Search for anomalous production in the highly-boosted all-hadronic final state

A search is presented for a massive particle, generically referred to as a Z′, decaying into a tt− pair. The search focuses on Z′ resonances that are sufficiently massive to produce highly Lorentz-boosted top quarks, which yield collimated decay products that are partially or fully merged into single jets. The analysis uses new methods to analyze jet substructure, providing suppression of the non-top multijet backgrounds. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 5 fb−1. Upper limits in the range of 1 pb are set on the product of the production cross section and branching fraction for a topcolor Z′ modeled for several widths, as well as for a Randall-Sundrum Kaluza-Klein gluon. In addition, the result contrain any enhancement in tt− production beyond expectations of the standard mode for tt invariant mass larger than 1 TeV/c2.


Introduction
Among scenarios for physics beyond the standard model (SM) are possibilities of new gauge interactions with large couplings to third-generation quarks [1][2][3][4][5][6][7][8][9][10][11]. These interactions predict new massive states, generically referred to as Z bosons, that can decay into tt pairs. Typical examples are the topcolor Z described in Refs. [4][5][6], and the Randall-Sundrum Kaluza-Klein (KK) gluons of Ref. [12]. Other models [13][14][15][16] have recently been proposed to resolve the discrepancy in the forward-backward asymmetry in tt production reported at the Tevatron [17][18][19][20][21]. Model-independent studies of the implications of a large forward-backward asymmetry suggest that a strong enhancement of the production cross section for tt pairs would be expected at the Large Hadron Collider (LHC) for invariant masses m tt > 1 TeV/c 2 , if the observed discrepancy with the predictions of the standard model (SM) is due to new physics at some large mass scale [22,23]. Searches for new physics in top-pair production have been performed at the Tevatron [24][25][26], and provide the most stringent lower limits on the mass (m Z ) of narrow-width (Γ Z ) resonances, e.g. excluding a topcolor tt resonance with Γ Z /m Z = 1.2% for masses below ≈ 0.8 TeV/c 2 .
In this Letter, several models of resonant tt production are considered, including a Z resonance with a narrow width of 1% of the mass, a Z resonance with a moderate width of 10% of the mass, as well as broader KK gluon (g ) states [12]. An enhancement over tt continuum production at large tt invariant masses is also considered.
This study examines decays of produced tt pairs in the all-hadronic channel, taking advantage of the large (46%) branching fraction of tt → W + bW − b → 6 quarks, and focuses on final states with m tt > 1 TeV/c 2 . For lower masses, the background from quantum-chromodynamic (QCD) production of non-top multijet events makes the search prohibitively difficult in this channel. At high m tt , using new techniques in jet reconstruction to identify jet substructure [27][28][29][30][31], it is possible to study highly boosted top quarks (E/m t c 2 > 2, where E and m t are the energy and mass of the top quark). The decay products of these highly boosted top quarks are collimated, and are partially or fully merged into single jets with several separate subjets corresponding to the final-state quarks (one from the bottom quark, and two light-flavor quarks from the W decay). The data sample corresponds to an integrated luminosity of 5 fb −1 collected by the Compact Muon Solenoid (CMS) experiment [32] in proton-proton collisions at a center-of-mass energy of 7 TeV at the LHC.
In the following Letter, Sec. 2 describes the CMS detector and the event reconstruction. Section 3 explains the strategy for the analysis and the derivation of the efficiency and misidentification probability of the substructure tools that were used. Section 4 gives the systematic uncertainties in the analysis. Section 5 describes the statistical methodology used. Section 6 presents a summary of the results.

CMS detector, event samples, and preselection
The CMS detector is a general-purpose detector that uses a silicon tracker, as well as finely segmented lead-tungstate crystal electromagnetic (ECAL) and brass/scintillator hadronic (HCAL) calorimeters. These subdetectors have full azimuthal coverage and are contained within the bore of a superconducting solenoid that provides a 3.8 T axial magnetic field. The CMS detector uses a polar coordinate system with the polar angle θ defined relative to the direction (z) of the counterclockwise proton beam. The pseudorapidity η is defined as η = − ln tan(θ/2), which agrees with the rapidity y = 1 2 ln 2 2 CMS detector, event samples, and preselection in the tracker for |η| < 2.5. The surrounding ECAL and HCAL provide coverage for photon, electron, and jet reconstruction for |η| < 3. The CMS detector also has extensive forward calorimetry that is not used in this analysis. Muons are measured in gas-ionization detectors embedded in the steel return yoke outside the solenoid.
Events were selected with an online trigger system, with decisions based on the transverse momentum (p T ) of a single jet measured in the calorimeters. The instantaneous luminosity increased with time, hence two thresholds were used for different running periods. Most of the data were collected with a threshold of jet p T > 300 GeV/c, and the rest with a threshold of 240 GeV/c. Offline, one jet is required to satisfy p T > 350 GeV/c.
There are several Monte Carlo (MC) simulated samples in the analysis. The continuum SM tt background is simulated with the MADEVENT/MADGRAPH 4.4.12 [33] and PYTHIA 6.4.22 [34] event generators. The MADGRAPH generator is also used to model generic high-mass resonances decaying to SM top pairs. In particular, a model is implemented with a Z that has SM-like fermion couplings and mass between 1 and 3 TeV/c 2 . However, in the MC generation of the Z , only decays to tt are simulated. The width of the resonance is set to 1% and 10% of m Z , so as to check the predictions for a narrow and a moderate resonance width, respectively. Here, the 10% width is comparable to the detector resolution. The PYTHIA 8.145 event generator [35] is used to generate Randall-Sundrum KK gluons with masses m g = 1, 1.5, 2, and 3 TeV/c 2 , and widths of ≈ 0.2m g . These Randall-Sundrum gluons have branching fractions to tt pairs of 0.93, 0.92, 0.90, and 0.87, respectively. PYTHIA6 is also used to generate non-top multijet events for background studies, cross-checks, and for calculating correction factors. The CTEQ6L [36] parton distribution functions (PDF) are used in the simulation. The detector response is simulated using the CMS detector simulation based on GEANT4 [37].
Events are reconstructed using the particle-flow algorithm [38], which identifies all reconstructed observable particles (muons, electrons, photons, charged and neutral hadrons) in an event by combining information from all subdetectors. Event selection begins with removal of beam background by requiring that events with at least 10 tracks have at least 25% of the tracks satisfying high-purity tracking requirements [39]. The events must have a well-reconstructed primary vertex, and only charged particles identified as being consistent with the highest Σp 2 T interaction vertex are considered, reducing the effect of multiple interactions per beam crossing (pile-up) by ≈ 60%.
The selected particles, after removal of charged hadrons from pile-up and isolated leptons, are clustered into jets using the Cambridge-Aachen (CA) algorithm with a distance parameter of R = 0.8 in η-φ space, where φ is the azimuthal angle [40,41], as implemented in the FAST-JET software package version 2.4.2 [42,43]. The CA algorithm sequentially merges into single objects, by four-vector addition, the pairs of particle clusters that are closest in the distance measure d ij = ∆R 2 ij /R 2 , where ∆R ij = (∆η) 2 + (∆φ) 2 and R = 0.8, until the minimum is less than or equal to the so-called beam distance d iB , which equals unity in the CA algorithm. More generally these distance measures are equal to i . In the more common cases of the k T and anti-k T algorithms [44], n = 1 and n = −1, respectively, however for the CA algorithm n = 0, and hence only angular information is used in the clustering. When the beam distance for particle cluster i is smaller than all of the other d ij , particle cluster i is identified as a jet and the clustering proceeds for the remaining particles in the event. Jet energy scale corrections are applied as documented in Ref. [45]. All jets are required to satisfy jet-quality criteria [38], as well as |y| < 2.5. The rapidity is used in this case because the jets acquire a finite mass as part of the imposed jet-quality criteria.

Analysis method
The analysis is designed for cases in which the tt system has sufficient energy for the decay products of each top quark to be emitted into a single hemisphere, implying that E/m t c 2 > 2. As a consequence, the top quarks can be either partially merged when only the W decay products are merged into a single jet, or fully merged when all top decay products are merged into a single jet. Thus, this analysis becomes inefficient for low masses, and upper limits are not evaluated for Z masses below 1 TeV/c 2 .
The largest background in this search is the non-top multijet (NTMJ) background. This is highly suppressed by requirements on the jet mass and substructure. The remaining NTMJ background is estimated by computing the probability for non-top jets to pass the top-jet selections (misidentification probability) in control regions of the data. These control regions are constructed by inverting substructure selections while keeping mass selections fixed. This mistagging probability is then applied to the signal region to estimate the contribution from the NTMJ background.
In this section, the jet topologies in the analysis are defined in Sec. 3.1, the signal estimate is described in Sec. 3.2, and the background estimate is shown in Sec. 3.3. Finally, the results of the event selection and the background estimate are presented in Sec. 3.4.

Analysis of jet topologies
The events are classified into two categories, depending on the number of final-state jets that appear in each hemisphere. The 1+1 channel comprises dijet events in which each jet corresponds to a fully merged top-quark candidate, denoted as a Type-1 top-quark candidate. The 1+2 channel comprises trijet events that fail the 1+1 criteria, with a Type-1 top-quark candidate in one hemisphere, and at least two jets in the other, one being a jet from a b quark (although no identification algorithms are applied) and the other a merged jet from a W. These two separate jets define a Type-2 top-quark candidate in the 1+2 channel. Further channels, such as 2+2, which would correspond to two Type-2 top quarks, are not considered in this analysis. The 1+1 and 1+2 selections are now discussed in detail.
The 1+1 events are required to have at least two Type-1 top-quark candidates, each reconstructed with p T > 350 GeV/c. Both candidates are tagged by a top-tagging algorithm [27, 28] to define merged top jets. In the case of more than two top-tagged jets, the two top-tagged jets with the highest p T are considered. The top-tagging algorithm is based on the decomposition of a jet into subjets, by reversing the final steps of the CA jet-clustering sequence. In this decomposition, particles that have small p T or are at large angles relative to the parent cluster are ignored. At least three subjets are required in each jet. While the subjets of generic jets tend to be close together, and one of them often dominates the jet energy because of gluon emission in the final state, the decay products of the top quark share the jet energy more equally and emerge at wider angles. The mass of the summed four-vector of the constituents of the hard jet must be consistent with the mass of a top quark m t ≈ 175 GeV/c 2 (140 < m jet < 250 GeV/c 2 , where the values chosen are optimized through MC simulation). Figure 1a shows the expected jet mass for the Z signal from MC as a dotted histogram, and the expected jet mass for the NTMJ background from MC as a solid yellow histogram. As expected, the Z signal has a peak at the top mass corresponding to fully merged top jets, and has a shoulder at the W mass corresponding to partially merged top jets. The minimum pairwise invariant mass of the three subjets of highest p T is required to be > 50 GeV/c 2 , because the combination with the minimum pairwise mass often (> 60%) consists of the jet remnants from the W decay.
The 1+2 events are required to have exactly one hemisphere containing a top-tagged Type-1 candidate with p T > 350 GeV/c. That is, only events that fail the 1+1 criteria are considered for the 1+2 selection. In the hemisphere opposite the top-tagged Type-1 candidate, there must be at least two jets, one identified as a W-jet candidate, with p T > 200 GeV/c, and another jet from a b quark (although no identification algorithm is used) with p T > 30 GeV/c. The W jet is required to be tagged by a W-tagging algorithm, based on the jet pruning technique [29,30]. The W-tagging algorithm requires two subjets, a total jet mass consistent with the mass of the W boson m W = 80.4 GeV/c 2 (60 < m jet < 100 GeV/c 2 ), and an acceptable "mass-drop" parameter µ of the final subjets relative to the hard jet [31]. The mass-drop µ is defined as the ratio of the mass of the more massive subjet m 1 to the mass of the complete jet m jet , and is required to be smaller than 40% (m 1 /m jet ≡ µ < 0.4). This selection helps to discriminate against generic jets, which usually have larger µ values. The W-jet and b-jet candidates combine to form the Type-2 top-quark candidate, whose mass must be consistent with that of the top quark (140 < m jet < 250 GeV/c 2 , where the values chosen are optimized using MC simulation). When there are more than two jets in the Type-2 hemisphere, the b-quark candidate is taken as the one closest to the W-tagged jet in η-φ space.
The jet-pruning technique used to select W jets removes a portion of the jet, which is not accounted by the ordinary jet energy scale corrections. The jet corrections used in this analysis are derived from unpruned jets, and the impact on pruned jets is therefore investigated using a dijet MC sample. In particular, the p T of reconstructed pruned jets are compared to the p T of matched generator-level particle jets, that also underwent the pruning procedure, and the difference of 2-3% observed in absolute response suggests a systematic uncertainty in the jet energy from this source. An uncorrelated 3% uncertainty is therefore added to the uncertainties for standard jet energy corrections. This uncertainty is applied for both the top-tagging and jet-pruning algorithms, and is added in quadrature to the general jet energy scale corrections of Ref. [45], which are ≈ 2-4%, depending on p T and rapidity.

Signal efficiency
For both the Z signal and the (subdominant) tt background, the efficiencies of the analysis selection are estimated from Monte Carlo simulation, with scale factors to account for measured differences with respect to the data. Figure 1b shows the efficiency for tagging a true top jet as a function of p T . Above ≈ 500 GeV/c, the efficiency plateaus between 50-60%.
Three scale factors are applied to the efficiency. The first scale factor is used to correct for the trigger in simulated signal events. Its value is equal to the trigger efficiency: it rises from ≈ 75% (60%) for 1+1 (1+2) events at m tt = 1.0 TeV/c 2 and becomes fully efficient for m tt > 1.5 TeV/c 2 . The value of the trigger efficiency is estimated per jet on a sample of simulated NTMJ events passing the top-quark candidate selections, it is then applied to simulated signal events. The systematic uncertainty is assigned to be 50% of the trigger inefficiency from MC. The difference between the measured trigger efficiency in data and MC is roughly in this range, but suffers from large statistical uncertainties. The second scale factor is used to correct for any differences in jet-energy scale for the subjets and for the full jets. This is referred to as the subjet jet-energy scale factor. The third scale factor is used to correct for the impact of any differences between data and MC in efficiencies for finding jets with substructure. This is referred to as the subjet selection-efficiency scale factor. The derivation of the second and third scale factors is now discussed in detail.
These second two scale factors are both determined in a control sample comprising events with a single muon (referred to as the muon control sample), usually from the decay of t → Wb,  with W → µν, and at least two jets. The event selection is nearly identical to that in Ref. [46], except for larger p T requirements for the jets. The leading jet is required to satisfy p T > 200 GeV/c, and the sub-leading jet is required to satisfy p T > 30 GeV/c. Due to a small number of fully-merged (Type-1) top jets in this sample, it is not possible to construct a sufficiently large number of true Type-1 top jets. Instead, the characterization of jets with substructure is studied with moderately-boosted tt events where there is a large fraction of partially-merged (Type-2) top-quark candidates and the W-jets within them.
The events in the muon control sample used to study W-tagging are dominated by tt decays, and the leading-jet p T requirement (> 200 GeV/c) favors the topology in which the two top quarks are produced back-to-back, thereby facilitating jet merging on the side of the "hadronic" top quark, containing jets from t → Wb → qq b. In the other hemisphere, these events contain one isolated muon, consistent with originating from the primary collision vertex, with p T > 45 GeV/c and |η| < 2.1. Events are rejected if they contain other isolated electrons or muons within |η| < 2.1 with p T > 15 GeV/c or p T > 10 GeV/c, respectively. The remaining events are then required to have ≥ 2 jets with p T > 30 GeV/c, and at least one jet with p T > 200 GeV/c. Unlike the all-hadronic channel discussed in this Letter, in the muon control sample, there are two well-separated jets originating from b quarks, so in order to enhance the tt fraction of this control region, the events are required to contain at least one jet tagged with a secondary-vertex b-tagging algorithm [47], also used in Ref. [46]. The b-tagging algorithm combines at least two tracks into at least one secondary vertex, and forms a discriminating variable based on the three-dimensional decay length of the vertex.
The subjet jet-energy scale factor is estimated by extracting a W mass peak in the muon control sample, and comparing the peaks in data and MC. The mass distribution of the jet of largest mass in the hadronic hemisphere is shown in Fig. 2a.
In this figure, the MC tt contribution is normalized to the approximate next-to-next-to-leadingorder (NNLO) cross section for inclusive tt production of 163 pb [48][49][50]. The non-W mulitjet component is based on sidebands in data that have the muon isolation criterion reversed. The contributing spectrum is normalized through a fit to the missing transverse energy. The stringent criteria of this analysis provide very few W+jets events that pass the required selections. This distribution is therefore taken to be the same as that of the generic non-W multijet background. This is acceptable because the mass structure within the candidate top-quark jets are very similar in these two samples, and the sideband data has many more events that pass the selection criteria. The W+jets contribution is normalized to the inclusive W production cross section of σ W→ +ν = 31.3 ± 1.6 nb computed at NNLO with FEWZ [51]. A fit of the sum of two Gaussian functional forms to data is given by the solid line, and a similar fit to the simulated events is shown as a dashed line. The centers of the main Gaussian distributions in data and MC are m DATA W = 83.0 ± 0.7 GeV/c 2 and m MC W = 82.5 ± 0.3 GeV/c 2 , respectively. The subjet jetenergy scale factor for W jets is determined by taking the ratio of these two values, and equals 1.01 ± 0.01, including statistical uncertainty only.
The subjet selection-efficiency scale factor is estimated by comparing the observed selection efficiency in the muon control sample in data and MC. The ratio of the number of events in the W mass window (60 < m jet < 100 GeV/c 2 ) in Fig. 2a, after W tagging, to the number of events in the muon control sample, defines the W selection efficiency within the mass window. the subjet selection-efficiency scale factor, to be applied to the MC to obtain the same efficiency as in data, is determined to be 0.97 ± 0.03. The same scale factor and uncertainty are assumed for Type-1 jets, which is consistent with results from the statistics-limited control sample of muon events that contain Type-1 jets. As two top-quark tags are required in each event, the correction for both 1+1 and 1+2 events is the square of the single-tag scale factor, yielding 0.94 ± 0.06.
The Type-1 jet selection cannot be checked at the same level of precision as the W-jet selection because of the small number of Type-1 jets in the muon control sample. However, the Type-2 top-quark candidate selection can be tested in the muon control sample, as shown in Fig. 2b. The same procedure is used to construct these Type-2 top-quark candidates as in the 1+2 selection, including the W-mass and mass-drop selections. Within the statistical uncertainty, good agreement is observed in the data and simulation. Since the selection of Type-2 top-quark candidates considers a boosted three-body decay as well as a W tag, the agreement between the characteristics of candidates in data and in MC provides further confidence for the assumption that the scale factor for the efficiency of W-tagging is appropriate for three-body decays such as the Type-1 top-quark system.
To check the dependability of our assumption, namely that the data-to-MC scale factors are the same for the muon control sample as for the Z signal, the scale factor is measured in a control sample using more stringent kinematic requirements to select a part of phase space similar to that of a Z signal with m ∼ 1 TeV/c 2 . The b-tagging requirement is dropped in order to collect more tt events. Also, to capture the kinematics of the background, instead of using the distribution for W+jets from the sidebands in data without isolated muon candidates, as is done in the fit to the W mass, the distribution for W+jets is taken instead from the W+jets MC.
In all samples with large p T thresholds, the data-to-MC scale factor is found to be consistent with the measured value of 0.97 ± 0.03. The selection that provides sideband regions most similar in kinematics to that of the signal region is a requirement that the Type-2 top candidate satisfy p T > 400 GeV/c. Fig. 3a shows the p T distribution for the Type-2 candidates in the muon control sample, and Fig. 3b shows the p T of the W-jet within the Type-2 top-quark candidate, as defined by the jet of largest mass in the event. Arbitrarily normalized distributions for a Z signal with m = 1 TeV/c 2 are overlaid for comparison. For completeness, Figs. 4a and 4b show plots identical to Figs. 2a and 2b, but with selections that require Type-2 top-quark candidates with p T > 400 GeV/c. The scale factor extracted from this higher-p T subsample is 0.99 ± 0.11, which is consistent with the quoted data-to-MC scale factor of 0.97 ± 0.03.

Background estimate
Since this analysis focuses on signatures with high-p T jets, the main backgrounds expected are from SM non-top multijet production and tt production. The background from NTMJ production is estimated from sidebands in the data as described below. For the Z masses considered in this analysis, the irreducible SM tt component is significantly smaller than the NTMJ background contribution, and is therefore estimated from MC simulation using the same correction factors as found for the Z MC described in Sec. 3.2. It is normalized to the approximate NNLO cross section described in Sec. 3.2.
In both 1+1 and 1+2 channels, estimates of the dominant NTMJ background are obtained from data as follows. First, the probability is estimated for mistaking a non-top jet as a top-quark jet through the top-tagging algorithm. This procedure defines the mistag probability (P m ). Higher momentum jets have a larger probability to radiate gluons, and as the jet p T increases, they are more likely to have top-like substructure and thereby satisfy a top tag [52]. The mistag    Figure 3a shows the distribution of the Type-2 top candidate p T . probability is therefore obtained as a function of total jet p T , using the following procedure. Events with ≥ 3 jets are selected for the 1+2 topology, with the three leading jets in the event required to pass p T thresholds of 350, 200, and 30 GeV/c, respectively, without any requirements placed on the jet mass of the Type-1 candidate. The mass of the W-boson candidate within the Type-2 candidate is required to fall within the W-boson mass window, and the invariant mass of the Type-2 candidate is required to fall within the top-quark mass window. However, the mass-drop requirement is inverted (µ > 0.4) to define a signal-depleted sideband. The small contribution from the SM tt continuum is subtracted using MC expectation, and the mistag probability P m (p T ) is defined by the fraction of Type-1 candidates that are top-tagged, as a function of their p T . The resulting mistag probability appears in Fig. 1b. Next, the 1+2 and 1+1 samples are defined using a loose selection: (i) in trijet events, two jets in one hemisphere are required to pass the Type-2 selection and (ii) in dijet events, one randomlychosen jet is required to pass the Type-1 selection. In both cases, the other high-p T jet in the event (the probe jet) is not required to be top-tagged. These samples are dominated by NTMJ events. For each event in the loose selection (i), the probability that the event would pass the full selection in the signal region (P i NTMJ ) equals the mistag probability (P m (p T )), evaluated at the p T of the probe jet in event i (p i T ), The total number of NTMJ events (N NTMJ ) is then equal to the sum of the weights from Eq. 1.
where N loose is the number of events passing the loose selection and the other quantities are defined above.
The ensemble of jets in the loose pretagged region have, on average, a lower jet mass than the jets in the signal region. Consequently, the m tt spectrum in this sideband is kinematically biased. To emulate the event kinematics of the signal region, the jet mass of the probe jet is ignored, and instead it is set to a value randomly drawn from the distribution of jet masses of probe jets from NTMJ MC events in the range 140 to 250 GeV/c 2 .
This procedure is cross-checked on a NTMJ MC sample to ensure that the methodology achieves closure. In this cross-check, half of the events in the MC are used to derive a mistag probability using the above procedure, and then used to predict the expected number of tags for the remaining events, which is compared to the observed number of tags in these events. The observed and expected number of tags agree within statistical uncertainties.
Possible biases in the calibration procedure from the presence of a new Z have also been investigated in the analysis. For instance, a Z signal with m Z = 3 TeV/c 2 and a width of 30 GeV/c 2 contributes less than 1% to the events defined through the loose selection criteria as well as to the sideband regions used to determine the probability of mistagging jets.
The uncertainty on this procedure is taken as half the difference between the m tt distributions obtained using the modified and unmodified probe-jet masses. Two choices of alternative prior distributions for the probe-jet mass were investigated, the MC-based prior described above, and a flat prior. The systematic uncertainty estimated with the current method is slightly more conservative.   Table 1 provides an estimate for the mistagged NTMJ background for two tt mass windows: 0.9-1.1 TeV/c 2 and 1.3-2.4 TeV/c 2 . The first row corresponds to the number of events observed in the loose selection (N loose from Eq. 2) to which the mistag probability is applied. The second row corresponds to the number of expected events from the mistagged NTMJ background in the signal region (N NTMJ in Eq. 2). As can be observed in Table 1, the primary uncertainty on the NTMJ background is from the systematic uncertainty assigned to the procedure for modifying probe-jet masses.

Results of event selection
Observed m tt distributions for 1+1 and 1+2 events in data are compared to the expected backgrounds in Fig. 5. The NTMJ background expectation determined from data is given by the yellow (light) filled histograms. The SM tt estimate is shown as red (dark) filled histograms, and the data are shown as solid black points. The hatched gray regions indicate the total uncertainty on the backgrounds. Figure 5 also shows for comparison the signal expectation from MC for several hypothetical Z signals with masses from 1 to 3 TeV/c 2 with a width of 1%, in the 1+1 and 1+2 samples, but with cross sections taken from the expected limits discussed in Sec. 5.1.
From Fig. 5, it is clear that the dominant background in this analysis is from NTMJ events rather than from SM tt production. The implementation of b-quark selections has not as yet been introduced to improve the sensitivity of this search, and must await an improvement in performance of b-tagging in merged top jets.
To demonstrate the components of the background estimate, Table 2 lists the number of events expected from background sources in the 1+1 and 1+2 channels, along with the observed number of events, for two tt mass windows: from 0.  Figure 5: Results for (a) 1+1 and (b) 1+2 event selections and background estimates. The yellow (light) histograms are the non-top multijet (NTMJ) estimates from data, as described in the text, and the red (dark) histograms are the MC estimates from SM tt production. The black points are the data. The hatched gray boxes combine the statistical and systematic uncertainties on the total background. For comparison, expectations for some Z hypotheses are shown for the assumption of 1% resonance width, with cross sections taken from the expected limits discussed in Sec. 5.1. Also shown are the ratio of the fractional difference between the data and the prediction, shown in red circles, with the y-axis on the right of the plot, and the number of standard deviations (N σ ) of the observation from the prediction, shown as a black histogram with the y-axis on the left of the plot, where the binning is adjusted to have at least 20 events in each bin.

5 Statistical treatment 4 Systematic uncertainties
The sources of systematic uncertainty on the tt invariant mass spectrum fall into three categories: (i) the determination of the efficiency, (ii) the mistag probability, and (iii) the shape of the tt invariant-mass distribution. Several sources of systematic uncertainties can simultaneously affect these three categories, and in such cases, any changes in parameters have to be varied in a correlated way. The uncertainties on efficiency include uncertainties in the overall jet-energy scale for tagged jets (≈ 2-4% from standard jet energy corrections, ≈ 3% from the application of the jet corrections to pruned jets, and ≈ 1% to account for the uncertainty on the determination of the W mass in data and MC, as described in Sec. 3.2), integrated luminosity (2.2%), subjet-selection efficiency (≈ 6%, as described in Sec. 3.2), jet energy resolution (< 1%), and jet angular resolution (< 1%). The trigger uncertainty for 1+1 events is 13% for m tt = 1 TeV/c 2 , and < 1% for tt masses above 1.5 TeV/c 2 . The trigger uncertainty is larger for 1+2 events: 20% for m tt = 1 TeV/c 2 , and 3% for m tt > 1.5 TeV/c 2 , as described in Sec. 2. The impact of changes in parton distribution functions [53] is found to be negligible.
Similar uncertainties affect the tt continuum background and are estimated in the same manner.
In addition, the large uncertainty on the renormalization and factorization scales (a factor of two) is found to have significant impact on SM tt production, resulting in a 50% variation in the yield, estimated from MC studies. This is reflected in the uncertainties on the number of tt events in Table 2. Table 3 provides a summary of this information. The uncertainties on the mistagged NTMJ background include the statistical uncertainty on the sample after loose selection, to which the mistag probability is applied; the statistical uncertainty on the mistag probability itself, ranging from < 1% at 1 TeV/c 2 to ≈ 10% at 3 TeV/c 2 as seen in Fig. 1b; and the systematic uncertainty on the mistag probability application, as described in Sec. 3.3, which is in the range of 1 to 5% depending on the tt mass. The total background uncertainty is ≈ 5% for the low-mass region, dominated by the systematic uncertainty, and ≈ 100% for the high-mass region, dominated by statistical uncertainty associated with the sample after loose selection.

Statistical treatment
The main result of this analysis is the fit to data assuming a resonance hypothesis for the new physics, in which a likelihood is fit to the expected tt invariant mass distributions for signal and background. The second result corresponds to a counting of events relative to some generic model of an enhancement of the tt continuum assuming the SM efficiency for the additional contribution. These two results are discussed below.

Resonance analysis
The first analysis uses a resonant signal hypothesis to search for localized contributions to the m tt spectrum. A cross-check of the analysis is performed by counting the number of events in a mass range defined for each resonant mass value. Two such mass ranges are shown in Tables 1-3. In the main resonance analysis and the cross-check, the number of observed events, N obs , is compared to the expectation N exp , based on the production cross section σ Z , branching fraction B(Z → tt), signal reconstruction efficiency , integrated luminosity L, and the predicted number of background events N B : The likelihood is computed using the Poisson probability to observe N obs , given a mean of N exp , with uncertain parameters L, , and N B , all defined through log-normal priors based on their mean values and their uncertainties. The shapes and normalizations of signal and background distributions are varied within their systematic uncertainties until the likelihood is maximized. This procedure effectively integrates over the parameters describing the systematic uncertainties, thereby reducing their impact.
The upper limits at 95% confidence level (CL) on the product of the Z production cross section and the branching fraction to the tt final state are extracted for the combination of the 1+1 and 1+2 tt mass spectra, as a function of m Z in a range from 1 to 3 TeV/c 2 with a 0.1 TeV/c 2 increment. A CL S method [54][55][56] is used to extract the 95% CL upper limits, with the posterior based on a Poisson model for each bin of the m tt distribution. Figure 6 shows the observed and expected upper limits for: (a) a Z hypothesis with Γ Z /m Z = 1%, (b) a Z hypothesis with Γ Z /m Z = 10%, and (c) a Randall-Sundrum Kaluza-Klein gluon hypothesis. Also shown are the theoretical predictions for several models to compare to the observed and expected limits. In Figure 6a, predictions are also shown for a topcolor Z model based on Refs. [4][5][6] updated to √ s = 7 TeV in Ref. [57], with Γ Z /m Z = 1.2% and Γ Z /m Z = 3%, compared to limits obtained assuming a 1% width. Higher-order QCD corrections to the Z production cross section were accounted for through a constant K-factor, computed to be 1.3. The same Z model, but for Γ Z /m Z = 10%, is compared to the limits obtained assuming a 10% width in Fig. 6b. Finally, in Fig. 6c, the prediction of the Randall-Sundrum Kaluza-Klein gluon model from Ref. [12] is compared to the limits from data.
Using the upper limits for the Z with 1% width, mass ranges for two Z models are excluded as seen in Fig. 6a. First, the mass range 1.0-1.6 TeV/c 2 is excluded for a topcolor Z with width Γ Z /m Z = 3%. Second, two mass ranges, 1.3-1.5 TeV/c 2 and a narrow range (smaller than the mass increment) close to 1.0 TeV/c 2 , are excluded for the same topcolor Z with width Γ Z /m Z = 1.2%. Similarly, using the upper limits for the Z with 10% width as seen in Fig. 6b, the mass range 1.0-2.0 TeV is excluded for a topcolor Z with width Γ Z /m Z = 10%.
Finally, as seen in Fig. 6c, upper limits in the range of 1 pb are set on σ g × B(g → tt) for m g > 1.4 TeV/c 2 for a specific Randall-Sundrum gluon model [12], which exclude the existence of this particle with masses between 1.4-1.5 TeV/c 2 , as well as in a narrow region (smaller than the mass increment) close to 1.0 TeV/c 2 .
The resonant analysis is cross-checked by counting events in specified mass windows of m tt . The signal region is defined by a window in m tt , and the background estimates from Figs. 5a and 5b are integrated over this range. The results obtained from this cross-check are consistent with the analysis of the m tt spectrum, but are not as sensitive. Table 2 shows the number   Figure 6: The 95% CL upper limits on the product of production cross section (σ) and branching fraction (B) of hypothesized objects into tt, as a function of assumed resonance mass. (a) Z production with Γ Z /m Z = 1% (1% width assumption) compared to predictions based on Refs. [4][5][6] for Γ Z /m Z =1.2% and 3.0%. (b) Z production with Γ Z /m Z = 10% (10% width assumption) compared to predictions based on Refs. [4][5][6] for a width of 10%. (c) Randall-Sundrum Kaluza-Klein gluon production from Ref. [12], compared to the theoretical prediction of that model. The ±1 and ±2 standard deviation (s.d.) excursions are shown relative to the results expected for the available luminosity.

tt enhancement analysis
In the second analysis, general enhancement is assumed in modeling the tt mass spectrum due to some new phenomenon (NP), assuming the same signal efficiency as for the SM tt continuum, as described in Refs. [22, 23]. The limit on any possible enhancement is presented in terms of a variable S, the ratio of the integral of the m tt distribution above 1 TeV/c 2 corresponding to SM tt production and a contribution from some NP, to that from just SM tt production: The events used for setting the limit are selected to have reconstructed m tt > 1 TeV/c 2 , which does not correspond to the same range for the true mass. Consequently, a correction factor must be applied to the reconstructed tt mass distribution to estimate the true mass distribution. This is estimated by dividing the number of simulated tt events with a reconstructed mass > 1 TeV/c 2 by the number of simulated tt events with a true mass > 1 TeV/c 2 . This ratio is 1.24 ± 0.08 for the Type 1+1 analysis and 1.41 ± 0.11 for the Type 1+2 analysis. These differences are applied as multiplicative factors to obtain the yields for the true tt mass above 1 TeV/c 2 . These factors do not affect the quantity S since they cancel in the ratio.
The approximate NNLO cross section for inclusive tt production is taken to be 163 pb [48][49][50]. The efficiency for Type 1+1 events, relative to inclusive SM tt production, is found to be (2.5 ± 1.3) × 10 −4 , and for Type 1+2, the efficiency is (1.6 ± 1.0) × 10 −4 . The numbers of observed and expected events for the SM tt and NTMJ backgrounds are shown in Table 4, along with these efficiencies. Following the statistical procedure outlined above, it follows that the enhancement factor to the tt production cross section for m tt > 1 TeV/c 2 (S in Eq. (4)) must be < 2.6. The a priori expectation is for this limit to lie in the interval 2.0-3.5 at 68% CL, and 1.7-5.5 at 95% CL, with a most probable value of 2.5.

Summary
In summary, a search is presented for a massive resonance (Z ) decaying into a tt pair in the all-hadronic final state using an integrated luminosity of 5 fb −1 collected with the CMS detector at 7 TeV. A Z with standard-model couplings is considered as a model of such a resonance. Two widths are considered (Γ Z /m Z = 1% and 10%), as well as an additional model of a Randall-Sundrum Kaluza-Klein gluon. The search focuses on high tt masses that yield collimated decay products, partially or fully merged into single jets. The analysis therefore relies on new developments in the area of jet substructure, thereby providing suppression of non-top multijet production.
No excess of events is observed over the expected yield from SM background sources. Upper limits in the range of 1 pb are set on the product of the Z cross section and branching fraction for a topcolor Z modeled for several widths, as well as for a Randall-Sundrum Kaluza-Klein gluon.
Finally, results are presented for any generic source of new phenomena with the same reconstruction efficiency as standard-model tt production, and limits are placed on any enhancement to the cross section from such a contribution. In particular, the tt production cross section (in total) must be less than a factor of 2.6 times that of the SM expectation for m tt > 1 TeV/c 2 . This constrains generic enhancements to standard-model tt production, which can be used to check models that seek to interpret the forward-backward tt production asymmetry observed at the Tevatron as a sign of new physics.
This is the first publication to constrain tt resonances in the kinematic region of m tt > 1 TeV/c 2 , and is also the first work to use the jet-substructure tools described above.