Search for supersymmetry in pp collisions at √ s = 8 TeV in events with a single lepton , large jet multiplicity , and multiple b jets

Article history: Received 20 November 2013 Received in revised form 18 March 2014 Accepted 10 April 2014 Available online 18 April 2014 Editor: M. Doser


Introduction
This paper presents results from a search for new physics in proton-proton collisions at a centerof-mass energy of 8 TeV in events with a single lepton (electron or muon), missing transverse momentum, and multiple jets, at least two of which are tagged as originating from bottom quarks (b-tagged jets). This signature arises in models based on supersymmetry (SUSY) [1][2][3][4][5][6], which potentially offers natural solutions to limitations of the standard model (SM). Large loop corrections to the Higgs boson mass could be cancelled by contributions from supersymmetric partners of SM particles. Achieving these cancellations requires the gluino ( g) and top squark ( t), which are the SUSY partners of the gluon and top quark, respectively, to have masses less than about 1.5 TeV [7][8][9][10]. Here and throughout this document we only consider the lighter of the two top squarks. Extensive searches at LEP, the Tevatron, and the Large Hadron Collider (LHC) have not produced evidence for SUSY (see  for recent results in the singlelepton topology). For scenarios with mass-degenerate scalar partners of the first-and secondgeneration quarks, the mass limits generally lie well above 1 TeV. However, viable scenarios remain with t and g masses below approximately 0.5 and 1.5 TeV, respectively.
In some of these scenarios top squarks are the lightest quark partners. In R-parity conserving models [18] this could lead to signatures with multiple W bosons, multiple b quarks, and two LSPs in the final state, where the LSP is the weakly interacting lightest SUSY particle. The search described in this paper is designed to detect these signatures. It focuses on gluino pair production, with subsequent gluino decay to two top quarks and the LSP ( χ 0 1 ) through either a virtual or an on-shell top squark: pp → g g with g(→ tt) → tt χ 0 1 . These decay chains result in events with high jet multiplicity, four b quarks in the final state, and large missing transverse momentum (E T / ). The probability that exactly one of the four W bosons decays leptonically is approximately 40%, motivating a search in the single-lepton channel.
Three variations of this scenario, denoted as models A, B, and C, are considered in this analysis and implemented within the simplified model spectra (SMS) framework [19][20][21]. In model A (models B and C), gluinos are lighter (heavier) than top squarks and gluino decay proceeds through a virtual (real) t. For model A, the gluino and LSP masses m g and m χ 0 1 are allowed to vary. For model B, we set m g = 1 TeV and vary m χ 0 1 and the top squark mass m t . For model C, m χ 0 1 = 50 GeV while m g and m t are varied.
The relevant backgrounds for this search arise from tt, W+jets, and single-top quark processes with small contributions from diboson, ttZ, ttW, ttH, and Drell-Yan (DY)+jets production. The non-tt backgrounds are strongly suppressed by requiring at least six jets, at least two of which are b-tagged. The remaining background is dominated by tt events with large E T / , generated either by a single highly boosted W boson that decays leptonically (single-lepton event) or by two leptonically decaying W bosons (dilepton event). Though tt decays produce two true b quarks, additional b-tagged jets can arise because of gluon splitting to a bb pair or from mistagging of charm-quark, light-quark, or gluon jets.
We search for an excess of events over SM expectations using two approaches. The first approach is based on the distribution of E T / in exclusive intervals of H T , where H T is the scalar sum of jet transverse momentum (p T ) values. In this approach, we evaluate the E T / distribution in the signal region of high H T in two different ways [12,13]: by extrapolating from lower H T and by using the charged-lepton momentum spectrum (this latter spectrum is highly correlated with the neutrino p T spectrum in events with a leptonically decaying W boson and so carries information about E T / ). In this approach combined signal regions for the e and the µ channels are used since the differences in terms of backgrounds and sensitivity are small.
The second approach, which is new and described in more detail in this paper, is based on the azimuthal angle, ∆φ(W, ), between the reconstructed W-boson direction and the lepton. The single-lepton background from tt is suppressed by rejecting events with small ∆φ(W, ). As will be shown later, this angle carries information similar to the transverse mass of the lepton and E T / , but has superior resolution. The search is performed in different regions of the quantity S lep T , defined as the scalar sum of the E T / and lepton p T . The S lep T variable is a measure of the leptonic energy in the event and does not necessarily require high E T / in order to be large. SUSY events are expected to appear at large S lep T , where the contribution from SM processes is small. The definition of signal regions in terms of S lep T allows the inclusion of events with lower E T / than are included in the first approach. Therefore the e channel receives a small, but non-negligible correction for the presence of multijet events, and the e and the µ channels are treated as separate signal regions.
The two approaches are complementary in the kinematic observables used and data samples exploited. The first approach searches the tails of the single-lepton tt-dominated sample at high E T / and H T with two independent methods, while the second approach uses ∆φ(W, ) to reject that background process and search in a low-background region dominated by dilepton events in which one lepton is not identified or lies outside the acceptance of the analysis. Together the two approaches provide a broad view of possible deviations from the standard model.

Data sample and event selection
The data used in this search were collected in proton-proton collisions at √ s = 8 TeV with the Compact Muon Solenoid (CMS) experiment in 2012 and correspond to an integrated luminosity of 19.3 fb −1 . The central feature of the CMS apparatus is a superconducting solenoid, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass-scintillator hadron calorimeter. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. The origin of the CMS coordinate system is the nominal interaction point. The polar angle θ is measured from the counterclockwise beam direction and the azimuthal angle φ (in radians) is measured in the plane transverse to the beam axis. The silicon tracker, the muon systems, and the barrel and endcap calorimeters cover the regions |η| < 2.5, |η| < 2.4, and |η| < 3.0, respectively, where η = − ln[tan(θ/2)] is the pseudorapidity. A detailed description of the CMS detector can be found elsewhere [22].
Simulated event samples based on Monte Carlo (MC) event generators are used to validate and calibrate the background estimates from data and to evaluate the contributions for some small backgrounds. The MADGRAPH [23] 5 generator with CTEQ6L1 [24] parton distribution functions (PDFs) is used for tt, W+jets, DY+jets, ttZ, ttW, and multijet processes and the POWHEG 1.0 [25] generator for single-top-quark production. The PYTHIA [26] 6.4 generator is used to generate diboson and ttH samples and to describe the showering and hadronization of all samples (the Z2 * tune [27] is used). The cross sections used to scale the yields of these samples are calculated at next-to-leading (NLO) or higher order. Decays of τ leptons are handled by TAUOLA [28]. The GEANT4 [29] package is used to describe the detector response.
The SUSY signals for the three scenarios considered in this analysis are generated with MAD-GRAPH and CTEQ6L1 PDFs. In these scenarios, gluinos are pair-produced and decay into tt χ 0 1 , assuming the narrow-width approximation. For the signal samples, the detector response is described using a fast simulation [30]. The fast simulation has been validated extensively against the detailed GEANT4 simulation for the variables relevant for this search and efficiency corrections based on data are applied. All simulated events are reweighted to match the multiplicity distribution of additional proton-proton collisions ("pileup") as observed in data.
Events are selected online with either triple-or double-object triggers. The triple-object triggers require a lepton with p T > 15 GeV, together with H T > 350 GeV and E T / > 45 GeV. The doubleobject triggers, which are used to select control samples and extend the E T / acceptance in the approach based on ∆φ(W, ), have the same H T requirement, no E T / requirement, and a lepton p T threshold of 40 GeV. The trigger object efficiencies are measured in independently triggered control samples and found to reach a plateau at approximately 95% for thresholds well below those used in the offline selection. The measured trigger efficiencies are used to correct the simulation.
The preselection of events is based on the reconstruction of an isolated lepton (e or µ) and multiple jets and follows the procedure described in Ref. [12]. Events are required to include at least one lepton with p T > 20 GeV and |η| < 2.5 (e) or |η| < 2.4 (µ). Standard identification and isolation requirements [31,32] are applied to reject backgrounds from jets mimicking the lepton signature and from non-prompt leptons produced in semileptonic decays of hadrons within jets. The isolation selection requires the sum of transverse momenta of particles in a cone of radius (∆η) 2 + (∆φ) 2 = 0.3 around the electron (muon) direction, divided by the p T of the lepton itself, to be less than 0.15 (0.12). The lepton efficiencies are measured with a "tag-and-probe" technique [33] to be approximately 80% for electrons and 95% for muons. The efficiencies vary by less than 20% over the selected kinematic range and the average values agree to better than 1% between data and simulation.
Jets are clustered from particles reconstructed with the particle-flow (PF) algorithm [34], which combines information from all components of the detector. The clustering is performed with the anti-k T clustering algorithm [35] with a distance parameter of 0.5. Jet candidates are required to satisfy quality criteria that suppress noise and spurious non-collision-related energy deposits. Jets with p T > 40 GeV and |η| < 2.4 are considered in the analysis and are used to determine the number of selected jets N j and H T . The missing transverse momentum is determined from the vector sum of the momenta of all particles reconstructed by the PF algorithm. Jet and E T / energies are corrected to compensate for shifts in the jet energy scale and the presence of particles from pileup interactions [36].
The number of b-tagged jets, N b , is determined by applying the combined secondary vertex tagger [37,38] to the selected jets. At the working point used, this tagger has a roughly 70% b-tag efficiency, and a mistag rate for light partons (charm quarks) of approximately 3% (15-20%). Scale factors for the efficiencies and mistag rates relative to simulation are measured with control samples in data and applied in the analysis.
As the signal events are expected to exhibit a high level of hadronic activity and contain a large number of b quarks, events are required to have H T > 400 GeV. In addition, at least two btagged jets and a total jet multiplicity N j ≥ 6 are required. The SM background in this sample is dominated by tt production. Samples selected with the requirements 3 ≤ N j ≤ 5 or N b < 2 are used to define background-dominated control regions. Events with a second isolated lepton with p T > 15 GeV are vetoed by the nominal signal selection to suppress contributions from dilepton tt decays, but such events are used as a control sample to measure the residual background from that process.

Search in missing transverse momentum and H T
We now describe the background estimation method based on the evaluation of the E T / spectrum. This method utilizes two techniques, as mentioned above, both of which were employed for previous CMS studies [12,13]. The lepton spectrum (LS) method makes use of the similarity between the neutrino and charged-lepton p T spectra in W decays to predict the high-side tail of the E T / distribution from single-lepton tt decays based on the p T distribution of charged leptons with high p T [39]. The contributions from dilepton and τ lepton decays are predicted from single-lepton and dilepton control samples. The missing transverse momentum template (MT) method uses a parametric description of the E T / spectrum based on a fit to control regions at low H T . Through extensive use of data control samples, we avoid uncertainties related to potential mismodelling of SM yields by the simulation in the high H T and high E T / tails.
We consider overlapping signal regions corresponding to lower limits for H T ranging from 400 to 1000 GeV, each of which provides sensitivity to a different SUSY-particle mass region. The E T / spectrum in these samples is divided into exclusive ranges: 150-250, 250-350, 350-450, and >450 GeV. To increase the sensitivity, the search regions are further divided into events with N b = 2 and ≥3. The two background estimation methods provide direct predictions for events with two b-tagged jets. The expected yields at higher N b are obtained by extrapolating those predictions to the ≥3 b-jet case.

Prediction of the single-lepton background for the LS method
The E T / spectrum of the single-lepton background is predicted with a method based on the similarity of the neutrino and charged lepton p T spectra in W decays. In each event, the charged and neutral lepton p T can be very different, but the distributions of the true neutrino p T and the true lepton p T are identical in the absence of W polarization. There are several effects that result in differences between the observed lepton and neutrino p T spectra and for which corrections are derived: W polarization, the effect of a lepton p T threshold, and the difference between the E T / and lepton-p T resolutions. The W-boson polarization in tt decays is the dominant effect that causes a difference between the neutrino and lepton p T spectra. This polarization is well understood theoretically [40] and accounted for in the simulation. The difference between the E T / and lepton-p T resolution is modeled with E T / resolution templates measured in multijet data samples. These samples are used because the E T / resolution is dominated by the measurement of the hadronic activity in an event, and these samples have little genuine E T / . These resolution templates are binned in H T and N j and are used to smear the lepton-p T spectrum to account for the difference with respect to the E T / resolution.
The single-lepton E T / spectrum is predicted from the lepton p T spectrum using the following steps. First, the lepton p T spectrum in a control sample, selected with lepton p T > 50 GeV and without a E T / requirement, is smeared with the resolution templates. The smeared distribution is then corrected with p T -dependent scale factors κ LS to obtain a predicted E T / spectrum. These scale factors are defined by κ LS (p T bin) = N true (E T / bin)/N pred (p T bin), where N pred is the MC yield in a given bin of the smeared p T distribution and N true is the MC yield in the same bin of E T / . The latter includes only events with a single lepton at generator level, while the former includes all events passing the selection of the control sample. This definition ensures that the scale factors model the E T / distribution from only the single-lepton background without contributions from τ leptons or dilepton backgrounds, which are predicted separately. The calculation of the scale factor is dominated by the contributions of tt events, but W+jets, DY+jets, single-top quark, ttZ, and ttW events are included as well; the contribution of diboson events is negligible. The impact of ttZ, ttW, and ttH events is insignificant, and for the results shown in this Section only the first two categories have been included. The dependence of the scale factor on lepton p T primarily reflects the effect of the W-boson polarization in tt decays. The scale factor varies from around 1.0 for lepton p T of 150 to 250 GeV, after E T / resolution smearing, to about 1.5 for p T > 450 GeV.
Systematic uncertainties are evaluated by calculating the change induced in the scale factors from various effects and propagating this change to the predicted yields. The sources of systematic uncertainty are the jet and E T / scale, W polarization in tt decays and direct W production, tt and sub-dominant background cross sections, lepton efficiency, muon p T scale, and DY+jets yield. The dominant uncertainties arise from the statistical uncertainties of the simulated samples used in the determination of the scale factor (9-49%), the jet and E T / scale (7-31%, depending on H T and E T / ), and the W polarization in tt decays (2-4%).

Predictions of τ lepton and dilepton backgrounds for the LS method
Neutrinos from τ lepton decays cause the E T / and charged-lepton p T spectra to differ. Therefore, the SM background from τ leptons is evaluated separately, following the procedure documented in Ref. [39]. While τ-lepton decays are well simulated, their p T spectra may not be. Thus we apply τ-lepton response functions derived from simulated tt events to the p T spectra of electrons and muons measured in single-lepton and dilepton control samples. To suppress DY events in these control samples, same flavor dilepton events are rejected if they have E T / < 40 GeV or a dilepton invariant mass within 20 GeV of m Z . In these control samples, the E T / requirement is removed and a selection to reject DY events is applied. The H T and N j requirements are loosened in the control sample used to estimate the background of events with hadronically decaying τ leptons. For leptonic (hadronic) τ-lepton decays, hereafter labelled τ (τ h ), the response function is the distribution of the daughter lepton (jet) p T as a fraction of the parent τ lepton p T . To predict the contribution to the E T / spectrum, the observed lepton in the control sample is replaced by a lepton (or jet), with the transverse momentum sampled from the appropriate response function; the difference between the sampled and original p T is added vectorially to the E T / . This procedure is used to predict three background categories: single τ , + τ h , and + τ events; the notation includes τ components.
The E T / spectrum obtained from applying the response functions to the control samples is corrected as a function of E T / and H T for branching fractions and efficiencies determined from MC simulation. These correction factors are roughly 0.2, 0.9, and 0.6 for the single τ , + τ , and + τ h backgrounds, respectively, in all H T bins. A correction is derived from simulation to account for a possible dependence on E T / of the event selection and acceptance (note that this correction is consistent with one within the uncertainties).
SM backgrounds also arise from dilepton events. There are two categories of these events: those with both leptons reconstructed but where only one of the leptons is selected, and those with one lepton that is not reconstructed, which can occur either because of a reconstruction inefficiency or because the lepton lies outside the η acceptance of the detector. The estimate of the background from these processes is given by the simulated E T / distribution, corrected by the ratio of the number of data to MC events in a dilepton control sample. This sample is the same as that used in the + τ background prediction, but with an additional requirement of E T / > 100 GeV used to retain high trigger efficiency. Systematic uncertainties for the dilepton background estimate arise from the uncertainty in the data/MC scale factor, pileup, trigger and selection efficiencies, and the top-quark p T spectrum.
The background composition is similar in each of the LS signal regions. For example, the signal region with H T > 500 GeV, N b = 2, and 350 < E T / < 450 GeV has predicted single-lepton and Table 1: Observed yields in data and SM background predictions with their statistical and systematic uncertainties from the LS and MT methods. For the MT method the low E T / (150-250 GeV) and low H T (400-750 GeV) regions in the N b = 2 sample are used as control regions and are not shown in the table.
single-τ backgrounds of 11.6 ± 5.2 and 1.8 ± 0.7, respectively. The remainder of the background prediction, consisting of + τ h , + τ , and dilepton events, is 2.0 ± 1.1. The total yields for all signal regions are given in Table 1 and Fig. 1 shows the E T / distributions.

The missing transverse momentum model in the MT method
For values of E T / well above the W boson mass, the SM E T / distribution primarily arises from neutrino emission (genuine E T / ) and has an approximately exponential shape. According to simulation, this distribution depends on H T and, to a lesser extent, N j and N b , with only a small variation predicted for the non-exponential tails. Empirically, we find that the genuine E T / distribution from tt events (the leading background term) can be parametrized well with the Pareto distribution [41], which is widely used in extreme value theory: where x min , α, and β are the position, scale, and shape parameters, respectively. Equation 1 yields an exponential function for β = 0. We set x min = 150 GeV, representing the lower bound of the E T / spectrum to be described, while α and β are determined from a fit to data.
Both the control regions used for a fit of the E T / model to data and the signal regions have selection criteria applied to H T . Because of the correlation between the momentum of the leptonically decaying W boson and the momenta of the jets balancing it, restrictions on H T af-fect the E T / spectrum. We describe the ratio between the E T / spectrum after imposing a lower bound on H T and the inclusive E T / spectrum by a generalized error function (corresponding to a skewed Gaussian distribution), similar to the approach described in Ref. [13]. The evolutions with H T of the location and variance parameters of this function are determined from simulation and found to be linear. The results in simulation are found to be consistent with the dependence measured from a tt-dominated control sample in data, defined by N j ≥ 4, N b ≥ 2, and H T > 400 GeV. Systematic uncertainties related to the error functions are determined from this comparison and from the difference between linear and quadratic models of the function parameters. The E T / spectrum in exclusive bins of N b is also affected by an acceptance effect due to the p T requirement on the b-tagged jets: in tt events at low H T , high values of E T / correspond to low values of the p T of the b quark associated with the leptonically decaying W boson and tend to move events to lower b-jet multiplicities. We therefore apply an acceptance correction when applying the E T / model to events with one or two b-tagged jets. For N b = 2 and 150 < E T / < 1000 GeV, the size of the correction is 12% for H T = 750 GeV and is smaller for larger H T .
The b-jet multiplicity distribution is used to estimate the ratio of the W+jets background to the tt background as a function of H T . The H T distribution of tt events is extracted from the N b = 2 sample as described in Ref. [13]. The contribution of W+jets events for E T / > 150 GeV is approximately 1%. Uncertainties related to other non-leading background components are estimated by varying the corresponding cross sections and are found to be small. Based on the measured ratio of W+jets to tt background events, the Pareto distribution describing the leading background term is combined with the shape of the W+jets E T / distribution from simulation to form the full model describing the genuine E T / distribution of SM events.

The fit to the missing transverse momentum spectrum in the MT method
The model for genuine E T / in SM events is convolved with the E T / resolution templates described in Section 3.1 and used in a simultaneous fit to the E T / shapes in control regions in the N b = 1 and N b = 2 bins. The control regions are chosen in order to ensure reasonably small statistical uncertainties and to limit potential contributions from signal events: for events with two btagged jets the control region is defined by 400 < H T < 750 GeV and 150 < E T / < 400 GeV, while for one b-tagged jet it is extended to 400 < H T < 2500 GeV and 150 < E T / < 1500 GeV.
Because of limited statistical precision in the control regions, we are unable to obtain a reliable estimate of β from data. We use a constraint from simulation together with an uncertainty derived from a comparison between data and simulation in control regions with lower jet multiplicity. The constraint is implemented as a Gaussian term corresponding to the value and its statistical uncertainty obtained from simulation, β = 0.03 ± 0.01. The prediction from simulation for N j = 3-5 is β = 0.15-0.05, consistent with the data. The maximum difference between data and simulation in any of these three N j bins of 0.05 is used to define a systematic uncertainty in the prediction. The parameters of the error function (Section 3.3) are constrained by Gaussian terms reflecting the respective values and covariance from simulation.
The predictions for the N b = 2 signal regions are obtained by integrating the function representing the E T / model over the relevant E T / range and summing over the H T bins. In each H T bin, the predicted distribution is scaled to match the observed number of events in the normalization region defined by 150 < E T / < 250 GeV. The statistical uncertainties of the predictions are evaluated by repeating the procedure using parameter values randomly generated according to the results of the fit, including the covariance matrix. The predictions are stable to within 1% if the E T / model described in Ref.
[13] is used in place of the model described here. The results of the MT method can be affected by several systematic uncertainties that are related to detector effects, assumptions made on the shape of the distribution, as well as theoretical uncertainties and the contamination due to non-leading backgrounds. Systematic uncertainties related to the jet and E T / scale, lepton reconstruction efficiencies, W-boson polarization in tt events, and cross sections of non-leading backgrounds are evaluated in the same way as for the LS method (Section 3.1). Effects due to b-jet identification efficiencies and pileup are also taken into account. In addition, the following uncertainties specific to the MT method are considered. The β parameter and parameters of the error function are varied as described above. The differences with respect to the standard result define the systematic uncertainty for each signal region. The effects of a possible residual non-linearity in the error function parameters versus H T are also taken into account. To test the validity of the method, the procedure is applied to simulated events. The resulting background predictions are found to be statistically consistent with the true numbers from simulation. Conservatively, the maximum of the relative difference and its uncertainty are assigned as a further systematic uncertainty ("closure"). The dominant contributions to the systematic uncertainty are related to the E T / model (1-35%, depending on the H T and E T / bin) and the closure (8-43%). Uncertainties related to the theoretical predictions of the cross section for SM backgrounds, the jet and E T / scale, and pileup contribute each with less than 5%.

Background estimation in the N b ≥ 3 bin
The numbers of data events in the N b ≥ 3 control samples are too low for an application of the LS or MT technique. Therefore we estimate the background for high b-jet multiplicities by applying to the background predictions for N b = 2 transfer factors (R 32 ) that give the ratio of the number of events with ≥ 3 and = 2 b-tagged jets for each of the signal regions. The central values for the R 32 factors are determined from simulation. The scale factors R 32 increase with jet multiplicity from approximately 0.05 for events with three jets to approximately 0.2 in events with ≥ 6 jets because of the higher probability of misidentifying one or more jets. For constant jet multiplicity they do not demonstrate a strong dependence on H T .
The ratios between N b ≥ 3 and = 2 events in data and simulation could differ because of incorrect modeling of the heavy-flavor content, the jet kinematics, and uncertainties in the btagged jet misidentification rates. To probe the impact of the first source of uncertainties, the weight of events with at least one c quark is varied by ±50%. A variation of the same size is applied to events with additional b-or c-quark pairs. The effect of possible differences between data and simulation in the kinematics of the system of non-b jets on R 32 is tested in a control sample with exactly two b-tagged jets. The remaining jets in the event are randomly assigned a parton flavor: one jet is marked as a c-quark jet, while the others are marked as light-quark jets. Based on this assignment the ratio of probabilities to tag at least one additional jet is calculated. This procedure is applied to both data and simulation. Good agreement is found and the residual difference is interpreted as a systematic uncertainty. The uncertainty related to b-tagged jet misidentification is evaluated from the uncertainties of the misidentification scale factors relative to simulation. The total systematic uncertainties for R 32 are approximately 9-19% depending on the signal region. An additional verification is performed in two control regions at higher lepton p T (>30 GeV), lower H T (<400 GeV) and E T / (150 < E T / < 250 GeV), and N j = 5 or ≥6. In both regions the values of R 32 obtained in simulation are compatible with the ones observed in data.
In the LS method, the transfer factors are applied to the signal regions for H T > 500, 750, and 1000 GeV. In the MT method, signal regions for H T > 400 GeV and 150 < E T / < 250 GeV are added for the N b ≥ 3 bin, corresponding to the limits of the control and normalization regions in the N b = 2 bin, respectively.

Results for signal regions in missing transverse momentum and H T bins
The predictions of both methods are compared with the observed number of events in Table 1. For the LS method the predictions consist of the single-lepton and τ-lepton backgrounds with a small contribution from dilepton events. Drell-Yan events are heavily suppressed by the N j , N b , and kinematic requirements. The yield of this small component of the background is taken from simulation. For the MT method the predictions consist of the inclusive estimation of the leading backgrounds. Additional contributions to the signal regions from multijet events are heavily suppressed, but their cross section is large and not precisely known. Therefore, they are predicted from data based on scaling the sideband of the relative lepton isolation distribution. These contributions are neglected as they are found to constitute 1% or less of the total background in all cases.
The corresponding observed and predicted E T / spectra are shown in Fig. 1 for the two b-jet multiplicity bins and different H T requirements. The two methods differ in their leading systematic terms and in the correlations they exhibit between the background predictions in different signal regions. The predictions are consistent, an indication of the robustness of the methods. No excess is observed in the tails of the E T / distributions with respect to the expectations from SM processes. The results are interpreted in terms of upper limits on the production cross section for different benchmark models in Section 5.

Search using S lep T and ∆φ(W, )
After applying the selection criteria in Section 2, the sample is dominated by single-lepton tt events. In the delta phi (∆φ) analysis method, this background is further reduced by applying a requirement on the azimuthal angle between the W-boson candidate and the charged lepton. The W-boson candidate transverse momentum is obtained as the vector sum of the lepton p T and the E T / vectors. For single-lepton tt events, the angle between the W-boson direction and the charged lepton has a maximum value, which is fixed by the mass of the W boson and its momentum. Furthermore, the requirement (direct or indirect) of large E T / selects events in which the W boson yielding the lepton and the neutrino is boosted, thus resulting in a fairly narrow distribution in ∆φ(W, ). On the other hand, in SUSY decays, the "effective W boson" that is formed from the vector sum of the transverse momenta of the charged lepton and the E T / vector will have no such maximum. Since the E T / results mostly from two neutralinos, the directions of which are largely independent of the lepton flight direction, the ∆φ(W, ) distribution is expected to be flat.
Distributions of ∆φ(W, ) in different S lep T bins are shown for the N b ≥ 3 and N j ≥ 6 samples in Fig. 2. We select ∆φ(W, ) > 1 as the signal region. The complementary sample, events with ∆φ(W, ) < 1, constitutes the control region. It can be seen that this selection is effective in reducing the background from single-lepton tt decays; the dominant background in the signal regions comes from dilepton tt events. Table 2 shows the event yields from simulation for the signal and control regions in different S lep T bins for events with N b ≥ 3, which have the highest sensitivity to the SUSY signal. The contributions from ttZ, ttW, ttH, and diboson events are insignificant and have not been used for the results shown in this Section. The search also uses events with N b = 2, albeit with smaller sensitivity.

Prediction of standard model background
The estimate of the SM background in the signal region is obtained using the data and some input from simulation. We define a transfer factor, R CS , as the ratio of the number of events with ∆φ(W, ) > 1 to the number with ∆φ(W, ) < 1. Figure 3 displays the value of R CS as a function of N b for the SM alone and also with the addition of signal from a SUSY benchmark scenario. In the absence of a SUSY signal, the value of R CS is roughly independent of the b-jet multiplicity. In the presence of a signal containing four top quarks, however, the value of R CS in the N b ≥ 2 bins changes significantly, whereas it remains unchanged in the N b = 1 bin, which is dominated by background from SM processes. Given this observation, we obtain the transfer factors used to predict the SM background for different values of Table 3) and κ CS is a correction factor obtained from simulation (Table 4), introduced to account for any residual dependence of R CS on N b . The transfer factors R  Table 4, which lists the yield without a κ CS factor correction, and the observed event yields, as well as the corresponding κ CS correction factors for N b ≥ 3. The κ CS factor ranges from 0.93 to 1.45 with statistical uncertainties up to ±0.6. The large statistical uncertainty reflects the very small event yields expected in the signal region from SM processes.  Table 4: Comparison of the simulated yields, combined for the e and µ channels, in the signal region and the estimate using R CS from the N b = 1 sample. The κ CS factor is calculated as the ratio of the true yield in the signal region ("MC truth") and the predicted number. We observe only a weak dependence of the transfer factor R CS on N j and, as stated above, on N b . Two sources of this dependence have been identified: the relative composition of SM samples (W+jets, tt (1 ), tt ( ), single top quark), and the residual dependence of R CS within each SM sample. The effect of each source on R CS is found to be <50%. The application of the κ CS factor compensates for these effects and incorporates their uncertainties. A potential signal would result in much larger values of R CS (e.g., of up to a factor of five larger for the benchmark points) than the variations above, as can be seen from Fig. 3.
The only elements of the background estimate that depend on simulation are the κ CS factors. Most potential sources of systematic uncertainties leave κ CS unaffected, since the correction factor reflects only residual changes in the value of R CS from N b = 1 to N b ≥ 3 (N b = 2) as a result of each systematic uncertainty. Systematic uncertainties are estimated as in Section 3, i.e. by calculating the change induced in the scale factor, κ CS , from various effects and propagating this change to the predicted yields. The jet /E T / energy scale and the b-tagging efficiencies are varied within their uncertainties. For each independent source (energy scale, heavy-and lightparton tagging efficiencies) the effects of the upwards and downwards variations are averaged. The W+jets cross section is varied by 30% as in Ref. [12]. The cross section for W+bb is varied by 100% [42,43] and that for single-top-quark production by 50% [44]. We assign an uncertainty of 5 and 10%, respectively, to the W boson and tt polarizations [40,45]. These effects are negligible.
Since the estimate of the background in the signal region is based on ratios of events in the data and the κ CS factor that only depends on the number of b-tagged jets, the systematic uncertainties of the background prediction are expected to be the same for the electron and muon samples. This is confirmed with an explicit calculation of these uncertainties, and thus the final result uses the combination of the uncertainties from the two lepton flavors. The overall systematic uncertainty found for κ CS , which is dominated by the limited statistics in the simulated samples, is 23%, 45% and 70%, respectively, in the three S lep T ranges. The total systematic uncertainty of the background prediction is dominated by the statistical uncertainty that arises due to the limited number of events in the data control samples.

Multijet background estimate
Contributions of multijet events to the control and signal regions could affect the correction factors. Therefore we estimate these contributions from data. For the muon channel, the MC prediction for the multijet background is smaller than all other backgrounds by two to three orders of magnitude. This was confirmed by an estimate from data in the previous singlelepton SUSY search [12].
In the electron channel, the multijet background is larger than in the muon channel, but it remains significantly smaller than the other backgrounds. We make use of the method described in Ref. [45], employing a control sample in data that is enriched in electrons from multijet events, obtained by inverting some of the electron identification requirements ("antiselected" sample). While the method works well at low N b and N j , it yields statistically limited results in the samples with higher N b and higher N j . To obtain more precise predictions for the multijet background in these regions, the estimate from the N b = 1 sample is extrapolated with two methods that rely on the relative insensitivity of the multijet background to N b . The results of these methods are found to be consistent, and the fraction of multijet events is determined to be less than 5-7% of the total number of data events observed in the control region. Based on the antiselected sample, the corresponding transfer factor for multijet events is estimated to be smaller than approximately 2%. The multijet contamination in the signal region (∆φ(W, ) > 1) is therefore determined to be negligible and so the multijet background is subtracted only in the control region.

T and N b
The background prediction method is validated with the 3 ≤ N j ≤ 5 control sample, which is background dominated with dilepton tt events and with a relative contribution from W+jets larger than in the signal region. The compatibility between the predicted and observed yields in this sample is demonstrated by the results shown in the left portion of Table 5.
The predicted and observed data yields in the signal regions are also presented in Table 5. In the single case of a control region with zero observed events the uncertainty is estimated assuming that one event was present. Combining all signal bins we predict 19.2±4.0 events and observe 26. In the N b ≥ 3 bins, which are the most relevant regions for the signal, we predict 5.3 ± 1.5 events and observe 4. For S lep T > 350 GeV we predict 5.6 ± 2.5 events and observe 4.

Interpretation
The compatibility between the observed and predicted event counts in the searches described above is used to exclude regions in the parameter space of the three models of gluino-mediated production of final states with four top quarks and two LSPs introduced in Section 2. The expected signal yield obtained from simulation is corrected for small differences in the efficiencies between data and simulation and for an overestimation of events with high-p T radiated jets in MADGRAPH, as described in Ref. [11]. Systematic uncertainties in the signal yield due to uncertainty in the jet/E T / scale [36], initial-state radiation, PDFs [46], pileup, b-tagging scale factors [37], lepton efficiency, and trigger efficiency are calculated for each of the models and Table 5: Event yields in data for the 3 ≤ N j ≤ 5 (validation) and N j ≥ 6 (signal) samples. The number of events in the control regions used for the predictions are also shown. For the lower jet multiplicity validation test, only the statistical uncertainties stemming from the event counts in the control regions are given, while statistical and systematic uncertainties are listed for the signal region prediction. for every mass combination. The uncertainty due to the measurement of the integrated luminosity is 2.6% [47]. For model A, the total uncertainty in the signal yields ranges from 20% to 60%. The largest uncertainties are related to the PDFs and occur in regions with small mass differences m g − m χ 0 1 and high m g .
The modified-frequentist CL S method [48][49][50] with a one-sided profile likelihood ratio test statistic is used to define 95% confidence level ( Upper limits on the cross section at a 95% CL are set in the parameter plane of the three models. Corresponding mass limits are derived with the next-to-leading order (NLO) + next-to-leading logarithm (NLL) gluino production cross section [51][52][53][54][55] as a reference. The uncertainty on this cross section is determined as described in Ref. [56]. These limits are summarized in Fig. 4, which shows a comparison of the mass limits obtained for signal regions in H T and E T / , cross section and mass limits for the signal regions in S lep T and ∆φ(W, ), and a comparison of the observed mass limits obtained by the three methods. For each of the considered models the LS and MT methods show a similar reach; the most stringent limits are set by the ∆φ method. For model A, with off-shell top squarks, the limits extend to a gluino mass of 1.26 TeV for the lowest LSP masses and to an LSP mass of 580 GeV for m g = 1.1 TeV. At low gluino masses the sensitivity extends to the region m χ 0 1 > m g − 2m t . For model B, where the top squarks are onshell, the limits for m χ 0 1 reach 560 GeV for m t = 800 GeV. For model C the gluino mass limits for low LSP mass are similar to model A for m t > 500 GeV but decrease to m g = 1.0 TeV for lower stop masses because the signal populates the lower E T / region, which has higher background. For m g = 1.0 TeV, the limits cover the full range of top-squark masses if the LSP mass lies below approximately 530 GeV. Conservatively, these limits are derived from the reference cross section minus one standard deviation [56].

Summary
A sample of proton-proton collisions recorded with the CMS detector at a center-of-mass energy of 8 TeV and corresponding to an integrated luminosity of 19.3 fb −1 has been used for a search for new physics in events with a single isolated electron or muon, multiple high-p T jets, including identified b jets, and missing transverse momentum. This event topology is a possible signature for the production of supersymmetric particles in R-parity conserving models, in particular the production of gluinos with subsequent decays into top squarks. The dominant standard model background in a search region defined by the presence of at least six jets, including at least two jets identified as originating from the fragmentation of b quarks, is due to tt production.
The search is performed with two sets of signal regions, and uses three different methods, each based on data, to estimate the leading background contributions. The lepton spectrum and the missing transverse momentum template methods are designed as searches in the high H T , high E T / region. They estimate the SM backgrounds (dominated by single-lepton tt decays) for events with two identified b jets and extrapolate these predictions to additional signal regions requiring ≥3 b-tagged jets. The first of these methods uses the lepton p T distribution to estimate the E T / spectrum while the second obtains the predictions in a parametrized form by fitting a E T / model to control regions in data. The delta phi method uses the azimuthal angle between the lepton and W boson directions as a discriminating variable, leading to a strong suppression of the single-lepton backgrounds and leaving dilepton tt events as the leading SM contribution. The signal regions are defined by the use of the same two b-jet multiplicity requirements and by bins in S lep T , which probes the total leptonic ( and ν) scalar transverse momentum in the event.
While the delta phi approach shows the highest sensitivity, the use of different methods, which probe complementary kinematic aspects and both hadronic and leptonic event characteristics, increases the robustness of this search. Together these methods examine the event sample in both high-and low-yield regions to provide sensitivity to signal topologies with high hadronic activity, missing transverse momentum, and at least two b jets.
No significant excess is observed in any of the signal regions. Upper limits are set at 95% CL on the product of production cross section and branching fraction for three benchmark models of gluino pair production with subsequent decay into virtual or on-shell top squarks, where each of the two top squarks decays in turn into a top quark and the lightest supersymmetric particle. In the case of decays via virtual top squarks and for light LSPs, gluino masses below [GeV] [GeV]

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 centres 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: BMWF and FWF  [11] CMS Collaboration, "Search for top-squark pair production in the single-lepton final state in pp collisions at √ s = 8 TeV", Eur. Phys. J. C 73 (2013) 2677, doi:10.1140/epjc/s10052-013-2677-2, arXiv:1308.1586.