A search for $t\bar{t}$ resonances using lepton-plus-jets events in proton-proton collisions at $\sqrt{s} = 8$ TeV with the ATLAS detector

A search for new particles that decay into top quark pairs is reported. The search is performed with the ATLAS experiment at the LHC using an integrated luminosity of 20.3 fb$^{-1}$ of proton-proton collision data collected at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The lepton-plus-jets final state is used, where the top pair decays to $W^+bW^-\bar{b}$, with one $W$ boson decaying leptonically and the other hadronically. The invariant mass spectrum of top quark pairs is examined for local excesses or deficits that are inconsistent with the Standard Model predictions. No evidence for a top quark pair resonance is found, and 95% confidence-level limits on the production rate are determined for massive states in benchmark models. The upper limits on the cross-section times branching ratio of a narrow $Z'$ boson decaying to top pairs range from 4.2 pb to 0.03 pb for resonance masses from 0.4 TeV to 3.0 TeV. A narrow leptophobic topcolour $Z'$ boson with mass below 1.8 TeV is excluded. Upper limits are set on the cross-section times branching ratio for a broad colour-octet resonance with $\Gamma/m =$ 15% decaying to $t\bar{t}$. These range from 2.5 pb to 0.03 pb for masses from 0.4 TeV to 3.0 TeV. A Kaluza-Klein excitation of the gluon in a Randall-Sundrum model is excluded for masses below 2.2 TeV.


Introduction
Many models of physics beyond the Standard Model (SM) predict production at the LHC of additional particles with masses near the TeV scale. This paper presents a search for such heavy particles decaying to top quark pairs (tt) using data from proton-proton collisions collected at a centre-of-mass energy √ s = 8 TeV with the ATLAS detector, corresponding to an integrated luminosity of 20.3 fb −1 .
Searches for production of heavy particles that decay to tt are of high interest at the LHC due to the role that the top quark plays in many models of physics beyond the SM (BSM). The top quark is the most massive of the fundamental particles in the SM, and it can have a large coupling to heavy Higgs bosons. Thus, heavy Higgs bosons in two-Higgs-doublet models [1,2] can have a large branching ratio to tt final states. Furthermore, many models that propose alternative mechanisms for electroweak symmetry breaking (EWSB) incorporate new heavy particles with a larger coupling to tt than to lighter quarks. Examples include strong EWSB models such as topcolour-assisted technicolour [3] (TC2) and Composite Higgs [4][5][6][7][8][9][10][11] scenarios. Models with warped extra dimensions [12][13][14][15] form an additional class of models that predict heavy particles that decay to tt pairs. In such models, the heavy particles are the counterparts of the gluon and graviton.
The search starts by selecting events with one isolated charged lepton (electron or muon), missing transverse momentum (whose magnitude is denoted by E miss T ) and hadronic jets, which are compatible with tt → W + bW −b , with one W boson decaying leptonically and the other hadronically. At least one of the hadronic jets is required to be consistent with having originated from a b-quark. An estimator of the tt invariant mass (m reco tt ) is constructed with the events divided into two orthogonal classes by topology: the boosted topology, where the decay products of the hadronically decaying top quark are expected to be fully enclosed within one large-radius jet, and the resolved topology where four small-radius jets are reconstructed and attributed to the bbqq ′ quarks. The m reco tt spectrum is scanned for localised deviations relative to the expectations from the background processes. The compatibility of the data and expectations is assessed, and limits on the production cross-section for new particles are set.
This search is designed to be sensitive to the production of any new particle that decays to tt. Nonetheless the selection efficiency and acceptance can differ between particular model choices. Hence the sensitivity to a variety of different new particles was evaluated to quantify the performance of the search. The benchmark models adopted in this search include colour-singlet and colour-octet bosons with spin 0, 1 and 2 and masses from 0.4 to 3 TeV. The resonance width for the specific models varies from very narrow (1%) to a size similar to that of the experimental resolution (15%). Furthermore, the dependence of the limits on the resonance width is explored for heavy gluons up to a width of 40%. With these results, it is possible to interpret the cross-section limits in the context of a search for other new particles with the same production modes.
In addition to making use of 8 TeV data, this search incorporates several improvements with respect to the previous most sensitive ATLAS collaboration search for the same signature [16], which used a similar strategy. Trimming [17] is now used to mitigate pile-up effects on large-radius jets, a new procedure is applied to recover efficiency loss from removal of overlap between electron and jet objects in the detector, and a χ 2 variable is exploited to remove events from non-tt background processes. Furthermore, the limits on production of spin 2 bosons and on heavy gluons of varying width represent an extension compared to previous searches by the ATLAS and CMS [18] Collaborations.

Models tested
The details of the benchmark models considered in this search are reviewed below. Interference between these processes and SM tt production is not considered in this search.

Spin-1 colour singlet
The first class of models explored produces spin-1 colour-singlet vector bosons, Z ′ . This search uses topcolour-assisted technicolour Z ′ TC2 [3,19, 20] as a benchmark. This is a leptophobic boson, with couplings only to first-and third-generation quarks, referred to as Model IV in ref. [19]. The properties of the boson are controlled by three parameters: cot θ H , which controls the width and the production crosssection, and f 1 and f 2 , which are related to the coupling to up-type and down-type quarks respectively. Here f 1 = 1 and f 2 = 0, which maximises the fraction of Z ′ TC2 that decay to tt. The parameter cot θ H is tuned for each mass point such that the resonance has a width of 1.2% of its mass. To account for higher-order contributions to the cross-section, the leading-order calculation is multiplied by a factor of 1.3 based on calculations performed at next-to-leading order (NLO) in QCD [21,22].

Spin-1 colour octet
The second class of models considered produces spin-1 colour-octet vector bosons. Specifically, heavy Kaluza-Klein gluons, g KK , as produced in Randall-Sundrum (RS) models with a single warped extra dimension [30], are used as a benchmark in this search. In this model, the g KK has a nominal width of 15.3% of its mass. Previous searches using √ s = 7 TeV ATLAS data [16] exclude a g KK with a mass less than 2.1 TeV. The CMS Collaboration searched for similar resonances [18], using a slightly different benchmark model [31]. The CMS choice leads to a larger natural width of 20% and a larger production cross-section, and, for such a scenario, CMS excludes the existence of a g KK with mass less than 2.5 TeV. In the analysis presented here, the sensitivity to the width of the colour octet is also tested for widths from 10% to 40% of the resonance mass.

Spin-2 colour singlet
The third class of models explored in this search produces spin-2 colour singlets, such as Kaluza-Klein excitations of the graviton, G KK . The search uses a Randall-Sundrum model with extra dimensions where the SM fields are in the warped bulk and the fermions are localised appropriately to explain the flavour structure of the SM [12,32,33]. This kind of graviton is commonly referred to as a "Bulk" RS graviton and is characterised by a dimensionless coupling constant k/M Pl ∼ 1, where k is the curvature of the warped extra dimension andM Pl = M Pl / √ 8π is the reduced Planck mass. For such gravitons, decays

Event selection
Events consistent with tt decaying to a single charged lepton together with hadronic jets and missing transverse momentum are selected. Electron candidates are required to have a transverse energy E T > 25 GeV and |η cluster | < 2.47, where η cluster is the pseudorapidity of the cluster of energy deposited in the electromagnetic calorimeter, computed with respect to the centre of ATLAS detector and matched to the candidate [84]. Electron candidates in the transition region 1.37 < |η cluster | < 1.52 between calorimeter barrel and endcap are excluded.
In order to reduce backgrounds from non-prompt sources and hadronic showers with a high electromagnetic energy fraction in the calorimeter, electron isolation is imposed using a mini-isolation variable MI 10 defined as the tracks p track T for all tracks (except the matched lepton track) with p T > 1 GeV satisfying quality selection criteria, and within a cone of size ∆R < 10 GeV/E T [16, 85] centred on the barycentre of the cluster. Electrons are defined to be isolated if MI 10 /E T < 0.05. The E T here is the transverse energy of the reconstructed electron. The isolation variable MI 10 is particularly useful in the case of boosted top quark decays since the p T -dependent cone size reflects the p T dependence of the separation between objects with a common boosted parent. The matching of the electron to the collision vertex [86] is imposed by requiring that the longitudinal impact parameter relative to it be less than 2 mm.
Muon candidates are required to have p T > 25 GeV and |η| < 2.5. The matching of the muon to the collision vertex is imposed by the requirements that the longitudinal impact parameter relative to the collision vertex be less than 2 mm and that the transverse impact parameter relative to the collision vertex divided by its uncertainty, |d 0 /σ d 0 |, be less than 3.0. Muons are also required to satisfy the same MI 10 requirement as electrons, with the cone centred on the inner-detector track associated with the muon. Only small-radius jets are considered for b-jet identification (b-tagging). The b-tagging algorithm uses a multivariate approach with inputs taken from the results of separate impact parameter, secondary vertex and decay topology algorithms [96]. The operating point of the algorithm is chosen such that the btagging efficiency for simulated tt events is 70%. In MC simulation, factors are applied to correct for the differences between the b-tagging efficiency in simulated events and that measured in data. The factors are adapted to be appropriate for b-jets from high-p T top quarks, for which the b-tagging efficiencies are lower.
The E miss T is calculated from the vector sum of the transverse energy of topological clusters in the calorimeter [97]. The clusters associated with the reconstructed electrons and small-radius jets are replaced by the calibrated energies of these objects. Muon transverse momenta determined from the ID and the muon spectrometer are also included in the calculation.
Overlap in identification of the relevant physics objects is possible and a procedure is implemented to remove duplication. Electrons and small-radius jets are considered for overlap removal if the cluster associated with the electron is within ∆R = 0.4 of the nearest jet. In such cases, the jets have their fourmomentum and jet vertex fraction recalculated after subtracting the electron four-momentum and then are removed if the recalculated values do not satisfy the original jet selection criteria. If the distance ∆R between the electron and the recalculated jet is < 0.2, the electron candidate is likely to be from the hadronic jet. Therefore the electron is removed from the electron candidate list and its four-momentum is added to that of the recalculated jet. Muons are removed from the muon candidate list if the distance ∆R between the muon and small-radius jet is less than 0.04 + 10 GeV/p T . This criterion exploits the anti-correlation between the muon p T and its angular distance from the b-quark, in an approach similar to the isolation variable. The parameters are tuned based on signal MC simulations in order to provide a constant high efficiency as a function of resonance mass.
A set of common preselection criteria is used for events to be considered for the boosted and resolved topologies. Events are required to have exactly one lepton (electron or muon) plus multiple jets. Events recorded by the lepton triggers are required to have lepton-trigger objects that match the selected lepton.
Additionally, events must have E miss T > 20 GeV and E miss T + m T > 60 GeV, where m T is the transverse mass calculated as m T = 2p T E miss T (1 − cos φ ℓν ) where p T is the transverse momentum of the lepton and φ ℓν is the angle between the p T and E miss T vectors.
Events are next checked against the boosted-topology selection. The selected lepton is required to have at least one small-radius jet within a distance of ∆R(ℓ, j) = 1.5 and, of these, the jet with highest p T is termed j sel . Boosted-topology events must have at least one large-radius jet with p T > 300 GeV (380 GeV for the muon-plus-jets events selected by the large-radius-jet trigger), |η| < 2.0, mass m jet > 100 GeV, first k t splitting scale [95] √ d 12 > 40 GeV, ∆R > 1.5 between the large-radius jet and j sel , and ∆φ > 2.3 between the large-radius jet and lepton. The jet mass is calculated using the four-momenta of its constituent clusters, which are taken as massless. If multiple large-radius jets satisfy these criteria, the highest-p T jet is chosen as the hadronically decaying top quark candidate. Finally, at least one of the small-radius jets in the event must be b-tagged and matched to either of the top quark candidates, as described in section 6.
Events that do not satisfy the boosted-topology selection are then tested against the criteria for the resolved-topology selection. These events are required to have at least four small-radius jets, with at least one of them b-tagged. A χ 2 algorithm is used to reconstruct the tt system, as described in section 6. The lowest χ 2 value is required to satisfy log 10 (χ 2 ) < 0.9.
The selection efficiencies for MC simulated signal events are given in figure 1, for different models of interest. For reference, the branching ratio for tt to electron-or muon-plus-jets is about 17% for each lepton flavour taking into account leptonic tau decays [98]. There are efficiency losses from both the large-radius jet requirements and b-tagging requirement for the boosted-topology selection. For resonance masses above 1.5 TeV, the efficiencies of the resolved selections are relatively insignificant due to the χ 2 requirements and the veto of boosted selections. It can also be seen that efficiency times acceptance is smaller for isolated electrons than isolated muons above the same resonance mass point, due to the inefficiency of electron identification and overlap removal in the boosted environment.

Event reconstruction
Signal tt resonances should appear in the m reco tt spectrum as an excess of events over the SM expectation clustered around the resonance mass. Events are reconstructed assuming the final state originated from a tt decay. To calculate m reco tt , the neutrino four-momentum must be determined. The neutrino transverse momentum is taken to be the E miss T vector. The longitudinal component of the neutrino momentum, p z , is calculated by constraining the lepton plus missing momentum system to have the W boson mass and solving the resulting quadratic equation in the neutrino's longitudinal momentum p z [99, 100]. If no real solution exists, the E miss T vector is varied by the minimal amount required to produce exactly one real solution. If two real solutions are found, the one with the smallest |p z | is used for the boosted-topology reconstruction, while the choice is made by the χ 2 algorithm described below for the resolved topology.
For the boosted topology, m reco tt is computed from the four-momenta of the neutrino, lepton, the previously selected small-radius jet, j sel , and the highest-p T large-radius jet. In this case the assignment of jets to the semileptonically decaying top quark and hadronically decaying top quark is unambiguous.
In calculating m reco tt for the resolved topology, a χ 2 algorithm is employed to find the best assignment of jets to the semileptonically and hadronically decaying top quarks. Using the four-momenta of the  neutrino, lepton and all small-radius jets in the event, a χ 2 is defined using the expected top quark and W boson masses: The first term is a constraint using the mass of the hadronically decaying W boson. The second term is a constraint using the mass difference between the hadronically decaying top quark and the hadronically decaying W boson. Since the mass of the hadronically decaying W boson, m j j , and the mass of the hadronically decaying top quark, m j jb , are highly correlated, the mass of the hadronically decaying W boson is subtracted from the second term so as to decouple it from the first term. The third term is a constraint using the mass of the semileptonically decaying top quark. The last term arises as a constraint on the expected transverse momentum balance between the two decaying top quarks. In the χ 2 definition above, t h and t ℓ refer to the hadronically and semileptonically decaying top quarks. The values of the χ 2 central-value parameters m W , m t h −W , m t ℓ and p T,t h − p T,t ℓ , and the values of the width parameters σ W , σ t h −W , σ t ℓ and σ diff p T are found through Gaussian fits to the distributions of relevant reconstructed variables, using reconstructible 3 MC events with Z ′ masses from 0.5 to 2.0 TeV. All possible neutrino p z solutions and jet permutations with at least one b-quark candidate satisfying the b-tagging requirement are tested, and the one with the lowest χ 2 value is adopted. About 80% of these reconstructible events have the correct assignment of reconstructed objects to the hadronically and semileptonically decaying top quarks.
The resulting m reco tt distributions for several signal masses from the resolved-and boosted-topology reconstruction are shown in figures 2 and 3. For these figures, all events satisfying the resolved-or boostedtopology selection criteria are used. The low-mass tails arise from two effects: firstly, extra radiation from the tt system that is not included in the reconstruction can shift the reconstructed mass to lower values; secondly, before reconstruction the Breit-Wigner signal shape in m tt has a tail at lower values due to the steep fall in parton luminosity with increasing partonic centre-of-mass energy. The former is particularly true for high-mass resonances, while the latter has a larger effect on broad resonances. The experimental resolution for the invariant mass of the tt system 4 is 8% for the resolved-topology selection at a resonance mass of 400 GeV improving to 6% for 1 TeV. It is 6% in the boosted-topology selection, independent of resonance mass.
With hadronically and semileptonically decaying top quarks identified for both the boosted-and resolvedtopology selections, three categories of b-tagged events are defined: those in which both decaying top quark candidates have a matching b-jet, those in which only the hadronically decaying top quark candidate has a matching b-jet and those in which only the semileptonically decaying top quark candidate has a matching b-jet. In the boosted-topology selection, the match is defined as either the selected jet, j sel , or a small-radius jet within ∆R = 1.0 of the large-radius jet as being a b-tagged jet. In the resolved-topology selection, the matching is determined by the χ 2 algorithm.

Background contributions estimated from data
Data are used to estimate the magnitudes and uncertainties of two important background contributions: W+jets and multi-jet production.

W+jets scale factors
For the W+jets background, data are used to derive scale factors that are applied to correct the normalisation and flavour fractions given by Alpgen MC simulations of this background.
For both the resolved-and boosted-topology event selection criteria, the normalisation scale factors are determined by comparing the measured W boson charge asymmetry in data [101,102] with that predicted by Alpgen MC simulation. For the resolved topology, all selection criteria are applied to the data except 3 Reconstructible events are those where there is a reconstructed object within ∆R = 0.4 of each visible parton from top decays, and the ∆φ between the neutrino and the E miss T is smaller than 1. Among the events satisfying the final selection critera, 70% (55%) are reconstructible for Z ′ mass of 750 GeV (400 GeV). 4 The experimental resolution is extracted from a Gaussian fit of the relative difference      for the b-tagging requirement. For the boosted topology, in order to decrease the statistical uncertainty on the scale factors, a relaxed set of selection criteria that does not include the b-tagging, ∆φ(jet, ℓ) > 2.3, jet mass and √ d 12 requirements is used. Any bias induced by relaxing the criteria for the boosted selection is found to be negligible compared to the statistical uncertainty in the scale factor determination. The total number of W+jets events in data, N W + + N W − , is given by: where r MC is the ratio given by MC simulation of the number of W+jets events with a positively charged lepton to that with a negatively charged lepton and D corr+(−) is the number of observed events with a positively (negatively) charged lepton. Contributions to D corr+(−) from charge-asymmetric processes such as single top, WZ and tt+W boson production are estimated from MC simulation and are subtracted. Contributions from charge-symmetric processes such as tt production cancel in the difference on the right-hand side of eq. (2). A scale factor, C A , applied to the MC simulated samples of W + jets events is then calculated as the ratio of N W + + N W − evaluated from data to that predicted from MC simulation.     The value and statistical uncertainty obtained for C A in the electron (muon) channel are 1.026 ± 0.011 (0.978 ± 0.010) with the resolved selection, and 0.89 ± 0.06 (0.81 ± 0.05) with the boosted selection.
Scale factors for the relative fraction of heavy-flavour contributions from W + bb, W + cc, W + c are also determined from data [102][103][104]. In determining these scale factors, events are required to satisfy all selection criteria common to the boosted-and resolved-topology selections. Exactly two small-radius jets are required without any b-tagging requirement.
The flavour fractions for W + bb, W + cc, W + c and W+light-quark flavours are first determined from MC simulation for this sample. The ratio of the W + bb to W + cc contribution is taken from MC simulation and fixed at that value. A system of three equations is used to fit to the two-jet data sample with at least one b-tagged jet in order to determine correction factors for each of the flavour fractions determined from MC simulation: where D W ± is the expected number of W+jets events with a positively charged or negatively charged lepton in the data. The flavour fraction is f flavour , and the correction factor for a given flavour component is K flavour . The different flavour labels are bb, cc, c, and light corresponding to W + bb, W + cc, W + c, and W+light-jets respectively. The numbers of positively charged and negatively charged leptons in the data are found by subtracting all non-W+jets contributions, which are determined from MC simulations as 35% (15%) of the selected events for the electron (muon) channel. An iterative process is used to find the K flavour factors, which are then used to correct the corresponding flavour fractions f flavour that are applied during the C A factor calculation. In this iterative process, only the K flavour and C A factors are allowed to vary. The K flavour factors are initially set to unity, thus altering the C A factor calculation. New correction factors K flavour are calculated by inverting eq. (3), and then the process is repeated ten times, with each repetition using the correction factors determined from the previous one. It was checked that using more than ten iterations produces only negligible changes in the extracted correction factors.
The correction factors found for the two-jet sample are extrapolated to higher jet multiplicities by keeping the same ratios between them while conserving the normalisation in each jet multiplicity bin. This method reduces the systematic uncertainties (from the jet energy scale, b-tagging and other uncertainties) compared to using W+jets MC simulation alone. Systematic uncertainties in the W+jets normalisation and flavour-fraction corrections are determined by rederiving these scale factors when a given systematic effect is applied. The new scale factors are then used in producing the m reco tt mass spectrum for that particular systematic uncertainty.

Multijet estimate
The multi-jet background in events satisfying the resolved or boosted selection criteria consists of events with a jet that is misreconstructed as a lepton or with a non-prompt lepton that satisfies the identification criteria. The normalisation, m reco tt shape, and statistical and systematic uncertainties associated with the multi-jet background are estimated from data using a matrix method [103, 105].
The matrix method utilises efficiencies for leptons produced by prompt and non-prompt sources. The efficiency f is defined as the probability that a non-prompt lepton from multi-jet production that satisfies the loose identification criteria [105] also satisfies the tight identification criteria. It is derived from data in control regions dominated by multi-jet events, with prompt-lepton contributions subtracted based on MC simulations. The efficiency ǫ is defined as the probability that a lepton from prompt sources (W or Z bosons) that satisfies the loose identification criteria also satisfies the tight identification criteria. It is determined using SM MC samples with a mixture of processes similar to that in the signal region, corrected using data versus MC correction factors derived from Z → ℓℓ events.
The number of multi-jet background events satisfying the resolved or boosted selection criteria is estimated using data events that satisfy all selection criteria, except that the loose lepton identification criteria are used. This sample contains prompt as well as non-prompt leptons.
The number of events with leptons satisfying the loose identification criteria, N L is defined as where N prompt is the number of events with prompt leptons satisfying the loose identification criteria and N multi-jet is the number of events satisfying the loose identification criteria with leptons from other sources. The number of events satisfying the tight identification criteria, N T is then Solving these two equations for N prompt and N multi-jet gives the multi-jet contribution from events satisfying all the selection criteria.
Good shape modelling of the m reco tt distributions is achieved by parameterising the efficiencies as functions of relevant kinematic variables, and validated in the multi-jet control regions. Systematic uncertainties are evaluated using several different definitions of multi-jet control regions that result in slightly different f estimations. Systematic uncertainties associated with object reconstruction and MC simulation are also considered, resulting in a total normalisation uncertainty of 20%.

Systematic uncertainties
The systematic uncertainties can be broadly divided into two categories: uncertainties that affect reconstructed objects (such as jets) and uncertainties that affect the modelling of certain background or signal processes. Some of the uncertainties affect both the shape and the normalisation of the m reco tt spectra, while others affect the normalisation only. In table 1, an overview of the effects of the dominant systematic uncertainties on the background and signal yields is given. Only the impact on the overall normalisation is shown in the table, but some of the systematic uncertainties have a significant dependence on the reconstructed tt mass, which is fully taken into account in the analysis for all of these uncertainties. The systematic uncertainties with the strongest dependence are those from the jet energy scale, parton distribution functions and b-jet identification.
The dominant uncertainty on the normalisation of the total background estimate is the NNLO+NNLL tt cross-section uncertainty of 6.5%. This uncertainty includes renormalisation and factorisation scale uncertainties, combined PDF and strong-coupling uncertainties evaluated following the PDF4LHC [106] recommendations, and uncertainties associated with the value of the top quark mass. The combined PDF and strong-coupling uncertainties are extracted for each of the three PDF sets: MSTW2008 68% confidence level (CL) NNLO [43,107], CT10 NNLO [52, 108] and NNPDF2.3 NNLO [109]; the total uncertainty associated with the PDF and strong-coupling uncertainties is one half of the size of the envelope of the three resultant error bands, with the central prediction being the midpoint of the envelope. Variations from changing the top quark mass by ±1.0 GeV are added in quadrature to the scale uncertainties, and combined PDF and strong-coupling uncertainties.
The W+jets normalisation, determined using data, is separately evaluated for each experimental source of systematic uncertainty. An additional systematic uncertainty on the prediction is evaluated by using the simulated samples generated with varied Alpgen matching parameters. The normalisation uncertainty on the multi-jet background is 20%, as described in section 7.
The single-top-quark background normalisation uncertainty is 7.7% [74][75][76]. The normalisation uncertainty on the Z+jets sample is 48%, estimated using Berends-Giele scaling [110]. The diboson normalisation uncertainty is 34%, which is a combination of the NLO PDF and scale uncertainties, and additional uncertainties from the requirements on the jet multiplicity. The uncertainty on the integrated luminosity is 2.8%. It is derived, following the same methodology as that detailed in Ref.
[111], from a preliminary calibration of the luminosity scale derived from beamseparation scans performed in November 2012. This uncertainty is applied to all signal and background samples except multi-jet and W+jets, which are estimated from data.
The effect of the PDF uncertainty on all MC samples is estimated by taking the envelope of the NNPDF2.3, MSTW2008NLO and CT10 PDF set uncertainties at 68% CL 5 following the PDF4LHC recommendation and normalising to the nominal cross-section. The PDF uncertainty on the tt mass spectrum has a much larger effect on the boosted sample than on the resolved sample. The effect on the total background yield is 2.1% (4.2%) after the resolved (boosted) selection. The size of the uncertainty grows with reconstructed mass, attaining values of 50% above 2 TeV in the boosted selection.
One of the dominant uncertainties affecting reconstructed objects is the jet energy scale (JES) uncertainty, especially for large-radius jets [91,92]. Uncertainties on the jet mass scale (JMS) and the k t splitting scales [92] are also important for this analysis. These uncertainties have an impact of 10% on the overall background yield in the boosted selection. The impact on the background estimates falls with increasing m reco tt , varying from 22% at lowest masses to about 7% above 1.5 TeV. The impact is smaller for the resolved selection, since the large-radius jets are only used indirectly there via the vetoing of events that satisfy the boosted selection. For large-radius jets, uncertainties on the jet energy resolution (JER) and jet mass resolution (JMR) are also considered. These are less significant than the JES. For small-radius jets, the uncertainties on the JES, the jet reconstruction efficiency and the jet energy resolution are considered [88, 90]. The small-radius JES uncertainty is one of the most significant systematic uncertainties in the resolved selection, affecting the overall expected yield by 6%. The effect of uncertainties associated with the jet vertex fraction is also considered. The b-tagging uncertainty is modelled through simultaneous variations of the uncertainties on the efficiency and rejection [112,113]. An additional b-tagging uncertainty 6 is applied for high-momentum jets (p T > 300 GeV) to account for uncertainties on the modelling of the track reconstruction in high-p T environments, which is one of the dominant uncertainties for high-mass signals.
For the leptons, the uncertainties on the isolation efficiency, the single-lepton trigger and the reconstruction efficiency are estimated using Z → ee and Z → µµ events. In addition, high-jet-multiplicity Z → ℓℓ events are studied, from which extra uncertainties on the isolation efficiency are assigned to account for the difference between Z and tt events. Uncertainties on the E miss T reconstruction, as well as on the energy scale and resolution of the leptons, are also considered, and generally have a smaller impact on the yield and the search sensitivity than the uncertainties mentioned above.
The uncertainty on the tt background due to uncertainties on the modelling of QCD initial-and finalstate radiation (ISR/FSR) is estimated using AcerMC v3. 8 [114] plus Pythia v6.426 MC samples by varying the Pythia ISR and FSR parameters within ranges allowed by a previous ATLAS measurement of tt production with a veto on additional central jet activity [115]. The QED ISR/FSR uncertainty is negligible at this level. The dependency of the m reco tt shape on the choice of NLO generator is accounted for by using the difference between samples generated with MC@NLO and Powheg-Box+Herwig as a systematic uncertainty. The parton showering and fragmentation uncertainty on the tt background is estimated by comparing the results from a sample generated with Powheg-Box [48], interfaced with Pythia or Herwig. The uncertainty on the m reco tt distribution arising from the uncertainty in the top quark mass is evaluated by comparing the m reco tt spectrum using the nominal sample to those generated with top quark masses of 170 and 175 GeV, and multiplying the difference by 0.4 (to approximate a one standard deviation uncertainty, corresponding to ±1.0 GeV). The uncertainty on the electroweak corrections to top quark pair production is modelled by changing the difference of each correction factor from unity by ±10%.
For the W+jets background, the uncertainty on the m reco tt distribution is estimated by reweighting the events to the kinematics of MC samples generated with a different matching scale or functional form of the factorisation scale [69].

Comparison of data with expected background contributions
After all event selection criteria are applied, 223,330 events remain for the resolved topology and 8,206 events are selected for the boosted topology. The event yields from data and from expected background processes are listed in table 2 together with the associated systematic uncertainties. Good agreement is observed between the data and the total expected background. Figure 4 shows the reconstructed mass of the semileptonically and hadronically decaying top quark candidates, and the mass of the hadronically decaying W boson candidate for the resolved selection. The equivalent distributions for the boosted selection are the mass of the semileptonically decaying top quark candidate and the mass of the large-radius jet; both are shown in figure 5. Figure 6 shows the distribution of the transverse momentum and first k t splitting scale of the selected large-radius jets.
The tt invariant mass spectra for the resolved and the boosted selections in the electron and muon channels, separated by b-tagging category, are shown in figures 7 and 8. Figure 9 shows the tt invariant mass spectrum for all channels added together. The data generally agree with the expected background with slight shape differences seen especially in the high-mass regions; these deviations are consistent with the uncertainties.

Results
The final discriminating observables that are used to search for a massive resonance are the twelve tt invariant mass spectra: three b-tag categories for two selections and two decay channels. After the reconstruction of the tt mass spectra, the data and expected background distributions are compared using BumpHunter [116], which is a hypothesis-testing tool that searches the data for local excesses or deficits compared to the expected background, taking the look-elsewhere effect [117] into account over the full mass spectrum. The search is performed on three combinations of the spectra: the six channels of the resolved selections, the six channels of the boosted selections and the twelve channels. The most significant deviation of the data from the expected background spectrum is required to appear at the same place in each of the channels of a combination. After accounting for the systematic uncertainties, no significant deviation from the total expected background is found. Upper limits are set on the crosssection times branching ratio for each of the signal models using a profile likelihood-ratio test. The CL s prescription [118] is used to derive one-sided 95% CL limits. The results are obtained using the Hist-Fitter [119] framework with all spectra from the 12 channels, excluding bins with few events with m reco tt below 400 GeV in the boosted channels or above 2 TeV in the resolved channels.
The statistical and systematic uncertainties on the expected distributions are included in this CL s procedure as nuisance parameters in the likelihood fits. The nuisance parameters for the systematic uncertainties are constrained by a Gaussian probability density function with a width corresponding to the size of the uncertainty considered. Correlations between different channels and bins are taken into account. The product of the various probability density functions forms the likelihood function that is maximised in the fit by adjusting the free parameter (the signal strength) and nuisance parameters. The expected m reco tt distributions are compared to data in figure 10 after a fit of nuisance parameters under the background-only hypothesis. It can be seen that the uncertainties are smaller than in figure 9 and that the procedure is able to produce a good-quality fit to the data.
The expected and observed limits using different signal models are presented in figure 11. Here the expected limits are obtained by taking the nominal background estimates as the expected data. For the Z ′ TC2 benchmark, limits on the production cross-sections vary from 4.2 pb to 0.03 pb for masses from 0.4 TeV to 3 TeV. A Z ′ TC2 of width 1.2% is excluded for masses less than 1.8 TeV, while masses below 2.0 TeV are expected to be excluded. The Z ′ TC2 mass limits are stronger for a width of 2% (3%), reaching 2.0 TeV (2.3 TeV). For the g KK benchmark, limits on the production cross-sections vary from 4.8 pb for a mass of 0.4 TeV, to 0.09 pb for a mass of 3 TeV. A g KK of width 15.3% is excluded for masses less than 2.2 TeV, while masses below 2.3 TeV are expected to be excluded. The cross-section limits in the G KK model range from 2.5 pb for a mass of 0.4 TeV to 0.03 pb for 2.5 TeV, with no mass range excluded in the benchmark scenario. The cross-section limits on a narrow scalar resonance range from 3.0 pb for a mass of 0.4 TeV to 0.03 pb for 2.5 TeV. The cross-section limits are generally stronger for the latter two benchmark models than those for the spin-1 resonances due to higher acceptance.
The width dependence of the cross-section limits was also evaluated for the g KK models. The results are presented in figure 12. For a 1 TeV resonance, the limits weaken by approximately a factor of two as the width increases from 10% to 40%. The effect is stronger for 2 TeV and 3 TeV resonances, where the limits weaken by a factor of three over this width range.
The observed upper limits on the cross-section times tt branching ratio are larger than the expected limits, especially for tt resonance masses greater than 1.8 TeV. This arises from the use of the profile likelihood method which allows the data to constrain the systematic uncertainties using the full m reco tt distribution,    thanks to the abundant data. The maximisation of the likelihood can change the central values of the nuisance parameters and their associated uncertainties. In the region of m reco tt above 1.5 TeV, the background prediction as seen in figure 9 is slightly higher than the data, which would lead to the anticipation that the observed limits should be slightly better than the expected ones. However, the central values of some nuisance parameters are significantly shifted in the fit. In the high-m reco tt region one of the dominant uncertainties is the high-p T jet b-tagging extrapolation uncertainty, as detailed in section 8. This uncertainty is reduced to half of its original size by the fit, and the central value is also shifted downwards by approximately one pre-fit standard deviation. As this uncertainty is associated with reconstructed physics objects, it has correlated effects on the predictions of BSM signal and SM background. The 1σ change in the central value of this nuisance parameter reduces the acceptance of high-mass signals in the boosted selection considerably: approximately 25% for a Z ′ with a mass of 2 TeV. As a consequence, the observed upper limits on the cross-section obtained from the fit to the data are larger than the expected ones fitted to the nominal background estimates. Constraints from the fit are also observed in the nuisance parameters associated with other major systematic uncertainties such as the PDF, the shape of W+jets background, the energy and mass scales for both the large-radius and small-radius jets, b-tagging efficiencies, and tt MC modelling. These constraints are understood through their impact on the fitted m reco tt distributions. A few of the other nuisance parameters also have their central values changed slightly by the fit, but their impact on the signal acceptance and hence cross-section limits are much smaller than the one detailed above.
Studies were done to understand the origin of the shifted nuisance parameter associated with the high-p T jet b-tagging extrapolation uncertainty, in particular to investigate its potential origin as a mis-modelling of the tt background. Indeed an equally good fit can be obtained by introducing an additional ad hoc uncertainty in the modelling of the SM tt background with a similar dependency on m reco tt . Such a mismodelling would not reduce the signal acceptance and results in more stringent limits on the cross-section times tt branching ratio. Ultimately, no method was found to unambiguously ascertain the origin of this mis-modelling. The limits presented here are those with a 1σ change in the fitted value of the nuisance parameter associated with the high-p T jet b-tagging extrapolation uncertainty, which correspond to more conservative results. An upper cross-section limit was generated using expected data constructed from a background-only model built from the nuisance parameters fitted to real data. It excludes a g KK of width 15.3% for masses less than 2.1 TeV, compared to 2.2 TeV generated using nominal background estimates.

Summary
A search for heavy particles decaying to tt in the lepton-plus-jets decay channel was carried out with the ATLAS experiment at the LHC. The search uses data corresponding to an integrated luminosity of 20.3 fb −1 of proton-proton collisions at a centre-of-mass energy of 8 TeV. No excess of events beyond the Standard Model predictions is observed in the tt invariant mass spectra. Upper limits on the cross-section times branching ratio are set for four different signal models: a narrow (≤ 3% width) Z ′ boson, a broad (15.3% width) Randall-Sundrum Kaluza-Klein gluon, a Bulk Randall-Sundrum Kaluza-Klein graviton, and a narrow scalar resonance. Based on these results, the existence of a narrow leptophobic topcolour Z ′ in the range 0.4 TeV < m Z ′ < 1.8 TeV is excluded at 95% CL. A broad Kaluza-Klein gluon with mass between 0.4 TeV and 2.2 TeV is also excluded at 95% CL. These results probe new physics at higher mass than previous ATLAS searches for the same signature, and the results are applicable to a broader variety of heavy resonances.

The ATLAS Collaboration
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