Search for resonant tt̄ production in proton-proton collisions at ffiffi s p 1⁄4 8 TeV

A search is performed for the production of heavy resonances decaying into top-antitop quark pairs in proton-proton collisions at sqrt(s) = 8 TeV. Data used for the analyses were collected with the CMS detector and correspond to an integrated luminosity of 19.7 inverse femtobarns. The search is performed using events with three different final states, defined by the number of leptons (electrons and muons) from the t t-bar to W b W b decay. The analyses are optimized for reconstruction of top quarks with high Lorentz boosts, where jet substructure techniques are used to enhance the sensitivity. Results are presented for all channels and a combination is performed. No significant excess of events relative to the expected yield from standard model processes is observed. Upper limits on the production cross section of heavy resonances decaying to t t-bar are calculated. A narrow leptophobic topcolor Z' resonance with a mass below 2.4 TeV is excluded at 95% confidence level. Limits are also derived for a broad Z' resonance with a 10% width relative to the resonance mass, and a Kaluza-Klein excitation of the gluon in the Randall-Sundrum model. These are the most stringent limits to date on heavy resonances decaying into top-antitop quark pairs.


I. INTRODUCTION
The top quark is the heaviest known fundamental particle, with a mass close to the electroweak scale. It has a Yukawa coupling to the Higgs potential close to unity and is, therefore, closely connected to the hierarchy problem, where the largest corrections to the mass of the Higgs boson arise from top-quark loops. Studies of topquark production may provide further insight into the mechanism of electroweak symmetry breaking, especially in light of the recent discovery of a Higgs boson [1-3] and a precision measurement of its mass [4][5][6].
Many theories beyond the standard model (SM) predict the existence of heavy resonances, generically referred to as Z 0 , that preferentially decay to tt pairs and manifest themselves as a resonant component on top of the SM tt continuum production. Examples of such models include colorons [7][8][9] including a leptophobic topcolor Z 0 [10], extended gauge theories with massive color-singlet Z 0 bosons [11][12][13], axigluons [14,15], and models in which a pseudoscalar Higgs boson may couple strongly to top quarks [16]. Furthermore, various extensions of the Randall-Sundrum model [17] with extra dimensions predict Kaluza-Klein (KK) excitations of gluons g KK [18] or gravitons G KK [19], both of which can have enhanced couplings to tt pairs. Direct searches for heavy tt resonances have been performed at the Fermilab Tevatron and the CERN LHC colliders, with no evidence for such signals. The experiments at the Tevatron have probed the mass range up to about 900 GeV [20][21][22][23][24][25], using the leptophobic Z 0 model, and the LHC experiments have set subpicobarn limits on the production cross section in the mass range of 1-3 TeV [26][27][28][29][30][31].
This paper presents a model-independent search for Z 0 → tt → W þ bW −b production, where the leptonic and hadronic decay modes of the W bosons are considered. Unless otherwise indicated, the symbol Z 0 is used in the following to refer to the resonance decaying to tt, irrespective of the specific model. This results in final states with two, one, or zero leptons, which are referred to as the dilepton, lepton þ jets, and all-hadronic channels, respectively. The search is based on pp collision data collected by the CMS experiment at the LHC at a center-of-mass energy ffiffi ffi s p ¼ 8 TeV, and corresponding to an integrated luminosity of 19.7 fb −1 . The final state of the dilepton channel consists of two leptons of opposite charge (ee, eμ, or μμ) with high transverse momentum (p T ), at least two jets from the fragmentation of b quarks, and missing transverse momentum due to escaping neutrinos. The final-state objects arising from decays of heavy tt resonances are collimated because of the large Lorentz boosts of the top quark decay products. Leptons from the W boson decay are reconstructed in the proximity of jets from the fragmentation of b quarks. Special selection criteria are used to preserve high lepton selection efficiency for nonisolated leptons at high resonance masses. The dominant irreducible background is the tt continuum production. Other SM processes contributing to the background are single top quarks, Z þ jets, and diboson production.
The final state considered in the lepton þ jets channel consists of one high-p T lepton (e or μ), at least two jets, of which at least one jet is identified to arise from the fragmentation of a b quark, and missing transverse momentum. As in the case of the dilepton analysis, special selection criteria are used to identify nonisolated leptons at high resonance masses. A top-quark tagging algorithm, referred to as a t-tagging algorithm, is applied to identify fully hadronic decays of the type t → Wb → qq 0 b merged into one single jet. The use of the t-tagging algorithm enhances the sensitivity of this channel at high resonance masses by about 30%-40%, and leaves tt continuum production as the dominant irreducible background. A bottom-quark tagging algorithm is also used to create regions enhanced in signal for the analysis.
The all-hadronic channel considers events with a dijet topology, where two wide jets are selected and required to be consistent with the decay of a top quark. Two separate regions are explored: a search region sensitive to Z 0 masses M Z 0 below 1 TeV, where Cambridge-Aachen (CA) jets [32,33] with a distance parameter of R ¼ 1.5 are considered and a search region for high resonance masses, using CA jets with R ¼ 0.8. Two distinct t-tagging algorithms [34,35] are used for these two regions. In both regions the dominant background from non-top-quark multijet production can be reduced considerably by requiring one identified subjet in each of the two top quark candidates to be consistent with the fragmentation of a b or c quark, leaving irreducible SM tt continuum production as the dominant background.
Except for the nontop multijet backgrounds in the allhadronic channels, the shapes of all SM backgrounds are estimated from simulation. The total yield of the simulated samples is obtained with a binned maximum likelihood fit to the reconstructed tt invariant mass (M tt ) distributions. A limit on the production cross section of heavy resonances is extracted by performing a template-based statistical evaluation of the M tt distributions of all channels. This paper is organized as follows: Section II gives a description of the CMS detector. The reconstruction and identification of electrons, muons, and jets is described in Sec. III. Section III also gives an overview of the t-tagging algorithms used. The data sets and simulated Monte Carlo (MC) samples used in the analysis are given in Sec. IV. Section V describes the event selection for the three different channels. Systematic uncertainties are discussed in Sec. VI, while Sec. VII describes the evaluation of the SM background processes. The statistical analysis and the results are given in Sec. VIII, and a summary is given in Sec. IX.

II. CMS DETECTOR
The central feature of the CMS detector 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, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. In addition to the barrel and end-cap detectors, CMS has extensive forward calorimetry. Muons are detected by four layers of gas-ionization detectors embedded in the steel flux-return yoke of the magnet. The inner tracker measures charged particle trajectories within the pseudorapidity range jηj < 2.5, and provides an impact parameter resolution of approximately 15 μm. A two-stage trigger system selects pp collision events of interest for use in physics analyses. 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. [36].

III. EVENT RECONSTRUCTION
The CMS experiment uses a particle-flow (PF)-based event reconstruction [37,38], which aggregates input from all subdetectors. This information includes charged-particle tracks from the tracking system and deposited energy from the electromagnetic and hadronic calorimeters, taking advantage of excellent granularity of the subsystems. Particles are classified as electrons, muons, photons, charged hadrons, and neutral hadrons. Primary vertices are reconstructed using a deterministic annealing filter algorithm [39]. The vertex with the largest squared sum of the associated track p T values is taken to be the primary event vertex.
Electrons are reconstructed in the pseudorapidity range jηj < 2.5, by combining tracking information with energy deposits in the electromagnetic calorimeter [40,41]. Electron candidates are required to originate from the primary event vertex. Electrons are identified using information on the shower shape, the track quality, and the spatial match between the track and electromagnetic cluster, and the fraction of total cluster energy in the hadron calorimeter. Electron candidates that are consistent with originating from photon conversions in the detector material are rejected.
Muons are detected and measured in the pseudorapidity range jηj < 2.4 using the information collected in the muon and tracker detectors [42]. Tracks from muon candidates must be consistent with a muon originating from the primary event vertex and satisfy track fit quality requirements.
Since the top-quark decay products can be collimated at high values of M Z 0 , no isolation requirements on the leptons are imposed in either the trigger or offline selections.
The missing transverse momentum vectorp miss T is 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 . Particle-flow candidates are clustered into jets using the FASTJET 3.0 software package [43]. Charged hadrons associated with other event vertices than the primary event vertex are removed prior to jet clustering. All jets are required to satisfy jηj < 2.4. The dilepton and lepton þ jets analyses use jets obtained by the anti-k T jet-clustering algorithm [44] with a distance parameter of 0.5 (AK5 jets). If a lepton candidate (electron or muon) is found within ΔR < 0.5 of an AK5 jet, its four-momentum is subtracted from that of the jet. In this paper the unmodified term 'jet' will refer to these AK5 jets. The allhadronic analyses use the CA jet-clustering algorithm [32,33] with distance parameters of 0.8 (CA8 jets) and 1.5 (CA15 jets) for the analyses at high and low values of the tt invariant mass, respectively. The CA algorithm has been chosen because of its use in the declustering of jets for the identification of jet substructure. The CA8 jets are also employed in the lepton þ jets analysis to identify the hadronic decay of top quarks with high p T in the hemisphere opposite to one defined by the momentum vector of the lepton. All jets contain neutral particles from additional collisions in the beam crossing (pileup). The extra contribution is subtracted based on the average expectation of the pileup in the jet catchment area [45]. This is done by calculating a correction for the average offset energy density in each event as function of the number of primary vertices [46]. Jets are identified as originating from the fragmentation of a b or c quark by the combined secondary vertex algorithm (CSV). The loose and medium operating points are used, which were chosen to have a misidentification probability of 10% and 1%, respectively, for tagging light-parton jets with an average p T of about 80 GeV. The efficiency for the medium operating point varies between 70%-75% for jet p T in the range 50-100 GeV, where it reaches a plateau. Above 200 GeV the efficiency decreases gradually to about 60% for p T values of 500 GeV [47]. All jets are required to satisfy quality selections to remove calorimeter noise and other sources of fake jets [48]. Events are required to also satisfy selection criteria to remove calorimeter noise from E miss T signals as described in Ref. [49]. The structure of CA jets is used to distinguish hadronically decaying top quarks merged into a single jet from light quark or gluon jets. For CA8 jets the CMS t-tagging algorithm is used [50,51], which is based on an algorithm studied in Ref. [34]. Only jets with p T > 400 GeV are considered, as at lower momenta the decay products of the hadronically decaying top quark are rarely merged into a single jet. The algorithm attempts to split the merged jets into subjets. In the process, soft and wide-angle particles relative to the parent in the clustering are ignored, enhancing the separation into subjets. CA8 jets that pass the CMS t-tagging algorithm (CA8 t-tagged jets) are required to have at least three subjets. The mass of the jet has to satisfy the condition 140 < M jet < 250 GeV, the minimum pairwise mass M min of the three highest p T subjets is required to be greater than 50 GeV, and the N-subjettiness [52,53] ratio τ 32 ≡ τ 3 =τ 2 must be smaller than the value of 0.7, which has been obtained from optimization studies. The Nsubjettiness observable τ N , defined through the relation is a measure of the consistency of a CA jet with N or fewer subjets, where i is a sum over all jet constituents, and the ΔR terms represent distances between a given constituent i and one of the N candidate subjet axes. The quantity d 0 is a normalization constant. The HEPTopTagger [35] algorithm is applied to CA15 jets. The larger distance parameter allows the identification of hadronic decays of top quarks with intermediate transverse momenta, p T > 200 GeV. The CA15 jet is decomposed according to the last clustering step of the CA algorithm. Subjets are identified by an iterative procedure: when undoing the last clustering of the jet into two subjets, the mass of the heavier subjet is required to be between 30 GeV and 80% of the mass of the original jet. The algorithm fails if fewer than three subjets are found. If three or more subjets are reconstructed, jet constituents are reclustered using the CA algorithm with filtering [54] until there are exactly three subjets. Additional criteria are applied to the invariant mass calculated from the three subjets and the pairwise masses using combinations of the three subjets to reject jets from light quarks or gluons [51]. Jets identified by the HEPTopTagger are referred to as CA15 t-tagged jets [55].
In the all-hadronic channel, additional discriminating power against background processes is obtained from the application of the CSV algorithm to the subjets of the CA jets. A CA jet is considered to be b-tagged if the subjet with the highest discriminator value satisfies the requirement for the medium operating point. This has an efficiency of about 65% and a misidentification probability of approximately 5%. In the following, this algorithm will be called subjet b tagging. Its performance has been studied in data, and shows a gain in efficiency for boosted topologies with respect to the standard b-tagging algorithm [56]. The same study also compared the b-quark efficiency in data and simulated events, and established that the measured data-tosimulation scale factor for b-tagged subjets is the same as for unmerged b jets.

IV. TRIGGER AND DATA SETS
Dilepton events are collected with single-lepton triggers. Events for the ee channel are selected using a single electron trigger with a p T threshold of 80 GeV and an efficiency of 90%. In all cases, no isolation requirement is applied to the leptons. Similarly, eμ and μμ events are recorded with a trigger requiring a single muon with p T > 40 GeV and jηj < 2.1. The efficiency for this trigger is 95% for muons measured within jηj < 0.9, and 85% if they are measured within 0.9 < jηj < 1.2 and 83% for 1.2 < jηj < 2.1.
The data used in the lepton þ jets channel also rely on single lepton triggers. The trigger for electron events requires one electron with p T > 35 GeV in conjunction with two jets that have p T > 100 and 25 GeV, respectively. The trigger for muon events is the same one used in the dilepton analysis. In both cases, no isolation requirement is applied to the leptons. A 10% increase in the signal efficiency at M Z 0 ¼ 2 TeV is gained in the electron channel by including events that are triggered by a single jet with p T > 320 GeV. The events recovered by the single-jet trigger contain an electron merged in a jet, which can not be resolved at the trigger level. The resulting trigger efficiency is 90% for events with a leading (highest p T ) jet with p T < 320 GeV. Above this value the trigger shows a turnon behavior and is fully efficient above a value of 350 GeV.
The all-hadronic data sample is based on two different triggers. The first requires the scalar sum of the p T of jets (H T ) to be greater than 750 GeV, with an efficiency of 95% or higher after the analysis selection. The second requires four jets with p T > 50 GeV at trigger level, used to gain efficiency in the low-mass regime with M Z 0 < 1 TeV. The efficiency of this trigger is 50% for events with the fourth leading jet having p T > 50 GeV, and increases to 100% for jets with p T > 100 GeV.
The total integrated luminosity associated with the data sets is 19.7 fb −1 , except for the four-jet data set, which corresponds to an integrated luminosity of 18.3 fb −1 . The lower integrated luminosity in the latter case is due to the unavailability of the four-jet trigger at the start of data taking. The efficiencies for all triggers are well modeled by the simulation.
The Z 0 → tt process is simulated using the MADGRAPH 4.4 [57] event generator, which produces a generic highmass resonance with the same left-and right-handed couplings to fermions as the SM Z boson. Higher-order parton radiations are calculated for up to three extra partons at tree level. The simulation is performed for masses M Z 0 of 0.75, 1, 1.25, 1.5, 2, and 3 TeV, and for relative decay widths Γ Z 0 =M Z 0 of 1% (narrow width) and 10% (wide width). Kaluza-Klein gluon excitations are simulated using PYTHIA 8 [58], where interference effects with SM tt production are neglected. The widths of the g KK signals are about 15%-20% of the resonance mass. For visualization purposes, the signal samples are scaled to an arbitrary cross section of 1 pb. This is about a factor of 30 larger than the cross section expected from the narrowwidth topcolor Z 0 model. Figure 1 shows the invariant mass of the tt quark system at the parton level for the Z 0 and g KK samples for two different invariant masses, 1.5 and 3 TeV. The samples at 1.5 TeV show a peaked structure, characteristic of a narrow-width resonance. The samples at 3 TeV exhibit a significant tail at low invariant mass values due to the interplay between the available partonic center-of-mass energy and the width of the resonance; this is most pronounced for g KK because of its very large width. Above 3 TeV, the resonant hypothesis for the signal samples is not valid anymore, thus signals with masses above 3 TeV are not considered in this paper.
All of the samples produced with MADGRAPH are interfaced to PYTHIA for parton showering and fragmentation. The MLM algorithm [64] is applied during the parton matching to avoid double counting of partons. The MADGRAPH samples use the CTEQ6L [65] parton distribution functions (PDF). For the POWHEG tt sample, the CT10 [66] PDF set is utilized, whereas the single top quark processes are produced with the CTEQ6M PDF set. The most recent PYTHIA 6 Z2* tune is used to model the  underlying event activity. It is derived from the Z1 tune [67], which uses the CTEQ5L parton distribution set, whereas Z2* uses CTEQ6L [68].
The leading-order (LO) cross sections for the topcolor Z 0 signal are taken from Ref. [10], whereas for g KK production, calculations from Ref. [18] are used. However, both cross sections are multiplied by a factor of 1.3 to approximate NLO effects [69]. The normalizations of the background samples are taken from the NLO þ next-to-next-to-leading logarithms (NNLL) calculation for the single top quark production [70], the next-to-next-to-leading order (NNLO) calculations for Wð→ lνÞ þ jets and Z=γ Ã ð→ llÞ þ jets [71][72][73], and the NLO calculation for diboson production [74]. The normalization for the continuum tt background uses NNLO calculations [75]. However, by comparing the number of simulated and data events in control regions, we determine additional cross section scale factors. This is discussed in Sec. V. A detailed simulation of particle propagation through the CMS apparatus and detector response is performed with GEANT4 v9.2 [76]. For all simulated samples, the hard interaction collision is overlaid with a number of simulated minimum bias collisions. The resulting events are weighted to reproduce the pileup distribution measured in data. The same event reconstruction software is used for data and simulated events. The resolutions and efficiencies for reconstructed objects are corrected to match those measured in data [40,42,47,49,51].

A. Dilepton channel
In the dilepton channel, the selection is based on the assumption that both W bosons decay leptonically. The selection requires two leptons and at least two jets. The lepton and the b quark from the decay of a highly Lorentz-boosted top quark are usually not well separated, resulting in a nonisolated lepton that partially or fully overlaps with the b-quark jet.
Offline, the following selection requirements are applied. In the ee channel, events are required to have two electrons with p T > 85 GeV and p T > 20 GeV, each within jηj < 2.5. In the eμ channel, there must be a muon with p T > 45 GeV with jηj < 2.1 and an electron with p T > 20 GeV with jηj < 2.5. Events in the μμ channel should contain two muons with p T > 45 GeV and p T > 20 GeV with jηj < 2.1 and jηj < 2.4, respectively. In all three channels, the two lepton candidates must have opposite charge. The invariant mass of the lepton candidates in the ee and μμ channels must be M ll > 12 GeV and outside the mass window of 76 < M ll < 106 GeV. These selections reduce the contribution from the production of low-mass resonances and from on-shell Z boson production. Events are required to contain at least two jets with p T > 100 GeV and p T > 50 GeV within jηj < 2.5.
Signal events are selected with a two-dimensional isolation variable that is efficient at high top-quark boosts yet reduces multijet backgrounds. This two-dimensional isolation requires ΔRðl; jetÞ > 0.5 or p T;rel ðl; jetÞ > 15 GeV, where ΔRðl; jetÞ is the distance in ðη; ϕÞ between the lepton and the nearest jet, and p T;rel ðl; jetÞ is the transverse momentum of the lepton with respect to the axis of the closest jet. In calculating these quantities only jets with p T > 30 GeV are considered. The efficiency of the two-dimensional isolation requirement has been studied in data and simulation in a Z=γ Ã ð→ llÞ þ jets sample. In this sample, one lepton, passing isolation criteria, is used as a tag, and the other lepton is used as a probe to study the efficiency. The dilepton invariant mass is used to determine the number of events passing and failing the twodimensional isolation criteria. Figure 2 shows the efficiency as function of ΔRðl; jetÞ for data and simulated events. At small ΔR separation between the lepton and the closest jet, the efficiency for electrons is 5%, increasing to 75% for larger ΔRðl; jetÞ. The corresponding values are 10% to 90% for muons. The efficiency is well described by the simulation and no correction is needed. The relative efficiency of the two-dimensional isolation requirement for the 1.5 TeV signal is approximately 70% independent of width.
A requirement of E miss T > 30 GeV in the ee and μμ channels additionally reduces the contribution from multijet and Z=γ Ã ð→ llÞ þ jets production. Given the presence of two b quarks in the events, a logical OR of two b-tagging algorithms is used: at least one of the two leading jets is required to be tagged as a b-quark jet by the CSV algorithm at the medium working point or both leading jets must be tagged using the loose working point of the CSV algorithm. After these requirements, the sample contains about 90% tt background.
The boosted nature of the signal events provides an additional handle for further reduction of the tt background: the separation in ΔR between each lepton and its nearest jet. Requiring ΔRðl 1 ; jetÞ < 1.2 and ΔRðl 2 ; jetÞ < 1.5, where l 1 and l 2 denote the leading and subleading leptons, reduces the tt background contribution by more than a factor of 2, while the loss for a Z 0 signal with mass of 1.5 TeV is about 10%. Additionally, the region with ΔRðl 2 ; jetÞ > 1.5 is dominated by events from continuum tt production and provides an independent sample to check the tt background normalization. The contamination from resonant tt production is expected to be less than 0.2% in this sample. The normalization of the tt background is found to be compatible with the SM expectation using the NNLO cross section calculations, and good agreement between the ee, eμ, and μμ channels is observed.
The resonant nature of the signal is exploited by constructing a mass variable from the four-momenta of the two leading leptons, the two leading jets, and the neutrinos, which approximates the invariant mass of the tt system. For the momentum components p x and p y of the pair of neutrinos, the x and y components ofp miss T are used, and the p z component of each neutrino is set to zero. Figure 3 shows the M tt distributions for the dilepton channel. The expected distribution from a Z 0 signal with M Z 0 ¼ 2 TeV is also shown. Good agreement between the data and the SM background expectation is found.

B. Lepton þ jets channel
The selection in the lepton þ jets channel is based on events with one W boson decaying leptonically, W → lν, and the other one decaying hadronically, W → qq 0 . It requires one lepton (electron or muon) and at least two jets with high p T , including events with nonisolated leptons and merged jets arising from decays of two high-p T top quarks.
Events are required to have exactly one electron with p T > 35 GeV and jηj < 2.5, or one muon with p T > 45 GeV and jηj < 2.1. The reconstructed lepton has to be consistent with originating from the primary event vertex. In order to avoid overlap with the dilepton sample, events with a second reconstructed lepton are removed. All events must have at least two jets with p T > 150 GeV and p T > 50 GeV, both with jηj < 2.4. In order to ensure that there is no overlap with the all-hadronic channel, events with two or more CA8 t-tagged jets are rejected. To reduce the background from multijet production, events are required to have E miss T > 50 GeV and the scalar sum of the lepton p T and E miss T has to be larger than 150 GeV. A further reduction of the multijet background contribution is achieved by applying a similar two-dimensional isolation criterion as described for the dilepton channel. It is applied for both the electron and muon channels, requiring ΔRðl; jetÞ > 0.5 or p T;rel ðl; jetÞ > 25 GeV, where only jets with p T > 25 GeV are considered when calculating these quantities.
In addition, in the electron channel topological requirements are imposed that ensure thatp miss T does not point along the transverse direction of the electron or the leading jet [29], jΔϕðfe or jetg;p miss T Þ − 1.5j < E miss T =50 GeV; with E miss T measured in GeV. The efficiency of this requirement is above 95% for all signal samples, while the background from multijet production is reduced significantly.
The tt system is reconstructed by assigning the fourvectors of the reconstructed final-state objects to either the leptonic or hadronic leg of the tt decay. This is done by constructing a two-term χ 2 function, based on the masses of the reconstructed tt candidates [29,31]. For each event, the hypothesis with the smallest χ 2 value is chosen. In case a CA8 t-tagged jet is found in the event, this jet is used for the hadronic leg of the tt decay and all jets with ΔR < 1.3 from the t-tagged jet are removed from the list of possible hypotheses. Events are required to have a minimum value of χ 2 smaller than 50, which reduces the contribution from background processes and enhances the sensitivity of the search. In the electron channel, the transverse momentum of the reconstructed leptonic leg of the top-quark decay is required to be larger than 140 GeV, to suppress the background from multijet production to a negligible level. Events are categorized based on the lepton flavor and on the number of CA8 t-tagged jets. In case no CA8 t-tagged jet is found, the events are further split into two categories, depending on if any jets are identified as originating from the fragmentation of a b quark using the medium working point of the CSV algorithm. This has a tagging efficiency of 65% per jet [47].
An independent control sample is used to validate the mistag rate of CA8 t-tagged jets in the W þ jets sample. This sample is obtained by inverting the χ 2 criterion, using the leptonic leg of the tt decay hypothesis only, and requiring that no jet has been tagged as a b-quark jet by the loose operating point of the CSV algorithm [47]. This removes most of the tt contamination while retaining events from W þ jets production. Figure 4 shows the p T and mass of the leading CA8 jet in this sample. These jets are used to determine the mistag rate of the CA8 t-tagged jets in data and simulated events that also contain a lepton. Such events have a higher fraction of jets from quark fragmentation than the non-top-quark multijet background for the all-hadronic channel, which has a higher fraction of , and μμ (bottom) channels for data and simulated events. Each background process is scaled by a factor derived from a maximum likelihood fit to data. The expected distribution from a Z 0 signal with M Z 0 ¼ 2 TeV and Γ Z 0 =M Z 0 ¼ 0.01, normalized to a cross section of 1 pb, is also shown. The uncertainty associated with the background expectation includes all the statistical and systematic uncertainties. For bins with no events in data but with nonzero background expectation, vertical lines are shown indicating the 68% confidence level coverage corresponding to an observation of zero events. The data-to-background ratio is shown in the bottom panel of each figure. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray. There is a systematic disagreement observed in the high-mass region that is accommodated by the renormalization and factorization scale uncertainty.
jets from gluon fragmentation. Good agreement is observed, with a mistag rate of 1.2% in data, and a data-to-simulation ratio of 0.83 AE 0.21. This factor is used to scale simulated events containing a misidentified topquark jet.
To validate the CA8 t-tagging efficiency, distributions of the jet mass, minimum pairwise mass, and the ratio τ 32 for CA8 t-tagged jets are shown in the lepton þ jets channel for data and simulated events in Fig. 5, where all SM components are normalized to the output of the maximum likelihood fit. Differences between the distributions in data and simulation lead to different efficiencies of the t-tagging algorithm. In order to account for these differences, a correction factor for simulated events is derived from a combined maximum likelihood fit. The fit is performed by comparing the yields in categories of events which pass and fail the CA8 t-tagging selection criteria, as explained in Sec. VII. The scale factor for t-tagged jets is estimated to be 0.94 AE 0.03, reflecting the somewhat better resolution of the reconstructed mass of CA8 jets in simulation.
The reconstructed top-quark candidates are used to calculate the tt invariant mass. The events are divided into six categories, three for each lepton þ jets channel, so in total six M tt distributions are obtained. The three categories for each lepton flavor are: events with one CA8 t-tagged jet, events without a CA8 t-tagged jet but at least one b tag, and events with neither a CA8 t-tagged jet nor a b tag. All six distributions are shown in Fig. 6.

C. All-hadronic channel
When the top quark has large p T and decays hadronically, all decay products frequently merge into a single jet. Events with high tt invariant mass, where both quarks decay hadronically, thus effectively result in a dijet topology. This forms the basis of the selection in the allhadronic channel. Two exclusive selections are made, one optimized for higher resonance masses, and one optimized for lower resonance masses where the decay products are still somewhat collimated.
To satisfy the high-mass selection, events are required to have two CA8 t-tagged jets with p T > 400 GeV and rapidity jyj < 2.4. The two jets have to be separated in azimuthal angle by jΔϕj > 2.1 radians. The rapidity difference between the two leading jets is also used to divide the events into two categories (jΔyj < 1.0 and jΔyj > 1.0), since the QCD multijet background with light-quark and gluon final states dominantly populates the jΔyj > 1.0 category, whereas the Z 0 signal with a mass of 2 TeV is equally split between the two. The two categories are further subdivided depending on the number of CA8 jets containing a b-tagged subjet: zero, one, or two. This results in six exclusive search regions, with the highest sensitivity in the categories with two b-tagged CA8 jets.
The low-mass selection is applied to events failing the high-mass selection and is designed to gain sensitivity in regions where the decay products are less collimated. Events are selected if two CA15 t-tagged jets with p T > 200 GeV and jyj < 2.4 are found. The sample is split into events with H T < 800 GeV and H T > 800 GeV, where H T is defined as the scalar sum of jet p T , including all jets with p T > 50 GeV. The sample is further categorized according to the number of b-tagged CA15 jets. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray.
In order to estimate the background for the all-hadronic analysis, an approach based on control samples in data is applied. A sideband is selected by inverting the CA8 t-tagging minimum mass requirement on one of the jets in the dijet sample. For the low-mass analysis, the CA15 t-tagging selection criteria based on the subjet invariant mass and pairwise masses are inverted. The other leading CA jet in the event provides a kinematically unbiased ensemble of non-top-quark jets to measure the mistag rate. This mistag rate is then applied to the events where exactly one jet passes the t-tagging selection. These events have a higher gluon fraction than the events used to derive the mistag rate for the lepton þ jets analysis, as mentioned above.
The misidentification probability, r, for a non-t-quark CA jet to be identified as a t-tagged CA jet, is parametrized by three variables, the jet p T , the N-subjettiness ratio τ 32 , and the jet b-tagging discriminant β (the output of the CSV algorithm described above), r ¼ rðp T ; τ 32 ; βÞ. The variable τ 32 is not used for the low-mass analysis because it does not enhance the sensitivity of the search. In this case, the mistag rate is parametrized as a function of two variables only, using the same procedure. The mistag rate is binned, defined as r i;j;k . To estimate the t-tagged jets in the lepton þ jets channel. The SM backgrounds are scaled by a factor derived from the maximum likelihood fit to data. The uncertainty associated with the background expectation includes all the statistical and systematic uncertainties.
The data-to-background ratio is shown in the bottom panel of each figure. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray. FIG. 6. Invariant mass of the reconstructed tt pair in data and simulation in the electron þ jets (left column) and muon þ jets (right column) channels. Events are separated into three categories: one CA8 t-tagged jet (top row), no CA8 t-tagged jet and at least one b tag (middle row), and no CA8 t-tagged jet and no b tag (bottom row). Each background process is scaled by a factor derived from the maximum likelihood fit to data. The expected distribution from a Z 0 signal with M Z 0 ¼ 2 TeV and Γ Z 0 =M Z 0 ¼ 0.01, normalized to a cross section of 1 pb, is also shown. The uncertainty associated with the background expectation includes all statistical and systematic uncertainties. For bins with no events in data but with nonzero background expectation, vertical lines are shown indicating the 68% confidence level coverage corresponding to an observation of zero events. The data-to-background ratio is shown in the bottom panel of each figure. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray.
non-top-quark multijet background arising from mistagging light jets, a four-dimensional array of counts N α;i;j;k is measured in the single t-tagged data sample, where α is the bin of the variable of interest (in this case, M tt ), given by N α ¼ P N jets a¼1 N α;i;j;k r i;j;k , where the indices i; j; k are the bins in p T , τ 32 , and β in which jet "a" lies. The four-dimensional parametrization properly accounts for correlated and uncorrelated statistical uncertainties. The uncertainty in each bin of the predicted mistagged distribution has two parts: one arises from the misidentification probability, and the other from the number of jets in the ensemble; they are uncorrelated and are added in quadrature. The details of this procedure are given in Appendix A. Figure 7 shows the CA8 t-tagging misidentification probability as a function of the CA8 jet p T for different bins of τ 32 and β. Figure 8 shows the CA15 t-tagging misidentification probability as a function of the CA15 jet p T for different values of β for the low-mass analysis. Figures 9 and 10 show validation of this procedure on QCD simulation in the various tagging categories for the high-and low-mass analysis, respectively. Good agreement between the predicted and selected contribution from QCD multijet production is observed in both analyses.
The results of the high-mass selection in the allhadronic channel are shown in Fig. 11 for events with jΔyj < 1.0 and jΔyj > 1.0 in the three b-tagged categories. The distributions of M tt obtained with the low-mass selection are shown in Fig. 12 for events with two subjet b tags, for H T > 800 GeV and H T < 800 GeV. The tt background process is scaled by a factor derived from the maximum likelihood fit to data as explained in Sec. VII, and the non-top-quark multijet background is obtained from data in a sideband region.

VI. SYSTEMATIC UNCERTAINTIES
The sources of systematic uncertainties considered in these analyses are summarized in Table I. Uncertainties originating from the same source are assumed to be 100% correlated between all channels. The uncertainties can affect the normalization, the shape, or both normalization and shape of the M tt distribution.

A. Uncertainties affecting the normalization
The following systematic uncertainties in the normalization of the background processes are considered. The uncertainty in the cross section for SM tt production is 15% [77]. Uncertainties in the production cross sections of W þ jets are 9% for light-flavor jets [78] and 23% for heavy-flavor jets [79]. An uncertainty of 50% is assigned to the cross section of Z þ jets production, obtained by varying the renormalization and factorization scales simultaneously by factors of 0.5 and 2. The largest background contribution from single top quark production originates from the tW channel, which has been measured with an accuracy of 23% [80]; this uncertainty is used for all electroweak single top production processes. The uncertainty in diboson production is 20% [81,82].
In addition, the following systematic uncertainties affect the normalization of all simulated processes, including signal processes. The uncertainty in the measurement of the integrated luminosity is 2.6% [83]. The combined trigger used in the electron category in the lepton þ jets channel has an efficiency uncertainty of 1%. The uncertainty due to the single-muon trigger efficiency is 1%, which affects the muon category in the lepton þ jets channel and the eμ and μμ categories in the dilepton channel.

B. Uncertainties affecting the shape
Systematic uncertainties due to the electron identification are applied as a function of electron p T and η to events with an identified electron in the dilepton and lepton þ jets channels. The uncertainty in the efficiency of the single electron trigger is applied as a function of electron p T and η and affects the ee dilepton channel. Systematic uncertainties due to the muon identification and trigger efficiencies are applied as a function of muon Results of the validation test for the high-mass allhadronic analysis, using simulated QCD multijet events, to validate the data-driven background method used to estimate the QCD multijet contribution. Events are shown without any selection or division applied based on the number of identified b-tagged jets for jΔyj < 1.0 (top) and jΔyj > 1.0 (bottom). The points show the selected QCD multijet events in the signal region, with the horizontal error bars indicating the bin width. The solid histogram shows the predicted number of QCD multijet events using the misidentification probability for CA8 t-tagged jets measured in a statistically independent sideband region. The statistical uncertainty is shown as a shaded region. The ratio of selected to predicted events is shown in the bottom panel of each figure.
p T and η and affect events with a muon in the dilepton and lepton þ jets channels. The efficiencies of the H T and four-jet triggers are measured as a function of H T and the p T of the fourth jet in the event, respectively. A correction is applied for the different behavior between data and simulation in the region where the triggers are not fully efficient.
A systematic uncertainty of half the size of this correction is assigned, with a minimum of 2% in regions where the triggers are fully efficient as determined from MC studies of the efficiency. These uncertainties affect the all-hadronic analyses. Uncertainties in the jet energy scale and resolution are of the order of a few percent, and are functions of jet p T and η. These are taken into account in all channels. These uncertainties are also propagated to the estimation of p miss T . The systematic uncertainty associated with the pileup reweighting procedure is assumed to be fully correlated among all channels and is evaluated by varying the minimum bias cross section.
Efficiencies and mistag rates of the b-tagging algorithm have been measured in data and simulated events for jets [47] and subjets with a spatial separation between them of ΔR > 0.3 [56]. The corresponding uncertainty is correlated between the dilepton, lepton þ jets, and the low-mass category of the all-hadronic channel. The highmass selection in the all-hadronic channel uses subjet b tagging in a collimated region, where the subjets are separated by ΔR < 0.3. The applicability of the standard b-tagging correction factors and uncertainties is not guaranteed in this kinematic regime, because of double-counting of tracks from subjets, which are used in the b-tagging algorithm. To account for this, the corresponding efficiency is measured simultaneously with the derivation of the cross section limits as described in Sec. VII, where the efficiency is left unconstrained in the maximum likelihood fit when deriving upper limits. This approach allows for a consistent extraction directly from the signal regions. The same procedure is used for the efficiency of the CA8 t-tagging algorithm, combined with the requirement on τ 32 .
The mistag rate of the CA8 t-tagging algorithm has been studied for data and simulated events in a sideband region of the lepton þ jets channel, dominated by W þ jets events (as described in Sec. V). An uncertainty of 25% is used for simulated events, which mostly affects the contribution of events from W þ jets processes in events with one misidentified top-quark jet in the lepton þ jets channel. Misidentified CA8 and CA15 t-tagged jets are the source of the QCD multijet background in the all-hadronic channel. The background estimation is obtained from data in sideband regions and the corresponding uncertainties are assumed to be fully uncorrelated between individual bins of the M tt distribution. The efficiency of CA15 t-tagged jets has been studied in data and simulated events [51]. The associated uncertainty affects only the low-mass selection of the all-hadronic channel.
In addition to the experimental uncertainties, the following uncertainties affecting the predictions of the SM background processes are considered. The effect due to missing higher-orders in the simulation of SM processes is estimated by variations of the renormalization and factorization scales. For the W þ jets and tt simulated samples, Results of the validation test for the low-mass allhadronic analysis, using simulated QCD multijet events, to validate the data-driven background method used to estimate the QCD multijet contribution for events with H T > 800 GeV (top), and events with H T < 800 GeV (bottom). The points show the selected QCD multijet events in the signal region, with the horizontal error bars indicating the bin width. The solid histogram shows the predicted number of QCD multijet events using the misidentification probability for CA15 t-tagged jets measured in a statistically independent sideband region. The statistical uncertainty is shown as a shaded region. The ratio of selected to predicted events is shown in the bottom panel of each figure. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray. The expected distribution from a Z 0 signal with M Z 0 ¼ 2 TeV and Γ Z 0 =M Z 0 ¼ 0.01 is also shown, normalized to a cross section of 1 pb.
the renormalization and factorization scales are varied simultaneously by factors of 0.5 or 2. The resulting uncertainty in continuum SM tt production affects all channels, while the uncertainty in W þ jets production affects only the lepton þ jets channel. The effect due to the uncertainty in extra hard-parton radiation is studied by varying the jet matching threshold for simulated W þ jets processes by factors of 0.5 and 2. This uncertainty applies only to the lepton þ jets channel. All simulated signal and background events are reweighted according to the uncertainties parametrized by the eigenvectors of the CTEQ6L and CT10 PDF sets. The shifts produced by the individual eigenvectors are added in quadrature in each bin of the M tt distribution. The resulting uncertainty is taken to be fully correlated among all channels. The impact of the systematic uncertainties on the normalization of the total background depends strongly on the channel considered. The following uncertainties are the dominant ones in the two channels with the highest sensitivity, the category with one CA8 t-tagged jet in the lepton þ jets analysis and the category with two b-tagged jets in the high-mass all-hadronic analysis. The dominant uncertainty comes from missing higher orders in the simulation of the tt background and is on average 17%. The uncertainty due to the uncertainties in the PDFs is 15%, which is the same size as the uncertainty in the total tt cross section in the phase space considered. The size of other experimental uncertainties, like the CA8 t-tagging efficiency, the subjet b-tagging efficiency, and uncertainties due to the jet energy scale and resolution, vary between 4%-12%.

VII. ESTIMATION OF THE BACKGROUND NORMALIZATION
The main source of irreducible background in all channels arises from SM tt production. In the lepton þ jets channels, W þ jets production contributes to events without a CA8 t-tagged jet. Single top quark, Z þ jets, and diboson production constitute small backgrounds overall, and contribute to the dilepton and lepton þ jets channels. In the following, these processes are combined into a single "others" category.
Except for the non-top-quark multijet backgrounds in the all-hadronic channels, the shapes of all SM backgrounds are estimated from simulation. The total yield of the simulated samples is obtained with a maximum likelihood fit to the M tt distributions. Nuisance parameters are included in the fit to take into account the effect of systematic uncertainties. The parameters are constrained using log-normal probability density functions and are fitted simultaneously with the parameters corresponding to the background normalization.
Since there is no control sample of highly-boosted SM tt events that is disjoint from the signal regions of this analysis, the maximum likelihood fit is also used to extract the efficiency of the CA8 t-tagging and subjet b-tagging algorithms simultaneously. This is accomplished by separating the sample into subsamples based on the tagging criteria, and allowing the fit to find the best values for the nuisance parameters corresponding to these efficiencies. For the ratio plot, the statistical uncertainty is shown in light gray, while the total uncertainty, which is the quadratic sum of the statistical and systematic uncertainties, is shown in dark gray. The expected distribution from a Z 0 signal with M Z 0 ¼ 1 TeV and Γ Z 0 =M Z 0 ¼ 0.01 is also shown, normalized to a cross section of 1 pb.
Higher-order calculations, as listed in Sec. IV, are used as prior assumptions on the cross sections of each background process, with the uncertainties discussed in Sec. VI. No assumption on the scale factor for the CA8 t-tagged jets is made and the corresponding nuisance parameter is left to float freely in the fit. The same is true for the subjet b-tagging scale factor for the high-mass selection in the allhadronic channel. This procedure effectively constrains the tagging efficiencies. No signal hypothesis is used in this procedure. Only the experimental uncertainties (see Sec. VI) are included in the likelihood fit. Uncertainties due to scale and matching systematics, as well as the uncertainties due to the PDF choice are not included. The list of uncertainties considered is given in the upper part of Table I. The fit converges with no parameter outside of two standard deviations of the prior assumption. A reduction of the uncertainty due to the tt normalization is obtained and a simultaneous measurement of the CA8 t-tagging and subjet b-tagging efficiencies is performed. These results do not TABLE I. Sources of systematic uncertainties and the channels they affect. The CA8 subjet b-tagging uncertainty includes the uncertainties in both the efficiency and mistag rate. Uncorrelated uncertainties that apply to a given channel are marked by ⊙. Uncertainties correlated between channels are marked by ⊕. The uncertainties listed in the upper part of the AE1σ ⊕ ⊕ ⊕ ⊕ tt ren. and fact. scales 4Q 2 and 0.25Q 2 ⊕ ⊕ ⊕ ⊕ W þ jets ren. and fact. scales 4Q 2 and 0.25Q 2 ⊙ W þ jets matching scale μ 2μ and 0.5μ ⊙ a AK5 and CA15 subjets.
TABLE II. Parameters for the background normalization of the given processes, the scale factor for CA8 t-tagged jets and the subjet b-tagging scale factor. The value of each parameter is obtained from a maximum likelihood fit. Also shown are the prior assumptions on the rate uncertainties and the posterior uncertainties obtained by the fit. In case of the subjet b-tagging scale factor, the best-fit value and the posterior uncertainty are given in units of the standard b-tagging scale factor and uncertainty. change when including different signal hypotheses in the maximum likelihood fit. The best-fit values are used to scale the predictions for the various background processes. The measured CA8 t-tagging efficiency is used to scale simulated events containing one CA8 t-tagged jet in the lepton þ jets channel and all categories of the high-mass all-hadronic channels. The nuisance parameter for the subjet b-tagging scale factor is used to scale all simulated events in the high-mass all-hadronic channels. The numerical values for the background normalization, the CA8 t-tagging scale factor, and the subjet b-tagging scale factor are given in Table II, together with the prior and posterior uncertainties.
The number of expected and observed events after the maximum likelihood estimation is shown in Tables III-VI for all categories in the three channels.

VIII. RESULTS
No significant excess of data over the expected SM background is observed. A Bayesian statistical method [84,85] is used to derive 95% confidence level (C.L.) upper limits on the cross section times branching fraction for Z 0 → tt production. The limits are derived employing a template based evaluation that uses the invariant mass distribution of the reconstructed tt pair. A likelihood fit TABLE III. Signal efficiency and number of events in the ee, eμ, and μμ channels. The yield of each MC background is obtained from NLO þ NNLL calculations, multiplied by a scale factor derived from the likelihood fit. The uncertainty given for each background process includes the MC statistical uncertainty added in quadrature with all systematic uncertainties. The resonance relative decay width Γ Z 0 =M Z 0 is indicated by w. ee channel eμ channel μμ channel  Signal efficiency and number of events in the e þ jets and μ þ jets channels. The yield of each MC background is obtained from NLO þ NNLL calculations, multiplied by a scale factor derived from the likelihood fit. The uncertainty given for each background process includes the MC statistical uncertainty added in quadrature with all systematic uncertainties. The resonance relative decay width Γ Z 0 =M Z 0 is indicated by w.
e þ jets channel μ þ jets channel is used to compare the signal and SM background expectations. To build the likelihood function, a Poisson probability is calculated in each bin of the mass distribution for each category in each channel. The parameters representing the Poisson mean of the signal strength and the background processes are determined in the fit. Pseudoexperiments are performed to extract expected limits under a background-only hypothesis. The systematic uncertainties discussed in Sec. VI are taken into account through nuisance parameters. These are randomly varied within their ranges of validity using log normal distributions as the probability density function. Correlations between the systematic uncertainties across all channels are taken into account. The statistical uncertainties of simulated samples are treated as an additional Poisson nuisance parameter in each bin of the mass distribution. Signal efficiency and number of events in the high-mass all-hadronic channel. The yield of the tt background is obtained from NLO þ NNLL calculations, multiplied by a scale factor derived from the likelihood fit. The multijet background is obtained from sideband regions in data. The uncertainty given for each background process includes the statistical uncertainty added in quadrature with all systematic uncertainties. The resonance relative decay width Γ Z 0 =M Z 0 is indicated by w.
jΔyj < 1.0 jΔyj > 1.0 Signal efficiency and number of events in the low-mass all-hadronic channel. The yield of the tt background is obtained from NLO þ NNLL calculations, multiplied by a scale factor derived from the likelihood fit. The multijet background is obtained from sideband regions in data. The uncertainty given for each background process includes the statistical uncertainty added in quadrature with all systematic uncertainties. The resonance relative decay width Γ Z 0 =M Z 0 is indicated by w. The median of the distribution of the upper limits at 95% C.L. in the pseudoexperiments and the central 68% (95%) interval define the expected upper limit and AE1σ (AE2σ) bands, respectively. Upper limits for three benchmark signal hypotheses are calculated: a topcolor Z 0 boson [10] with relative widths Γ Z 0 =M Z 0 ¼ 1.0% or Γ Z 0 =M Z 0 ¼ 10%, and a Randall-Sundrum KK gluon with coupling as described in Ref. [18]. Resonance masses between 0.75 and 3 TeV are considered using simulated samples with mass values given in Sec. IV. Above mass values of 3 TeV, narrow-width signals would have cross sections below 1 fb, placing them beyond the reach of Run 1 at the LHC, and signals with relative widths larger than 10% would show no resonance structure at the collision energy of 8 TeV. All limits are given at 95% C.L.
A comparison of the expected limits obtained from the individual channels is shown in Fig. 13. Also shown are the results from a search optimized for threshold production of the tt pair in the lepton þ jets channel [31]. This channel has the best sensitivity for resonance masses below 0.75 TeV. Above this value, the combination of the boosted analyses described in this paper places better limits on the production cross section times branching fraction. The best overall sensitivity is obtained in the lepton þ jets channel. The high-mass selection of the allhadronic channel has comparable sensitivity in the mass region above 2 TeV. Figure 14 shows the results for each of the three signal hypotheses. The cross section limits for the narrow signal hypothesis are compared to the cross section for the production of a Z 0 boson with 1.2% width. This width is chosen for comparison with theoretical results and previous measurements. Resonances with masses up to 2.4 TeV (2.4 expected) for the narrow Z 0 hypothesis are excluded. These cross section limits are model independent, meaning that they are valid for any resonance decaying to tt, with a width well below the experimental resolution of about 10%. Wide resonances with 10% width are excluded up to 2.9 TeV (2.8 expected). The better limits with respect to narrow resonances are due to the higher production cross section of the wider Z 0 resonance. Randall-Sundrum KK gluons decaying to tt are excluded with masses below 2.8 TeV (2.7 expected). This model exhibits the weakest upper limits on the production cross section, because of the long tails towards low resonance masses present in the predicted M tt distribution. These tails are introduced by the interplay between the large natural width of the KK gluons and the parton luminosity, causing masses that are far below the resonance mass to have a larger probability than events near the resonance itself. The expected and observed exclusion limits for different resonance masses are given in Table VII.
The upper limits on the production cross section times branching fraction into tt are given in Table VIII, for different resonance masses. The upper limits on the cross sections show improvements of about 50% with respect to a previous combination of results from a search in the lepton þ jets and all-hadronic channels [31]. These improvements are mostly due to the use of t tagging in the lepton þ jets channel, and the application of b tagging on subjets in the all-hadronic channel. The limits for M Z 0 < 1 TeV are improved with the addition of the dilepton channel and the low-mass selection in the all-hadronic channel.

IX. SUMMARY
A search has been performed for the production of heavy tt resonances in final states including two, one, or no leptons. The analysis is based on a data sample corresponding to an integrated luminosity of 19.7 fb −1 recorded in 2012 with the CMS detector in proton-proton collisions at ffiffi ffi s p ¼  Cross sections times branching fractions above 11 fb are excluded at 95% C.L. for the process pp → Z 0 → tt with a Z 0 resonance [10] with mass of 2 TeV and width Γ Z 0 =M Z 0 ¼ 1%. The corresponding 95% C.L. expected   to the combination, in providing the best expected limit. Below this dashed line, only the results of the low-mass analysis with resolved jets are quoted; above this line, the results from the combination of the boosted channels are given. The limits are shown as a function of the resonance mass and are compared to predictions for the cross section of a Z 0 boson with relative width of 1.2% and 10% [10] and the prediction for the production of a KK gluon [18]. The predictions are multiplied by a factor of 1.3 to account for higher-order corrections [69]. TABLE VII. Expected and observed lower mass limits for the three benchmark models. Mass limits are given for the dilepton analysis, the lepton þ jets analysis, the combination of the two all-hadronic analyses and the full combination of all four analyses. All limits are given at 95% C.L. cross section limit is 13 fb. The 95% C.L. observed lower mass limit for a topcolor narrow Z 0 resonance with Γ Z 0 =M Z 0 ¼ 1.2% corresponds to 2.4 TeV, which agrees with the expected limit. Observed and expected 95% C.L. upper limits of 18 fb (23 fb) are set for a Z 0 boson [10] with a mass of 2 TeV and width Γ Z 0 =M Z 0 ¼ 10%. The respective 95% C.L. observed and expected lower mass limits are 2.9 and 2.8 TeV for a wide topcolor Z 0 resonance.

Mass limit [TeV
For the production of Kaluza-Klein gluon excitations pp → g KK → tt predicted in Randall-Sundrum models [18], an upper limit on the cross section of 38 fb is observed (50 fb expected) at 95% C.L. for a mass of 2 TeV. The observed and expected lower mass limits are 2.8 and 2.7 TeV.
These mass limits represent significant improvements over previous ones set at ffiffi ffi s p ¼ 7 TeV [26,29,30]. An improvement by about 50% on the 95% C.L. upper limits with respect to an earlier search optimized for high masses at ffiffi ffi s p ¼ 8 TeV [31] is achieved by the application of additional jet substructure information and the addition of the dilepton channel. The results presented provide the most stringent constraints on resonant tt production 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:  VIII. Expected and observed limits for the production cross section times branching fraction of a Z 0 boson decaying to tt with a width of 1%, 10% and a KK gluon in the RS model. All limits are given at 95% C.L.  As mentioned in Section V, in the high-mass allhadronic analysis, the mistag rate r is parametrized as a function of the jet p T , the N-subjettiness ratio τ 32 , and the b-tagging discriminant β, of the jet "a". In the lowmass analysis, the mistag rate is parametrized as a function of jet p T and β only, but the procedure is otherwise identical.
Taking the high-mass analysis as an example, the nontop-quark multijet background arising from events with mistagged light jets is estimated by dividing the data into bins along four dimensions: jet p T , τ 32 , β, and the variable of interest α (in this case M tt , although the procedure is applicable to any other variable).
The expected background yield for this 4-dimensional bin is obtained by multiplying the events in this bin before the application of t tagging, NðM tt ; p T ; τ 32 ; βÞ ¼ N α;i;j;k , by the mistag rate rðp T ; τ 32 ; βÞ ¼ r i;j;k . Summing all the predictions along indices i, j, and k then yields the total prediction for the bin α: N α ¼ X N jets a¼1 N α;i;j;k r i;j;k ; where N jets is the number of jets in the event. The four-dimensional parametrization properly accounts for correlated and uncorrelated statistical uncertainties. The uncertainty in each bin of the predicted mistagged distribution σðm α Þ has two parts: one arises from the misidentification probability (σðr i;j;k Þ), and the other from the number of jets in the ensemble ð ffiffiffiffiffiffiffiffiffiffiffiffiffi N α;i;j;k p Þ: σðm α Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X N jets a¼1 ððN α;i;j;k σðr i;j;k ÞÞ 2 þ ð ffiffiffiffiffiffiffiffiffiffiffiffiffi N α;i;j;k p r i;j;k Þ 2 Þ v u u t ; The first term accounts for all uncertainties in the i; j; kth bin of the mistag probability. The second term accounts for statistical uncertainties in the jet ensemble. Both of these terms are individually added linearly since they are fully correlated within each bin. The two pieces are added in quadrature since they are fully uncorrelated.
[1] ATLAS Collaboration, Observation of a new particle in the search for the  D 85, 051101 (2012).
[24] T. Aaltonen et al. (CDF), Search for resonant production of tt decaying to jets in pp collisions at ffiffi ffi s p ¼ 1.96 TeV, Phys.