentum over the whole p T spectrum and detector acceptance. Jet energy corrections are derived from the simulation, and are confirmed with measurements of the energy balance of dijet and photon þ jet events [42]. The jet energy resolution is typically 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV, to be compared to about 40%, 12%, and 5% obtained when the calorimeters alone are used for jet clustering.
Neutrinos escape the detector undetected and give rise to the missing transverse momentum vector, defined as the projection on the plane perpendicular to the beams of the negative vector sum of the momenta of all reconstructed particles in an event. Its magnitude is referred to as E miss T . The jets contain neutral particles from pileup events. The contribution from these additional particles is subtracted based on the average expectation of the energy deposited from pileup in the jet area, using the methods described in Ref. [43].
For the identification of jets resulting from fragmentation of b quarks ("b jets"), an algorithm is used that combines information from reconstructed tracks and from secondary vertices, both characterized by a displacement with respect to the PV. This information is combined into a single discriminating variable and jets are tagged as b jets based on its value. The algorithm is referred to as "combined secondary vertex tagger" and is described in Ref. [44]. In most of the analyses described in the following, a minimum value of this variable (medium operating point) is chosen such that the b tagging efficiency is 70% and the light-flavor jet misidentification rate is 1% in tt events. The analyses presented in Secs. V B and V E also use a smaller minimum value of the discriminating variable (loose operating point), yielding a higher efficiency of approximately 80%, with a light-flavor misidentification rate of 10%.

A. Jet substructure methods
Because of the possible large mass of the T quarks, the top quarks, Higgs and W bosons from T quark decays might have significant Lorentz boosts. Daughter particles produced in these decays would therefore not be well separated. In many cases, all decay products are clustered into a single large jet by the event reconstruction algorithms. These merged jets exhibit an intrinsic substructure that can be analyzed with dedicated jet substructure algorithms. In order to cluster the decay products from top quarks and Higgs boson into wide jets, the CA algorithm is used with size parameters R ¼ 1.5 (CA15 jets) or R ¼ 0.8 (CA8 jets). A number of jet substructure algorithms are then used in different analyses to identify jets from top quark or Higgs boson decays. This process is known as t or H tagging, and in some cases relies on b tagging of individual subjets.
The inclusive T quark search in final states with leptons discussed in Sec. VA uses the CMSTOPTAGGER [45], which is based on the algorithm developed in Ref. [46]. The tagger identifies a top quark decay if a CA8 jet with p T > 400 GeV is found with a mass between 140 and 250 GeV and at least three subjets with a minimum mass of subjet pairs larger than 50 GeV. The sensitivity of the CMSTOPTAGGER is suitable for a regime with jet p T > 400 GeV where the decay products are collimated to be within the acceptance of a jet with the size parameter of 0.8.
The search for T → tH in the hadronic final state (Sec. V C) adopts the HEPTOPTAGGER algorithm [47,48], which employs CA15 jets to increase the acceptance to top quarks with a moderate Lorentz boost (p T > 200 GeV). This facilitates a smooth transition between the boosted and resolved regimes. A CA15 t jet candidate is required to exhibit a substructure compatible with a three-body decay. If this requirement is satisfied, the HEPTOPTAGGER clustering algorithm identifies the three subjets, and then requires that the mass of a subjet pair be consistent with the W boson mass and the mass of the three subjets be consistent with the top mass. The t tagging performance is further enhanced by the application of b tagging to subjets of CA15 jets [49]. Subjet b tagging is also used to identify decays of boosted Higgs bosons into a bottom quark-antiquark pair. The subjets of CA15 jets are reconstructed using the filtering algorithm described in Ref. [50]. Two filtered subjets of CA15 jets are required to have a di-subjet invariant mass larger than 60 GeV. Both subjets are tagged using the subjet b tagging algorithm, which is based on the same algorithm used for regular anti-k T jets, discussed above, with the difference that only tracks and secondary vertices associated with the individual subjets are used to build the b tag discriminator.
For the identification of boosted W bosons, two subjets are required to be reconstructed by a pruning algorithm [50][51][52]. The mass of the pruned jet has to be compatible with the mass of the W boson, within a mass window that differs slightly depending on the analysis considered. The inclusive analysis in Sec. VA requires a W jet to have p T > 200 GeV and a mass between 60 and 130 GeV. The search for T → bW with single leptons (Sec. V B) applies the same p T selection, but the mass window is tightened to 60 to 100 GeV. The search for T → bW in hadronic final states (Sec. V D) requires p T > 150 GeV in combination with a jet mass m j requirement of 60 < m j < 100 GeV. Additionally, this analysis complements pruning with a selection on the mass drop [50], which is defined as the ratio of the largest subjet mass to that of the original jet. Requiring the mass drop to be < 0.4 rejects events containing massive jets from QCD multijet processes.
The different performance of the t tagging and W tagging algorithms in data and simulation is taken into account with scale factors that are applied to the simulated events [48,53].

V. ANALYSIS CHANNELS
In this section, five distinct searches for T quarks are presented, each optimized for a different topology. The analyses described in Secs. VA and V B are based on leptonic final states. While the former is an inclusive search covering all possible decay modes, the latter is a search specifically optimized to find T → bW decays. The searches presented in Sec. V C and Sec. V D are optimized for boosted event topologies in hadronic final states and make use of jet substructure techniques. Finally, the search treated in Sec. V E is sensitive to T → tH decays, where the Higgs boson decays to a pair of photons.

A. Inclusive search with single and multiple leptons
The inclusive search described in this section is sensitive to all decay modes of the T quark, i.e., T → tH, T → tZ, and T → bW. It is divided into two channels: one channel in which exactly one lepton is selected and the other channel with at least two leptons. Further details are given in Ref. [15].

Single-lepton channel
Single-lepton events must contain exactly one isolated muon or electron with p T > 32 GeV. In addition to the lepton, events must also have at least three AK5 jets with p T > 120, 90, and 50 GeV. A fourth AK5 jet with p T > 35 GeV is required if no W jet is identified in the event. To fulfill the lepton isolation requirement, jets must be separated by ΔR > 0.4 from muons and by ΔR > 0.3 from electrons. The requirement on the jet multiplicity and p T significantly suppresses background processes. The contribution from QCD multijet events is further reduced by selecting events with E miss T > 20 GeV. The major selection requirements are summarized in Table II.
Some background events from W þ jets production remain after the event selection. This process is not well modeled by simulations and the normalization is determined from a control sample in data. This sample is defined by single-lepton events fulfilling the signal selection criteria, but failing the requirement that a fourth jet with p T > 35 GeV or alternatively a W jet is identified in the event.
A boosted decision tree (BDT) [54] is used to discriminate between signal and background events. Different BDTs are implemented for events with and without identified W jets and for each hypothetical value of the mass of the T quark. The use of dedicated BDTs for different T quark decay modes does not improve the performance, so the BDTs are trained irrespective of the branching fraction of the T quark.
The variables used for the calculation of the BDT discriminant are jet multiplicity, b -tagged jet multiplicity, E miss T , lepton p T , p T of the third jet, p T of the fourth jet, and H T , where H T is defined as the scalar p T sum of all jets with p T > 30 GeV. For events with at least one W jet, the multiplicity and p T of W-tagged jets and the numbers of t-tagged jets are also included in the BDT training. These variables are chosen based on their discrimination power as calculated by the BDT algorithm, and on the absence of significant correlations between the different variables. The final BDT distributions are shown in Ref. [15]. The total numbers of events predicted for background processes and observed in collision data are shown in Table III.
The predicted contributions for each background process are available in Ref. [15]. The signal selection efficiencies are between 7.5% and 9.4% which corresponds to an expected number of 850 events for a T quark mass of 500 GeV and 6 events for a T quark mass of 1000 GeV assuming branching fractions to tH, tZ, and bW of 25%, 25%, and 50%, respectively. A detailed table with selection efficiencies and expected number of events is available in Ref. [15].

Multilepton channel
This channel uses four mutually exclusive subsamples with at least two leptons: two opposite-sign dilepton samples (referred to as OS1 and OS2 samples) which differ by the required numbers of jets in the event, a samesign dilepton sample (the SS sample) and a multilepton sample. The division into opposite-and same-sign dilepton events is based on the charge of the leptons.
Multilepton events must contain at least three leptons with p T > 20 GeV. To reject backgrounds from heavyflavor resonances and low-mass Drell-Yan (DY) production, multilepton events must contain a dilepton pair of the same flavor and of opposite charge with an invariant mass above 20 GeV. Events in which E miss T ≤ 30 GeV are discarded. Jets must be separated by ΔR > 0.3 from the selected leptons and at least one of the jets has to fulfill the b tagging criteria.
The OS1 dilepton sample targets events in which both T quarks decay to bW [13]. This dilepton sample contains events with either two or three jets, H T > 300 GeV, and S T > 900 GeV, where S T is the sum of H T , E miss T , and the transverse momenta of all leptons. Events are discarded where there is a dilepton pair with same-flavor leptons and a mass M ll consistent with that of a Z boson (76 < M ll < 106 GeV). To reduce the tt background, all the possible pair-wise combinations of a lepton and a b jet are considered and their invariant masses are all required to be larger than 170 GeV.
The DY background is not modeled reliably in the selected kinematic region and is controlled using a data sample consisting of events with no b-tagged jets, E miss T < 10 GeV, S T < 700 GeV, and H T > 300 GeV. The OS2 dilepton sample consists of events with at least five jets, two of which must be identified as b jets. Events are also required to have H T > 500 GeV, and S T > 1000 GeV. This sample is mostly sensitive to signal events where both T quarks decay to tZ. The dominant background is tt production.
The SS sample selection criteria target events in which at least one T quark decays to tZ or tH. Besides the lepton selection criteria, at least three jets are required, H T > 500 GeV, and S T > 700 GeV.
Different processes contribute to the background in the SS sample. A minor contribution is given by SM processes leading to prompt SS dilepton signatures, which have very small cross sections. These processes can be simulated reliably. The prompt OS dilepton production can also contribute if one lepton is misreconstructed with the wrong sign of the charge. The misreconstruction probability of the charge sign is negligible for muons in the kinematic range considered, while for electrons it is determined from control data samples. We determine the probability to misreconstruct the charge sign of an electron from events with a dileptonic Z decay, selected with the same criteria as in the signal selection except for the charge requirement. Instrumental backgrounds in which misidentified jets create lepton candidates are determined from control data samples in which nonprompt and fake leptons are enriched. The multilepton sample, like the SS sample, is mostly sensitive to signal events in which at least one T quark decays to tZ or tH. The backgrounds are suppressed by selecting events with at least three jets, H T > 500 GeV, and S T > 700 GeV. Prompt backgrounds in this channel are due to SM processes with three or more leptons in the final state, such as diboson and triboson production. These are correctly modeled by simulation. Nonprompt backgrounds are caused by the misidentification of one or more leptons, by tt production, and by other processes. As for the dilepton samples, data control samples are used to evaluate these sources of background.
The main selection requirements for the four samples are summarized in Table IV.
The numbers of events in the multilepton samples are given in Table V, both for data and for estimated background contributions. The predicted contributions for each background process are available in Ref. [15]. The selection efficiencies for signal events are between 0.15% and 0.44% which corresponds to an expected number of 16.7 events for a T quark mass of 500 GeV and 0.28 events for a T quark mass of 1000 GeV, assuming branching fractions to tH, tZ, and bW of 25%, 25%, and 50%, respectively. A detailed table with selection efficiencies and expected number of events is available in Ref. [15]. The numbers of background and signal events are of similar order of magnitude. The sensitivity to the signal is enhanced by further splitting the samples according to the lepton flavor. The dilepton samples are separated into three subsamples, μμ, μe, and ee. The multilepton sample is divided into a μμμ subsample, an eee subsample, and a third subsample with events with mixed lepton flavors. Data and SM background expectations are found to be in agreement.

B. Search for T → bW with single leptons
The analysis described in this section is optimized for the event topology in which both T quarks decay into a bottom quark and a W boson.
Events are required to have one isolated muon or electron, where muon candidates must have p T > 45 GeV and electron candidates must have p T > 30 GeV. At least four jets are required, either at least four AK5 jets or at least three AK5 jets plus at least one CA8 jet. The AK5 jets are required to have p T > 30 GeV and CA8 jets are required to have p T > 200 GeV. Both types of jets must have jηj < 2.4.
The CA8 jets are used to identify merged hadronic decays of W bosons with high Lorentz boost. The AK5 jets are replaced by the two pruned subjets of W-tagged CA8 jets if the angular distance between AK5 and CA8 jets fulfills the matching criterion ΔRðJet CA8 ; Jet AK5 Þ < 0.04. Unmatched AK5 jets and the subjets of matched W-tagged CA8 jets are used as input for a kinematic fit, which is described below. The four jets or subjets are required to satisfy p T > 120, 90, 50, and 30 GeV. At least one of the AK5 jets has to satisfy the b tagging criteria.
A kinematic fit is made to each event for the hypothesis TT → bW þb W − → lνbqq 0b , subject to the constraints, mðlνÞ ¼ mðqq 0 Þ ¼ M W , and mðlνbÞ ¼ mðqq 0 bÞ ¼ M fit , the fitted mass of the selected T candidate. The E miss T in the event is attributed to the undetected neutrino from leptonic W decays. If a selected event has more than four jets, the fifth jet with highest p T is also considered and all the possible combinations of four jets are tested in the kinematic fit.
Only events containing fit combinations with χ 2 probability pðχ 2 Þ > 1% are retained. The efficiency of the pðχ 2 Þ criterion is 62% for signal events with a T quark mass of 800 GeV while 76% of background events are rejected. The pðχ 2 Þ criterion removes badly reconstructed TABLE IV. Main selection requirements for the four multilepton channels: the opposite-sign dilepton samples with two or three jets (OS1) and with at least five jets (OS2), the same-sign dilepton sample (SS), and the multilepton sample. The smallest mass obtained from all the possible combinations of leptons and b jets is indicated by M bl .

OS1
OS2 SS Multileptons events with poor mass resolution and improves the signal-to-background ratio in the reconstructed mass spectrum.
To reduce the large combinatorial background, the b tagging and the W tagging information is used. If a W tag is present, only those combinations where the subjets of the W jet match the W decay products are considered. The best combination is selected from groups of fit combinations with decreasing b tag multiplicity, ranked by the b tagging operating point (OP), as listed below: (i) 2 b tags at medium OP; (ii) 1 b tag at medium OP and 1 b tag at loose OP; (iii) 1 b tag at medium OP; (iv) 2 b tags at loose OP.
Decay products of T quarks have on average higher p T than those from the SM backgrounds. To suppress the backgrounds and enhance the signal significance, we select events with large values of the S T variable, which is defined here as a sum of E miss T , p T of the lepton, and p T of the four jets that minimize the χ 2 in the kinematic fit. Figure 1 demonstrates that SM backgrounds and a T quark signal populate different regions in the two-dimensional S T and M fit distribution.
We test the modeling of the shape of the reconstructed mass, and verify how well the SM background expectations agree with data, as a function of S T . Figure 2 shows the reconstructed mass distributions separately for μ þ jets and e þ jets events with the S T > 1000 GeV requirement. Correctly reconstructed tt events peak near the top quark mass value, while events with misassigned jets constitute a combinatorial background, and populate a region of higher masses, where the potential signal is expected to appear. Table VI (left columns) presents the event yields of SM backgrounds and data for this selection. The dominant background process is tt production. Smaller but still significant backgrounds come from W þ jets and single top quark production. In the e þ jets channel there is also a contribution from QCD multijet production. Other backgrounds have been found to be negligible. Data and SM background expectations agree in both shape and total normalization. We apply a requirement of S T > 1240 GeV in the final event selection. This condition is optimized to enhance the sensitivity to the signal, based on SM backgrounds and T signal expectations. The major selection requirements are summarized in Table VII. Table VI (right columns) presents the event yields for expected SM backgrounds and data. Signal efficiencies are of the order of 0.5%-4% for T quark masses from 500 to 1000 GeV. They are summarized in Table VIII.
The M fit distribution for the final event selection is shown in Fig. 3. The μ þ jets and e þ jets final states give very similar results. The observed data are compatible with background expectations from SM processes. The μ þ jets and e þ jets channels are combined to improve the statistics for the simulated SM backgrounds.

C. All-hadronic search for T → tH
This channel is optimized for the event topology in which at least one T quark decays to T → tH, where the top quark decays into bW and the W boson decays   hadronically, and the Higgs boson decays into two b quarks. Because of the expected high mass of the T quarks, the top quarks and Higgs bosons can have significant Lorentz boost; therefore the event selection is based on jet substructure requirements, as described in Sec. IVA. At least one t-tagged and one H-tagged CA15 jet are required, where the t-tagged jets must have p T > 200 GeV and the H-tagged jets must have p T > 150 GeV. Two variables are used to further distinguish the signal from the background events after the event selection. These variables are H sub T , defined here as the scalar p T sum of subjets of CA15 jets, and the invariant mass m bb of two b-tagged subjets in the H-tagged jets. These two variables are used for setting upper limits on the T quark production cross section. The major selection requirements are summarized in Table IX.
Backgrounds due to QCD multijet production are determined from data using signal-depleted sideband regions. These sidebands are defined by inverting the jet substructure criteria. Backgrounds due to tt events are determined from simulation; other backgrounds are found to be negligible.
To maximize the sensitivity of the analysis, the events are divided into two categories: a category with a single H tag and a category with at least two H tags. The background estimates are well matched to the observed data, as discussed in Ref. [19]. For the final event selection, the H sub T and m bb variables are combined into a single discriminator using a likelihood ratio method. The numbers of expected background events and events observed in data after the full selection are shown in Table X. The observed data are compatible with background expectations from SM processes. The signal selection efficiencies are between 2.5% and 7.2% which corresponds to an expected number of 283 signal events for a T quark mass of 500 GeV and 4.9 events for a T quark mass of 1000 GeV, assuming BðT → tHÞ ¼ 100%. A detailed table with selection efficiencies and expected numbers of signal events is available in Ref. [19].

D. All-hadronic search for T → bW
This channel is optimized for the event topology in which both T quarks decay to T → bW, where the W bosons decay hadronically. Events are selected by requiring two W-tagged CA8 jets with p T > 150 GeV. At least two additional AK5 jets with p T > 50 GeV are required, one of which must be b-tagged. Events are divided into categories defined by the numbers of b-tagged jets: one or at least two.
After the event selection, two T candidates T 1 and T 2 are reconstructed using combinations of the W jets and the AK5 jets. The order of T 1 and T 2 is arbitrary. The reconstruction is performed by identifying the combinations of W jets and AK5 jets having the smallest invariant mass difference. Figure 4 shows the two-dimensional distribution of the masses of each reconstructed T candidate in a signal sample with a simulated T quark mass of 800 GeV. The reconstructed mass peak is clearly visible at the expected value. The misreconstruction rate, where the wrong combination of jets is chosen, is small and does not affect the signal acceptance. Additional event requirements are then applied to increase sensitivity to the signal process. The T candidate masses must be greater than 200 GeV, and the fractional difference a f in the masses of the two T candidates mðT 1 Þ and mðT 2 Þ, where a f ¼jmðT 1 Þ−mðT 2 Þj= ðmðT 1 ÞþmðT 2 ÞÞ, must be less than 10%. The two T  candidates must fall in opposite hemispheres of the detector, ΔϕðT 1 ; T 2 Þ > 5π=6, and finally H 4jet T must be above 1000 GeV, where H 4jet T is defined as the scalar p T sum of the four jets used to reconstruct the T candidates. The major selection requirements are summarized in Table XI.
The dominant backgrounds are due to QCD multijet production and tt production. Other background contributions are negligible.
To obtain the shape of the QCD multijet background, a control region is defined by requiring H 4jet T > 1000 GeV, but inverting the requirement on the fractional mass difference, a f > 0.1. This control region is enriched in multijet events and has a negligible signal contamination. The shape of the H 4jet T distribution in the control region, after subtracting the expected tt contribution, is used to model the QCD multijet events entering the signal region. The H 4jet T distribution in the signal region agrees with the distribution in the sideband region for simulated QCD multijet events. The normalization of the QCD multijet background is not fixed, and is determined in the limit setting procedure. This procedure is done independently for events containing one and at least two b-tagged jets. Figure 5 shows the post-fit H t T ext4jet distributions obtained with the above method. Data are found to be in agreement with the expected background contributions. The numbers of expected background events and events observed in data after full selection are shown in Table XII. The numbers of expected signal events and selection efficiencies assuming BðT → bWÞ ¼ 100% are summarized in Table XIII.

E. Search for T → tH with H → γγ
The analysis described in this section is optimized for events with one T quark decaying to tH, where the Higgs boson decays into a pair of photons. The main advantage of this channel is the possibility to precisely measure the invariant mass of the diphoton system (m γγ ) so that a peak in the m γγ distribution would be present for signal events. The disadvantage is the small Higgs branching fraction of the order of 2 × 10 −3 [55]. The analysis concept is the same as for searches of the SM Higgs boson in the H → γγ decay channel [56].
Events with two isolated photons are selected. Additional leptons and jets coming from the decay of top quarks or a second Higgs boson are required. In order to maximize the sensitivity of the analysis, two search channels are defined, targeting different decay modes of the top quark:  (i) the leptonic channel searches for events with a pair of photons and at least one isolated high-p T muon or electron; (ii) the hadronic channel searches for events with a pair of photons and no isolated muons or electrons. The resonant contributions from the ttH background are determined from simulation. The nonresonant contribution is composed of events with two prompt photons arising from QCD multijet production as well as for emission in top quark production (γγ þ jets, tt þ γγ, t þ γγ). The tt events are more likely to have a jet misreconstructed as a photon, because of the large numbers of jets in the final state. The simulation of such sources of instrumental background is not completely reliable. The background model is therefore derived from data.
The control sample used to estimate the nonresonant background consists of events where at least one photon passes loose identification requirements but does not pass the final event selection. This sample is enriched with events containing one misidentified photon. A reweighting is applied, in order to match the p T and η spectra of the photons in this control sample to those obtained after the signal selection. This is done independently for each photon.
The event selection is based upon six quantities that have the largest discriminating powers between signal and backgrounds and that have small correlations. They include the transverse momenta of the larger p T photon (γ 1 ) and smaller p T photon (γ 2 ). The selection criteria are optimized to produce the most stringent limits on the signal cross

Variable
Leptonic channel Hadronic channel    The nonresonant background contributions are obtained from unbinned maximum likelihood fits to the diphoton mass distribution over the range 100 < m γγ < 180 GeV, under the hypothesis of no signal. An exponential function is chosen for these fits. Studies of pseudoexperiments showed that the use of an exponential function does not introduce a bias in the estimation of the numbers of background events in both categories. In Fig. 6, the observed diphoton mass distribution in each event category is shown, together with the expected signal and the expected resonant background contribution. The error bands show the uncertainty in the background shapes associated with the statistical uncertainties of the fits. The numbers of expected background events and events observed in data after final selection are shown in Table XV. The numbers of expected signal events and selection efficiencies assuming BðT → tHÞ ¼ 100% are summarized in Table XVI.
The data in the signal window are compatible with background expectations from SM processes.

VI. COMBINATION STRATEGY
The event samples selected by the five analyses are almost entirely distinct and therefore, signal limits extracted from those analyses are statistically independent. They can be combined to yield a result that is more stringent than any of the inputs. Because the backgrounds are largely common to all analyses, the background estimates are largely correlated but well determined by the multiple independent samples. In particular, most analyses have top quark pair production as a background process. This background normalization is correlated among the analyses in the combination, providing for the combination a better background estimation than in the individual analyses. Similar arguments hold for the TABLE XV. Expected yields for ttH and nonresonant background (from the fit to data) and the numbers of observed events in data after full event selection for the two channels of the T → tH search in the final state with photons. All the yields are computed in a window of 1 full width at half maximum i.e., 125 AE 1.5 GeV. The ✓ symbol indicates that the uncertainty has been taken into account in the analysis, but it is not correlated with any of the other analyses. The ✓ symbol indicates that the uncertainty has been taken into account and that it is correlated with the other analysis that have a ✓ sign as well. A missing symbol indicates that this uncertainty is not relevant for this analysis channel.

Uncertainty
Single leptons Inclusive leptons Multiple leptons All-had. T → bW All-had. T → tH H → γγ correlated systematic uncertainties, which are discussed in more detail in Sec. VI A. The inclusive analysis with single and multiple leptons described in Sec. VA is able to set limits for all T quark decay modes. Dedicated optimizations to enhance the sensitivity for T → bW decays are described in Sec. V B. These optimizations use single-lepton events. To avoid double counting of events we replace the single-lepton part of the inclusive approach (Sec. VA) with the single-lepton analysis described in Sec. V B. This is done for scenarios with BðT → bWÞ values of at least 80%. For lower BðT → bWÞ values this approach is inferior and we use the inclusive results from Sec. VA only. At every point the approach used is that which gives the best expected limit. The other three analyses described in Secs. V C to V E do not have any overlap so they are always combined with the cases above.
For the statistical combination a Bayesian method [57] has been adopted in which the systematic uncertainties are taken into account as nuisance parameters with their corresponding priors as discussed in Sec. VI A. Upper limits on the T quark production cross section are obtained with the Theta framework [58]. Systematic uncertainties are taken into account as global normalization uncertainties and as shape uncertainties where applicable. More details about the treatment of systematic uncertainties are given in the next section.

A. Systematic uncertainties
Some of the individual analyses are sensitive to the same systematic uncertainties, for example the uncertainty in the integrated luminosity, the jet energy scale and the b tagging efficiency. Such uncertainties are treated as fully correlated, as is done technically by correlating the corresponding nuisance parameters in the limit setting procedure. This treatment allows improved constraints to be obtained on these parameters than is possible in the standard analyses.
The systematic uncertainties fall into two types: those which affect the normalization of the signal and background samples, and those which also affect the shapes of distributions. The uncertainty in the tt cross section is 13%. It is obtained from the tt cross section measurement [59] for large invariant mass values of the tt system. The uncertainty in the integrated luminosity is 2.6% [60]. FIG. 7. Expected limits at 95% C.L. of the individual analyses in comparison to the combination for exclusive decays of the T quark to tH, tZ, and bW.    XVIII. Branching fractions (first three columns) and the observed and expected upper limits on the T quark production cross section at 95% C.L. for different values of the T quark mass. The expected limits are quoted with their corresponding uncertainties, for different branching fractions hypotheses. The cross section limits are given in units of pb.
T quark mass (GeV)  D 93, 012003 (2016) Shape uncertainties include the jet energy scale, the jet energy resolution and the b tagging efficiency uncertainties. We also consider the uncertainties in the efficiencies of the t tagging, W tagging, and H tagging algorithms [48,49,53]. The uncertainty due to the energy deposits not associated with jets (unclustered energy) has an impact on the missing p T . This effect is taken into account in the single-lepton channel. The size of this uncertainty typically varies from a few percent up to 10%.
The systematic uncertainty in the pileup jet identification is taken into account in the analysis with H → γγ. It is derived through the use of the data/simulation scale factors (SF), which are binned in jet η and p T [56].
For the photon identification efficiency, the uncertainty in the SF is taken into account. The SF corrects the efficiency in simulation to the efficiency as measured in data using a "tagand-probe" technique [61] applied to Z → e þ e − events. The uncertainty applied to this SF amounts to 3% in the barrel region of the calorimeter and 4% in the endcaps.
Lepton trigger efficiencies, lepton identification efficiencies, and corresponding correction factors for simulated events are obtained from data using decays of Z bosons to dileptons. These uncertainties are ≤3%.
For simulated tt and ttH events, uncertainties due to renormalization and factorization scales (μ R and μ F ) are taken into account by varying both scales simultaneously up and down by a factor of two. Uncertainties arising from the choice of PDFs are taken into account. Simulated background events are weighted according to the uncertainties parametrized by the CTEQ6 eigenvectors [31].
The shifts produced by the individual eigenvectors are added in quadrature in each bin of the relevant distributions.
A systematic uncertainty of 50% is assigned to the diboson backgrounds, single top quark production and the W and Z boson background. This accounts for the effects of the μ R and μ F variations in simulation and the uncertainties in the determination of the W þ jets SF from data.
Modified "template" distributions of those quantities that are affected by the respective uncertainties are obtained by varying the respective quantity by its uncertainty, namely by AE1 standard deviation. In the limit setting procedure a likelihood fit is performed in which the nominal distribution and the modified templates are interpolated. The corresponding uncertainty is represented as a nuisance parameter, which receives its prior constraints from the template distributions. In the fit, the templates are allowed to be extrapolated beyond AE1 standard deviation, but this happens rarely. The resulting fit values are always within AE1.5 standard deviations of their prior values.
The list of nuisance parameters of all analysis channels is shown in Table XVII. This table also indicates which parameters are correlated and which uncorrelated.

VII. RESULTS
No significant deviation from the SM prediction is observed. The expected limits of the individual analysis channels at a 95% confidence level (C.L.) are displayed in Fig. 7 for exclusive decays of the T quark to tH, tZ, and bW. This figure also shows the result of the combination, where only the nonoverlapping part of the individual analyses are combined, as discussed in Sec. VI. The observed limits and the expected one and two standard deviation uncertainties are displayed in Fig. 8 for exclusive T quark decays.
The lower limits on the mass of the T quark are obtained by determining the intersection between expected (observed) limits with the theoretical prediction, based on the cross section versus T quark mass distributions shown in Fig. 8. The results are visualized graphically in the triangular plane of branching fractions in Fig. 9. The numerical upper limits on the T quark production cross section are given in Table XVIII for a full range of branching fractions and the numerical results of the limits on the mass of the T quark are given in Table XIX. A different visualization of the mass limits is presented in Fig. 10.
Depending on the assumed branching fractions, the expected limits lie between 790 and 890 GeV, while the observed limits are in a range between 720 and 920 GeV. In much of the triangular plane of branching fractions these are the most stringent limits on T quark pair production to date.

VIII. SUMMARY
A search for pair production of vectorlike T quarks of charge 2=3 has been performed. In most models the hypothetical T quark has three decay modes: T → tH, T → tZ, and T → bW. The following five distinct topologies have been investigated: inclusive lepton events covering all possible decay modes, single-lepton events optimized to find T → bW decays, all-hadronic events optimized either for T → tH or T → bW decays, and events containing a Higgs boson decaying to a pair of photons.
Data and SM background expectations are found to be in agreement. Upper limits on the production cross sections of vector-like T quarks are set. The expected 95% C.L. lower mass limits are between 790 and 890 GeV depending on the branching fraction of the T quark. For a branching fraction of BðtHÞ ¼ 100% an expected (observed) limit of 840 (770) GeV is found. For BðtZÞ ¼ 100% the expected (observed) limit is 830 (790) GeV and for BðbWÞ ¼ 100% the limit is 890 (920) GeV. These are among the strongest limits on vectorlike T quarks obtained to date.

ACKNOWLEDGMENTS
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: